MS and CT list / Aug. 21, 13:20-15:00.

MS [00795] Topological data analysis and machine learning

room : G301

• [03334] Topological Data Analysis of Spatial Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Mason Alexander Porter (UCLA)
  • Abstract : I discuss several applications of topological data analysis to spatial systems. I will consider examples from voting, city streets, the spread of COVID-19.
• [03341] Bigraded persistence barcodes and their stability
  • Format : Talk at Waseda University
  • Author(s) :
    • Anthony Bahri (Rider University)
    • Ivan Limonchenko (Higher School of Economics)
    • Taras Evgenievich Panov (Moscow State University)
    • Jongbaek Song (Pusan National University)
    • Donald Stanley (University of Regina)
  • Abstract : We define the bigraded persistent homology modules and the bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. Then we discuss the stability for the bigraded persistent double homology modules and corresponding bigraded barcodes.
• [03617] Learning visual representation with homological labels
  • Format : Talk at Waseda University
  • Author(s) :
    • Shizuo Kaji (Kyushu University)
    • Yohsuke Watanabe (ZOZO inc.)
  • Abstract : We propose a new scheme for convolutional neural networks to learn visual representation with synthetic images and mathematically-defined labels that capture topological information. Our scheme can be viewed as a type of self-supervised learning, where the regression of vectorised persistent homology of an image is learned. We show that the acquired visual representation supplements the one obtained by the usual supervised learning with manually-defined labels by confirming an improved convergence in training for image classification. Our method provides a simple way to encourage the model to learn global features through a specifically designed task based on topology. It requires no real images nor manual labels and can be utilised at a minimal extra cost.
• [03647] Exact multi-parameter persistent homology of time-series data: Fast and variable one-dimensional reduction of multi-parameter persistence theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Keunsu Kim (POSTECH)
    • Jae-Hun Jung (POSTECH)
  • Abstract : Time-series data can be inferred as a periodic signal, enabling a continuous approximation with discrete Fourier transform to reveal the relation between its Fourier modes and topology of the data. We introduce an exact multi-parameter persistent homology construction utilizing the fast Fourier transform and Künneth formula, which computes and interprets the corresponding persistent barcode in a fast and efficient manner. This work is based on https://arxiv.org/abs/2211.03337

MS [00444] Complex Systems: Advances in Theory and Applications

room : G304

• [01282] Time Series Analysis with Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Small (University of Western Australia)
    • Braden John Thorne (University of Western Australia)
    • Eugene Tan (University of Western Australia)
    • Débora Corrêa (University of Western Australia)
    • Ayham Zaitouny (University of Western Australia)
    • Thomas Stemler (University of Western Australia)
  • Abstract : Machine learning is widely applied to model dynamical systems and make predictions. Instead of doing this, We will introduce the concept of Reservoir Time Series Analysis - using a particular flavour of machine learning (reservoir computing) to represent the state of a dynamical system and characterise the dynamical evolution of that state. How much can we infer about the changing behaviour of a system from the internal representation of these states within a reservoir machine learning model? A second strategy within machine learning for time series analysis is to use the machine learning model as a proxy for the original dynamics - but how well do such models capture chaotic dynamics? I will show via some short examples that persistent homology can be used as an effective tool to quantify that structure. These methods will be illustrated with applications to machine vibration and pump cavitation in industrial processes.
• [01306] On constructing directed networks from multivariate time series
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomomichi Nakamura (University of Hyogo)
    • Toshihiro Tanizawa (Toyota)
  • Abstract : We consider a problem of constructing networks for multivariate time series. To construct networks from multivariate time series, we first need to detect relationships among them. However, it is difficult, because the relationships among multivariate time series are diverse. The time series might contain components that have large differences in the amplitude and the time scales of the fluctuations. We consider this problem using the transfer entropy, one of the common techniques for detecting causal relationships and Reduced Auto-Regressive (RAR) model, an information theoretic reduction of auto-regressive model.
• [05563] Optimal network synchronization and a higher-order topological approach
  • Author(s) :
    • Guanrong (Ron) Chen (City University of Hong Kong )
  • Abstract : In this talk, we will discuss the optimal network synchronization problem. The totally homogenous network approach will be reviewed, and a higher-order topological approach will be introduced, with some preliminary results reported.
• [01273] Evaluating the Network Robustness: A Convolutional Neural Network Approach
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yang Lou (Osaka University)
    • Junli Li (Sichuan Normal University)
    • Guanrong Chen (City University of Hong Kong)
  • Abstract : Evaluating network robustness by attack simulations is computationally time-consuming. In this talk, a convolutional neural network (CNN)-based robustness estimation is presented, which has three schemes, including the straightforward scheme, the learning feature-assisted scheme, and the pyramid pooling-assisted scheme. Experimental studies demonstrate that: 1) the prediction error is low; 2) the runtime is significantly lower than that of attack simulations; and 3) it provides a good indicator for robustness, better than the classical spectral measures.

MS [02396] Recent Advances on Polynomial System Solving

room : G305

• [03796] Polynomial System Solving in a Nutshell
  • Format : Talk at Waseda University
  • Author(s) :
    • Chenqi Mou (Beihang University)
  • Abstract : In this introductory talk of the minisympoisum “Recent Advances on Polynomial System Solving”, I will give a brief overview of the problem of solving polynomial systems, including its theories, methods, softwares, and applications. In particular, basic concepts of three typical methods of Gröbner bases, triangular decomposition, and homotopy continuation for solving polynomial systems will be presented, serving as an introduction of other talks in this minisympoisum to a wider audience of different backgrounds.
• [04394] Signature-based algorithm and change of ordering for Groebner basis
  • Format : Talk at Waseda University
  • Author(s) :
    • Masayuki Noro (Rikkyo University)
  • Abstract : Although the termination is not guaranteed, signature-based algorithm under non-compatible term orderings may give good performance for computing Groebner bases. In such cases, we can apply the notion of Hilbert function for guaranteeing the termination. The Hilbert function is given by a Groebner basis with respect to another term ordering and thus this algorithm is a kind of change of ordering. We compare its performance with the usual Hilbert driven algorithm.
• [03913] Dimension results for polynomial systems over complete toric varieties
  • Format : Talk at Waseda University
  • Author(s) :
    • Matías Bender (INRIA - CMAP, École polytechnique, IPP)
    • Pierre-Jean Spaenlehauer (INRIA Nancy)
  • Abstract : A common computational approach to study affine varieties is to first homogenize the input defining equations. Among other reasons, we do so because the new equations have an associated grading that allows us to reduce our computations to a linear algebra problem. However, the homogenization process might introduce higher components at infinity, changing drastically the geometry of the affine object that we want to study. This is what happens when we homogenize, in the classical sense, sparse polynomials. To overcome this issue, a possible approach is to homogenize the input equations, using their Newton polytopes, over a Cox ring or a polytopal graded subring of it. However, other simpler homogenizations might be possible. In this work, we prove a combinatorial criterion to decide when a candidate homogenization is good, in the sense that it does not introduce higher components at infinity. Additionally, we use our criterion to decide which families of degrees on polytopal algebras lead to regular sequences.
• [03633] On the computation of staggered linear bases
  • Format : Talk at Waseda University
  • Author(s) :
    • Amir Hashemi (Isfahan University of Technology)
    • Hans Michael Moller (Technical University Dortmund)
  • Abstract : Grobner bases are a powerful tool in polynomial ideal theory with many applications in various areas of science and engineering. Considering an ideal as a vector space, we investigate for such an ideal a particular linear basis, so-called staggered linear basis, which contains a Grobner basis as well. This notion was first introduced by Gebauer and Moller in 1988, however the algorithm that they described for computing these bases was not complete. In this talk, we present a simple and efficient algorithm to compute an staggered linear basis. The new framework is equipped with some novel criteria (including both Buchberger's criteria) to detect superfluous reductions. Finally, we discuss the efficiency of this algorithm compared to the existing methods using a set of benchmark polynomials.

MS [01211] Generalized and non-Gaussian Tensor Decompositions

room : G306

• [05616] Generalized Canonical Polyadic Tensor Decomposition: Algorithms and Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • David Hong (University of Delaware)
  • Abstract : Canonical polyadic (CP) tensor decomposition is a fundamental method for finding underlying patterns in data tensors by fitting a low-rank tensor to the data with respect to the least-squares loss. This talk gives an introduction to the generalized CP (GCP) tensor decomposition, which allows general user-selected losses (i.e., non-Gaussian/non-Euclidean/non-least-squares losses). We will describe first-order algorithms for computing GCP and show various demonstrations of GCP on data from science and engineering.
• [05224] Recent Improvements in CP Poisson Tensor Algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jeremy Myers (Sandia National Laboratories)
    • Daniel Dunlavy (Sandia National Laboratories)
  • Abstract : The challenge of fitting a low-rank, non-negative canonical polyadic tensor model to Poisson-distributed multi-way data is often formulated as a nonconvex optimization problem. A common approach is to use local methods initialized from many random starting points to improve the probability of convergence to the global minimum, which is costly. Our mitigation is a heuristic that identifies and teleports away from suboptimal solutions to improve the probability of convergence and reduce computational cost.
• [04808] Second-order algorithms for canonical polyadic decomposition with non-least-squares cost functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Michiel Vandecappelle (Televic Rail NV)
    • Nico Vervliet (KU Leuven)
    • Lieven De Lathauwer (KU Leuven)
  • Abstract : Signal processing and data analysis applications often rely on rank-1 terms to extract meaningful information from tensor data. By using the least-squares loss when computing this canonical polyadic decomposition, one implicitly assumes normally distributed errors, which might not be suitable for, e.g., count data. Therefore, we derive a generalized Gauss-Newton-type algorithm for non-least-squares loss functions and discuss how exploiting tensor structure and randomization lead to an efficient algorithm.
• [05553] Efficient Algorithms and Software for Generalized Tensor Completion
  • Format : Online Talk on Zoom
  • Author(s) :
    • Navjot Singh (University of Illinois Urbana-Champaign)
    • Edgar Solomonik (University of Illinois at Urbana-Champaign)
  • Abstract : We present novel algorithms and systems infrastructure which enable efficient parallel implementation of algorithms for CP tensor completion with generalized loss functions. Specifically, we consider alternating minimization, coordinate minimization, and a quasi-Newton (generalized Gauss-Newton) method. By extending the Cyclops library, we implement all these methods in high-level Python syntax using new sparse tensor kernels. We demonstrate the generalizability of our framework with the first large-scale implementation for Poisson loss completion.

MS [02067] Recent topics on generalized orthogonal polynomials and their applications

room : G401

• [04542] Meta algebras, biorthogonal rational functions and the Askey scheme
  • Format : Talk at Waseda University
  • Author(s) :
    • Satoshi Tsujimoto (Kyoto University)
    • Luc Vinet (IVADO & CRM, Université de Montréal)
    • Alexei Zhedanov (School of Mathematics, Renmin University)
  • Abstract : Algebras that subsume those of the Askey-Wilson type and are designated by the suffix meta are introduced to explain in a unified way the bispectral properties of the orthogonal polynomials of the Askey scheme and of biorthogonal rational functions that can be associated to the entries of that scheme. The Hahn and Racah families will be used to illustrate the framework.
• [04588] Introducing q→-1 limits of biorthogonal rational functions: two instructive examples
  • Format : Talk at Waseda University
  • Author(s) :
    • Julien Gaboriaud (Kyoto University)
    • Satoshi Tsujimoto (Kyoto University)
  • Abstract : We recall how $q\to-1$ limits of orthogonal polynomials have been introduced and we introduce analogous limits for biorthogonal rational functions (BRF). In order to illustrate the main properties of these $q\to-1$ BRF, we look at two "extremal" cases: the most general one (Wilson) and one of the simplest ones (Pastro).
• [03379] CMV bispectrality of polynomials orthogonal on the unit circle
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexei Zhedanov (School of Mathematics, Renmin University)
  • Abstract : We present new explicit results and examples concerning CMV bispectrality of the polynomials orthogonal on the unit circle.
• [04976] The Element Distinctness Problem Revisited
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hajime Tanaka (Tohoku University)
  • Abstract : The element distinctness problem is the problem of deciding whether or not a list contains identical elements. In this talk, I will revisit Ambainis' famous quantum algorithm for the problem (2007) and its refinement by Portugal (2018) in terms of the Grover quantum walk on the Johnson graphs. I will explain how a result about orthogonal polynomials (i.e., Leonard pairs) plays a role here.

MS [00988] Treatment of infinity and finite-time singularities in differential equations

room : G402

• [01480] Finite-time singularity and dynamics at infinity: characterization and asymptotic expansions
  • Format : Talk at Waseda University
  • Author(s) :
    • Kaname Matsue (Kyushu University)
  • Abstract : Finite-time singularities in differential equations, in particular finite-time blow-up, from the viewpoint of dynamical systems are discussed in this talk. Using compactifications of phase spaces and time-scale desingularization naturally introduced by the quasi-homogeneity of vector fields in an asymptotic sense, blow-up characterization is reduced to dynamics at infinity. We also discuss a systematic calculations of multi-order asymptotic expansion of blow-up solutions with a natural correspondence to dynamical properties of invariant sets at infinity.
• [01461] Compactification for Asymptotically Autonomous Dynamical Systems with Applications to Tipping Points.
  • Format : Talk at Waseda University
  • Author(s) :
    • Sebastian Wieczorek (University College Cork)
    • Christopher K.R.T. Jones (University of North Carolina)
  • Abstract : We develop a general compactification framework for non-autonomous ODEs, where non-autonomous terms decay asymptotically. The aim is to use compact invariant sets of the autonomous limit systems from infinity to analyse non-autonomous instabilities in the original problem, in the spirit of dynamical systems theory. We illustrate our framework using rate-induced tipping instability that occurs in natural systems when external inputs, such as climatic conditions, vary faster than some critical rate.
• [01512] Rate-induced tipping in heterogeneous reaction-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Cris Hasan (University of Glasgow)
    • Sebastian Wieczorek (University College Cork)
    • Ruaidhrí Mac Cárthaigh (University College Cork)
  • Abstract : We propose a framework to study nonlinear waves in reaction-diffusion equations (RDEs) based on a compactification technique and Lin’s method for constructing heteroclinic orbits. We identify generic instabilities of travelling pulses in an RDE with a fold of heteroclinic orbits in the compactified system. In an illustrative model of a habitat patch that is geographically shrinking or shifting due to climate change, we combine our framework with numerical continuation to study tipping points to extinction.
• [01527] Using Geometric Singular Perturbation Theory to Understand Singular Shocks
  • Format : Talk at Waseda University
  • Author(s) :
    • Barbara Lee Keyfitz (The Ohio State University)
  • Abstract : Solutions to hyperbolic conservation laws (quasilinear hyperbolic partial differential equations) typically satisfy the equations in the sense of distributions. But there are examples of systems whose solutions have even lower regularity, solutions known as singular shocks or delta shocks. In some of these examples, candidates for solutions that exhibit singular shocks have been found as limits of approximations. An unusual model in two-component chromatography, discovered by Marco Mazzotti, provides the first physically significant example of a system where singular shocks appear. This model does not fit into the existing theory. Here, I present new approach. Singular perturbation theory (SPT), long a mainstay of classical applied mathematics, has been put on a new footing by an approach developed by Fenichel in the 1970's and since then extended by many other researchers. This approach uses manifold and dynamical systems theory to replace the formal constructions of SPT. It was first applied to singular shocks by Stephen Schecter. Using geometric singular perturbation theory, Ting-Hao Hsu, Martin Krupa, Charis Tsikkou and I can give a singular shock structure to Mazzotti's unusual chromatography equations.

MS [00699] Delay and stochastic differential equations in life sciences and engineering

room : G404

• [04596] Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects
  • Format : Talk at Waseda University
  • Author(s) :
    • Yun Kang (Arizona State University)
    • Tao Feng (Yangzhou University,)
    • Hongjuan Zhou (Arizona State University)
    • Zhipeng Qiu (Nanjing University of Science and Technology)
  • Abstract : This work provides rigorous analysis on stochastic persistence and extinction, ergodicity, and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics with component Allee effects. We show that stochasticity may affect population dynamics differently for different strength of Allee effects. Moreover, in the extinction case, demographic and environmental stochasticity can not change the trend of population extinction, but they can delay or promote population extinction.
• [03954] Recent advances in modeling tick-borne dynamics using delay differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianhong Wu (York University)
  • Abstract : We provide a short survey of recent advances in modeling tick-borne disease transmission dynamics using structured population dynamics models and delay differential equations. Focus will be on those studies relevant to diapause, that introduces additional delays in the modeling system (and periodic variation of the environment), and on co-feeding transmission route that requires incorporation of individual infestation dynamics into the tramsmission dynamics at the population level.
• [03402] Delay and Resonance: From Differential Equations to Random Walks
  • Format : Talk at Waseda University
  • Author(s) :
    • Toru Ohira (Graduate School of Mathematics, Nagoya University)
  • Abstract : Various types of oscillatory dynamics are associated with systems with delayed feedback. We present two simple models that take advantage of these oscillations to induce resonating behaviors. The first model is a simple first-order delay differential equation with a time linear coefficient. The other model is a simple stochastic binary bit with delayed feedback. Both models produce transient oscillatory dynamics that can show resonance with the tuned value of the delay.
• [03310] Evolutionary Games with Strategy-Dependent Time Delays
  • Format : Talk at Waseda University
  • Author(s) :
    • Jacek Miękisz (University of Warsaw)
  • Abstract : We present a new behavior of systems with time delays. We show that in differential replicator equations with strategy-dependent time delays, interior stationary states, describing the level of cooperation in evolutionary games of social dilemmas, depend continuously on time delays, they may also disappear or additional states can emerge. A Prisoner’s Dilemma model with an asymptotically stable population with just cooperators is presented. We will also discuss some results for finite populations.

MS [00982] Partial Differential Equations in Fluid Dynamics

room : G405

• [04512] Two-Dimensional Riemann Problems: Transonic Shocks and Free Boundary Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gui-Qiang George Chen (University of Oxford)
  • Abstract : We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional Riemann problems involving transonic shock waves and free boundary problems through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.
• [05347] Global stability of steady supersonic flow for 1D Compressible Euler system
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianli Liu (Shanghai University)
  • Abstract : It is more important to consider the stability of compressible flow with some phyical effects. In this talk, we will give the global nonlinear stability of steady supersonic flows for one dimensional unsteady compressible Euler systems with physical effect, such as a nonlinear damping representing frictions, heat transfer term or mass addition.
• [04192] Scaling limit of vortex dynamics on the filtered-Euler flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Gotoda (Tokyo Institute of Technology)
  • Abstract : We consider weak solutions of the 2D filtered-Euler equations, which describe a regularized Euler flow. We show that, in the limit of the filtering scale, filtered weak solutions converge to weak solutions of the 2D Euler equations and an energy dissipation rate for the filtered weak solution converges to zero for initial vorticity in a certain class.
• [05331] Characteristic Decomposition for Hyperbolic System
  • Format : Talk at Waseda University
  • Author(s) :
    • Wancheng Sheng (Shanghai University)
  • Abstract : In this talk, we show the method of characteristic decompositions for hyperbolic conservation laws. By this methods, we give some results on the multidimensional Riemann problems of compressible Euler equations.

MS [00085] Singular Problems in Mechanics

room : G406

• [00222] Recent progress on the irreversible fracture phase field model
  • Format : Talk at Waseda University
  • Author(s) :
    • Masato Kimura (Kanazawa University)
  • Abstract : We would like to present our recent progress in the study of the fracture phase field model of the irreversible type. It not only enables us to simulate various kinds of crack propagation phenomena but also realizes a non-healing property and a natural energy gradient structure simultaneously.
• [00267] Fractional Korn inequalities in bounded domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Davit Harutyunyan (University of California Santa Barbara)
    • Hayk Mikayelyan (University of Nottingham Ningbo China)
  • Abstract : The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in the case $ps>1$ for fractional $W^{s,p}_0(\Omega)$ Sobolev fields in open and bounded $C^{1}$-regular domains $\Omega\subset \mathbb R^n$. Also, in the case $ps<1,$ for any open bounded $C^1$ domain $\Omega\subset \mathbb R^n$ we construct counterexamples to the inequality, i.e., Korn's first inequality fails to hold in bounded domains. The proof of the inequality in the case $ps>1$ follows a standard compactness approach adopted in the classical case, combined with a Hardy inequality, and a recently proven Korn second inequality by Mengesha and Scott [\textit{Commun. Math. Sci.,} Vol. 20, N0. 2, 405--423, 2022]. The counterexamples constructed in the case $ps<1$ are interpolations of a constant affine rigid motion inside the domain away from the boundary, and of the zero field close to the boundary.
• [00266] On Phase Field Approach for Crack Propagation due to Water Pressure in Porous Medium
  • Format : Talk at Waseda University
  • Author(s) :
    • Sayahdin Alfat (Kanazawa University)
    • Masato Kimura (Kanazawa University)
  • Abstract : The crack propagation in the material due to water pressure was studied. This study involved the poroelasticity theory proposed by M. A. Biot. This study is divided into two parts. In the first part, we derived the poroelasticity theory, and its energy equality and presented several numerical examples. In the second part, we introduce our phase field model with unilateral contact conditions for desiccation cracking by coupling with the Biot model and show energy equality.
• [00171] Asymptotic series solution of variational Stokes problems in planar domain with crack-like singularity
  • Format : Talk at Waseda University
  • Author(s) :
    • Victor Kovtunenko (University of Graz)
  • Abstract : Variational problems for incompressible fluids and solids descried by stationary Stokes equations in a planar domain with crack are considered. Based on the Fourier asymptotic analysis, general solutions are derived analytically as power series with respect to the distance to the crack tip. The logarithm terms and angular functions are accounted in the asymptotic expansion using recurrence relations. Boundary conditions of Dirichlet, Neumann, impermeability, non-penetration, and shear at the crack faces determine admissible exponents and parameters in the power series. The principal asymptotic terms are derived in the sector of angle 2π, which determine a square-root singularity at the crack tip and presence of log-oscillations of variational solutions for the Stokes problems.

contributed talk: CT027

room : G501

[02184] Oscillatory Translational Instability of Localized Spot Patterns in the Schnakenberg Reaction-Diffusion System in Defected 3D Domains

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
• Type : Contributed Talk
• Abstract : For a two-component reaction-diffusion system in a bounded $3D$ domain, we investigate oscillatory instabilities of $N$-spot equilibrium. An $N$-spot equilibrium consists of localized spots in which the activator concentration is exponentially small everywhere except localized regions. In the stability analysis, we consider the translation mode and obtain the eigenvalue $\lambda$ is $\mathcal{O}(\varepsilon^2)$, which is the same order as the spot dynamics, while $\tau $ is $\mathcal{O}(\varepsilon^{-3})$. As a result, the system which contains the behavior of $\lambda$ and $\tau \lambda$ falls into the $\mathcal{O}(\varepsilon^2)$ correction. We later find that stability of these solutions is governed by a $3N \times 3N$ nonlinear matrix eigenvalue problem. Entries of the $3N \times 3N$ matrix involves terms calculated from certain Green’s function that contains information about the domain’s geometry. In the nonlinear matrix eigenvalue system, the most unstable eigenvalue decides the oscillation frequency at onset while the corresponding eigenvector determines the mode of spot oscillations. Further, we demonstrate the impact of various types of localized heterogeneity on this instability. An example of localized domain defects that we consider is to analyze the effect of perturbing the system by removing a small ball in the domain, which therefore allows a leakage of the chemical species out of the domain. Perturbation techniques is employed to compute Green’s function of near-spherical and near-cubic domains to gain analytic insight into how domain geometry select the dominant mode of oscillation. We show full solutions of the $3$-$D$ Schnakenberg PDE to confirm our asymptotic results.
• Classification : 35B36, 35B35, 35B25
• Format : Talk at Waseda University
• Author(s) :
  • Siwen Deng (Macquarie University)
  • Justin Tzou (Macquarie University)

[02006] Dynamics of localization patterns in some nonlocal evolution equations

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
• Type : Contributed Talk
• Abstract : Recently, studies have been proposed to simplify biological pattern formation problems by using nonlocal evolution equations to capture the self-organization caused by complex interactions with many factors. Especially, it has been reported that linear reaction-diffusion networks reduce to some nonlocal evolution equations reproducing patterns. Also, nonlocal effects are derived to reduce the structure of the network. In this talk, we report the influence of nonlocal effects on pattern dynamics for this reduced equation.
• Classification : 35B36, 92C15, 35K57
• Format : Talk at Waseda University
• Author(s) :
  • Hiroshi Ishii (Kyoto University)

[00956] Inner Structure of Attractors for a Nonlocal Chafee-Infante Problem

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
• Type : Contributed Talk
• Abstract : The structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem is studied. The existence and properties of stationary points are analysed. Also, the study of the stability and connections between them are carried out, establishing that the semiflow is a dynamic gradient. As a consequence, the attractor consists of the stationary points and their heteroclinic connections.
• Classification : 35B40, 35B41, 35B51, 35K55, 35K57
• Format : Online Talk on Zoom
• Author(s) :
  • RUBEN CABALLERO (UNIVERSIDAD MIGUEL HERNANDEZ DE ELCHE)

[00495] Input-state finite time stabilization of singular Markov fuzzy system.

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
• Type : Contributed Talk
• Abstract : This work aims to examine the problem of Input-state finite-time stabilization of singular Markov T-S fuzzy systems with input time delay and disturbance. The sampled-data control for a singular Markov T-S fuzzy system with the quantized state has been designed. Using Lyapunov stability theory and linear matrix inequalities we guarantee that the singular fuzzy system is Input state Finite time stable. Finally, a numerical example is used to show the effectiveness of the proposed method.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Format : Online Talk on Zoom
• Author(s) :
  • Keerthana N (Anna University )

[01539] Actuator fault reconstruction-based tracking control for periodic piecewise polynomial systems

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
• Type : Contributed Talk
• Abstract : The problem of actuator fault reconstruction and fault-tolerant tracking control for periodic piecewise polynomial systems with time-varying delay is investigated. The observer system is configured with periodic piecewise polynomial character to concurrently reconstruct the actuator faults and states of the system. Based on these configurations, the fault-tolerant tracking control is proposed, which aids in tracking the reference system by compensating the actuator faults. Numerical example is provided to validate the competence of proposed control scheme.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Author(s) :
  • Aravinth Narayanan (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

MS [00276] Interplay of Numerical and Analytical Methods in Nonlinear PDEs

room : G502

• [05323] Hartree-Fock theory with a self-generated magnetic field
  • Format : Talk at Waseda University
  • Author(s) :
    • Carlos J. Garcia Cervera (UCSB)
    • Rafael Lainez Reyes (UCSB)
  • Abstract : The study of a quantum system of N electrons interacting with K nuclei through the Coulomb potential has a long history in the mathematics community. In the first part of my talk, I will go over some of the quantum mechanical models developed to describe these systems, focusing on their mathematical structure and properties. Following that, I will describe how these theories change when a magnetic field is present. In particular, I will define the Hartree-Fock ground state problem for a system of N electrons and K nuclei in the presence of self-generated magnetic fields and direct coupling and we will study the existence of the ground state and excited states, as well as some numerical approaches for its computation. The work I present is in collaboration with Rafael Lainez Reyes.
• [02913] Uniform flow in axisymmetric devices through permeability optimization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Harbir Antil (George Mason University)
    • Drew P Kouri (Sandia National Labs)
    • Denis Ridzal (Sandia National Labs)
    • David Robinson (Sandia National Labs)
    • Maher Salloum (Sandia National Labs)
  • Abstract : Porous media enable the intimate contact between a fluid and a functional solid that can accomplish tasks valuable to chemical engineers, such as catalytic reaction, chemical separations, chemical species detection, and filtration. New additive manufacturing technologies enable the creation of porous media with precise control of the geometry of each pore, which could enable improved performance and more flexible design of chemical engineering devices. However, new design tools are needed to accomplish this. In this talk, we analyze an optimization problem, constrained by Darcy's law, to design porous media columns that achieve uniform fluid flow properties despite having nonuniform geometries. We prove existence of solutions to our problem, as well as differentiability, which enables the use of rapidly converging, derivative-based optimization methods. We demonstrate our approach on two axisymmetric columns where we achieve a desired velocity field with uniform transit times despite varying device cross sections.
• [03496] Regularised stochastic Landau-Lifshitz equations and their application in numerical analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Chunxi Jiao (RWTH Aachen University )
  • Abstract : We revisit a regularised stochastic Landau-Lifshitz equation (sLLE) with bi-Laplacian in the effective field and study a similarly regularised stochastic Landau-Lifshitz-Bloch equation (sLLBE) in a two-dimensional domain. We derive the rate of convergence (in probability) of numerical solutions of a finite-element scheme for the regularised sLLBE to the solution of sLLBE, and outline the difficulty of applying this approach to sLLE. This talk is based on a joint work with Beniamin Goldys and Ngan Le.
• [03482] A least squares Hessian/Gradient recovery method for fully nonlinear PDEs in Hamilton--Jacobi--Bellman form
  • Format : Talk at Waseda University
  • Author(s) :
    • Omar Lakkis (University of Sussex)
    • Amireh Mousavi (Jena Universität)
  • Abstract : Least squares recovery methods provide a simple and practical way to approximate linear elliptic PDEs in nondivergence form where standard variational approach either fails or requires technically complex modifications. This idea allows the creation of relatively efficient solvers for fully nonlinear elliptic equations, the linearization of which leaves us with an equation in nondivergence form. An important class of fully nonlinear elliptic PDEs is that of Hamilton--Jacobi--Bellman form. Suitable functional spaces and penalties in the cost functional must be carefully crafted in order to ensure stability and convergence of the scheme with a good approximation of the gradient and Hessian which is useful, for example, for Newton--Raphson, semismooth Newton, or a policy iteration (Howard) approximation of a Hamilton--Jacobi--Bellman equation. We prove convergence and provide convergence rates under a Cordes condition.

MS [00642] Traveling Waves in Mathematical Epidemiology

room : G601

• [05106] Traveling wave solutions for an epidemic model with free boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoichi Enatsu (Tokyo University of Science)
    • Emiko Ishiwata (Tokyo University of Science)
    • Takeo Ushijima (Tokyo University of Science)
  • Abstract : Free boundary problems are recently used to model phenomena of biological invasion for species such as migration into a new habitat. In this talk, we consider a diffusive epidemic model with free boundary. We prove the existence and nonexistence of a traveling wave solution of the model. We numerically observe the traveling wave and the front motion of the model. This is a joint work with Takeo Ushijima and Emiko Ishiwata.
• [01447] Traveling Wave Solutions for Discrete Diffusive SIR Epidemic Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Ran Zhang (Heilongjiang University)
    • Jinliang Wang (Heilongjiang University)
    • Shengqiang Liu (Tiangong University)
  • Abstract : In this talk, we deal with the conditions of existence and nonexistence of traveling wave solutions for a class of discrete diffusive epidemic model. In addition, the boundary asymptotic behavior of traveling wave solutions is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Our result could answer some unsolved problems in the previous studies on discrete diffusive epidemic model.
• [04496] Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase
  • Format : Talk at Waseda University
  • Author(s) :
    • Mostafa Adimy (Inria and UCBL 1, Lyon)
    • Abdennasser Chekroun (University of Tlemcen)
    • Toshikazu Kuniya (Kobe University)
  • Abstract : We consider a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder’s fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.

MS [00036] Different perspectives in non-linear and non-local PDEs

room : G602

• [04031] Quantified overdamped limit for Vlasov-Fokker-Planck equations with singular interaction forces
  • Format : Talk at Waseda University
  • Author(s) :
    • Young-Pil Choi (Yonsei University)
  • Abstract : In this talk, I will discuss a quantified overdamped limit for kinetic Vlasov-Fokker-Planck equations with nonlocal interaction forces. We provide explicit bounds on the error between solutions of that kinetic equation and the limiting equation, which is known under the names of aggregation-diffusion equation or McKean-Vlasov equation. Our strategy only requires weak integrability of the interaction potentials, thus in particular it includes the quantified overdamped limit of the kinetic Vlasov-Poisson-Fokker-Planck system to the aggregation-diffusion equation with either repulsive electrostatic or attractive gravitational interactions.
• [04055] A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Noemi David (University of Lyon)
    • Tomasz Dębiec (University of Warsaw)
    • Mainak Mandal (Technische Universität Dresden)
    • Markus Schmidtchen (Technische Universität Dresden)
  • Abstract : In recent years, there has been a spike in interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law or Darcy's law. While each of these velocity-pressure relations has been studied in the literature, little emphasis has been placed on the fine relationship between them. In this paper, we want to address this dearth in the literature, providing a rigorous argument that bridges the gap between a viscoelastic tumour model (of Brinkman type) and an inviscid tumour model (of Darcy type).
• [03802] Nonlocal particle approximations of the porous medium equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Katy Craig (University of California, Santa Barbara)
    • Olga Turanova (Michigan State University)
    • Karthik Elamvazhuthi (University of California, Riverside)
    • Matt Haberland (Cal Poly, San Luis Obispo)
  • Abstract : Given a desired target distribution and an initial guess of its samples, what is the best way to evolve the locations of the samples so that they accurately represent the desired distribution? A classical solution to this problem is to evolve the samples according to Langevin dynamics, a stochastic particle method for the Fokker-Planck equation. In today’s talk, I will contrast this with a nonlocal, deterministic particle method inspired by the porous medium equation. Using the Wasserstein gradient flow structure of the equations and Serfaty’s scheme of Gamma-convergence of gradient flows, I will show that, as the number of samples increases and the interaction scale goes to zero, the interacting particle system indeed converges to a solution of the porous medium equation. I will close by discussing practical implications of this result to both sampling and the training dynamics two-layer neural networks. This is based on joint work with Karthik Elamvazhuthi, Matt Haberland, and Olga Turanova.
• [05056] A convergent discretization of the porous medium equation with fractional pressure
  • Format : Talk at Waseda University
  • Author(s) :
    • Félix del Teso (Universidad Autónoma de MadridU)
  • Abstract : We carefully construct and prove convergence of what is to our knowledge the first numerical discretization of the porous medium equation with fractional pressure, \begin{equation}\tag{FPE} \frac{\partial u}{\partial t}-\nabla\cdot\left(u^{m-1}\nabla(-\Delta)^{-\sigma}u\right)=0, \end{equation} for $\sigma\in(0,1)$. The model was introduced by Caffarelli and Vázques in 2011, and is currently one of two main nonlocal extensions of the local porous medium equation. It has finite speed of propagation and comes from a nonlocal Fick's law, but as opposed to the other extension, it does not satisfy the comparison principle. Without comparison, the analysis is difficult. Uniqueness is only known in 1d, where one can exploit that the ``cumulative density'' $v(x,t)=\int_{-\infty}^yu(y,t)dy$ satisfies \begin{equation} \frac{\partial v}{\partial t}+|\partial_xv|^{m-1}(-\Delta)^s v=0,\quad s=1-\sigma, \end{equation} which is a nonlocal quasilinear parabolic equation in nondivergence form that can be analyzed through viscosity solution methods. Our numerical method then loosely speaking consists in discretizing this ``integrated'' equation with a difference quadrature scheme and then compute the solution $u$ of (FPE) via numerical differentiation. Using upwinding in non-traditional way, we obtain a new type of monotone schemes that allows for convergence analysis via the Barles-Perthame-Souganidis half-relaxed limit method. Combining this result with tightness arguments, we then prove convergence of the approximations of the original problem in the Rubinstein-Kantorovich/Wasserstein-1 distance uniformly in time. Our results cover both absolutely continuous and Dirac or point mass initial data, and in the latter case, machinery for discontinuous viscosity solutions are needed in the analysis.

MS [00559] DNB Theory and its Applications

room : G605

• [05643] Introduction to DNB Theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuyuki Aihara (The University of Tokyo)
  • Abstract : As the opening talk of this minisymposium, I introduce the concept of DNB (Dynamical Network Biomarkers) theory, its experimental proof of concept and its possible applications to ultra-early precision medicine.
• [05641] DNB-based intervention for ultra-early treatment
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun-ichi Imura (Tokyo Institute of Technology)
  • Abstract : The process leading to the onset of disease may be understood as a rapid transition in the complex interactions between genes. This talk proposes a DNB-based intervention approach for preventive treatment just before such transitions, i.e., in the pre-disease state, by combining DNB theory with control theory to build a theory that estimates which nodes of the relevant gene expression network should be intervened and how they should be intervened.
• [05343] Change-point detection in temporal complex systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Huanfei Ma (Soochow University)
  • Abstract : We develop a model-free approach, named temporal change-point detection (TCD), and integrate both dynamical and statistical methods to achieve accurate detection of the time instant at which a system changes its internal structures. The proposed approach is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner.
• [05637] Alerting for the critical transition of complex systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Rui Liu (South China University of Technology)
  • Abstract : It is a challenging task to accurately predict the future critical state of a short-term time-series. The major difficulty to solve such a task is the lack of the information, which typically results in the failure of most existing approaches due to the overfitting problem of the small sample size. To address this issue, we proposed a computing framework: auto-reservoir neural network, to efficiently and accurately make the multi-step-ahead prediction based on a short-term high-dimensional time-series. Different from traditional reservoir computing whose reservoir is an external dynamical system irrelevant to the target system, ARNN directly transforms the observed high-dimensional dynamics as its reservoir, which maps the high-dimensional/spatial data to the future temporal values of a target variable based on a spatiotemporal information (STI) transformation. Combining with the dynamic network biomarker (DNB), it is possible to detect the early-warning signal of critical transitions of real-world complex systems.

MS [00528] High order and well-balanced methods and stability analysis for non-linear hyperbolic systems

room : G606

• [01682] High order well-balanced finite volume and discontinuous Galerkin schemes for a first order hyperbolic reformulation of the coupled Einstein-Euler system in 3+1 general relativity
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Dumbser (University of Trento)
  • Abstract : We present new well-balanced finite volume and discontinuous Galerkin schemes for the solution of a new first order hyperbolic Z4 formulation of the Einstein-Euler system of general relativity. Nonlinear involutions are accounted for via a covariant GLM cleaning technique. We introduce a new, simple and efficient type of well-balancing that automatically applies to any numerical discretization and arbitrary equilibria in multiple space dimensions. We show numerical results for vacuum spacetimes and for a TOV star.
• [01699] Numerical approximation of non-convex relativistic hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Susana Serna (Universitat Autonoma de Barcelona)
    • Antonio Marquina (Universidad de Valencia)
  • Abstract : We explore the rich and complex dynamics that a phenomenological equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects. We study the parameter space of the EoS to ensure its causality and thermodynamical consistency. We approximate the non-conventional dynamics developed in the evolution of relativistic blast waves by means of a high order shock capturing scheme.
• [01720] Recovering primitive variables in special relativistic hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Antonio Marquina (Universidad de Valencia)
    • Susana Serna (Universitat Autonoma de Barcelona)
    • Jose M Ibanez (Universidad de Valencia)
  • Abstract : We study an iterative procedure based on fixed-point strategy to recover primitive variables in each time step of the evolution of Special Relativistic Hydrodynamic equations. Given a set of three conserved values we start the iteration by prescribing an initial zero pressure so that if the first iterate is strictly positive, then, the fixed-point iteration monotonically converges to the unique pressure associated to the conserved variables.
• [01290] Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Ernesto Guerrero Fernández (National Oceanic and Atmospheric Administration (NOAA))
    • Cipriano Escalante Sanchez (Universidad de Málaga)
    • Manuel Castro Díaz (Universidad de Málaga)
  • Abstract : This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced character of the resulting numerical method for smooth stationary solutions. The strategy can be adapted to some well-known different time marching DG discretisations. Particularly, in this article, Runge--Kutta DG and ADER DG methods are studied. Additionally, a limiting procedure based on a modified WENO approach is described to deal with the spurious oscillations generated in the presence of non-smooth solutions, keeping the well-balanced properties of the scheme intact. The resulting numerical method is then exactly well-balanced and high-order in space and time for smooth solutions. Finally, some numerical results are depicted using different systems of balance laws to show the performance of the introduced numerical strategy.

MS [00108] Recent Advances on Kinetic and Related Equations

room : G702

• [01451] Boundary singularity of a mono-speed Lorentz model for molecules with the infinite-range potential
  • Format : Talk at Waseda University
  • Author(s) :
    • Shigeru Takata (Kyoto University)
    • Masanari Hattori (Kyoto University)
    • Hayato Iida (Kyoto University)
  • Abstract : Possibility of the diverging gradient of the macroscopic quantity near the boundary is investigated by a mono-speed Lorentz-gas model, with a special attention to the regularizing effect of the grazing collision for the infinite-range potential on the velocity distribution function (VDF) and its influence on the macroscopic quantity. By careful numerical analyses of the steady one-dimensional boundary-value problem, it is confirmed that the grazing collision suppresses the occurrence of a jump discontinuity of the VDF on the boundary. However, as the price for that regularization, the collision integral becomes no longer finite in the direction of the molecular velocity parallel to the boundary. Consequently, the gradient of the macroscopic quantity diverges, even stronger than the case of the finite-range potential. A conjecture about the diverging rate in approaching the boundary is made as well for a wide range of the infinite-range potentials, accompanied by numerical evidences.
• [01849] On the Existence and Regularity for the Stationary Linearized Boltzmann Equation in a Small Domain
  • Format : Talk at Waseda University
  • Author(s) :
    • I-Kun Chen (National Taiwan University)
    • Ping-Han Chuang (National Taiwan University)
    • Jhe-Kuan Su (National Taiwan University)
    • Chun-Hsiung Hsia (National Taiwan University)
    • Daisuke Kawagoe (Kyoto University)
  • Abstract : We consider the incoming boundary value problem for the stationary linearized Boltzmann equation in a bounded domain with C^2 boundary of positive Gaussian curvature. We prove the existence of H^1 of solutions under assumptions that the boundary data is good enough and the domain is small enough. A counter example is provided to demonstrate the role of the geometry.
• [05464] Regularity estimates for the non-cutoff soft potential Boltzmann equation with typical rough and slowly decaying data
  • Format : Talk at Waseda University
  • Author(s) :
    • Lingbing He (Tsinghua University)
    • Jie Ji (Peking University)
  • Abstract : or the non-cutoff soft potential Boltzmann equation, if the Boltzmann collision operator is strictly elliptic in the $v$ variable, it is conjectured that the solution to the equation will become infinitely smooth instantly for both spatial and velocity variables for any positive time, even if the initial data has only polynomial decay in high velocity regimes. This conjecture is significant because it is closely connected to the regularity problem of weak solutions, especially for the smoothing property of so-called ``regular point''. In this work, we show that the conjecture may not hold for the general weak solution due to the degenerate and non-local properties of the collision operator. We demonstrate this in three steps: (i) constructing so-called ``typical rough and slowly decaying data''; (ii) proving that such data induces only finite smoothing effect for weak solutions in Sobolev spaces; and (iii) proving that this finite smoothing property induces local properties for any positive time, including that the Leibniz rule does not hold for high derivatives of the collision operator (even in the weak sense) and that there is a discontinuity in the $x$ variable for the average of weak solutions on certain domains.
• [00646] Vanishing angular singularity limit to the hard-sphere Boltzmann equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jin Woo Jang (Pohang University of Science and Technology)
    • Bernhard Kepka (University of Bonn)
    • Alessia Nota (Università degli Studi dell'Aquila)
    • Juan J. L. Velázquez (University of Bonn)
  • Abstract : In this talk we consider Boltzmann's collision kernel for inverse power law interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $ d=3 $. We introduce the proof of the limit of the non-cutoff kernel to the hard-sphere kernel and give precise asymptotic formulas of the singular layer near $\theta\simeq 0$ in the limit $ s\to \infty $. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions.

MS [01191] Recent advances on regularity and irregularity of fluids flows

room : G703

• [03313] Singularity formation for models of fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Mimi Dai (University of Illinois at Chicago)
  • Abstract : Finite time singularity formation for fluid equations will be discussed. Built on extensive study of approximating models, breakthroughs on this topic have emerged recently for Euler equation. Inspired by the progress for pure fluids, we attempt to understand this challenging issue for magnetohydrodynamics (MHD). Finite time singularity scenarios are discovered for some reduced models of MHD. The investigation also reveals connections of MHD with Euler equation and surface quasi-geostrophic equation.
• [03731] Vorticity estimates for the 3D incompressible Navier-Stokes equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jincheng Yang (University of Chicago)
  • Abstract : We show some a priori regularity estimates for the vorticity and its trace in the three-dimensional incompressible Navier-Stokes equation. These a priori estimates are obtained via the blow-up method and a novel averaging operator. The averaging operator can be used to provide regularity and trace estimates for PDEs with $\varepsilon$-regularity.
• [04943] On criticality of the Navier-Stokes diffusion
  • Format : Online Talk on Zoom
  • Author(s) :
    • zoran grujic (university of virginia)
  • Abstract : The main purpose of this talk is to present a mathematical evidence of criticality of the Navier-Stokes diffusion. In particular, considering a plausible candidate for a finite time blow-up, a two-parameter family of the dynamically rescaled profiles, we show that as soon as the hyper-diffusion exponent is greater than one, a new region in the parameter space (completely in the super-critical regime) is ruled out. As a matter of fact, the region is a neighborhood (in the parameter space) of the self-similar profile, i.e., the `approximately self-similar' blow-up is ruled out for all hyper-diffusive models.
• [05062] Well-posedness of mildly regularized active scalars in Sobolev spaces
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anuj Kumar (Florida State University)
    • Vincent Ryan Martinez (CUNY Hunter College)
  • Abstract : In this work, we consider the initial value problem for a family of active scalar equations when perturbed by a logarithmic order regularization in dissipation. These equations, commonly known as generalized surface quasi-geostrophic equations (gSQG) interpolate between the 2D incompressible Euler equation and the 2D SQG equation, and extrapolate beyond SQG to a family with more singular velocities. Ill-posedness at the threshold regularity for the unperturbed models has been established in the celebrated works of Bourgain and Li, and Elgindi and Masmoudi for the 2D Euler equation, and recently by Cordoba and Zoroa-Martinez, and Jeong and Kim for the 2D SQG equation. In this work, we treat the positive side of well-posedness and consider a minimally dissipative regularization to recover local well-posedness (in the Hadamard sense) in the threshold Sobolev regularity. The proof is based on developing estimates for a suitably identified linear system that preserves the underlying commutator structure of the nonlinearity.

MS [01532] Recent Trends in Fluid Mechanics and its Applications

room : G704

• [01972] Global BV solution and relaxation limit for Greenberg-Klar-Rascle model
  • Author(s) :
    • Ying-Chieh Lin (National University of Kaohsiung)
    • Shih-Wei Chou (Soochow University)
    • John M. Hong (National Central University)
    • Hsin-Yi Lee (National Cheng Kung University)
  • Abstract : In this talk, we consider the Greenberg-Klar-Rascle multi-lane traffic flow model. This model is a relaxation system with the equilibrium state that is a discontinuous function of the car density. We study the existence of global entropy solutions and the relaxation limit for the GKR model. To construct the approximate solutions, we find two sequences of invariant regions under some suitable condition of initial data. As the relaxation time approaches 0, we prove that the limit of the entropy solutions for the GKR model is a weak solution of its equilibrium equation. It is interesting that the equilibrium equation is a scalar conservation law with discontinuous flux.
• [02450] Global Transonic Solutions of Compressible Euler-Poisson Equations in Semiconductors
  • Author(s) :
    • Shih-Wei Chou (Soochow University)
    • Chia-Chieh Jay Chu (National Tsing Hua University)
    • John M Hong (National Central University)
  • Abstract : In this talk, we consider an initial-boundary value problem of compressible Euler-Poisson equations arising in semiconductors. The equations form a 3-by-3 hyperbolic system of balnace laws with the global source. We establish the global existence of the transonic entropy solution by framework of a generized Glimm scheme. This is a joint work with John Hong and Jay Chu.
• [02456] Finite Speed of Propagation of the Relativistic Landau and Boltzmann Equations
  • Author(s) :
    • Ming Jiea Lyu (Chung Yuan Christian University)
    • Kung Chien Wu (National Cheng Kung University,)
    • Baoyan Sun (Yantai University)
  • Abstract : In this talk, we will study the relativistic Boltzmann and Landau equations in the whole space ${\mathbb{R}}^{3}$ under the closed to equilibrium setting. We recognize the finite speed of propagation of the solution in $L^{\infty}_{v,p}L^{\infty}_{x}$ and $L^{2}_{v}L^{\infty}_{x}$.
• [02865] Global Transonic Solutions of Hot-Jupiter Model for exoplanetary atmosphere
  • Author(s) :
    • Po-Chih Huang (Natonal Chung Cheng University)
  • Abstract : The hydrodynamic escape problem (HEP) for Hot Jupiter model, which is characterized by a inital-boundary value problem of Euler equation with exoplanetary gravity, heat, and tidal force cuased by star, is crucial for investigating the evolution of planetary atmospheres. In this paper, the global existence of transonic solutions to the HEP is established using the generalized Glimm method. The new version of Riemann and boundary-Riemann solvers, are provided as building blocks of the generalized Glimm method by inventing the contraction matrices for the homogeneous Riemann or boundary-Riemann solutions. The extended Glimm-Goodman wave interaction estimates are investigated for obtaining a stable scheme and the lower bound of the gas velocity, which matches the physical observation. The limit of approximation solutions serves as an entropy solution of bounded variations. Moreover, the range of the feasible hydrodynamical region is also obtained.

MS [00024] Geometric methods in machine learning and data analysis

room : G709

• [03148] Geometric Data Analysis via Discrete Curvature
  • Format : Talk at Waseda University
  • Author(s) :
    • Melanie Weber (Harvard University)
  • Abstract : The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of Machine Learning. In this talk, we approach this problem from the perspective of Discrete Geometry. We begin by reviewing discrete notions of curvature, where we focus especially on discrete Ricci curvature. Then we consider a setting, where a given point cloud was sampled from an (unknown) manifold. We give pointwise consistency results for the discrete curvature of a geometric graph build from the point cloud and the curvature of the manifold. We further show that if the manifold has curvature bounded from below by a positive constant, the geometric graph will inherit this global structural property with high probability. Finally, we discuss applications of discrete curvature and our consistency results in Geometric Data Analysis, including graph-based clustering and regression. The talk is based on joint work with Nicolas Garcia Trillos, Zachary Lubberts and Yu Tian.
• [02978] Large data limit of the MBO scheme for data clustering
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jona Lelmi (University of Bonn)
    • Tim Laux (University of Bonn)
  • Abstract : The MBO scheme is a highly performant scheme used for data clustering. Given some data, one constructs the similarity graph associated with the data points. The goal is to split the data into meaningful clusters. The algorithm produces the clusters by alternating between diffusion on the graph and pointwise thresholding. In this talk, I will present the first theoretical studies of the scheme in the large data limit. We will see how the final state of the algorithm is asymptotically related to minimal surfaces in the data manifold and how the dynamic of the scheme is asymptotically related to the trajectory of steepest descent for surfaces, which is mean curvature flow. The tools employed are variational methods and viscosity solutions techniques. Based on joint work with Tim Laux (U Bonn).
• [03210] Topologies of convergences for discrete-to-continuum limit on Poission point clouds
  • Format : Talk at Waseda University
  • Author(s) :
    • Marco Caroccia (Politecnico di Milano)
  • Abstract : Energies on point clouds have attracted increasing attention in the last decades, especially due to their application to machine learning and data analysis. What seems to arise from the collection of the results at several scales is that a change in the topology of Gamma-convergence occur when the point clouds is connected at a very short-range interaction scale. Typically, in literature, the interaction range considered is big enough to neglect the defects arising from the stochastic geometry of the point clouds. In the small range interaction regime instead the geometry of the point clouds cannot be neglected in the analysis of the discrete-to-continuum limit. We will present the various topologies of convergence and the different techniques that are required to obtain the discrete-to-continuum limit at different scales.
• [03219] Spectral Methods for Data Sets of Mixed Dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Leon Bungert (Technical University of Berlin)
    • Dejan Slepcev (Carnegie Mellon University)
  • Abstract : High dimensional data often consist of parts with different intrinsic dimension. We study how spectral methods on graphs adapt to data containing intersecting pieces of different dimensions. We show that unnormalized Laplacian strongly prefer the highest dimension, while appropriately normalized Laplacian converges to Laplace-Beltrami operator in all dimensions simultaneously. For intersecting manifolds we identify when and how is the information transferred between manifolds.

MS [00038] Frontiers of gradient flows: well-posedness, asymptotics, singular limits

room : G710

• [05191] Existence for a class of fourth-order quasilinear parabolic systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Michal Lasica (Polish Academy of Sciences)
    • Yoshikazu Giga (the University of Tokyo)
  • Abstract : We consider a class of nonlinear fourth-order parabolic systems of PDEs formally arising as gradient flows of $p$-Dirichlet type energies with respect to $H^{-1}$ metrics weighted by spatial derivatives of the solution up to second order. PDEs with such structure appear for example in modeling of thermal fluctuations in crystal surfaces. We prove global existence of weak solutions. Our tools include a variant of Galerkin scheme, monotonicity methods, and interpolation.
• [03572] Evolutionary limit of gradient flows in heterogeneous Wasserstein space
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuan Gao (Purdue University)
  • Abstract : The Fokker-Planck equation with fast oscillated coefficients can be regarded as a gradient flow in Wasserstein space with heterogeneous medium. We will use an evolutionary variational approach to obtain the homogenized dynamics, which preserves the gradient flow structure in a limiting homogenized Wasserstein space. Equivalent formulations for heterogeneous Wasserstein distance and their limits will also be discussed.
• [04719] The fourth-order total variation flow in R^n
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirotoshi Kuroda (Hokkaido University)
    • Yoshikazu Giga (the University of Tokyo)
    • Michał Łasica (Polish Academy of Sciences)
  • Abstract : We characterize the solution in terms of what is called the Cahn-Hoffman vector field, and introduce a notion of calibrability of a set in our fourth-order setting. This notion is related to whether a characteristic function preserves its form throughout the evolution. If $n \neq 2$, all annuli are calibrable. In the case $n=2$, if an annulus is too thick, it is not calibrable.
• [05426] Global existence for the p-Sobolev flow
  • Format : Online Talk on Zoom
  • Author(s) :
    • Masashi Misawa (Kumamoto University)
  • Abstract : We shall talk about the global existence of the p-Sobolev flow. The p-Sobolev flow is regarded as the heat flow associated with the Sobolev inequality and the nonlinear eigenvalue problem corresponding to it. We shall study the asymptotic behavior of the p-Sobolev flow and present the so-called volume concentration phenomenon at time-infinity.

MS [00090] Recent advances in the theory of rogue waves: one- and multi-component models in 1+1 and 2+1 dimensions

room : G801

• [03779] Maximal Amplitudes of N-Phase Solutions of a Modified NLS Equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Otis Wright (Cedarville University)
  • Abstract : An effective method for finding the maximal amplitudes of N-phase solutions of a modified nonlinear Schrödinger equation is discussed.
• [05214] The effects of damping on rogue wave formation and permanent downshifting
  • Format : Online Talk on Zoom
  • Author(s) :
    • Cosntance Schober (University of Central Florida)
    • Annalisa Maria Calini (College of Charleston )
  • Abstract : The effects of damping on the B-F instability, rogue wave formation, and permanent downshifting are discussed in the framework of the viscous damped higher order nonlinear Schrodinger (v-HONLS) equation. The linear stability analysis of the damped Stokes wave solution is presented. Numerical simulations of the v-HONLS with unstable Stokes wave initial data indicate the inclusion of viscosity enables permanent downshifting and rogue waves typically do not develop after the time of permanent downshift.
• [04450] Rogue-wave formation scenarios for focusing NLS with parabolic initial data
  • Format : Talk at Waseda University
  • Author(s) :
    • Francesco Demontis (University of Cagliari)
    • Giovanni Ortenzi (University of Torino)
    • Giacomo Roberti (Northumbria University)
    • Matteo Sommacal (Northumbria University)
  • Abstract : We study focussing NLS for compactly-supported parabolic initial data with constant chirp. In the absence of dispersion, we provide a criterion for blow-up, generalising a result by Talanov et al. In the presence of dispersion, the same criterion determines, even beyond the semi-classical regime, the formation of rogue-waves, whose onset time is predicted by the corresponding dispersionless catastrophe time. Numerics suggest that the chirp controls the prevailing scenario among two competing mechanisms for rogue-wave formation.
• [04494] Stability of plane waves for the Yajima-Oikawa-Newell equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Marcos Caso-Huerta (Northumbria University)
  • Abstract : A new, integrable long wave-short wave model is proposed, encompassing Yajima-Oikawa and Newell systems as particular choices of the coefficients. The stability of its plane waves is studied in an algebraic-geometric approach making use of its Lax pair. The stability spectra are explicitly computed, leading to identifying a relation between the topology of the spectra and the gain of the system. This allows one to predict regions of existence for rogue wave type solutions.

MS [00957] Mathematics of thin structures

room : G802

• [04690] Rod shaped structures in plants
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Dondl (Albert-Ludwig-University Freiburg)
  • Abstract : During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to adapt to changing environmental conditions. The trade-off between flexural and torsional rigidity is an important example of sometimes conflicting mechanical requirements, the adaptation to which can be quantified by the dimensionless twist-to-bend ratio. In this work, we derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. Using a phase field approximation of the optimization problem we compute optimal structures and relate the resulting shapes to the morphology of plant stems.
• [04525] A homogenized bending theory for prestrained plates
  • Format : Talk at Waseda University
  • Author(s) :
    • Klaus Böhnlein (TU Dresden)
    • Stefan Neukamm (TU Dresden)
    • David Padilla-Garza (TU Dresden)
    • Oliver Sander (TU Dresden)
  • Abstract : Nonlinear plate theory described the energy of an incompressible and inextensible thin elastic sheet. In this work, we show a general rigorous derivation of a generalization of such a model for non-euclidean plates with microheterogeneous structures. We also analyze the limiting energy in some examples and discover interesting and counter-intuitive phenomena.
• [01825] Variational Modeling of Stress-Driven Rearrangement Instabilities
  • Format : Talk at Waseda University
  • Author(s) :
    • Paolo Piovano (Politecnico di Milano)
  • Abstract : Variational models in the context of the theory of stress-driven rearrangement instabilities are considered to describe the morphology of crystalline materials under stress due to the interaction with other adjacent materials. The existence and regularity of energy minimizers is discussed in various settings, from two to higher dimensions, and in the framework of a two-phase free-boundary problem by letting free also the contact interface with the other materials, both in its coherent and incoherent portions.

MS [02616] Recent Developments in Applied Inverse Problems

room : G808

• [04397] Perturbation of Surface Waves in Piezoelectric Media
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazumi Tanuma (Gunma University)
    • Xiang Xu (Zhejiang University)
    • Gen Nakamura (Hokkaido University)
  • Abstract : We study Bleustein-Gulyaev (BG) waves which propagate along the surface of a homogeneous $C_6$ hexagonal piezoelectric half-space under the mechanically-free and electrically-closed condition at the surface. We prove stability of the BG waves, to investigate the perturbations of their phase velocity and polarization when a fully anisotropic perturbation is added to the hexagonal material constants. The inverse problem to obtain material information from measurements of BG waves will be discussed.
• [04646] Quantitative Parameter Reconstruction from Optical Coherence Tomographic Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Leopold Veselka (University of Vienna)
  • Abstract : We discuss the quantification of the refractive index from data obtained by optical coherence tomography - an imaging modality based on the interferometric measurement of back-scattered light. We consider samples with layered structure, where the refractive index as a function of depth is a piece-wise constant function. The applicability of the reconstruction method, where the refractive index is obtained layer-by-layer via least squares minimization, is verified by numerical examples for both simulated and experimental data. This is a joint work with Peter Elbau (University of Vienna, Austria) and Leonidas Mindrinos (Agricultural University of Athens, Greece).
• [04241] Landweber-Kaczmarz for full datacube modelling in Extragalactic Archaeology
  • Format : Talk at Waseda University
  • Author(s) :
    • Fabian Hinterer (JKU Linz)
  • Abstract : We consider the problem of reconstructing a galaxy’s stellar population distribution function from spectroscopy measurements. These quantities can be connected via the single-stellar population spectrum, resulting in a very large scale integral equation with a system structure. To solve this problem, we propose a projected Nesterov-Kaczmarz reconstruction (PNKR) method, which efficiently leverages the system structure and incorporates physical prior information such as smoothness and non-negativity constraints.

MS [00876] Inverse Problems in Partial Differential Equations and Graphs

room : G809

• [04431] Geophysics and algebraic geometry
  • Format : Talk at Waseda University
  • Author(s) :
    • Joonas Ilmavirta (University of Jyväskylä)
  • Abstract : Many areas of interest within the Earth are anisotropic, meaning that the speed of sound is different in different directions. It turns out that pressure waves are far better behaved than shear waves, but fortunately the different polarizations are coupled together through algebraic geometry. I will explain the surprising power of algebraic geometry in the study of anisotropic inverse problems.
• [03655] Retrieving coupled Yang-Mills-Higgs fields
  • Format : Talk at Waseda University
  • Author(s) :
    • Xi Chen (Fudan University)
    • Matti Lassas (University of Helsinki)
    • Gabriel Paternain (University of Cambridge)
    • Lauri Oksanen (University of Helsinki)
  • Abstract : The pure Yang-Mills theory is only able to describe the behavior of massless gauge bosons. But experiments show massive gauge bosons do exist. According to the Higgs mechanism of mass generation, the mass of gauge bosons is acquired through the interactions with Higgs bosons. Therefore, the combined Yang-Mills-Higgs Lagrangian together with its Euler-Lagrange equation is of great scientific significance. We show that one can detect the coupled Yang-Mills-Higgs fields from active local measurements of Yang-Mills-Higgs equations.
• [03095] Inverse problems for the graph Laplacian
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinpeng Lu (University of Helsinki)
  • Abstract : We study the discrete version of Gel'fand's inverse spectral problem, of determining the graph structure of a finite weighted graph from the spectral data of its graph Laplacian. We prove that the problem is uniquely solvable under a novel Two-Points Condition. We also consider an inverse problem for random walks on finite graphs and its unique solvability under this condition. This is a joint work with E. Blåsten, H. Isozaki and M. Lassas.
• [03169] Quantum computing algorithms for inverse problems on graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Joonas Ilmavirta (University of Jyväskylä)
    • Matti Lassas (University of Helsinki)
    • Jinpeng Lu (University of Helsinki)
    • Lauri Oksanen (University of Helsinki)
    • Lauri Ylinen (University of Helsinki)
  • Abstract : We consider a quantum algorithm for an inverse travel time problem on a graph. This problem is a discrete version of the inverse travel time problem encountered in seismic and medical imaging and the boundary rigidity problem studied in Riemannian geometry. We also consider the computational complexity of the inverse problem, and show that the quantum algorithm has a quadratic improvement in computational cost when compared to the standard classical algorithm.

MS [00593] Advances in Nonlinear Dynamics

room : F308

• [02779] Polynomial discretisations of transfer and Koopman operators in chaotic dynamics
  • Author(s) :
    • Caroline Wormell (The Australian National University)
  • Abstract : Many long-term statistical properties of chaotic systems are encoded by transfer or Koopman operators. Orthogonal polynomial-based operator discretisations are generally very efficient, and I will show in expanding dynamics these operators are no exception: a Chebyshev discretisation allows fast, very accurate, rigorous estimates of expanding dynamics, even with parabolic fixed points. Furthermore, a theoretical extension to general orthogonal polynomials proves fast convergence of Extended Dynamical Mode Decomposition, a data-driven algorithm commonly used across physical sciences.
• [03719] Estimating the spectra for annealed transfer operators of random dynamical systems
  • Author(s) :
    • Alex Blumenthal (Georgia Tech)
    • Isaia Nisoli (Universidade Federal de Rio de Janeiro)
    • Toby Taylor-Crush (University of Loughborough)
  • Abstract : I will describe some recent efforts with my collaborators Toby Taylor-Crush and Isaia Nisoli towards the computer-validated estimation of spectra for annealed transfer operators of random dynamical systems. Applications include the study of various stochastic bifurcations associated to the explosion of the support of a stationary measure as some underlying parameter is varied.
• [03734] Energy growth in Hamiltonian systems with small dissipation
  • Author(s) :
    • Marian Gidea (Yeshiva Univesity)
  • Abstract : We consider a model for an energy harvesting device consisting of a rotator and a pendulum subject to a small perturbation given by a time-periodic Hamiltonian vector field plus a conformally symplectic vector field. In general, the system has energy dissipation. We provide explicit conditions so that the system exhibits energy growth. In theory, this shows Arnold diffusion in Hamiltonian systems with small dissipation. In practice, this translates into continuous generation of electricity.
• [03874] A dynamical systems approach to low-damage seismic design
  • Author(s) :
    • Hinke M Osinga (University of Auckland)
  • Abstract : An example of low-damage seismic design is the post-tensioned moment-resisting frame, which exhibits geometric nonlinearity under large deformations. Whether the tilt angle of the frame exceeds a prescribed maximum depends on the forcing properties. We show that this failure boundary is organised by so-called grazing orbits, which reach but do not move beyond the design limit of the frame. We consider both harmonic and aperiodic waves with a broader frequency content.

MS [02072] Theory and applications of random/non-autonomous dynamical systems: Part I

room : F309

• [03478] New characterizations of noise-induced order
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuzuru Sato (Hokkaido University)
  • Abstract : This talk includes a brief review of phenomenologies of non-autonomous / random dynamical systems, followed by a few examples of typical noise-induced phenomena in random dynamical systems. In particular, we present recent results on new characterizations of noise-induced order.
• [04094] Time-delayed feedback control for random dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Miki Kobayashi (Rissho University)
    • Yuzuru Sato (Hokkaido University)
  • Abstract : We propose a framework of Pyragas control for random dynamical systems. The deterministic Pyragus control adopts delayed feedback controls to stabilize a UPO in the original deterministic strange attractor. We demonstrate a few examples including stochastic Rossler dynamics.
• [03936] Rigorous enclosure of spectra and its applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Isaia Nisoli (Universidade Federal do Rio de Janeiro)
    • Alex Blumenthal (Georgia Tech)
    • Toby Taylor-Crush (Loughbourugh University)
    • Yuzuru Sato (Hokkaido University)
  • Abstract : In this talk I will introduce a tool developed in collaboration with Dr. A. Blumenthal and Dr. T. Taylor-Crush to rigorously enclose the finite spectrum of a Markov operator. I will then introduce some applications to the study of the phenomenology of important examples of random dynamical systems developed by Prof. Y. Sato.
• [03935] Recent developments on Lorenz-like attractors
  • Format : Talk at Waseda University
  • Author(s) :
    • MARIA JOSE PACIFICO (Federal University of Rio de Janeiro)
  • Abstract : The Lorenz attractor has been playing a central role in the research of singular flows, i.e., flows generated by smooth vector fields with singularities. In this talk I shall survey about old and new results describing the dynamics of this kind of attractors from the topological as well as the ergodic point of view. I will end sketching the proof of my result establishing that in a C1-open and densely family of vector fields (including the classical Lorenz attractor), if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state supported on Λ. In particular, there exists a unique measure of maximal entropy for the ow X|Λ.

contributed talk: CT058

room : F310

[02073] Graph convolutional networks for graph signal processing

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F310
• Type : Contributed Talk
• Abstract : We propose novel graph convolution models for analyzing graph-structured time series data. Graph convolutional networks (GCNs) is a generalization of convolutional neural networks from regular grid data to irregular graph data. The major building block of a GCN is the filter. Graph filters are designed for graph convolution in spatial and spectral domains. We also propose novel graph wavelet transform methods to be jointly used with graph convolution filters, which can further improve the results.
• Classification : 42BXX, Machine learning, graph signal processing
• Format : Talk at Waseda University
• Author(s) :
  • Jia He (Illinois Institute of Technology)
  • Maggie Cheng (Illinois Institute of Technology)

[01472] The Arithmetic Mean iterative methods for solving brain glioma growth models

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F310
• Type : Contributed Talk
• Abstract : Brain tumour is the uncontrolled growth of normal brain cells and most malignant form is known as glioma. In this work, the formulation and implementation of the Arithmetic Mean iterative methods for solving glioma growth models are presented. Numerical results and convergence analysis are included to verify the performance of the proposed methods.
• Classification : 41A55, 45A05, 45B05, 65D32, 65F10
• Format : Talk at Waseda University
• Author(s) :
  • Mohana Sundaram Muthuvalu (Universiti Teknologi PETRONAS)
  • Jumat Sulaiman (Universiti Malaysia Sabah)
  • Elayaraja Aruchunan (Universiti Malaya)
  • Majid Ali (Universiti Sains Malaysia)
  • Ramoshweu Solomon Lebelo (Vaal University of Technology)

[00542] Approximations of quasi-linear elliptic optimal control problems under variational and virtual discretizations

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F310
• Type : Contributed Talk
• Abstract : This talk will discuss virtual and variational discretizations for the numerical approximation of optimal control problems governed by the quasi-linear elliptic equation with distributed control. A conforming virtual element method is employed for the discretization of state and co-state equations that appeared in the model problem. The numerical approximation of the control variable is based on two different discretizations: variational and virtual. In the variational approach, the discrete space associated with the control is not discretized explicitly, whereas, for the virtual discretizations, the discrete spaces are taken as virtual element spaces that include linear polynomials and non-polynomials functions over the polygonal mesh, and a discretize-then-optimize approach is used for the computation of control. With the help of certain projection operators, optimal a priori error estimates are established for the control, state, and co-state variables in suitable norms. Numerical experiments are presented under general polygonal meshes to illustrate the performance of the proposed scheme and verify the theoretical convergence rate.
• Classification : 49M29, 49M41, 65K15, 90C46
• Format : Talk at Waseda University
• Author(s) :
  • Anil Kumar (BITS Pilani KK Birla Goa Campus, Goa (India))
  • Jai Tushar (BITS Pilani KK Birla Goa Campus, Goa (India))
  • Sarvesh Kumar (Indian Institute of Space Science and Technology, Thiruvananthapuram)

[00986] Approximation results for Gradient Descent trained Shallow Neural Networks

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F310
• Type : Contributed Talk
• Abstract : Neural networks show strong performance for function approximation, but provable guarantees typically rely on hand-picked weights and are therefore not fully practical. The aim for a small number of weights in approximation is opposed to over-parametrization by very wide or even infinitely wide networks in contemporary optimization results. The talk reconciles approximation and optimization results and provides approximation bounds that are guaranteed for gradient descent trained neural networks.
• Classification : 41A46, 65K10, 68T07
• Author(s) :
  • Gerrit Welper (University of Central Florida)
  • Russell Gentile (n/a)

[02401] A low-degree normalized B-spline-like representation for Hermite osculatory interpolation problems

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F310
• Type : Contributed Talk
• Abstract : This talk deals with Hermite's osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with super-smoothness at the vertices of the initial partition, and of the lowest possible degree. A normalized B-spline-like representation for the considered spline space is provided. In addition, several quasi-interpolation operators based on blossoming and control polynomials have also been developed. Some numerical tests are presented and compared with some recent works to illustrate the performance of the proposed approach.
• Classification : 41A15
• Author(s) :
  • Mohamed BOUSHABI (Abdelmalek Essaadi University, LaSAD, ENS, 93030 Tetouan, Morocco)
  • Salah Eddargani ( University of Rome Tor Vergata Rome)
  • María José Ibáñez (University of Granada)
  • Abdellah Lamnii (Abdelmalek Essaadi University, LaSAD, ENS, 93030 Tetouan, Morocco)

contributed talk: CT060

room : F311

[01251] Integral Equations Techniques for Floating Flexible Membrane

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F311
• Type : Contributed Talk
• Abstract : Scattering of obliquely incident gravity waves by a horizontal floating flexible porous membrane in the water of finite depth having a variable bottom bed is analyzed. A coupled eigenfunction expansion - boundary element method is used for the solution purpose. The effect of sinusoidally varying bottom topography, membrane porosity and heading angle of the incident wave on the Bragg resonance is analyzed.
• Classification : 45B05, 76B15, Integral Equations
• Format : Talk at Waseda University
• Author(s) :
  • SANTANU KOLEY (Birla Institute of Technology and Science - Pilani, Hyderabad Campus)

[01489] Mathematical modelling of hybrid wave energy converter device

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F311
• Type : Contributed Talk
• Abstract : The hydrodynamics of a hybrid wave energy converter device is investigated. For the sake of mathematical modeling, the associated boundary value problem is converted into a system of Fredholm integral equations and solved using the boundary element method. To incorporate the higher order plate boundary condition, central difference scheme is used. Primary emphasis is given to analyze the power extraction of the hybrid wave energy converter device for various incident wave parameters associated with the hybrid wave energy converter device.
• Classification : 45B05, 76B15, 76B07
• Format : Talk at Waseda University
• Author(s) :
  • KSHMA TRIVEDI (Birla Institute of Technology and Science-Pilani, Hyderabad campus)
  • SANTANU KOLEY (Birla Institute of Technology and Science-Pilani, Hyderabad campus)

[01478] Water wave interaction with porous wave barriers placed over stepped-seabed.

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F311
• Type : Contributed Talk
• Abstract : This study examines the dispersion of water waves by inverted semicircular surface-piercing wave barriers installed on a stepped seabed. The “Boundary element method” is applied to handle the present “Boundary value problem”. In addition to this energy identity is derived to estimate the dispersion of wave energy by the pair of perforated wave barriers. In addition, the influence of porosity, geometrical configurations of pair of porous barriers, and stepped seabed on the energy dissipation are investigated. The study reveals that for smaller Keulegan-Carpenter (KC) number, the “energy dissipation” due to the perforated barriers is higher. However, the reflection coefficient shows the opposite pattern.
• Classification : 45B05, 45G15, 45F05
• Format : Online Talk on Zoom
• Author(s) :
  • SANTANU KUMAR DASH (Birla Institute of Technology and Science-Pilani, Hyderabad campus)
  • SANTANU KOLEY (Birla Institute of Technology and Science - Pilani, Hyderabad Campus)

[01479] Water wave trapping by porous barriers using boundary element method.

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F311
• Type : Contributed Talk
• Abstract : This study examines the dispersion of water waves by inverted semicircular surface-piercing wave barriers installed on a stepped seabed in presence of a rigid wall in the right far-field boundary. The boundary element method is applied to handle the present boundary value problem. In addition, the energy identity is derived to estimate wave energy dispersion by the pair of perforated wave barriers. The influence of porosity, geometrical configurations of pair of porous barriers, and stepped seabed on the energy dissipation are investigated. The study reveals that for smaller Keulegan-Carpenter (KC) number, the energy dissipation due to the perforated barriers is higher. However, the reflection coefficient shows the opposite pattern.
• Classification : 45B05, 45G15, 45F05
• Format : Online Talk on Zoom
• Author(s) :
  • KAILASH CHAND SWAMI (Birla Institute of Technology & Science-Pilani,Hyderabad Campus)
  • SANTANU KOLEY (Birla Institute of Technology and Science - Pilani, Hyderabad Campus)

[01540] Composite Disturbance Rejection and Stabilization for Periodic Control Systems

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @F311
• Type : Contributed Talk
• Abstract : The stabilization and disturbance rejection issues for periodic control systems with actuator faults and external disturbances are investigated through a proportional integral observer approach. An equivalent-input-disturbance approach is employed to estimate the external disturbances. Moreover, proportional integral observer provides more design freedom and enhances the estimation precision of equivalent-input-disturbance. A periodic time-varying control framework is proposed to guarantee robust performance of the system. The potential of the proposed control design is validated via numerical simulations.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Author(s) :
  • Satheesh Thangavel (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

MS [01200] New Trends in Optimal Control and Their Applications

room : F312

• Type : Proposal of Minisymposium
• Abstract : This proposal belongs to the area of optimal control for sweeping processes and their applications to optimization-related and control problems, as well as some practical models. By now, the sweeping process has been recognized as a class of nonsmooth dynamical systems involving normal cones to moving sets. The controlled sweeping processes have been studied with applications relating to the theory of plasticity, ferromagnetism, ferroelectricity, and elastoplasticity. Further developments also apply to various problems of hysteresis, phase transitions, modelling systems with contact, friction, and impacts. These systems frequently arise in applications such as mechanical systems, switched electrical circuits, and biological systems.
• Organizer(s) : Leonardo Colombo, Dao Nguyen
• Classification : 47J20, 49J40, 49J53, 65K10, 90C99
• Minisymposium Program : No registered information

MS [00711] Recent Advances in Optimal control and optimization

room : F401

• [02838] PDE Constrained Optimization with Non-smooth Learning Informed Structures
  • Author(s) :
    • Michael Hintermueller (Weierstrass Institute Berlin)
  • Abstract : A class of optimization problems subject to PDEs with components resulting from ReLU-based neural network models is studied analytically and numerically. Concerning the analysis it is shown that direct classical smoothing of the non-smooth structures leads to issues concerning the existence of solutions. Further, for the non-smooth setting stationarity conditions are derived and used numerically. With respect to the numerical solution, a bundle-free minimization algorithm relying on possible smoothing on the level of directional derivatives is introduced and analyzed, and a brief report on computational tests is provided.
• [03725] Some optimal control problems in metric spaces
  • Author(s) :
    • Hasnaa Zidani (INSA Rouen Normandie)
    • Othmane Jerhaoui (INSA Rouen Normandie)
    • Averil Prost (INSA Rouen Normandie)
  • Abstract : In this talk, we will discuss some optimal control problems in metric spaces (e.g. stratified systems, centralized control problems in Wasserstein space). We are mainly interested in the characterisation of the value function as viscosity solution of an adequate Hamilton-Jacobi (HJ) equation. For this, we introduce a notion of viscosity solutions for HJ equations in some metric spaces. This notion is based on test functions that are directionally differentiable and can be represented as a difference of two semi-convex functions. Under mild assumptions on the Hamiltonian and on the metric space, we can derive the main properties of viscosity theory: the comparison principle and Perron's method.
• [03787] Exact controllability for systems describing plate vibrations. A perturbation approach.
  • Author(s) :
    • Marius Tucsnak (University of Bordeaux)
  • Abstract : The aim of this talk is to describe new exact controllability properties of systems described by perturbations of the classical Kirchhoff plate equation. We first consider systems described by an abstract plate equation with a bounded control operator. The generator of these systems is perturbed by bounded operators which are not necessarily compact, thus not falling in the range of application of compactness-uniqueness arguments. Our first main result is abstract and can be informally stated as follows: if the system described by the corresponding unperturbed abstract wave equation, with the same control operator, is exactly controllable (in some time), then the considered perturbed plate system is exactly controllable in arbitrarily small time. The employed methodology is based, in particular, on frequency-dependent Hautus type tests for systems with skew-adjoint operators. When applied to systems described by the classical Kirchhoff equations, our abstract results, combined with some elliptic Carleman-type estimates, yield exact controllability in arbitrarily small time, provided that the system described by the wave equation in the same spatial domain and with the same control operator is exactly controllable. The same abstract results can be used to prove the exact controllability of the system obtained by linearizing the von K\'arm\'an plate equation around a real analytic stationary state. This leads, via a fixed-point method, to our second main result: the nonlinear system described by the von K\'arm\'an plate equations is locally exactly controllable around any stationary state defined by a real analytic function.
• [03789] A Perturbation Framework for Convex Minimization with Nonlinear Compositions
  • Author(s) :
    • Luis Briceño-Arias (Universidad Técnica Federico Santa María)
    • Patrick L. Combettes (North Carolina State University)
  • Abstract : We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions.

MS [01547] Optimization in BV and Measure Spaces: Theory and Algorithms

room : F402

• [02974] Proximal methods for point source localisation
  • Format : Talk at Waseda University
  • Author(s) :
    • Tuomo Valkonen (Escuela Politécnica Nacional & University of Helsinki)
  • Abstract : Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in such non-Hilbert spaces are not yet very well understood. Most numerical algorithms are based on the Frank-Wolfe conditional gradient method. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy.
• [04816] Nonsmooth minimization in Banach spaces meets sparse dictionary learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Walter (Humboldt Universität zu Berlin)
  • Abstract : We propose a novel method for problems involving nonsmooth regularization terms over infinite dimensional function spaces . It resembles a dictionary learning algorithm which updates a dictionary $\mathcal{A}_k$ of extremal points of the unit ball of the regularizer and of a sparse represenation of the iterate $u_k$ in its conic hull. Imposing additional assumptions on the dual variables, its asymptotic linear convergence is shown.
• [04270] L^q-quasinorm sparse optimal control problems with controls in BV functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Pedro Martín Merino (Escuela Politécnica Nacional)
  • Abstract : We consider an elliptic optimal control of elliptic linear partial differential equations that involves a nonconvex regularization in terms of the $L^q$ quasi–norm (with $q$ in (0, 1)) together with a TV penalization in the cost function, given by: $$\mathcal{F}(y,u)=\frac{1}{2}\| y-y_d \|^2_{L^2(\Omega)}+\frac{ \alpha}{2}\|u\|^2_{L^2(\Omega)}+\beta \int_\Omega |u|^{q} dx + \gamma \int_\Omega |Du|, $$ where $u$ is control and $y$ are the control and state variables, respectively. When $\gamma=0$, the classical direct method fails to argue the existence of solutions due to the lack of lower semicontinuity of $\mathcal{F}$. However, given the topological properties of $BV(\Omega)$ and the continuity of the $L^q$-quasinorm in $L^1(\Omega)$, the existence of solutions can be obtained for controls in $BV(\Omega)$. In this talk, we address the optimality conditions for this problem and a numerical approach for its numerical solution based on primal-dual splitting methods.
• [04282] Robust Optimal Experimental Design for Bayesian Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ahmed Attia (Argonne National Laboratory)
    • Todd Munson (Argonne National Laboratory)
    • Sven Leyffer (Argonne National Laboratory)
  • Abstract : An optimal design is defined as the one that maximizes a predefined utility function which is formulated in terms of the elements of an inverse problem. An example being optimal sensor placement for parameter identification. This formulation generally overlooks misspecification of the elements of the inverse problem such as the prior or the measurement uncertainties. In this talk, we present efficient recipes for designing optimal experimental design schemes, for Bayesian inverse problems, such that the optimal design is robust with respect to misspecification of elements of the inverse problem.

MS [00635] Mean field games and optimal transport with applications in data science and biology

room : F403

• [05205] Manifold Interpolating Optimal-Transport Flows for Trajectory Inference
  • Format : Online Talk on Zoom
  • Author(s) :
    • Smita Krishnaswamy (Yale University)
    • Guillaume Huguet (University of Montreal)
    • Alexander Tong (University of Montreal )
    • Oluwadamilola Fasina (Yale University)
    • Daniel Sumner Magruder (Yale University)
    • Manik Kuchroo (Yale University)
    • Guy Wolf (University of Montreal)
  • Abstract : We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) that learns stochastic, continuous population dynamics from static snapshot samples taken at sporadic timepoints. MIOFlow combines dynamic models, manifold learning, and optimal transport by training neural ordinary differential equations (Neural ODE) to interpolate between static population snapshots as penalized by optimal transport with manifold ground distance. Further, we ensure that the flow follows the geometry by operating in the latent space of an autoencoder that we call a geodesic autoencoder (GAE). In GAE the latent space distance between points is regularized to match a novel multiscale geodesic distance on the data manifold that we define. We show that this method is superior to normalizing flows, Schrödinger bridges and other generative models that are designed to flow from noise to data in terms of interpolating between populations. Theoretically, we link these trajectories with dynamic optimal transport. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
• [01462] A Distributed Algorithm for Wasserstein Proximal Operator Splitting
  • Format : Online Talk on Zoom
  • Author(s) :
    • Iman Nodozi (University of California Santa Cruz)
    • Abhishek Halder (University of California Santa Cruz)
  • Abstract : Many time-stepping algorithms are available to numerically realize the Wasserstein proximal updates, which generalize the concept of gradient steps to the manifold of probability measures. This talk will present a distributed algorithm to perform the Wasserstein proximal updates. The proposed algorithm generalizes the finite dimensional Euclidean consensus ADMM to the measure-valued Wasserstein, and to its entropy-regularized version. We will explain how the proposed algorithm differs compared to the Euclidean case, and will provide numerical case-studies.
• [05216] Wasserstein gradient flows and Hamiltonian flows on the generative model
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shu Liu (Math department, UCLA)
    • Wuchen Li (University of South Carolina)
    • Hao Wu (Georgia Institute of Technology)
    • Xiaojing Ye (Georgia State University)
    • Haomin Zhou (Georgia Institute of Technology)
  • Abstract : In this talk, we introduce a series of sampling-friendly, optimization-free methods for computing high-dimensional gradient flows and Hamiltonian flows on the Wasserstein probability manifold by leveraging generative models from deep learning. Such methods project the corresponding probability flows to parameter space and obtain finite-dimensional ordinary differential equations (ODEs) which can be directly solved by using classical numerical methods. Furthermore, the computed generative models can efficiently generate samples from the probability flows via pushforward maps.
• [05393] Linear Optimal Transport (LOT) Framework for Graph-Based Semi-Supervised Learning using Point Cloud Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Mary Chriselda Antony Oliver (University of Cambridge)
    • Michael Roberts (University of Cambridge)
    • Matthew Thorpe (University of Manchester)
  • Abstract : In this study, we introduce a novel application of the linear optimal transport (LOT) framework, leveraging the geometrical structure of its linear embeddings. We incorporate these embeddings in the form of projections (velocity fields) post dimensionality reduction using graph-based semi-supervised algorithms. Additionally, we compute the shortest path between two prominent nodes (geodesic) for the feature vector within the graphical setting. Finally, we demonstrate the performance through numerical experiments conducted on benchmark 3-D point cloud data.

MS [00966] Theoretical and computational advances in measure transport

room : F411

• [05226] Optimal transport map estimation in general function spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Vincent Divol (Université PSL)
    • Jonathan Niles-Weed (New York University)
    • Aram Pooladian (New York University)
  • Abstract : We consider the problem of estimating the optimal transport map between a (fixed) source distribution P and an unknown target distribution Q, based on samples from Q. The estimation of such optimal transport maps has become increasingly relevant in modern statistical applications, such as generative modeling. At present, estimation rates are only known in a few settings (e.g. when P and Q have densities bounded above and below and when the transport map lies in a Hölder class), which are often not reflected in practice. We present a unified methodology for obtaining rates of estimation of optimal transport maps in general function spaces. Our assumptions are significantly weaker than those appearing in the literature: we require only that the source measure P satisfies a Poincaré inequality and that the optimal map be the gradient of a smooth convex function that lies in a space whose metric entropy can be controlled. As a special case, we recover known estimation rates for bounded densities and Hölder transport maps, but also obtain nearly sharp results in many settings not covered by prior work. For example, we provide the first statistical rates of estimation when P is the normal distribution and the transport map is given by an infinite-width shallow neural network.
• [04080] TBA
  • Author(s) :
    • Augusto Gerolin (Canada Research Chair and University of Ottawa)
  • Abstract : TBA
• [04165] Efficient subspace modeling via transport transforms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shiying Li (University of North Carolina - Chapel Hill)
    • Gustavo Rohde (University of Virginia)
    • Akram Aldroubi (Vanderbilt University)
    • Abu Hasnat Rubaiyat (University of Virginia)
    • Yan Zhuang (NIH)
    • Mohammad Shifat-E-Rabbi (University of Virginia)
    • Xuwang Yin (Center for AI Safety )
  • Abstract : When data is generated though deformations of certain template distributions, transport-based transforms often linearize data clusters which are nonlinear in the original domain. We will describe convexification properties of several transport transforms under various generative modeling assumptions, enabling efficient modeling of data classes as subspaces in the transform domain. Such subspace representations also give rise to accurate machine learning algorithms with low computational cost. We will show applications for image and signal classification.
• [04063] Conditional simulation through the data-driven optimal transport barycenter problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Esteban Gregorio Tabak (New York University, Courant Institute)
  • Abstract : A methodology is proposed to generate samples from a conditional probability distribution, with factors that are either known explicitly, up to discovery or only by association.The procedure pushes forward the conditional distribution to its barycenter through particle flows, whose inverse provides the simulation sought. Idiosyncratic factors are included through subsampling. The methodology serves as a conditional generator, to eliminate batch effects, to uncover hidden factors and to predict and optimize trajectories under treatment.

MS [00533] Recovery and robustness of geometric fingerprints for point clouds and data

room : F412

• [04178] Recovering discrete Fourier spectra from random perturbations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mircea Petrache (Pontificia Catolica Universidad de Chile)
    • Rodolfo Viera (Pontificia Universidad Católica de Chile)
  • Abstract : In this talk I will discuss the behaviour of the Fourier Transform of (quasi-)periodic sets under random perturbations. We will see that for i.i.d random perturbations of a quasi-periodic set X in the Euclidean space, the effect of the perturbations is almost surely that of multiplying the Fourier Transform of X by a weight which depends on the law of the perturbation. Also we will see quantitative versions of the previous discussion in finite groups which we will use to obtain, after passing to the limit, the almost sure recovery of the Fourier Transform of lattices in some non-abelian instances, such as the Heisenberg group.
• [04956] An information-theoretic perspective on the turnpike and beltway problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shuai Huang (Emory University)
  • Abstract : Reconstructing a set of points on a line or a loop from their unlabelled pairwise distances is known as the turnpike or beltway problem. Some point configurations are easy to reconstruct, while others are more difficult. We show that the difficulty of problem can be characterized by the mutual information $I(X;Y)$ between the point variable $X$ and distance variable $Y$. Experiments show that $I(X;Y)$ decreases when there are more repeated distances.
• [04313] Curvature sets and curvature measures over persistence diagrams
  • Format : Talk at Waseda University
  • Author(s) :
    • Facundo Memoli (Ohio State University)
  • Abstract : We study an invariant (i.e. a feature) of compact metric spaces which combines the notion of curvature sets introduced by Gromov in the 1980s together with the notion of Vietoris-Rips persistent homology. For given integers k≥0 and n≥1 these invariants arise by considering the degree k Vietoris-Rips (VR) persistence diagrams of all finite point clouds with cardinality at most n sampled from a given metric space. We call these invariants \emph{persistence sets}. This family of invariants contains the usual VR persistence diagram of the original space (when n is large enough). We argue that for a certain range of values of parameters n and k, (1) the family of these invariants 'sees' information not detected by the VR persistence diagrams of the whole space and (2) computing these invariants is significantly easier than computing the usual VR persistence diagrams. We establish stability results for our persistence sets and also precisely characterize some of them in the case of spheres with geodesic and Euclidean distances. We identify a rich family of metric graphs for which the invariant determined by n=4 and k=1 fully recovers their homotopy type. Along the way we prove some novel properties of VR persistence diagrams.
• [05121] Learning with persistence diagrams
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose Perea (Northeastern University)
    • Iryna Hartsock (University of Florida)
    • Alex Elchesen (Colorado State University)
    • Tatum Rask (Colorado State University)
  • Abstract : Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an optimal transport distance. Examples of such measures are expectations of probability distributions on the space of persistence diagrams. In this talk, I will present methods for approximating continuous functions on the space of Radon measures supported on the birth-death plane, as well as their utilization in supervised learning tasks.

MS [02700] Recent developments on Infinite Dimensional Analysis, Stochastic Analysis and Quantum Probability

room : E501

• [02940] Note on complexities for the quantum compound systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Noboru Watanabe (Tokyo University of Science)
  • Abstract : In order to discuss the efficiency of information transmission of the quantum com- munication processes consistently, we consider the entropy type functional and the mutual entropy type functional with respect to the initial state and the quantum communication channel. In this study, the mutual entropy type measures are con- structed by the compound states between the initial and final systems. We modify the compound states and examine the entropy functional and the mutual entropy functional defined by the modified compound states by means of the initial state and the completely positive channel to study the efficiency of information transmission of the quantum communication processes.
• [03589] Asymptotics of densities of first passage times for spectrally negative Lévy processes
  • Format : Talk at Waseda University
  • Author(s) :
    • shunsuke kaji (meijo university)
  • Abstract : We study a first passage time of a Lévy process over a positive constant level. In the spectrally negative case we give conditions for absolutely continuity of the distributions of the first passage times. The tail asymptotics of their densities are alsoclarified, where the asymptotics depend on tail behaviour of the corresponding Lévy measures.
• [03953] A combinatorial formula of the moments of a deformed filed operator
  • Format : Talk at Waseda University
  • Author(s) :
    • Nobuhiro ASAI (Aichi University of Education)
  • Abstract : We shall construct the two parameterized deformed Fock space obtained from the weighted $q$-deformation technique. We shall explain a combinatorial moment formula of a Poisson type filed operator defined on this Fock space by using the set partitions with their statistics. In addition, we shall mention relationships with the recurrence formula for the orthogonal polynomials of the deformed Poisson distribution. This talk is based on the joint work with H. Yoshida (Ochanomizu Univ, Tokyo).

MS [00603] Mean field stochastic control problems and related topics

room : E502

• [01320] Stochastic maximum principle for weighted mean-field system
  • Format : Talk at Waseda University
  • Author(s) :
    • Jie Xiong (Southern University of Science and Technology)
  • Abstract : We study the optimal control problem for a weighted mean-field system. A new feature of the control problem is that the coefficients depend on the state process as well as its weighted measure and the control variable. By applying variational technique, we establish a stochastic maximum principle. Also, we establish a sufficient condition of optimality. As an application, we investigate the optimal premium policy of an insurance firm for asset–liability management problem. This talk is based on a joint paper with Yanyan Tang.
• [00653] The mass-conserving stochastic partial differential equaton coming from spatial mean-field term
  • Format : Talk at Waseda University
  • Author(s) :
    • Qi Zhang (Fudan University)
  • Abstract : In this talk, I will introduce our study about the mass-conserving stochastic partial differential equaiton. It is a kind of equation with spacial mean-field term such that its solution satisfies a mass-conservative property. We prove the existence and uniqueness of solution, and then construct a stationary solution by the nonlinear Feynman-Kac formula under Lipschitz assumption. Moreover, the existence of solution in the non-Lipschitz case is considered.
• [01321] A quadratic mean-field BSDE with its applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Huilin Zhang (Shandong University)
  • Abstract : In this talk I will introduce the well-posedness of a quadratic mean-field BSDE. Moreover we show its several applications, in particular in the utility theory.
• [01324] Mean field stochastic control under sublinear expectation
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Li (Shandong University)
  • Abstract : In this talk we study Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a SDE driven by a $G$-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the $G$-expectation. Also the associated cost functional is of mean-field type. We give a necessary optimality condition for control processes, and also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the $G$-expectation of parameterized random variables. Based on joint work with Rainer Buckdahn (UBO, France), Bowen He (SDU, China).

MS [00059] Numerical solutions for differential equations: Probabilistic approaches and statistical perspectives

room : E503

• [00066] Probabilistic Numerical Methods
  • Format : Online Talk on Zoom
  • Author(s) :
    • Chris Oates (Newcastle University)
  • Abstract : The scale and complexity of modern scientific computer codes typically precludes a detailed analysis of how the code is numerically implemented. For example, multi-scale and multi-physics models of the human heart call on diverse numerical sub-routines to integrate differential equations, perform interpolation and optimise over some parameters of the model. As such, the computer output is acknowledged to be inexact and some alternative form of uncertainty quantification is needed for the output to be properly interpreted. This talk will provide an introduction to probabilistic numerical methods, which aim to provide probabilistic uncertainty quantification for computer code output. These methods are composed of "modules", such that a probabilistic description of numerical error can be automatically propagated, and some of the most useful modules will be discussed.
• [04930] Prior models for enforcing boundary constraints in state-space probabilistic PDE solvers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Oksana Chkrebtii (The Ohio State University)
    • Yue Ma (The Ohio State Univeristy)
  • Abstract : Probabilistic numerics is an active field of research that seeks to construct stochastic analogues of numerical methods, including the solution of ordinary and partial differential equations. Probabilistic solvers for partial differential equations require the specification of flexible prior models that respect physical constraints while allowing for computational efficiencies of the sequential updates. We focus on state-space based probabilistic PDE solvers and describe advances in nonparametric modeling of system states with boundary constraints.
• [04408] GParareal: Towards a time-parallel probabilistic ODE solver
  • Format : Talk at Waseda University
  • Author(s) :
    • T J Sullivan (University of Warwick)
    • Kamran Pentland (University of Warwick)
    • Massimiliano Tamborrino (University of Warwick)
    • Lynton Appel (Culham Centre for Fusion Energy)
    • James Buchanan (Culham Centre for Fusion Energy)
  • Abstract : Numerical solution of complex ODEs can be accelerated with time-parallel integration, predicting the solution serially using a cheap solver and correcting these values in parallel using an expensive solver. We propose a time-parallel ODE solver (GParareal) that models the prediction-correction term using a Gaussian process emulator. GParareal compares favourably with the classic parareal algorithm, locates solutions to certain ODEs where parareal fails, and can also use archives of legacy solutions to further accelerate convergence.
• [00148] Theoretical Guarantees for the Statistical Finite Element Method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yanni Papandreou (Imperial College London)
    • Jon Cockayne (University of Southampton)
    • Mark Girolami (University of Cambridge)
    • Andrew B. Duncan (Imperial College London)
  • Abstract : The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesized with the numerical solution of a PDE intended to describe it in a coherent statistical framework, to compensate for model error. This work presents a new theoretical analysis of the statistical finite element method demonstrating that it has similar convergence properties to the finite element method on which it is based. Our results constitute a bound on the Wasserstein-2 distance between the ideal prior and posterior and the StatFEM approximation thereof, and show that this distance converges at the same mesh-dependent rate as finite element solutions converge to the true solution. Several numerical examples are presented to demonstrate our theory, including an example which test the robustness of StatFEM when extended to nonlinear quantities of interest.

MS [00260] Statistics for random dynamics

room : E504

• [03955] Online parametric estimation of stochastic differential equations with discrete observations
  • Format : Talk at Waseda University
  • Author(s) :
    • Shogo Nakakita (University of Tokyo)
  • Abstract : We consider online parametric estimation for stochastic differential equations based on discrete observations. The proposed method uses an online gradient descent method for negative quasi-log-likelihood functions with convexity and achieves low computational complexity. We derive a non-asymptotic uniform upper bound for the risk of the estimation by our results on stochastic optimization and ergodicity.
• [03956] Weighted block bootstrap for misspecified ergodic Lévy driven SDE models
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuma Uehara (Kansai University)
  • Abstract : In this talk, we consider possibly misspecified stochastic differential equation models driven by L\'{e}vy processes. Under some regularity conditions, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, especially in the misspecified case, it is hard to construct a consistent estimator of the asymptotic variance directly. For such a problem, we propose a weighted block bootstrap procedure to evaluate the asymptotic distribution.
• [04399] Robustifying Gaussian quasi-likelihood inference for random dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Shoichi Eguchi (Osaka Institute of Technology)
  • Abstract : We consider Gaussian quasi-likelihood inference for stochastic differential equations. In this study, suppose that the observations are obtained from the L\'{e}vy process with the compound-Poisson jumps and spike noises, and we regard jumps and spike noises as outliers that disturb the parameter estimation. We construct an estimator without reference to the presence of the jump component and some spike noises, in addition to that of the drift term.
• [04695] Asymptotic expansion of estimator of Hurst parameter of SDE driven by fractional Brownian motion
  • Format : Talk at Waseda University
  • Author(s) :
    • Hayate Yamagishi (University of Tokyo)
  • Abstract : Asymptotic expansion is presented for an estimator of the Hurst coefficient of a stochastic differential equation driven by a fractional Brownian motion of H>1/2. While applying a recently developed theory of asymptotic expansion of Wiener functionals to the estimator, the main difficulty is to estimate orders of complicated functionals appearing in expanding the estimator and identifying the limit random symbols. To overcome the difficulty, we introduce a theory of an exponent based on weighted graphs.

MS [00379] Numerical techniques for coarse-graining, model reducing and simulation of complex physical systems

room : E505

• [02156] Ahyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Lijie Ji (Shanghai Jiao Tong University)
  • Abstract : The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous a posteriorerror estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and often degrade the offline and online computational efficiency. In this talk, I will introduce an adaptive enrichment strategy for R2-ROC rendering it capable of handling parametric fluid flow problems. Tests on lid-driven cavity and flow past a backward-facing step problems demonstrate its high efficiency, stability and accuracy.
• [02166] Hybrid Projection Methods for Solution Decomposition in Large-scale Bayesian Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiahua Jiang (University of Birmingham)
    • Julianne Chung (Emory University)
    • Arvind Krishna Saibaba (North Carolina State University)
    • Scot Miller (John Hopkins )
  • Abstract : We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection in atmospheric emissions tomography) where the reconstructed solution can be represented as a combination of two or more components and each component contains different smoothness or stochastic properties. In a deterministic inversion or inverse modeling framework, these assumptions correspond to different regularization terms for each solution in the sum. Although various prior assumptions can be included in our framework, we focus on the scenario where the solution is a sum of a sparse solution and a smooth solution. For computing solution estimates, we develop hybrid projection methods for solution decomposition that are based on a combined flexible and generalized Golub-Kahan processes. This approach integrates techniques from the generalized Golub-Kahan bidiagonalization and the flexible Krylov methods. The benefits of the proposed methods are that the decomposition of the solution can be done iteratively, and the regularization terms and regularization parameters are adaptively chosen at each iteration. Numerical results from photoacoustic tomography and atmospheric inverse modeling demonstrate the potential for these methods to be used for anomaly detection.
• [02484] A reduced basis method for the parametrized Monge-Ampere equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Shijin Hou (University of Science and Technology of China)
  • Abstract : In this talk, we first introduce a highly efficient solver for the parameterized optimal mass transport problem by adapting the reduced residual reduced over-collocation approach to the parameterized Monge-Amp$\grave{\rm e}$re equation. This new reduced basis technique allows us to handle the strong and unique nonlinearity pertaining to the Monge-Amp$\grave{\rm e}$re equation achieving online efficiency. After that, several numerical tests will be presented to demonstrate the accuracy and high efficiency of our reduced solver.
• [04068] Novel Reduced Basis Method for Radiative Transfer Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • ZHICHAO PENG (Michigan State University)
    • Yanlai Chen (University of Massachusetts Dartmout)
    • Yingda Cheng (Michigan State University)
    • Fengyan Li (Rensselaer Polytechnic Institute)
  • Abstract : One prominent computational challenge to simulate radiative transfer (RTE),  a fundamental kinetic description of energy or particle transport through mediums affected by scattering and absorption processes, comes from the high dimensionality of the phase space. Leveraging the existence of a low-rank structure in the solution manifold induced by the angular variable in the scattering dominating regime, reduced order models are designed and tested here for the linear RTE model based on reduced basis methods.

MS [00886] Numerical methods for stochastic partial differential equations

room : E506

• [05603] Convergence Analysis of splitting up method for nonlinear filtering problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanzhao Cao (Auburn University)
  • Abstract : Abstract: We consider a nonlinear filtering model where correlated Wiener processes and point processes drive observations. We first derive a Zakai equation that provides the filter solution's unnormalized probability density function. We then use a splitting-up technique to decompose the Zakai equation into three stochastic differential equations. Based on this, we construct a splitting-up approximate solution. We will present a half-order convergence result. Additionally, we will present a finite difference method to create a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.
• [04327] CLT for approximating ergodic limit of SPDEs via a full discretization
  • Format : Talk at Waseda University
  • Author(s) :
    • Chuchu Chen (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Tonghe Dang (Academy of Mathematics and Systems Science，Chinese Academy of Sciences)
    • Jialin Hong (Academy of Mathematics and Systems Science，Chinese Academy of Sciences)
    • Tau Zhou (Academy of Mathematics and Systems Science，Chinese Academy of Sciences)
  • Abstract : The approximation of the ergodic limit is of fundamental importance in many applications. In this talk, we focus on characterizing quantitatively the fluctuations between the ergodic limit and the time-averaging estimator of the full discretization for the parabolic stochastic partial differential equation. We establish a central limit theorem, which shows that the normalized time-averaging estimator converges to a normal distribution with the variance being the same as that of the continuous case, where the scale used for the normalization corresponds to the temporal strong convergence rate of the considered full discretization.
• [04355] Energy regularized approximations for stochastic logarithmic Schrodinger equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianbo Cui (Hong Kong Polytechnic University )
    • Jialin Hong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Liying Sun (Capital Normal University)
  • Abstract : In this talk, we first prove the global existence and uniqueness of the solution of the stochastic logarithmic Schroedinger (SlogS) equation driven by additive noise or multiplicative noise. The key ingredient lies on the regularized stochastic logarithmic Schroedinger (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of RSlogS equations. Then we present energy regularized numerical schemes and their strong convergence rates.
• [05599] Density approximation for stochastic heat equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Derui Sheng (The Hong Kong Polytechnic University)
    • Chuchu Chen (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Jianbo Cui (Department of Applied Mathematics, The Hong Kong Polytechnic University)
    • Jialin Hong (Academy of Mathematics and Systems Science，Chinese Academy of Sciences)
  • Abstract : This talk presents the numerical approximation of the density of the stochastic heat equation via the accelerated exponential Euler scheme. The existence and smoothness of the density of the numerical solution are proved through Malliavin calculus. By presenting a test-function-independent weak convergence analysis, we show that the convergence orders of the density in uniform convergence topology are 1/2 and nearly 1 in the nonlinear drift case and in the affine drift case, respectively.

MS [00465] Linear and Non-linear Approximation of Curves and Surfaces

room : E507

• [01862] Stable nonlinear inversion : a general framework for interface reconstruction from cell-average
  • Format : Talk at Waseda University
  • Author(s) :
    • Albert Cohen (Sorbonne Universite)
  • Abstract : In this lecture, we present a general framework for solving inverse problem using nonlinear approximation spaces. The main principles build up on the so called Parametrized Background Data Weak method (PBDW) which can be thought as a linear counterpart. As a main and motivating application we discuss the reconstruction of sharp interfaces from cell average at coarse resolutions for which linear methods are known to be uneffective. We discuss the convergence rates of these reconstructions and their optimality.
• [02134] Adaptive Multi-Quadric Interpolation: Applications in Image Compression.
  • Format : Talk at Waseda University
  • Author(s) :
    • Rosa Donat (Universitat de Valencia)
    • Francesc Aràndiga (Universitat de Valènciacia)
    • Daniela Schenone (Leonardo Sistemi Integrati S.L.R.)
  • Abstract : Multi-Quadric interpolation techniques depend on a shape parameter that has a direct influence on its accuracy. The computation of the shape parameter can be performed using 'linear' (e.g. data-independent) estimates or by incorporating adaptive techniques, similar to those used in ENO/WENO schemes to maximize the region of accuracy when using piecewise polynomial interpolatory techniques. We design 2D Prediction operators within Harten's Multiresolution Framework based on non-separable multi-quadric approximation that incorporates a WENO-type selection of the local shape parameter. We explore the compression properties of the resulting MR transformation, and also the combination of these techniques with the construction of edge maps of the image.
• [01772] Reconstructing a Digital Elevation Model from C2 quasi-interpolation
  • Format : Talk at Waseda University
  • Author(s) :
    • Domingo Barrera (University of Granada)
    • Salah Eddargani (University of Rome Tor Vergata)
    • Juan Francisco Reinoso (University of Granada)
  • Abstract : Quasi-interpolation spline in the Bernstein basis is a low-cost computational method for approximating functions or data in one or several variables. Although linked to the degree, regularity and exactness are parameters available to the user. In this contribution we propose to define a one-dimensional quasi-interpolation operator that achieves the optimal approximation order and provides C2 continuous approximants. It will be used to reconstruct a Digital Elevation Model using a tensor product type scheme.
• [01766] Low-degree quasi-interpolation in the Bernstein basis
  • Format : Talk at Waseda University
  • Author(s) :
    • María José Ibáñez (University of Granada)
    • Salah Eddargani (University of Rome Tor Vergata)
    • Sara Remogna (University of Torino)
  • Abstract : Spline quasi-interpolation is an effective tool for approximating functions or data. Usually, the quasi-interpolant is defined as a linear combination of the B-splines of a basis of the linear space in which the approximant is to be constructed. In this contribution we present a procedure for constructing quasi-interpolants by directly defining the coefficients of the expression in the Bernstein basis of its restriction to each subinterval induced by a uniform partition of the real line.

MS [00810] Recent Developments on the Numerical Solution of Least Squares Problems

room : E508

• [01652] MinAres: An Iterative Solver for Symmetric Linear Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexis Montoison (GERAD and Polytechnique Montréal)
    • Dominique Orban (GERAD and Polytechnique Montréal)
    • Michael Saunders (Stanford University)
  • Abstract : We introduce an iterative solver named MinAres for symmetric linear systems $Ax \approx b$, where $A$ is possibly singular. MinAres is based on the symmetric Lanczos process, like Minres and Minres-QLP, but it minimizes $\|Ar_k\|$ in each Krylov subspace rather than $\|r_k\|$, where $r_k$ is the current residual vector. In our experiments, MinAres terminates significantly earlier than Minres on ill-conditioned and singular linear systems.
• [02064] Fast inverse LU preconditioner based on the Sherman--Morrison formula
  • Format : Talk at Waseda University
  • Author(s) :
    • José Mas (Universitat Politècnica de València)
    • José Marín (Universitat Politècnica de València)
    • Juana Cerdán (Universitat Politècnica de València)
    • Rafael Bru (Universitat Politècnica de València)
  • Abstract : A fast version of an approximate inverse $LU$ preconditioner to solve linear systems is constructed based on the Sherman--Morrison formula. A multiplicative decomposition of the approximate inverse of the coefficient matrix is obtained applying recursively the inversion formula. Moreover, this recursion can be expresed in a compact form which is used to compute the preconditioner. The method is stable for nonsingular $M$-matrices and $H$-matrices. Numerical results show that the new proposal is robust and competitive compared with other preconditioners.
• [01679] GMRES using pseudoinverse for range symmetric singular systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Kota Sugihara (National institute of informatics)
    • Ken Hayami (Professor Emeritus, National Institute of Informatics/The Graduate University for Advanced Studies (SOKENDAI))
  • Abstract : For range symmetric singular linear systems, GMRES converges to the least squares solution in exact arithmetic. We derive necessary and sufficient conditions for GMRES to converge assuming exact arithmetic except for the computation of the elements of the Hessenberg matrix. In practice, GMRES may not converge due to numerical instability. Thus, we propose using the pseudoinverse for the solution of severely ill-conditioned Hessenberg systems. Numerical experiments indicate that the method is effective.
• [02051] Solving rank deficient mixed sparse-dense linear least-squares problems by updating preconditioned iterative methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Ning Zheng (The Institute of Statistical Mathematics)
  • Abstract : We consider the preconditioning of linear least squares problem when the large sparse coefficient matrix contains a few dense rows. Such mixed sparse dense least squares problem arises from many scientific practical problems. We propose preconditioned iterative methods for solving the problem when the sparse part is rank deficient and the whole system is rank deficient, respectively. Numerical experiments are presented to show the feasibility and efficiency of the proposed methods.

MS [00404] Large-Scale Eigenvalue Computations and Optimization

room : E603

• [03074] Consistent Estimation Using SVD for a Linear Regression Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Kensuke Aishima (Hosei University)
  • Abstract : In this talk, we consider parameter estimation of an errors-in-variables linear regression model. The standard approach to such parameter estimation is to formulate an optimization problem and solve it numerically using the singular value decomposition (SVD). Using the property that the SVD identifies the image and null spaces of a matrix, with orthogonal projections to the subspaces, we derive a consistent estimator for a linear regression model with the errors in a subset of variables.
• [04078] Fast optimization of eigenvalues for frequency-based damping of second-order systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nevena Jakovčević Stor (University of Split)
    • Tim Mitchell (Queens College / CUNY)
    • Zoran Tomljanović (University of Osijek)
    • Matea Ugrica (Max Planck Institute for Dynamics of Complex Technical Systems)
  • Abstract : We consider optimizing eigenvalues of certain parametric second-order systems that model vibrating mechanical systems, where the goal is to achieve frequency-weighted damping by moving eigenvalues away from undesirable areas on the imaginary axis. We present two new complementary approaches for this task. First, we propose determining damper viscosities via solving new nonsmooth constrained optimization problems. Second, we also propose a fast new eigensolver for the structured quadratic eigenvalue problems that appear in such vibrating systems.
• [02304] Rectangular multiparameter eigenvalue problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Bor Plestenjak (University of Ljubljana)
    • Michiel E Hochstenbach (TU Eindhoven)
    • Tomaž Košir (University of Ljubljana)
  • Abstract : In a rectangular multiparameter eigenvalue problem we have a $k$-variate, $k\ge 2$, polynomial pencil of rectangular matrices $W(\lambda)\in{\mathbb C}^{(n+k-1)\times n}$ and $\lambda_0\in{\mathbb C}^k$ is an eigenvalue if ${\rm rank}(W(\lambda_0))
• [04501] Simultaneous diagonalization and new bounds on shared invariant subspaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Brian Sutton (Randolph-Macon College)
  • Abstract : Commuting Hermitian matrices may be simultaneously diagonalized by a common eigenvector matrix. However, the numerical aspects are delicate, and existing Jacobi-like algorithms have a prohibitively large operation count on large matrices. We derive new error bounds on shared invariant subspaces and use them to develop a new simultaneous diagonalization algorithm with a running time that is a small multiple of a single eigenvalue-eigenvector computation.

MS [01161] Error-Controlled Adaptive Algorithms in Full-Order and Reduced-Order Model Simulations

room : E604

• [01786] Modeling and multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq modell
  • Format : Talk at Waseda University
  • Author(s) :
    • Sven Beuchler (IfAM, Leibniz University Hanover)
    • Bernhard Endtmayer (IfAM, Leibniz University Hanover)
    • Johannes Lankeit (IfAM, Leibniz University Hanover)
    • Thomas Wick (IfAM, Leibniz University Hanover)
  • Abstract : In this presentation, we develop a posteriori error control for a generalized Boussinesq model. The stationary Navier- Stokes equations with temperature dependent viscosity are coupled with a stationary heat equation. We use the dual- weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is done with the help of a partition- of-unity in a weak formulation. The resulting error estimators are used within an adaptive algorithm. Finally, numerical examples are presented.
• [04451] Error-Controlled Local Interpolation of Moment Matching Reduced Order Models for Vibroacoustics
  • Format : Talk at Waseda University
  • Author(s) :
    • Harikrishnan K. Sreekumar (Technische Universität Braunschweig, Institut für Akustik)
    • Ulrich Römer (Technische Universität Braunschweig, Institut für Dynamik und Schwingungen)
    • Matthias Bollhöfer (Technische Universität Braunschweig, Institut für Numerische Mathematik)
    • Christopher Blech (Technische Universität Braunschweig, Institut für Akustik)
    • Sabine C. Langer (Technische Universität Braunschweig, Institut für Akustik)
  • Abstract : Surrogate modeling for high-dimensional parametric problems is computationally challenging and therefore demands techniques to capture the essential features with the least effort. To this end, we present an adaptive error-controlled strategy to drive accurate modeling at two levels: moment matching reduced-order models approximating the frequency response and sparse grid interpolation for parametric approximation. We compare dimension-adaptive and spatially-adaptive refinement strategies with respect to convergence, demonstrated using problems from vibroacoustics.
• [04671] Advances in A Posteriori Error Estimation and Adaptive Model Order Reduction
  • Format : Talk at Waseda University
  • Author(s) :
    • Sridhar Chellappa (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)
    • Lihong Feng (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)
    • Peter Benner (MPI for Dynamics of Complex Technical Systems, Magdeburg)
  • Abstract : Reduced-order models (ROMs) play an important role in applications such as engineering design, control, optimization, etc. which require reliable simulations of large-scale systems in real-time. We discuss our recent work on a posteriori error estimation and adaptivity. The objective of this work is to reduce the training cost for ROM. We discuss several new error estimators and illustrate their use in adaptive basis enrichment and adaptive parameter sampling. The benefits of the adaptive methods are demonstrated on several numerical examples.
• [05257] Stable Linear Solves in Parametric Model Order Reduction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kapil Ahuja (Indian Institute of Technology Indore (IIT Indore))
    • Navneet Pratap Singh (Bennett University)
  • Abstract : We study stability of class of algorithms for model order reduction (MOR) of parametric linear dynamical systems, with respect to inexact linear solves. Our most novel contribution is achieving backward stable MOR algorithms. To achieve this, we first adapt the underlying linear solver such that it satisfies orthogonalities required for stability. Next, we demonstrate that by suitably using a recycling variant of the solver, these orthogonalities can be satisfied without any code changes and cheaply.

MS [00622] Inverse Problems and Imaging

room : E605

• [01259] Testing statistical hypothesis in Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Frank Werner (Universität Würzburg)
    • Remo Kretschmann (Universität Würzburg)
    • Daniel Wachsmuth (Universität Würzburg)
  • Abstract : In this talk, we propose a regularized approach to hypothesis testing in Inverse Problems in the sense that the underlying estimators or test statistics are allowed to be biased. As one major result we prove that regularized testing is always at least as good as classical unregularized testing. We furthermore provide an adaptive test by maximizing the power functional, which outperforms unregularized tests in numerical simulations by several orders of magnitude.
• [01346] Disentangling domain bias in medical images for meaningful embeddings
  • Format : Talk at Waseda University
  • Author(s) :
    • Samuel Tull (University of Cambridge)
  • Abstract : Machine learning models using imaging have been promising to revolutionise healthcare for many years but are rarely deployed in the clinic due to underlying dataset biases and distribution shifts. In medical images, several sources of bias cause a distribution shift: image acquisition protocols, the instrument used and any image processing. We discuss a method giving meaningful image embeddings, useful for downstream tasks, that have been disentangled from sources of bias, achieving improved generalisability and interpretability.
• [01553] A Bregman-Kaczmarz method for nonlinear systems of equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Maximilian Winkler (TU Braunschweig)
  • Abstract : We propose a new randomized method for solving systems of nonlinear equations for sparse solutions or solutions which are subject to simple additional constraints. The method uses only gradients of component functions and is based on Bregman projections. Convergence is established for convex nonnegative functions and for functions that fulfill the local tangential cone condition. We demonstrate in examples that the method can find sparse or simplex-constrained solutions of inverse problems.
• [01556] A complementary $\ell^1$-TV reconstruction algorithm for limited data CT
  • Format : Talk at Waseda University
  • Author(s) :
    • Simon Goeppel (University of Innsbruck)
    • Jürgen Frikel (OTH Regensburg)
    • Markus Haltmeier (University of Innsbruck)
  • Abstract : In this talk, we introduce a new variational reconstruction framework for inverse problems, suffering from incomplete data. As it is known that a single regularizer does not work flawlessly for noise reduction and artifact removal simultaneously, we instead adress both problems by subsequent reconstructions. These reconstructions are connected by a data-consistency term, which enables us to uitilize both properties of $\ell_1$-curvelet and total variation regularization in the example of limited angle tomography.

MS [02404] New Trends in Hierarchical Variational Inequalities and Optimization Problems

room : E606

• [03031] Self-adaptive subgradient extragradient method with extrapolation procedure for MSVIs
  • Author(s) :
    • Lu-Chuan Ceng (Shanghai Normal University)
  • Abstract : This article introduces a self-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality with common fixed points constraint of finite nonexpansive mappings. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established. A numerical example is used to demonstrate the viability of the proposed rule.
• [03050] Subgradient-extragradient method for SEP, VIP and FPP of multi-valued mapping
  • Author(s) :
    • Yun-shui Liang (Yichun Vocational Technique College)
  • Abstract : In this paper, via a subgradient extragradient implicit rule, we introduce a new iterative algroithm for solving split equilibrium problems, variational inequality problem and fixed point problem of nonspreading multi-valued mapping in Hilbert space. We show that the iteration converges strongly to a common solution of the considered problems. Our results extend and improve some well-known results in the literature. Finally, a numerical example is provided to verify the validity of the proposed algorithm.
• [03061] Modified subgradient-extragradient method for monotone-bilevel-equilibria with VIP and CFPP constraints
  • Author(s) :
    • Hui-ying Hu (shanghai normal university)
  • Abstract : In a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints. Some strong convergence results for the proposed algorithms are established under the mild assumptions.
• [03072] New strong convergence theorems of generalized quasi-contractive mappings
  • Author(s) :
    • Yangqing Qiu (Shanghai Polytechnic University)
  • Abstract : In this paper, the strong convergences and estimates of convergence rate for generalized quasi-contractive mappings and generalized set-valued quasi-contractive mappings are studied in a real Hilbert space. Firstly, the Picard iterative process is used to approximate the fixed point. Secondly, a characterization of strong convergence theorem of the Mann iterative sequence is proved. By virtue of the mean value theorem of integrals, the convergence rate and the error estimate of the iterative processes are given.

MS [00296] Recent advances on two-phase flows, fluid-structure interactions, and interface problems

room : E701

• [02815] High Order Compact Finite Difference Schemes for Helmholtz Interface Problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Bin Han (University of Alberta)
    • Qiwei Feng (University of Alberta)
    • Michelle Michelle (Purdue University)
    • Yau Shu Wong (University of Alberta)
  • Abstract : The Helmholtz equation is numerically challenging to solve, due to highly oscillating solutions and ill-conditioned huge matrices. Introducing Dirac-Assisted-Tree DAT method and high-order compact FDMs, we can handle 1D-heterogeneous and special 2D-Helmholtz interface problem with large wavenumbers by only solving small linear systems. We present 5th-order compact FDMs for 2D-Helmholtz interface problem with discontinuous wavenumbers and reduced pollution effect. Numerical experiments demonstrate effectiveness and superior performance of our proposed methods for Helmholtz interface problem.
• [03418] Cubic Hermite splines plus correction terms: a way of adaption to the presence of singularities
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Ruiz-Alvarez (Universidad Politecnica de Cartagena)
    • Zhilin Li (North Carolina State University)
    • Sergio Amat (Universidad Politécnica de Cartagena)
    • Juan Carlos Trillo (Universidad Politécnica de Cartagena)
    • Concepción Solano (Universidad Politécnica de Cartagena)
  • Abstract : Hermite interpolation is classically used to reconstruct smooth data when the function and its derivatives are available at certain nodes. If derivatives are not available, it is easy to set a system of equations imposing some regularity conditions at the data nodes in order to obtain them. This process leads to the construction of a Hermite spline. The problem of the described Hermite splines is that the accuracy is lost if the data contains singularities. The consequence is the appearance of oscillations, if there is a jump discontinuity in the function, that globally affects the accuracy of the spline, or the smearing of singularities, if the discontinuities are in the derivatives of the function. This work is devoted to the construction and analysis of a new technique that allows for the computation of accurate derivatives of a function close to singularities using a Hermite spline. The idea is inspired in the immersed interface method (IIM) and aims to correct the system of equations of the spline in order to attain the desired accuracy even close to the singularities. Once we have computed the derivatives with enough accuracy, a correction term is added to the Hermite spline in the intervals that contain a singularity. The aim is to reconstruct piecewise smooth functions with $O(h^4)$ accuracy even close to the singularities. The process of adaption requires some knowledge about the position of the singularity and the values of the function and its derivatives at the singularity. The whole process can be used as a post-processing, where a correction term is added to the classical cubic Hermite spline. Proofs for the accuracy and regularity of the corrected spline and its derivatives are given. We also analyse the mechanism that eliminates the Gibbs phenomenon close to jump discontinuities in the function. The numerical experiments presented confirm the theoretical results obtained.
• [02836] Difference Finite Element Method for 3D Steady Navier-Stokes Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Xinlong Feng (Xinjiang University)
  • Abstract : In this work, a difference finite element (DFE) method for the 3D steady Navier–Stokes (N–S) equations is presented. This new method consists of transmitting the FE solution of 3D steady N–S equations into a series of the FE solutions of 2D steady Oseen iterative equations, which are solved by using the finite element pair (P1b,P1b,P1)×P1 satisfying the discrete inf-sup condition in a 2D domain ω . In addition, we use finite element pair ((P1b,P1b,P1)×P1)×(P1×P0) to solve 3D steady Oseen iterative equations, where the pair satisfies the discrete inf-sup condition in a 3D domain Ω under the quasi-uniform mesh condition. To overcome the difficulty of nonlinearity, we apply the Oseen iterative method and present the weak formulation of the DFE method for solving 3D steady Oseen iterative equations. Moreover, we provide the existence and uniqueness of the DFE solutions of 3D steady Oseen iterative equations and deduce the first order convergence with respect to the discrete step parameter of the DFE solutions to the exact solution of 3D steady N–S equations. Finally, numerical tests are presented to show the accuracy and effectiveness of the proposed method.
• [03698] Finite difference method on staggered grids for Stokes-Biot problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hongxing Rui (Shandong University)
  • Abstract : In this talk, we will present a looking-free finite difference method based on staggered grids for coupled Stokes-Biot problems. The model problems are used to describe Stokes fluid coupled with a poroelastic flow with a interfece. The construction of the finite difference schemes, analysis for the existence and uniqueness of the approximation solutions, superconvergence will be presented. Numerical experiments are presented to confirm the theoretical results. Then we will present a semi-decoupled scheme for the Stokes-Biot system, where the displacement of structure is split from the whole system using the time-lagging scheme. We will also present some ongoing works on coupled problem briefly.

MS [00952] Numerical methods for emerging flow problems in geosciences

room : E702

• [03640] Non-stationary probabilistic tsunami hazard assessments incorporating the influence of tides and sea level rise
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ignacio Sepulveda (San Diego State University)
  • Abstract : Tides are often the largest source of sea levels fluctuations. Two probabilistic-tsunami-hazard-assessments (PTHA) methods are proposed to combine the tidal-phase uncertainty with other tsunami uncertainties. The first method adopts a Stochastic-Reduced Order-Model (SROM) producing sets of tidal phase samples to be used in tsunami simulations. The second method uses tsunami simulations with prescribed collocation-tidal-phases and probability distributions to model the uncertainty. The methods are extended to non-stationary-probabilistic-tsunami-hazard-assessments (nPTHA), combining tsunamis, tides and sea level rise.
• [02149] A hybrid numerical method for dispersive multiphase porous media flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Prabir Daripa (Texas A&M University, College Station)
  • Abstract : We discuss a recently developed model of multiphase multicomponent porous media flows in the context of shear-thinning polymer flooding. This model is based on Darcy’s law, Buckley-Leverett equations and shear-thinning constitutive laws. A multiscale hybrid numerical method based on a combination of discontinuous finite element method, modified method of characteristics, and data driven strategies is developed to solve this model. We study effects of dispersion and shear-thinning on the advective transport of constituents like polymers.
• [01968] Ocean canyon dynamics modeled using Mimetic Curvilinear Coastal Ocean Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Jared Brzenski (San Diego State University)
  • Abstract : A 3D case study for Monterey Bay, CA, is performed to validate and demonstrate the capabilities of the Mimetic Coastal Ocean Model (MCCOM) model for simulating non-hydrostatic flows. The MCCOM model can resolve features such as stratified flows, internal bore formation, and strongly nonlinear internal wave processes inside the steep bathymetry of the Monterey Canyon system by implementing the model on a fully 3D curvilinear mesh.
• [01610] Hierarchical models for the numerical simulation of shallow water flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Julian Koellermeier (University of Groningen)
  • Abstract : We introduce hierarchical moment models as a flexible way to derive hierarchies of models for shallow flows. The new hierarchical models are based on an expansion of the velocity profile. The equations for the expansion coefficients constitute an hierarchical system. We will exemplify the hierarchical models for 1D and 2D application cases including their analysis and the extension to complex fluids. We highlight runtime and accuracy improvements with respect to standard shallow water equations.

MS [00749] Recent Advances on Preconditioners and Fast Solvers for Nonlinear PDEs

room : E703

• [04011] Nonlinear FETI-DP domain decomposition methods combined with deep learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Axel Klawonn (University of Cologne)
    • Martin Lanser (University of Cologne)
    • Janine Weber (University of Cologne)
  • Abstract : In nonlinear-FETI-DP domain decomposition methods the choice of the nonlinear elimination set and of the coarse space have a huge impact on the nonlinear and linear convergence behavior. In this talk, we will show new results combining recently developed approaches for the adaptive choice of the nonlinear elimination set with adaptive coarse spaces. Additionally, we will discuss approaches to improve the computational efficiency and nonlinear convergence by enhancing Nonlinear-FETI-DP with techniques from machine learning.
• [03539] A quasi-Newton method with a secant-like diagonal approximation of Jacobian for symmetric sparse nonlinear equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Duc Quoc Huynh (National Central University)
    • Feng-Nan Hwang (National Central University)
  • Abstract : We propose and study a new variant of the quasi-Newton method with a secant-like diagonal approximation of Jacobian (QN-SDAJ) for solving sparse symmetric nonlinear equations (SSNEs). Such problems appear in various scientific computing applications, such as finding critical points that satisfy the first-order necessary condition of unconstrained optimization problems and numerical semilinear elliptic partial differential equations. The advantages of the proposed method are conceptually simple and easy to implement. We establish the global convergence of the proposed method in conjunction with a nonmonotone line search technique under some appropriate assumptions. Several numerical experiments for some benchmark problems demonstrate the efficiency of QN-SDAJ, which outperforms the alternatives, including exact Newton, nonlinear conjugate gradient, and Broyden--Fletcher--Goldfarb--Shanno (BFGS) methods. In addition, the proposed method can also be used as an effective nonlinear preconditioner to enhance the robustness and speed up the convergence of BFGS, especially for test cases with large dimensions.
• [02038] Robustness and Adaptivity of Iterative Solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • Chensong Zhang (AMSS)
  • Abstract : Linear systems arising from coupled PDEs in multiphysics applications could cause robustness problems for iterative solution methods. Solving large-scale linear algebraic systems in an efficient and robust manner is a dream for many computational scientists who work on practical engineering applications. In this talk, we review some old and new techniques for improving the robustness of iterative solvers for large-scale sparse linear equations. In particular, we will discuss methods based on machine learning to select solver components automatically to improve overall simulation performance. Based on this algorithm selection model, a self-adaptive procedure can be derived to improve the robustness of iterative solvers.
• [01782] Generalized multiscale finite element method for highly heterogeneous compressible flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Shubin Fu (Eastern Institute for Advanced Study)
    • Lina Zhao (City University of Hong Kong)
    • Eric Chung (The Chinese University of Hong Kong)
  • Abstract : I will present generalized multiscale finite element method for highly heterogeneous compressible flow. We follow the major steps of the GMsFEM to construct a permeability dependent offline basis for fast coarse-grid simulation. To further increase the accuracy of the multiscale method, a residual driven online multiscale basis is added to the offline space. Rich numerical tests on typical 3D highly heterogeneous media are presented to demonstrate the impressive computational advantages of the proposed multiscale method.

MS [02402] Numerical methods for a class of time-dependent PDEs

room : E704

• [02681] Unconditionally MBP-preserving linear schemes for conservative Allen-Cahn equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jingwei Li (Lanzhou University)
  • Abstract : The maximum bound principle MBP, is an important property for semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initial and boundary conditions and nonlinear operator preserves for all time a uniform pointwise bound in absolute value. It has been a challenging problem to design unconditionally MBP-preserving high-order accurate time-stepping schemes for these equations. Du Qiang et al have estiblished a unified analysical framework on the MBP preserving scheme for the semilinear parabolic equations which in this talk will be extended to conservative Allen-Cahn equation with the introduced Lagrange multiplier enforcing the mass conservation. Some sufficient conditions on the nonlinear potentials will be given under which the MBP holds and then the stabilized exponential time differencing scheme is proposed for time integration, which are linear schemes and unconditionally preserve the MBP in the time discrete level. Convergence of these schemes is analyzed as well as their energy stability. Various two and three dimensional numerical experiments are also carried out to validate the theoretical results and demonstrate the performance of the proposed schemes. These work are joint with Cai Yongyong, Feng Xinlong, Huang Qiumei, Jiang Kun, Ju Lili, Li Xiao, Lan Rihui et al.
• [02717] Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schr\"{o}dinger equation in the nonrelativistic regime
  • Format : Online Talk on Zoom
  • Author(s) :
    • xuanxuan zhou (beijing normal university)
  • Abstract : We establish a class of uniformly accurate nested Picard iterative integrator (NPI) Fourier pseudospectral methods for the nonlinear Klein-Gordon-Schr\"{o}dinger equation (KGS) in the nonrelativistic regime, involving a dimensionless parameter $\varepsilon\ll1$ inversely proportional to the speed of light. Actually, the solution propagates waves in time with $O(\varepsilon^2)$ wavelength when $0<\varepsilon\ll1$, which brings significant difficulty in designing accurate and efficient numerical schemes. The NPI method is designed by separating the oscillatory part from the non-oscillatory part, and integrating the former exactly. Based on the Picard iteration, the NPI method can be applied to derive arbitrary higher-order methods in time with optimal and uniform accuracy (w.r.t. $\varepsilon\in(0,1]$), and the corresponding error estimates are rigorously established. In addition, the practical implementation of the second-order NPI method via Fourier pseupospectral discretization is clearly demonstrated, with extensions to the third order NPI. Some numerical examples are provided to support our theoretical results and show the accuracy and efficiency of the proposed schemes.
• [02550] Structure-preserving scheme for the PNP equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Fenghua Tong (Beijing Normal University)
  • Abstract : Poisson-Nernst-Planck system is a macroscopic model to describe the ion transport process. We propose a novel method to construct the positivity preserving and mass conservation scheme for the Poisson-Nernst-Planck equations. The method is based on the discrete $L^2_h$ or $H^1_h$ projection strategy in which the solution projected from the intermediate solution computed by semi-implicit scheme inherits the positivity preservation and mass conservation with negligible additional computational cost resulting from the nonlinear algebraic equation.
• [02553] Numerical simulation of rotational nonlinear Schrodinger equations with attractive interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Wu (Beijing Normal University)
  • Abstract : We consider the focusing Schr$\ddot{o}$dinger equation with rotation and numerically simulate the ground state and dynamic properties. We take the gradient flow with Lagrange multiplier (GFLM) method to compute the ground state and time splitting pseudospectral method to simulate dynamics. We numerically verify the nonexistence of vortices in harmonic symmetry potential and analytically derive that the symmetric state energy (m=0) is always lower than the central vortex state energy (m=1) when the attractive interaction is sufficiently small. For dynamics properties, we mainly simulated the condensate widths, a stationary state with a shifted center and stability of central vortex states and found that the conclusion is completely consistent with the repulsive interaction. Finally, we numerically simulate the global existence and finite time blow-up of solution in mass-supercritical case.

MS [00052] Efficient numerical methods for high-dimensional PDEs

room : E705

• [04856] Sparse grid techniques for particle-in-cell simulation of kinetic plasmas
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lee Forrest Ricketson (Lawrence Livermore National Laboratory)
  • Abstract : The Vlasov equation, which models collisionless plasma dynamics, is six-dimensional in general. To combat this high dimensionality, the most prevalent numerical method has long been particle-in-cell (PIC), in which the plasma is represented by particles which interact with electromagnetic fields specified on a spatial mesh. However, the inclusion of particles subjects the scheme to slow-converging sampling errors, while use of a spatial mesh admits only partial mitigation of the curse of dimensionality. We show that using sparse grids with PIC makes the algorithm’s complexity only logarithmically dependent on dimension and dramatically reduces the impact of sampling noise. We report recent progress combining sparse PIC advanced symplectic and implicit methods. Finally, we report on ongoing work toward adaptively choosing suitable coordinates for these sparse grid computations. *Prepared by LLNL under Contract DE-AC52-07NA27344.
• [03639] Nonlinear model reduction with adaptive bases and adaptive sampling
  • Format : Online Talk on Zoom
  • Author(s) :
    • Benjamin Peherstorfer (Courant Institute of Mathematical Sciences, New York University)
  • Abstract : We introduce an online-adaptive model reduction approach that can efficiently reduce convection-dominated problems. It exploits that manifolds are low dimensional in a local sense in time and iteratively learns and adapts reduced spaces from randomly sampled data of the full models to locally approximate the solution manifolds. Numerical experiments to predict pressure waves in combustion dynamics demonstrate that our approach achieves significant speedups in contrast to classical, static reduced models.
• [04871] Quantum Algorithms for Accelerating the Solution of Partial Differential Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ilon Joseph (Lawrence Livermore National Laboratory)
  • Abstract : Quantum algorithms have been proposed to accelerate the solution of linear partial differential equations (PDEs) with polynomial to exponential speedup. Recent progress has significantly improved these algorithms with respect to numerical methods and error convergence. Due to the “no-cloning” theorem, solving nonlinear PDEs is more challenging. Newly proposed Koopman and Carleman approaches solve for the linear evolution of the probability distribution function of the solution and are closely related to simulating stochastic PDEs and quantum fields.
• [03854] A Hybrid AMR Low-Rank Tensor Approach for Solving the Boltzmann Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • William Tsubasa Taitano (Los Alamos National Laboratory)
    • Samuel Jun Araki (Air Force Research Laboratory)
  • Abstract : The Boltzmann equation describes the time evolution of a particle distribution function in a six-dimensional position-velocity phase space. The exponential growth in computational complexity often challenges a grid-based approach to modeling the Boltzmann equation as the dimensionality grows. Scalable low-rank tensor decomposition techniques have recently been developed with applications to high-dimension PDEs to address this issue. Despite the remarkable progress made in the community, low-rank structures in the phase-space are not evident in realistic engineering systems with complex geometries (e.g., electric propulsion systems and fusion reactors), where discontinuities, shocks, complex boundary conditions, and material-dependent physics (e.g., collisions, fusion reactions, ionization/excitation, charge-exchange processes) pose formidable challenges. In this talk, we propose a novel hybrid algorithm where quad-tree adaptive mesh refinement (AMR) is applied in real space while a low-rank approximation is applied in the velocity space. The AMR algorithm efficiently handles challenges pertaining to complex structures in real space, while the low-rank formulation targets dimensionality challenges in the velocity space. We present preliminary results on the new algorithm applied to challenging multi-dimensional gas kinetics problems.

MS [00708] Computational medicine of the heart: towards cardiac digital twins

room : E708

• [04495] Multiphysics, multiscale, and computational models for simulating the cardiac function
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Dede' (Politecnico di Milano)
  • Abstract : We present our novel 4-chambers model of the human heart. We couple state-of-the art models of electrophysiology, mechanical activation, passive mechanical response, and blood circulation, leading to a coupled electromechanical problem. Our multiscale model accounts for miscroscopic active force generation that exploits Machine Learning algorithms. We numerically solve the model in the HPC framework. We also present a Machine Learning method for real-time numerical simulations that allows efficient construction of cardiac digital twins.
• [03710] Virtual Populations of Heart Chimaeras: Generative Compositional Learning from Datasets of Datasets
  • Format : Talk at Waseda University
  • Author(s) :
    • Alejandro Federico Frangi (University of Leeds)
    • Haoran Dou (University of Leeds)
    • Seppo Virtanen (University of Leeds)
    • Nishant Ravikumar (University of Leeds)
    • Zeike Taylor (University of Leeds)
  • Abstract : Virtual populations capturing sufficient anatomical variability while remaining plausible are central to conducting in-silico trials of medical devices. Unfortunately, not all anatomical information is available from a single data sample or modality given a population. Instead, data with missing/partially overlapping anatomical information is often available from independent data samples and/or modalities. We introduce a generative anatomical model capable of learning complex anatomical structures from datasets of unpaired datasets and synthesising anatomical assemblies coined virtual chimaeras.
• [03238] The role of the Eikonal model in personalized cardiac modeling from parameter acquisition to arrhythmia simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Cristian Alberto Barrios Espinosa (Karlsruhe Institute of Technology (KIT))
    • Jorge Sanchez Arciniegas (Valencia Polytechnic University )
    • Laura Unger (Karlsruhe Institute of Technology (KIT))
    • Marie Houillon (Karlsruhe Institute of Technology (KIT))
    • Armin Luik (Städtisches Klinikum Karlsruhe)
    • Axel Loewe (Karlsruhe Institute of Technology (KIT))
  • Abstract : The Eikonal model is widely used to simulate wave propagation in different fields, including cardiac modeling. A modified version of the Eikonal model can help to customize model parameters, like conduction velocity accounting for anisotropic propagation. Moreover, the modified Eikonal model can be used to simulate arrhythmia by allowing for reactivation, overcoming challenges of the fast iterative method. Finally, we show applications of the enhanced Eikonal models as a valuable tool for cardiac research applications.
• [03521] An anisotropic eikonal model for cardiac repolarization and arrhythmias
  • Format : Talk at Waseda University
  • Author(s) :
    • Simone Pezzuto (Università di Trento)
    • Lia Gander (Università della Svizzera italiana)
    • Rolf Krause (Università della Svizzera italiana)
    • Martin Weiser (Zuse Institute Berlin)
    • Francisco Sahli Costabal (Pontificia Universidad Católica de Chile)
  • Abstract : State-of-the-art computational models of cardiac electrophysiology are computationally expensive. Their clinical applicability is, therefore, limited. In the talk, we will present a lightweight eikonal approximation for real-time simulation of cardiac arrhythmias on a desktop computer. We provide several numerical tests and comparisons, including atrial fibrillation, ventricular tachycardia, and with fibrosis. Finally, we consider the problem of estimating the inducibility of fibrillation with a multi-fidelity framework by combining the eikonal approach with the high-fidelity model.

MS [02014] High-order numerical methods: recent development and applications

room : E709

• [03002] High-order Structure-Preserving Schemes for Special Relativistic Hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Huazhong Tang (Nanchang Hangkong University and Peking University)
  • Abstract : Abstract: This talk mainly reviews two high-order accurate structure-preserving finite difference schemes for the special relativistic hydrodynamics (RHD). The first is the physical-constraints-preserving (PCP) scheme, which preserves the positivity of the rest-mass density and the pressure and the bounds of the fluid velocity and is built on the local Lax-Friedrichs (LxF) splitting, the WENO reconstruction, the PCP flux limiter, and the high-order strong stability preserving time discretization. The key to developing such scheme is to prove the convexity and other properties of the admissible state set and to discover a concave function with respect to the conservative vector. The second is the entropy stable (ES) scheme, whose semi-discrete version satisfies the entropy inequality. The key is to technically construct the affordable entropy conservative (EC) flux of the semi-discrete second-order accurate EC schemes satisfying the semi-discrete entropy equality for the found convex entropy pair. As soon as the EC flux is derived, the dissipation term can be added to give the semi-discrete ES schemes satisfying the semi-discrete entropy inequality. The WENO reconstruction for the scaled entropy variables and the previous time discretization are implemented to obtain the fully-discrete high-order “ES” schemes. The performance of the proposed schemes has been demonstrated by numerical experiments. By the way, we also briefly review other relative works on the structure-preserving schemes for the special RHDs. Those works have been further to the general equation of state and the special relativistic magnetohydrodynamics etc., see our papers listed below for details. References 1. Wu, K.L. and Tang, H.Z., “High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics”, J. Comput. Phys., Vol. 298, 2015, pp. 539-564. 2. Wu, K.L. and Tang, H.Z., “Physical-constraints-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state”, Astrophys. J. Suppl. ser., Vol. 228, 2017, 3. 3. Wu, K.L. and Tang, H.Z., “Admissible states and physical constraints preserving numerical schemes for special relativistic magnetohydrodynamics”, Math. Mod. and Meth. Appl. Sci., Vol. 27, 2017, pp. 1871-1928. 4. Wu, K.L. and Tang, H.Z., “On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state”, Z. Angew. Math. Phys., Vol. 69, 2018, 84. 5. Ling, D., Duan, J.M. and Tang, H.Z., “Physical-constraints-preserving Lagrangian finite volume schemes for one- and two-dimensional special relativistic hydrodynamics”, J. Comput. Phys., Vol. 396, 2019, pp. 507-543. 6. Ling, D. and Tang, H.Z., “Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics”, submitted to Commun. Comput. Phys., March 4, 2023. arXiv: 2303.02686. 7. Duan, J.M. and Tang, H.Z., “High-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamics”, Adv. Appl. Math. Mech., Vol. 12, 2020, pp. 1-29. 8. Duan, J.M. and Tang, H.Z., “High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics”, J. Comput. Phys., Vol. 421, 2020, 109731. 9. Duan, J.M. and Tang, H.Z., “Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics”, J. Comput. Phys., Vol. 426, 2021, 109949.
• [03400] High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Cheng (Institute of Applied Physics and Computational Mathematics)
  • Abstract : The nonlocal electron heat transport model in laser heated plasmas plays a crucial role in inertial confinement fusion (ICF), and it is important to solve it numerically in an accurate and robust way. In this talk, we develop a class of high-order entropy stable discontinuous Galerkin methods for the nonlocal electron heat transport model. We further design our DG scheme to have the positivity-preserving property, which is shown, by a computer-aided proof, to have no extra time step constraint than that required by L2 stability. Numerical examples are given to verify the high-order accuracy and positivity-preserving properties of our scheme. By comparing the local and nonlocal electron heat transport models, we also observe more physical phenomena such as the flux reduction and the preheat effect from the nonlocal model.
• [02764] A new cut-cell interface treating method for compressible multi-medium flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Chunwu Wang (Nanjing University of Aeronautics and Astronautics)
  • Abstract : In this work, a conservative sharp interface treating method is proposed for solving compressible multi-medium flow based on the cut-cell method. To overcome the small cell problem, which causes standard explicit scheme unstable, the most common approach is generating interface cells by merging small cut cells with their neighbors. We present a new and simple way to construct interface cells. Rather than considering various complex cell merging cases, we select some Cartesian cell nodes near the interface, and then connect these nodes to form the interface cells. Meanwhile, at the edges of the cell coinciding with the interface, the numerical fluxes are obtained by solving the local Riemann problem, thus the conservation of the flow variables is effectively maintained. Several numerical experiments indicate that our proposed method can capture the shock wave and material interface accurately and sharply, as well as being stable even for problems with significant density and pressure gradients.
• [02690] A hybrid WENO scheme for steady Euler equations in curved geometries on Cartesian grids
  • Format : Talk at Waseda University
  • Author(s) :
    • Yifei Wan (University of Science and Technology of China)
    • Yinhua Xia (University of Science and Technology of China)
  • Abstract : For steady Euler equations in complex boundary domains, high-order shock-capturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian grids to achieve uniform high-order accuracy. In this work, we utilize a fifth-order finite difference hybrid WENO scheme to simulate steady Euler equations, and the same fifth-order WENO extrapolation methods are developed to handle the curved boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform the tangential derivatives along the curved solid wall boundary. This hybrid WENO scheme is robust for steady-state convergence and maintains high-order accuracy in the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows that this hybrid WENO scheme possesses low dispersion and dissipation errors. Numerical examples are presented to validate the high-order accuracy and robust performance of the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.

MS [00319] Robust formulations for coupled multiphysics problems – Theory and applications

room : E710

• [01558] A diffuse interface method for fluid-poroelastic structure interaction
  • Format : Talk at Waseda University
  • Author(s) :
    • Martina Bukač (University of Notre Dame)
    • Boris Muha (University of Zagreb)
    • Sunčica Čanić (University of California, Berkeley)
  • Abstract : The interaction between a free flowing fluid and a poroelastic structure, commonly formulated as a Navier-Stokes/Biot coupled system, has been used to describe problems arising in many applications, including environmental sciences, hydrology, geomechanics and biomedical engineering. Many existing numerical for this problem are based on a sharp interface approach, in the sense that the interface between the two regions is parametrized using an exact specification of its geometry and location, and the nodes in the computational mesh align with the interface. However, the exact location is sometimes not known, or the geometry is complicated, making a proper approximation of the integrals error-prone and difficult to automate. Hence, in this talk, we present a diffuse interface method for the coupled fluid-poroelastic structure interaction. The method uses a phase-field function which transitions from 1 in one region to 0 in the other region. We will first present the analysis of convergence of the discrete diffuse interface solution to the continuous sharp interface solution for the Stokes-Darcy problem. Then, we will discuss the extensions to Navier-Stokes/Biot system, and apply the method to study the optimal design of a bioartificial pancreas.
• [01781] Parameter-robust methods for the Biot-Stokes interfacial coupling
  • Format : Talk at Waseda University
  • Author(s) :
    • Martin Hornkjøl (University of Oslo)
    • Wietse Boon (KTH Royal Institute of Technology)
    • Miroslav Kuchta (Simula Research Laboratory)
    • Kent-Andre Mardal (University of Oslo)
    • Ricardo Ruiz Baier (Monash University)
  • Abstract : In this talk I will discuss a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. I will present a five-field mixed-primal finite element scheme, with a preconditioner, for solving the Stokes velocity-pressure and Biot displacement-total pressure-fluid pressure. With adequate inf-sup conditions the stability of the formulation is established robustly in all material parameters.
• [02817] Robust parallel solvers in cardiac modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolás Alejandro Barnafi Wittwer (University of Chile)
  • Abstract : We will see the physics involved in cardiac modeling, and focus on their efficient solution in an HPC infrastructure measured in both CPU time and scalability. As we will see, one of the main tools for improving performance is quasi-Newton methods, which do not sacrifice on scalability when initialized adequately. In some contexts, it will be possible to circumvent the solution of a linear system, which drastically reduces the complexity of the proposed solvers.
• [02934] Stochastic Galerkin mixed finite element approximation for poroelasticity with uncertain inputs
  • Format : Talk at Waseda University
  • Author(s) :
    • Arbaz Khan (IIT Roorkee)
    • Catherine E Powell (University of Manchester, UK)
  • Abstract : Linear poroelasticity models have important applications in biology and geophysics. In particular, the well-known Biot consolidation model describes the coupled interaction between the linear response of a porous elastic medium {saturated with fluid} and a diffusive fluid flow within it, assuming small deformations. This is the starting point for modeling human organs in computational medicine and for modeling the mechanics of permeable rock in geophysics. Finite element methods for Biot's consolidation model have been widely studied over the past four decades. In the first part of talk, we discuss a novel locking-free stochastic Galerkin mixed finite element method for the Biot consolidation model with uncertain Young's modulus and hydraulic conductivity field. After introducing a five-field mixed variational formulation of the standard Biot consolidation model, we discuss stochastic Galerkin mixed finite element approximation, focusing on the issue of well-posedness and efficient linear algebra for the discretized system. We introduce a new preconditioner for use with MINRES and establish eigenvalue bounds. Finally, we present specific numerical examples to illustrate the efficiency of our numerical solution approach. In the second part of the talk, we discuss a posteriori error estimators for SGFEM of Biot's consolidation model with uncertain inputs.

MS [01681] Recent advances in numerical methods for partial differential equations

room : E711

• [03945] Geometrical degrees of freedom for high order Whitney forms
  • Format : Talk at Waseda University
  • Author(s) :
    • Ana María Alonso Rodríguez (University of Trento)
    • Francesca Rapetti (Université Côte d’Azur)
    • Ludovico Bruni Bruno (Università dell'Insumbria)
  • Abstract : Finite element spaces extending Whitney forms to higher polynomial degrees are widely used for discretizing partial differential equations in electromagnetism, fluid dynamics or elasticity, and different degrees of freedom (dofs) can be considered for interpolation. In particular the so-called weights preserve the meaning of the natural degrees of freedom associated with Whitney forms as circulation, fluxes or densities since they are the integrals of a k-form on k-chains. Weights are a generalization of the evaluations of a scalar function at a set of nodes in view of its reconstruction on multivariate polynomial bases and allows to extend in a natural way well- known concepts as the Lebesgue constant. We rely on the flexibility of the weights with respect to their geometrical support to reduce the growth of the Lebesgue constant when increasing the degree of the polynomial interpolation of differential k-forms.
• [02919] Energy-preserving Mixed finite element methods for a ferrofluid flow model
  • Format : Talk at Waseda University
  • Author(s) :
    • Yongke Wu (University of Electronic Science and Technology of China)
    • Xiaoping Xie (Sichuan University)
  • Abstract : In this talk, we introduce a class of mixed finite element methods for the ferrofluid flow model proposed by Shliomis [Soviet Physics JETP, 1972]. We show that the energy stability of the weak solutions to the model is preserved exactly for both the semi- and fully discrete finite element solutions. Furthermore, we prove the existence of the discrete solutions and derive optimal error estimates for both the the semi- and fully discrete schemes. Numerical experiments confirm the theoretical results.
• [03132] Immersed CR element methods for the elliptic and Stokes interface problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Haifeng Ji (Nanjing University of Posts and Telecommunications)
    • FENG WANG (NanJing Normal University)
    • Jinru Chen (NanJing Normal University)
    • Zhilin Li (North Carolina State University)
  • Abstract : In this talk, we shall discuss the immersed CR element method for solving the elliptic and Stokes interface problems with piecewise constant coefficients that have jumps across the interface. In the method, the triangulation does not need to fit the interface and the IFE spaces are constructed from the traditional CR element with modifications near the interface according to the interface jump conditions. The stability and the optimal error estimates of the proposed methods are also derived rigorously. The constants in the error estimates are shown to be independent of the interface location relative to the triangulation. Numerical examples are provided to verify the theoretical results.
• [02917] A fast Cartesian grid method for unbounded interface problems with non-homogeneous source terms
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiahe Yang (Shanghai Jiao Tong University)
    • Wenjun Ying (Shanghai Jiao Tong University)
  • Abstract : A Cartesian grid method is presented for interface problems of PDEs with non-homogeneous source terms on unbounded domains. The method adapts a compression-decompression technique and has algorithm complexity of only $O(n^2\log n)$ as compared to $O(n^3)$ by traditional methods. This Cartesian grid method is an extension of the kernel-free boundary integral method, which avoids direct evaluation of singular or nearly singular integrals by reformulating them into solutions of equivalent but much simpler interface problems.

MS [00782] Recent Advances on Mimetic Difference Methods

room : E802

• [01714] Fourth-order Mimetic Differential Operators Applied to the Convection-Diffusion Equation: A matrix Stability Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Jorge VILLAMIZAR (Universidad Industrial de Santander/Universidad de Los Andes)
    • Larry Mendoza (Universidad Central de Venezuela)
    • Giovanni Calderon (Universidad Industrial de Santander)
    • Otilio Rojas (Universidad Central de Venezuela)
    • Jose E Castillo (Computational Science Research Center at San Diego State University)
  • Abstract : The convection-diffusion equation describes physical phenomena where particles or energy are transferred within a physical system due to the processes of diffusion and convection. In this work, we investigate discretization framework based on the mimetic fourth-order finite-difference staggered-grid Castillo-Grone $(CG)$ operators, which has a sextuple of free parameters. We study the dependency of the stability and precision properties of our numerical scheme based on these CG free parameters, and propose parameters that favor both properties. We compare our results with CG parameters previously mentioned in the literature, including those leading to mimetic operators of minimum bandwidth.
• [01788] Discrete mollification results in mimetic difference schemes applied to the convection-diffusion-reaction equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Julio Cesar Carrillo-Escobar (Professor)
    • Giovanni Ernesto Calderon-Silva (Universidad Industrial de Santander)
  • Abstract : It is usual to have stability restrictions when using either an explicit finite differences or a mimetic differences schemes, proposed by Castillo in 2003, to obtain numerical solutions for the convection-diffusion-reaction equation of an incompressible fluid with a source term. In this work, we analyze the effects, in precision and stability, when applying the discrete mollification proposed by Acosta in 2008 to these schemes in mimetic differences.
• [01936] Numerical Energy Conservation Mimetic Scheme For The Advection Equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anand Srinivasan (San Diego State University)
    • Jose E Castillo (Computational Science Research Center at San Diego State University)
  • Abstract : The advection equation $u_t + \nabla \cdot u = 0$ is a hyperbolic partial differential equation that conserves energy. The numerical solution of the advection equation obtained using the traditional finite difference methods often fails to discretely conserve this numerical energy. Mimetic finite difference methods are structure-preserving and are thus well-suited for hyperbolic problems such as the advection equation. The Mimetic methods of Castillo et al discretely mimic the extended Gauss' divergence theorem, and are therefore a faithful discretization of the continuum vector calculus identities. These methods work on a staggered spatial grid and achieve even order of accuracy at the boundaries as well as the interiors of the domain. The temporal discretization obtained from the Leapfrog scheme is staggered in time. The staggered Mimetic-Leapfrog scheme conserves the numerical energy for the advection equation. In this talk, we present the numerical results illustrating the energy-conserving property of the second order Mimetic-Leapfrog scheme. Stability results of the scheme are also presented.
• [01939] Energy Conservation for Mimetic Scheme for Advection Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose E Castillo (Computational Science Research Center at San Diego State University)
  • Abstract : Mimetic difference schemes are based on discrete analogs of differential operators, gradient, divergence, and curl, that not only preserve their vector calculus identities but also hold discrete counterparts of integral formulas. A proof of the energy conservation property of second-order mimetic difference schemes is presented for the one-dimensional advection PDE. This proof leverages on the discrete analog of the integration by parts mimetic difference property

MS [01060] Exploring Arithmetic and Data Representation Beyond the Standard in HPC

room : E803

• [01783] FP-ANR: A representation format to handle floating-point cancellation at run- time
  • Format : Talk at Waseda University
  • Author(s) :
    • David DEFOUR (Universite de Perpignan)
  • Abstract : When dealing with floating-point numbers there are several sources of error which can drastically reduce the numerical quality of computed results. Among those errors, the loss of significance, or cancellation, occurs during for example the subtraction of two nearly equal numbers. In this article, we propose a representation format named Floating-Point Adaptive Noise Reduction (FP-ANR). This format embeds cancellation information directly into the floating-point representation format thanks to a dedicated pattern. With this format, unsignificant trailing bit lost during cancellation are removed from every manipulated floating-point number. The immediate consequence is that it increases the numerical confidence of computed values. The proposed representation format corresponds to a simple and efficient implementation of significance arithmetic based and compatible with the IEEE-754 standard.
• [01812] Precision autotuning using stochastic arithmetic
  • Format : Talk at Waseda University
  • Author(s) :
    • Quentin Ferro (Sorbonne University)
    • Stef Graillat (Sorbonne University)
    • Thibault Hilaire (Sorbonne University)
    • Fabienne Jezequel (Sorbonne University)
  • Abstract : We present PROMISE, a tool that makes it possible to provide a mixed precision version of a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using Discrete Stochastic Arithmetic that enables one to estimate round-off errors. PROMISE has been used for floating point auto-tuning on neural networks to lower their precision while keeping an accurate output.
• [01839] Implementation of highly optimized multiple precision BLAS: Strassen vs. Ozaki scheme
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomonori Kouya (Shizuoka Institute of Science and Technology)
  • Abstract : We have already developed a highly optimized extended multiple precision basic linear algebra subprogram library using various technologies such as AVX2 and OpenMP. In particular, Strassen algorithm and Ozaki scheme we employed are distinctive methods for accelerating matrix multiplication. In this talk, we describe the software structure of our library and highlight the advantages and disadvantages of Strassen algorithm and Ozaki scheme through benchmark tests using fixed- and arbitrary-precision floating-point arithmetic.
• [03869] Accelerating 128-bit Matrix Multiplication for Applications using FPGAs
  • Format : Talk at Waseda University
  • Author(s) :
    • Fumiya Kono (Shizuoka Institute of Science and Technology)
  • Abstract : General Matrix Multiplication (GEMM) is a core of various scientific applications. Since the requirement for the number of bits representing floating-point numbers depends on individual applications, the precision of GEMM is critical. Particularly, Semidefinite Programming requires higher precision, such as binary128. We researched methods of accelerating GEMM in binary128 using FPGAs because arithmetic in binary128 was very slow without hardware unit support. This talk presents an evaluation of our designs on several Intel FPGAs.

MS [00390] Recent Advances in Machine Learning Theory and Applications

room : E804

• [03668] Learning through empirical gain maximization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yunlong Feng (State University of New York at Albany)
    • Qiang Wu (Middle Tennessee State University)
  • Abstract : In this presentation, we introduce a novel empirical gain maximization (EGM) framework for addressing robust regression problems with heavy-tailed noise or outliers in the response variable. EGM focuses on approximating the noise distribution's density function rather than directly approximating the truth function. This approach, stemming from minimum distance estimation, allows for the exclusion of abnormal observations, unlike traditional maximum likelihood estimation. We demonstrate that well-known robust nonconvex regression techniques, such as Tukey regression and truncated least square regression, can be reformulated within this new framework. By developing a learning theory for EGM, we provide a unified analysis for these established, yet not fully-understood, regression methods. This framework offers fresh insights into existing bounded nonconvex loss functions and reveals close connections between seemingly unrelated terminologies, such as Tukey's biweight loss and the triweight kernel. We also show that other prevalent bounded nonconvex loss functions in machine learning can be reinterpreted from specific smoothing kernels in statistics. Lastly, our framework facilitates the creation of new bounded nonconvex loss functions for robust learning.
• [01357] SKELETAL BASED IMAGE PROCESSING FOR CNN BASED IMAGE CLASSIFICATION
  • Format : Online Talk on Zoom
  • Author(s) :
    • Cen Li (Middle Tenn State University)
    • Tsega Tsahai (Middle Tenn State University)
  • Abstract : This work studies image processing techniques as a preprocessing step in image classification. Deep Learning based Human Pose Estimation was used to preprocess raw image to extract key posture information, and CNN was applied to learn the classification models for human postures. Two applications have been developed: (1) teaching a humanoid robot to play an interactive game of Simon Says, (2) a fall detection system for elderly residents in an assisted living facility.
• [01023] Total stability of kernel methods and localized learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andreas Christmann (University of Bayreuth)
    • Hannes Koehler (University of Bayreuth)
  • Abstract : Regularized kernel-based methods typically depend on the underlying probability measure P and very few hyperparameters. We investigate the influence of simultaneous slight pertubations of P, the hyperparameters, and the kernel on the resulting predictor. Furthermore, kernel methods suffer from their super-linear computational requirements for big data. Hence we extend our results to the context of localized learning. The talk is based on Koehler and Christmann, JMLR, 23, 1-41, 2022.

MS [00168] Applications of evolutionary algorithms in differential equation models

room : E811

• [03121] Spherical search with multi-operator differential evolution for constrained optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman)
    • Jongmin Lee (Konkuk University)
    • Victoria May Paguio Mendoza (University of the Philippines Diliman)
    • Eunok Jung (Konkuk University)
  • Abstract : We propose a new method, SASS-MODE, for solving constrained optimization problems by combining the self-adaptive spherical search (SASS) with the improved multi-operator differential evolution (IMODE). We adapted IMODE to handle constraints with three modifications and tested our method on 57 benchmark problems and an optimal control problem from an infectious disease model. SASS-MODE outperforms recent algorithms and achieves state-of-the-art results.
• [02925] Minimizing infections and intervention cost: multi-objective approach with user-friendly dashboard
  • Format : Talk at Waseda University
  • Author(s) :
    • Jongmin Lee (Department of Mathematics, Konkuk University)
    • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman)
    • Victoria May P. Mendoza (Institute of Mathematics, University of the Philippines Diliman)
    • Eunok Jung (Department of Mathematics, Konkuk University)
  • Abstract : During the COVID-19 pandemic, the world faces the challenge of reducing the number of infections while simultaneously minimizing the cost of intervention policies. This study proposes a deterministic model and multi-objective optimization approach that balances these conflicting objectives. Metropolis-Hastings algorithm estimated parameters, and the genetic algorithm found multi-objective optimization solutions. From Pareto solutions, users can select the most suitable solution by considering economic-related parameters. Additionally, we develop a user-friendly, web-based dashboard for ease of use.
• [02755] Comparative Study of Heuristic Algorithms for Electrical Impedance Tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Arrianne Crystal Velasco (Institute of Mathematics, University of the Philippines Diliman)
    • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman)
    • Marion Darbas (LAGA CNRS UMR 7539, University Sorbonne Paris Nord)
    • Monica Bacon (Institute of Mathematics, University of the Philippines Diliman)
    • Johm Cedrick de Leon (Institute of Mathematics, University of the Philippines Diliman)
  • Abstract : Based on electrical measurements from electrodes placed around the boundary of a body, electrical impedance tomography (EIT) is an imaging procedure that recovers the spatial distribution of the conductivities in the interior of a body. This work presents a study of the applicability of six heuristic algorithms for the EIT image reconstruction problem.
• [03163] Bi-objective optimization considering bed capacity and timing of interventions
  • Format : Talk at Waseda University
  • Author(s) :
    • Victoria May Paguio Mendoza (University of the Philippines Diliman)
    • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman)
    • Youngsuk Ko (Department of mathematics, Konkuk university)
    • Jongmin Lee (Konkuk University)
    • Eunok Jung (Konkuk University)
  • Abstract : Without vaccines and medicine, non-pharmaceutical interventions are the main strategy for controlling the spread of diseases. A bi-objective optimization problem is formulated that allows for the easing of restrictions at an earlier time and minimizes the number of additional beds ensuring sufficient capacity in healthcare facilities. We utilize a compartmental model that distinguishes mild from severe cases. The multiple optimal solutions of the bi-objective problem offer trade-off solutions that can be useful decision-support tools.

MS [00211] Mathematics of Geometric Deep Learning

room : E812

• [03411] On the stability of spectral graph filters and beyond
  • Author(s) :
    • Xiaowen Dong (University of Oxford)
  • Abstract : Data collected in network domains, hence supported by an (irregular) graph rather than a (regular) grid-like structure, are becoming pervasive. Typical examples include gene expression data associated with a protein-protein interaction graph, or behaviours of a group of individuals in a social network. Graph-based signal processing and machine learning are recent techniques that have been developed to handle such graph-structured data and have seen applications in such diverse fields as drug discovery, fake news detection, and traffic prediction. However, a theoretical understanding of the robustness of these models against perturbation to the input graph domain has been lacking. In this talk, I will present our results on the stability bounds of spectral graph filters as well as other recent work on the robustness of graph machine learning models, which together will contribute to the deployment of these models in real-world scenarios.
• [01565] Spherical Framelets with Directionality for Spherical Neural Networks
  • Author(s) :
    • Jianfei Li (City University of Hong Kong)
    • Han Feng (City University of Hong Kong)
    • Xiaosheng Zhuang (City University of Hong Kong)
  • Abstract : In this talk, we shall focus on the constructions and applications of directional framelets beyond the Euclidean domain, i.e., on the 2-sphere. We shall discuss their characterizations in terms of the affine systems. Fast algorithmic framelet transforms associated with the underlying filter banks or multiscale structures will be investigated. Moreover, based on our spherical framelets with directionality, we shall consider the development of spherical convolutional neural network (SNN) model for deep learning tasks.
• [01568] Some Applications of Hyperplane Arrangements in Deep Learning
  • Author(s) :
    • Huan Xiong (HIT and MBZUAI)
  • Abstract : In this talk, we build some connections between hyperplane arrangements and Piecewise Linear Convolutional Neural Networks (PLCNNs), and use them to derive maximal and average numbers of linear regions for one-layer PLCNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer PLCNNs. Our results suggest that deeper ReLU CNNs have more powerful expressivity than their shallow counterparts, while ReLU CNNs have more expressivity than fully-connected ReLU NNs per parameter.
• [02341] Generalization Capabilities of Graph Neural Networks
  • Author(s) :
    • Gitta Kutyniok (LMU Munich)
    • Sohir Maskey (LMU Munich)
    • Ron Levie (Technion)
    • Yunseok Lee (LMU Munich)
  • Abstract : The tremendous importance of graph structured data due to recommender systems, social networks, or biological applications led to the introduction of graph neural networks. One key question in machine learning is the ability of a learnt model to generalize to unknown data sets. In this talk, we will present several results on the generalization capabilities of graph neural networks, focussing on both message passing and spectral graph neural networks.

MS [00718] Data-driven and physics-informed techniques in Data Assimilation

room : E817 -> A715 (changed)

• [02864] Consistency Results for some Bayesian PDE inverse problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nathan Glatt-Holtz (Tulane)
  • Abstract : Frequently one would like to estimate functional parameters $u$ in a physical model defined by a partial differential equation from a collection of sparse and uncertain observations. Here a Bayesian methodology provides an attractive statistical approach for many such estimation problems, one which provides a comprehensive picture of uncertainties in the unknown. An important step in the validation of this Bayesian methodology is to establish conditions for posterior consistency. Specifically we would like to determine when $\mu_N \rightharpoonup \delta_{u_*}$ where $\mu_N$ is the Bayesian posterior conditioned on $N$ observations of the solution and $u_*$ is the true value of the unknown. In this talk we describe some rigorous approaches that we have recently developed tailored to address consistency for PDE inverse problems involving the recovery of an infinite dimensional unknown. We describe how our approach applies to a gallery of model problems including the recovery of a divergence free velocity field from the measurement of a solute which is advecting and diffusing in the fluid medium. This is joint work with Jeff Borggaard, Christian Frederiksen and Justin Krometis.
• [05063] Data-driven and model-driven techniques in DA: applications, numerics, rigorous results
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jochen Broecker (Department of Mathematics and Statistics, University of Reading)
  • Abstract : Data Assimilation permeates all contributions in at least three ways: Firstly, novel approaches to data assimilation use machine learning and Bayesian inference to identify the current state as well as components of the system, two inextricably linked aims. Secondly, data assimilation has become an interesting application of (stochastic) PDE~theory. Thirdly, ergodic theory of infinite dimensional dynamical systems (asymptotic coupling) calls for sophisticated nudging or error feedback schemes. Finally, new venues for research will be sketched.
• [02753] Nonparametric Bayesian inference of discretely observed diffusions
  • Format : Talk at Waseda University
  • Author(s) :
    • Jean-Charles Croix (Amazon)
    • Masoumeh Dashti (University of Sussex)
    • Stylianos Katsarakis (University of Sussex)
    • Istvan Kiss (University of Sussex)
    • Tanja Zerenner (University of Bristol)
  • Abstract : We consider the inverse problem of recovering the diffusion and drift functions of a stochastic differential equation from discrete measurements of its solution. We show the stability of the posterior measure with respect to appropriate approximations of the underlying forward model allowing for priors with unbounded support. We then look at the approximated posterior obtained by Gaussian approximation of transition densities in the case where the diffusion coefficient is small.
• [02850] A general involution framework for Metropolis-Hastings algorithms and applications to Bayesian inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Cecilia Mondaini (Drexel University)
    • Nathan Glatt-Holtz (Tulane University)
  • Abstract : We consider a general framework for Metropolis-Hastings algorithms used to sample from a given target distribution on a general state space. Our framework has at its core an involution structure, and is shown to encompass several popular algorithms as special cases, both in the finite- and infinite-dimensional settings. In particular, it includes random walk, preconditioned Crank-Nicolson (pCN), schemes based on a suitable Langevin dynamics such as the Metropolis Adjusted Langevin algorithm (MALA), and also ones based on Hamiltonian dynamics including several variants of the Hamiltonian Monte Carlo (HMC) algorithm. In addition, our framework comprises algorithms that generate multiple proposals at each iteration, which allow for greater efficiency through the use of modern parallel computing resources. Aside from encompassing existing algorithms, we also derive new schemes from this framework, including some multiproposal versions of the pCN algorithm. To illustrate effectiveness of these sampling procedures, we present applications in the context of certain Bayesian inverse problems in fluid dynamics. In particular, we consider the problem of recovering an incompressible background fluid flow from sparse and noisy measurements of the concentration of a passive solute advected by the flow. This talk is based on joint works with N. Glatt-Holtz (Tulane U), A. Holbrook (UCLA), and J. Krometis (Virginia Tech).

MS [00448] Particle based methods

room : E818

• [02827] Constrained sampling
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Tong (National University of Singapore)
  • Abstract : Sampling-based inference and learning techniques, especially Bayesian inference, provide an essential approach to handling uncertainty in machine learning (ML). As these techniques are increasingly used in daily life, it becomes essential to safeguard the ML systems with various trustworthyrelated constraints, such as fairness, safety, interpretability. We propose a family of constrained sampling algorithms which generalize Langevin Dynamics (LD) and Stein Variational Gradient Descent (SVGD) to incorporate a moment constraint or a level set specified by a general nonlinear function. By exploiting the gradient flow structure of LD and SVGD, we derive algorithms for handling constraints, including a primal-dual gradient approach and the constraint controlled gradient descent approach.We investigate the continuous-time mean-field limit of these algorithms and show that they have O(1/t) convergence under mild conditions.
• [03107] Subsampling in ensemble kalman inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • Matei Hanu (Free University of Berlin)
    • Jonas Latz (Heriot-Watt-University)
    • Claudia Schillings (Free University of Berlin)
  • Abstract : The Ensemble Kalman Inversion (EKI) is an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. For large data sets, the EKI becomes computationally infeasible as the data misfit needs to be evaluated for each particle in each iteration. Randomised algorithms can successfully overcome this issue by using only a random subset of the data in each iteration, so-called subsampling techniques. In this talk we present subsampling-techniques within Ensemble Kalman Inversion.
• [03842] Ensemble Inference Methods for Models with Noisy and Expensive Likelihoods
  • Format : Talk at Waseda University
  • Author(s) :
    • Marie-Therese Wolfram (University of Warwick)
    • Andrew Stuart (California Institute of Technology)
    • Andrew Duncan (Imperial College London)
    • Oliver Dunbar (California Institute of Technology )
  • Abstract : This talk concerns interacting particle systems to solve inverse problems where the forward model evaluations present rapid fluctuations over the smoothly varying quantity of interest. After comparing the performance of ensemble Kalman methods (EKS) and Langevin-based methods (ELS) using formal multiscale analysis, we introduce a new class of algorithms, named ensemble Gaussian process samplers, which combine the main benefits of both approaches while avoiding their flaws.
• [04379] Projected ensemble data assimilation
  • Format : Talk at Waseda University
  • Author(s) :
    • Svetlana Dubinkina (VU Amsterdam)
    • Jana de Wiljes (University of Potsdam)
  • Abstract : Ensemble data assimilation is unable to reduce the error estimate for high-dimensional systems when used with a small ensemble. A typical remedy is dimesion reduction by localization. Though localization reduces the error substantially for both linear and nonlinear data-assimilation methods, the former ones considerably outperform the latter ones in quasi-linear regimes. We propose a further dimension reduction based on projection and show numerically considerable error decrease when used with small ensemble.

MS [00475] Variational methods and periodic solutions in the n-body problem

room : E819

• [04108] Regularizing Fuel-Optimal, Multi-Impulse Trajectories with Second-Order Derivatives
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenta Oshima (Hiroshima Institute of Technology)
  • Abstract : The present work implements analytical second-order derivatives for a direct multiple shooting-based regularized method of minimizing the fuel expenditure for spacecraft trajectories. The high-order dynamical information, such as the state transition tensor, expresses the Hessian matrix of the Lagrange function in the nonlinear programming problem. The result is an efficient tool for robustly and accurately computing fuel-optimal, multi-impulse trajectories in the regularized framework of removing singularities associated with null thrust impulses.
• [04642] Floquet Mode-Based Transfer between Halo Orbits Using Solar Sails
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshihiro Chujo (Tokyo Institute of Technology)
  • Abstract : Transfer between halo orbits around the sun-Earth L2 using solar sails is discussed in the circular restricted three-body problem. The path planning and the corresponding tilting angle of the sail are determined based on the Floquet mode, such that the coefficient of the center manifold for transition to another family of the halo orbit is maximized while that of the unstable manifold is suppressed under a certain threshold.
• [04549] Low-energy Transfer to the Earth-Moon Periodic Orbit: CubeSat Application
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuya Chikazawa (The University of Tokyo)
  • Abstract : This work investigates trajectories design for the ride-share spacecraft that begin with the Moon swing-by. In this type of trajectory design, mission designers need to consider uncertainties under limited propulsion capability. To aid trajectories design, established theory, such as manifold from periodic orbit in circular restricted three-body system, are often used. We demonstrate how to use such theory in actual mission design and operation phases.
• [04028] Transfer between Resonances via Lobe Dynamics in the Standard Map
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoki Hiraiwa (Kyushu University)
    • Isaia Nisoli (Universidade Federal do Rio de Janeiro)
    • Yuzuru Sato (Hokkaido University)
    • Mai Bando (Kyushu University)
    • Shinji Hokamoto (Kyushu University)
  • Abstract : Lobe dynamics is a useful structure to reveal phase space transport of chaotic trajectories by stable and unstable manifolds of resonant orbits. Based on lobe dynamics, this study formulates the transfer problem between two quasi-periodic orbits to find the optimal lobe sequence. Especially, the lobe dynamics of resonant orbits of the standard map are extracted and used to solve the problem. Applications to spacecraft trajectory design are also discussed.

MS [00558] Bifurcations, periodicity and stability in fluid-structure interactions

room : E820

• [04678] Weak solutions in fluid-structure interactions: Cauchy and periodic problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Boris Muha (University of Zagreb)
    • Sebastian Schwarzacher (Charles University and Uppsala University)
    • Justin Thomas Webster (University of Maryland, Baltimore County)
  • Abstract : In this talk, we will provide an overview of the latest developments in the theory of weak solutions to fluid-structure interaction problems. We will specifically explore the difficulties and distinctions that arise when moving from the Cauchy problem to that of obtaining periodic solutions. We will examine a simple heat-wave system, which serves as a representative example for a fluid-structure interactions; for this system, we present some new existence results for periodic solutions.
• [02192] Modelling and analysis of solids floating in a viscous fluid
  • Format : Talk at Waseda University
  • Author(s) :
    • Marius Tucsnak (University of Bordeaux)
  • Abstract : We describe some recent advances on the mathematical modelling of the interaction of water waves with floating objects. The main applications we have in mind are point absorber type devices for producing marine energy and floating platforms used to support wind turbines. The mathematical challenge here is the existence of two free boundaries: the free surface of the fluid and the solid-fluid interface. The presentation is essentially devoted to wellposedness and large time behavior issues.
• [02207] Time-periodic solutions to an interaction problem between a compressible fluid and a viscoelastic structure
  • Format : Talk at Waseda University
  • Author(s) :
    • Srđan Trifunović (Faculty of Sciences, University of Novi Sad)
    • Šárka Nečasová (Institute of Mathematics AS CR)
    • Ondřej Kreml (Institute of Mathematics AS CR)
    • Václav Mácha (Institute of Mathematics AS CR)
  • Abstract : In this lecture, I will talk about the problem of interaction between a compressible fluid and a viscoelastic beam under the influence of time-periodic external forces in 2D. For this problem, at least one weak solution is constructed which is periodic in time and perserves the mass which is a given constant. The approximate solution is obtained via a decoupling scheme in finite bases for time and space.
• [02722] Artificial boundary conditions for time-periodic flow past a body
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Eiter (Weierstrass Institute for Applied Analysis and Stochastics)
  • Abstract : Consider the time-periodic viscous flow past an obstacle. Numerical implementations require to reduce the problem to a bounded domain by introducing an artificial boundary. In this talk, we study a choice of associated boundary conditions such that this perturbed problem suitably approximates the original one. These boundary conditions reflect the asymptotic behavior of the flow, which is studied in terms of new representation formulas relying on time-periodic fundamental solutions to the linearized Navier-Stokes equations.

MS [00666] Simulations and Algorithms for Materials Sciences

room : D101

• [02135] ESES, a Eulerian and Lagrangian molecular surface generator
  • Format : Talk at Waseda University
  • Author(s) :
    • Weihua Geng (Southern Methodist University)
  • Abstract : The Poisson-Boltzmann (PB) model is numerically solved either on grid based meshes using finite difference/element methods or on body-fitted meshes using boundary element methods. In this talk, we investigate the distinguished features of the Eulerian Solvent Excluded Surface (ESES) software with which both Eulerian and Lagrangian surfaces are produced. We investigate the performance with these two types of surface discretization usingthe grid based MIBPB solver and body-fitted TABI-PB solvers.
• [02756] From nanocrystals to glasses: a strengthening mechanism analysis for amorphization.
  • Format : Talk at Waseda University
  • Author(s) :
    • Chuqi CHEN (Hong Kong University of Science and Technology)
    • Yang Xiang (Hong Kong University of Science and Technology)
  • Abstract : Recently, many studies investigated the correlation between the strength of the polycrystals, and the grain size and grain boundary width through both experimental and molecular dynamics simulation approaches. Results reveal that as grain boundary width increases, the crystalline structure of the grain boundary region transforms into an amorphous state. We propose mechanism analysis to elucidate the underlying mechanisms that govern the aforementioned relationships.
• [02794] Sum-of-Gaussians method with applications to molecular dynamics simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiuyang Liang (Shanghai Jiao Tong University)
  • Abstract : Sum-of-Gaussians (SOG) method has attracted attention in many applications. In this talk, we will review some recently-developed SOG methods. Based on a sum-of-Gaussians decomposition of the Coulomb kernel, we develop an accurate, highly efficient, and scalable random batch sum-of-Gaussians (RBSOG) method for molecular dynamics simulations of systems with long-range interactions. Numerical results, including SPC/E bulk water and phase-separated electrolytes, are presented to show the attractive performance of the algorithm, including the superscalability in parallel computing.
• [03201] Random-batch Ewald method for molecular dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhenli Xu (Shanghai Jiao Tong University)
  • Abstract : We present a random-batch Ewald method for molecular dynamics of particle systems with long-range interactions. It takes advantage of the random minibatch strategy for particles, leading to an order N algorithm. It is based on the Ewald splitting of the Coulomb kernel and the random importance sampling is employed in the Fourier part such that the force variance can be reduced. Numerical results are presented to show the attractive performance of the algorithm.

MS [00062] Analysis and computation of vortical flows

room : D102

• [00106] Logarithmic vortex spirals
  • Format : Talk at Waseda University
  • Author(s) :
    • In-Jee Jeong (Seoul National University)
  • Abstract : We investigate the dynamics of logarithmic vortex for the two-dimensional incompressible Euler equations. More precisely, we consider vorticity which is invariant under the transformation $(r,\theta) \mapsto (\lambda r, \theta + c \ln(\lambda))$ for any $\lambda>0$ and some $c>0$. Within this class of vorticities, one can consider various types, including patches and sheets. We derive the equations of motion for logarithmic vortex and consider the limit problem where patches become sheets.
• [00069] Dynamics of elliptical vortices
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ling Xu (North Carolina Agricultural and Mechanical State University)
    • Robert Krasny (University of Michigan, Ann Arbor)
  • Abstract : We examine the dynamics of elliptical vortices in 2D ideal fluid using an adaptively refined and remeshed vortex method. Four cases are considered: the compact MMZ and POLY vortices, and noncompact Gaussian and smooth Kirchhoff vortices (SK). The vortices have the same maximum vorticity and 2:1 initial aspect ratio, but unlike the top-hat Kirchhoff vortex, they have continuous profiles with different regularity. In all cases the co-rotating phase portrait has two hyperbolic points. At early time two filaments emerge and form a halo around the core as vorticity is advected along the unstable manifold of each hyperbolic point. The Gaussian vortex rapidly axisymmetrizes, but later on the core begins to oscillate and two small lobes emerge adjacent to the core; this is attributed to a resonance. For the MMZ, POLY, and SK vortices, the core maintains its ellipticity for longer time and the filaments entrain fluid into two large lobes forming a non-axisymmetric tripole state; afterwards the lobes repeatedly detrain fluid into the halo; this is attributed to a heteroclinic tangle. While prior work suggested that elliptical vortices evolve to either an axisymmetric state or a non-axisymmetric tripole state, our results suggest that such vortices may oscillate between these states.
• [00121] The N-vortex problem in doubly-periodic domains with background vorticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Vikas Krishnamurthy (IIT Hyderabad)
    • Takashi Sakajo (Kyoto University)
  • Abstract : We study the N-vortex problem in a doubly periodic rectangular domain in the presence of a constant background vorticity field. Using a conformal mapping approach, we derive an explicit formula for the hydrodynamic Green's function. We show that the point vortices form a Hamiltonian system and that the two-vortex problem is integrable. Several fixed lattice configurations are obtained for general N, some of which consist of vortices with inhomogeneous strengths and lattice defects.
• [00127] Swimming of a Fish-like Body by using a Vortex Shedding Model
  • Format : Talk at Waseda University
  • Author(s) :
    • SUNG-IK SOHN (Gangneung-Wonju National University)
  • Abstract : We consider the undulatory motion of a body translating through a quiescent fluid, which is motivated by the anguilliform swimming of aquatic animals, e.g., eels. We use an inviscid vortex shedding model to investigate the swimming dynamics. The model demonstrates the self-propulsion of the swimming body and yields pairs of anti-rotating vortices shed from the body. We examine the wake pattern and swimming efficiency which depends on the recoil motions of a body.

MS [00263] Problems in incompressible fluid flows: Stability, Singularity, and Extreme Behavior

room : D401

• [00695] Enforcing conservation laws in truncated fluid models: the effect on heavy-tailed statistics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mohammad Farazmand (North Carolina State University)
    • Zack Hilliard (North Carolina State University)
  • Abstract : A significant class of partial differential equations (PDEs) have conserved quantities, arising from conservation of mass, energy, momentum, etc. These conserved quantities are not necessarily preserved when the PDE is discretized for numerical simulations. A recent method called reduced-order nonlinear solutions (RONS) allows us to ensure these conserved quantities are preserved after a Galerkin-type truncation of the PDE. We apply RONS to the Euler equation for ideal fluids, Navier--Stokes equations for incompressible flow, and shallow water equation modeling tsunamis. In each case, we discuss the effect of conserved quantities on the extreme events and energy fluxes and compare the results to conventional Galerkin truncations.
• [00308] Verifying global stability of fluid flows despite transient growth of energy
  • Format : Online Talk on Zoom
  • Author(s) :
    • David Goluskin (University of Victoria)
    • Federico Fuentes (Pontificia Universidad Católica de Chile)
    • Sergei Chernyshenko (Imperial College London)
  • Abstract : To verify nonlinear stability of a laminar fluid flow against all perturbations, all past results rely on monotonic decrease of perturbation energy or a similar quadratic generalized energy. This "energy method" cannot show stability if perturbation energy can grow transiently, as in parallel shear flows at moderate Reynolds numbers. I will describe a more general approach that uses sum-of-squares polynomials to computationally construct non-quadratic Lyapunov functions that verify stability. Computational implementation for the example of 2D plane Couette flow verifies global stability at Reynolds numbers above the energy stability threshold found by Orr in 1907.
• [01836] Invariant solutions representing extreme behaviour in turbulence
  • Format : Talk at Waseda University
  • Author(s) :
    • Genta Kawahara (Osaka University)
  • Abstract : Invariant solutions to the incompressible Navier-Stokes equations are reviewed to theoretically interpret extreme behaviour observed in turbulent flows. Turbulent bursting in near-wall turbulence is characterised in terms of homoclinic orbits to the periodic edge state at low Reynolds numbers, while it is discussed using another vigorous turbulent saddle at high Reynolds numbers. The ultimate state, i.e. anomaly of energy and scalar dissipation, of turbulent thermal convection is represented by steady solutions.
• [03543] Numerical simulation of the convex integration for the dissipative Euler flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Matsumoto (Department of physics, Kyoto university)
  • Abstract : Weak solutions to the three-dimensional, incompressible Euler equations, which can dissipate the energy, were constructed with the convex integration by De Lellis, Szekelyhidi and collaborators. We develop a numerical simulation of the physically appealing construction by Buckmaster et al. Specifically, we study the solutions with the standard tools in physics of analyzing turbulent flows, such as the structure functions. We discuss insights obtained from them and also limitations of the simulation.

MS [00118] On mathematical modeling and simulation of droplets

room : D402

• [03374] Plug formation in models of falling viscous films inside tubes
  • Format : Online Talk on Zoom
  • Author(s) :
    • H. Reed Ogrosky (Virginia Commonwealth University)
  • Abstract : Falling viscous liquid films coating the interior of a tube occur in a variety of applications. If the film is thick enough, it may pinch off and form a plug, occluding the tube. In this talk I will discuss recent work examining the impact of surfactant, slip, viscoelasticity, and viscosity stratification on plug formation in a model for film flow. Implications for understanding occlusion in human airways will be discussed.
• [03547] Dipole-type solutions to the thin-film equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Mark Bowen (Waseda University)
    • Thomas Witelski (Duke University)
  • Abstract : We investigate the dynamics of a thin liquid film spreading in a semi-infinite domain $x\ge0$, so that $x=0$ corresponds to an edge over which fluid can drain. In particular, we investigate self-similar solutions of the one-dimensional "thin-film" equation (a fourth order degenerate parabolic equation) on $x\ge0$. We find classes of first- and second-kind similarity solutions and describe how these classes are connected. We also discuss the extension of our results to self-similar solutions featuring sign-changes.
• [02422] Thermally-driven coalescence in thin liquid film flowing down a fiber
  • Format : Talk at Waseda University
  • Author(s) :
    • Hangjie Ji (North Carolina State University)
    • Claudia Falcon (Wake Forest University)
    • Erfan Sedighi (University of California, Los Angeles)
    • Abolfazl Sadeghpour (University of California, Los Angeles)
    • Y. Sungtaek Ju (University of California, Los Angeles)
    • Andrea L. Bertozzi (University of California, Los Angeles)
  • Abstract : This paper presents a study on the dynamics of a thin liquid film flowing down a vertical cylindrical fibre under a streamwise thermal gradient. Previous works on isothermal flows have shown that the inlet flow and fibre geometry are the main factors that determine a transition from the absolute to the convective instability flow regimes. Our experiments demonstrate that an irregular wavy pattern and bead coalescence, which are commonly seen in the convective regime, can also be triggered by applying a thermal gradient along the fibre. We develop a lubrication model that accounts for gravity, temperature-dependent viscosity and surface tension to describe the thermal effects on downstream bead dynamics. Numerical simulations of the model show good agreement between the predicted droplet coalescence dynamics and the experimental data.

MS [01933] Fluid-structure interactions in Stokes flows

room : D403

• [04825] Cross-stream migration of vesicles in vortical flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gokberk Kabacaoglu (Bilkent University )
  • Abstract : We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number).
• [04962] Confinement effects on a suspension of squirmers
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuan Nan Young (New Jersey Institute of Technology)
    • Bryan Quaife (Florida State University)
    • Henry Shum (University of Waterloo)
    • Sangwoo Shin (University at Buffalo)
  • Abstract : Using a model recently developed for the many-body hydrodynamics of amphiphilic JPs suspended in a viscous background flow (JFM, 941, 2022), we investigate how various swimming dynamics of squirmers that interact with the solvent through a hydrophobic potential (HP) may vary from tuning the hydrophobicity/hydrophilicity of the squirmers. In the absence of such HP, several configurations of squirmers are known to be stable for squirmers to swim together. We numerically investigate how HP may help stabilize/destabilize these configurations. These results are further compared with the Vicek model for schooling and flocking of swimmers. We further investigate the effects of confinement and how active control of HP may be used for a cluster of swimmers to swim in specific fashions, indicating that the squirmers may actively change their surface properties so the collective of squirmers may swim in certain ways.
• [04477] Hydrodynamics and rheology of fluctuating, semiflexible, inextensible, and slender filaments in Stokes flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Aleksandar Donev (Courant Institute, New York University)
  • Abstract : Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible filaments / bio-polymers, such as microtubules, actin filaments, and intermediate filaments, all suspended in a viscous fluid. Similar suspensions of elastic filaments or polymers are widely used in materials processing. Numerical simulation of such gels is challenging because the filament aspect ratios are very large. We have recently developed new methods for rapidly computing the dynamics of non-Brownian and Brownian inextensible slender filaments in periodically-sheared Stokes flow. We apply our formulation to a permanently and dynamically cross-linked actin mesh in a background oscillatory shear flow. We find that nonlocal hydrodynamics can change the visco-elastic moduli by as much as 40% at certain frequencies, especially in partially bundled networks. I will focus on accounting for bending thermal fluctuations of the filaments by first establishing a mathematical formulation and numerical methods for simulating the dynamics of stiff but not rigid Brownian fibers in Stokes flow. I will emphasize open questions for the community such as whether there is a continuum limit of the Brownian contribution to the stress tensor from the filaments.
• [04813] Numerical simulations of swimming with multiple bacterial flagella
  • Format : Talk at Waseda University
  • Author(s) :
    • Henry Shum (University of Waterloo)
    • Vahid Nourian (University of Waterloo)
  • Abstract : To understand some of the consequences of different morphologies of flagellated bacteria, we numerically simulate their swimming motion using a boundary element-regularized Stokeslet method. The flagella are modelled as discretized Kirchhoff rods. We apply our model to: (i) bacteria with a pulling flagellum in front and a pushing flagellum at the rear, and (ii) bacteria with three pushing flagella. Bacterial hook flexibility and flagellar placement are important considerations, especially near a no-slip wall.

MS [00221] Analysis of Fluid Dynamics and Free Boundary Problems

room : D404

• [03643] Transonic flows and free boundary problems in gas dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Dehua Wang (University of PittsburghUniversity of Pittsburgh)
  • Abstract : In this talk, the transonic flows and free boundary problems in gas dynamics will be considered. The existence and stability of solutions will be presented for transonic flows past an obstacle and in a nozzle.
• [03380] Regularity and asymptotics for porous medium equations in bounded domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Tianling Jin (The Hong Kong University of Science and Technology)
    • Xavier Ros-Oton (Universitat de Barcelona)
    • Jingang Xiong (Beijing Normal University)
  • Abstract : We prove the optimal global regularity of nonnegative solutions to the porous medium equation in smooth bounded domains with the zero Dirichlet boundary condition after certain waiting time. This allows us to refine the asymptotics of solutions for large times. We establish faster rate of convergence and prove that the convergence holds in the regular topology.
• [03966] Energy concentration and weak stability in fluid dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Xianpeng Hu (City University of Hong Kong)
  • Abstract : The weak stability is an important issue in fluid dynamics. We will discuss the mathematical understudying of concentration phenomena in the framework of weak solutions with either critical or subcritical energy. Two typical examples, including two dimensional incompressible Euler equations and compressible Navier-Stokes equations, will be discussed.
• [03949] On Ericksen-Leslie system with free boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Yu (The Chinese University of Hong Kong)
    • Chenyun Luo (The Chinese University of Hong Kong)
    • Kaihui Luo (The Chinese University of Hong Kong)
  • Abstract : In this talk, we discuss a 3D simplified Ericksen-Leslie system subjected to the free boundary condition with surface tension. Dynamical stability of the classical planar wave solutions will also be addressed when the liquid crystal droplet is thin.

MS [00814] Inverse Problems for Moving Targets

room : D405

• [03803] Direct reconstruction methods for moving sources in the wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Ohe (Okayama University of Science)
  • Abstract : In this talk, we consider the reconstruction problem of moving wave sources under different observation conditions; one is observations on the boundary, and the other is observations on a small number of points. For each observation condition, we propose a direct reconstruction procedure for the parameters of moving wave sources. We also discuss the common and different issues between reconstruction procedures.
• [03831] An inverse problem in mean field game from partial boundary measurement
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yat Tin Chow (University of California, Riverside)
    • Samy Wu Fung (Colorado School of Mines)
    • Siting Liu (University of California, Los Angeles)
    • Levon Nurbekyan (University of California, Los Angeles)
    • Stanley Osher (University of California, Los Angeles)
  • Abstract : In this work, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the population dynamics under the limited aperture. Due to its severe ill-posedness, obtaining a good quality reconstruction is very difficult. Nonetheless, it is vital to recover the model parameters stably and efficiently in order to uncover the underlying causes for population dynamics for practical needs. Our work focuses on the simultaneous recovery of running cost and interaction energy in the MFG equations from a finite number of boundary measurements of population profile and boundary movement. To achieve this goal, we formalize the inverse problem as a constrained optimization problem of a least squares residual functional under suitable norms with L1 regularization. We then develop a fast and robust operator splitting algorithm to solve the optimization using techniques including harmonic extensions, three-operator splitting scheme, and primal-dual hybrid gradient method. Numerical experiments illustrate the effectiveness and robustness of the algorithm. This is a joint work with Samy W. Fung (Colorado School of Mines), Siting Liu (UCLA), Levon Nurbekyan (UCLA), and Stanley J. Osher (UCLA)
• [02996] Factorization method for recovering moving objects with dynamic near-field data
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hongxia Guo (Nankai University)
  • Abstract : In this talk, I will present the factorization method for recovering the trajectory of a moving point source from multi-frequency data with one or sparse dynamic near-field observation points . The observable and non-observable points in the near field region are introduced. At an observable point, it is verified that the smallest annular containing the trajectory and centered at the observable point can be imaged, provided the orbit function possessing a certain property.
• [04620] Imaging a moving point source from multi-frequency data measured at one and sparse observation directions (part I): far-field case
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hongxia Guo (Nankai University)
    • Guanghui Hu (Nankai University, Tianjin, China)
    • Guanqiu Ma (Nankai University)
  • Abstract : We propose a multi-frequency algorithm for recovering partial information on the trajectory of a moving point source from one and sparse far-field observation directions in the frequency domain. The starting and terminal time points of the moving source are both supposed to be known. We introduce the concept of observable directions (angles) in the far-field region and derive all observable directions (angles) for straight and circular motions. The existence of non-observable directions makes this paper much different from inverse stationary source problems. At an observable direction, it is verified that the smallest trip containing the trajectory and perpendicular to the direction can be imaged, provided the angle between the observation direction and the velocity vector of the moving source lies in $[0,\pi/2]$. If otherwise, one can only expect to recover a strip thinner than this smallest strip for straight and circular motions. The far-field data measured at sparse observable directions can be used to recover the $\Theta$-convex domain of the trajectory. Both two- and three-dimensional numerical examples are implemented to show effectiveness and feasibility of the approach.

MS [00915] The mathematics of quantum interaction models

room : D407

• [03491] Quantum computation and its viewpoint from spectral zeta functions
  • Format : Talk at Waseda University
  • Author(s) :
    • MASATO WAKAYAMA (NTT Institute for Fundamental Mathematics)
  • Abstract : We discuss the spectrum of the quantum interaction models such as the quantum Rabi models, non-commutative harmonic oscillators and their important derived models from the viewpoints of quantum computation and number theory via the corresponding heat kernels, partition functions and spectral zeta functions.
• [03218] New mathematics and machine learning applications from qubits and oscillators
  • Format : Talk at Waseda University
  • Author(s) :
    • Sahel Ashhab (National Institute of Information and Communications Technology (NICT))
  • Abstract : I will present some of our studies on the physics of qubits and oscillators that produced interesting results that go into the realms of mathematics and computer science. In studying the dynamics of strongly driven qubits, we obtained a new approximation for Bessel functions. Our studies on the Landau-Zener problem, a hard problem that has a simple solution, inspired us to explore the use of symbolic regression to solve theoretical physics and mathematics problems.
• [03683] Design and optimization of fault-tolerant quantum computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasunari Suzuki (Nippon Telegraph and Telephone)
  • Abstract : To demonstrate scalable quantum computing, we need to suppress the high error rates of quantum devices. While they can be reduced with quantum error correction (QEC) technology, it requires large overheads on computing resources. Thus, optimization methods and co-design of hardware and software for fault-tolerant quantum computing are demanded. In this talk, I will explain the recent progress relevant to computer architecture and compiler optimization technologies based on the QEC framework.
• [04189] Energy spacing and time evolution for asymmetric quantum Rabi models
  • Format : Talk at Waseda University
  • Author(s) :
    • Linh Thi Hoai Nguyen (Institute of Mathematics for Industry, Kyushu University)
    • Cid Reyes Bustos (NTT IFM)
    • Masato Wakayama (NTT Institute for Fundamental Mathematics)
  • Abstract : In this study, we describe the methods for numerical computations of the energy spacing distribution and time evolution for the asymmetric (or biased) quantum Rabi model (AQRM). The first several tens of thousands of eigenvalues are achieved by using the Truncated Hamiltonians method. From that, we observe the periodicity and symmetry of the consecutive energy spacing distribution with respect to the bias parameter. The time evolution is studied based on an explicit heat kernel formula.

MS [02557] Collaboration of machine learning and physics-based simulation on earthquake disasters

room : D408

• [04544] Physics-based long-period ground motion simulation for megaquakes
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahiro Maeda (National Research Institute for Earth Science and Disaster Resilience)
  • Abstract : There are limited seismic observation records directly linked to damage, such as ground motions caused by huge earthquakes and those near seismic faults. In order to evaluate such ground motions, physics-based seismic-ground-motion simulation using the three-dimensional subsurface structure and seismic-source models is carried out, which are used to clarify the causes of damage and predict future seismic motions. In this presentation, we will introduce ground-motion simulation methods and examples of their application to huge earthquakes.
• [03695] A smoothing scheme for seismic wave propagation simulation with SDWave
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ryuta Imai (Mizuho Research & Technologies, Ltd.)
  • Abstract : We propose a smoothing scheme SDWave for seismic wave propagation simulation. The SDWave is based on a diffusionized wave equation with the fourth-order spatial derivative term. We mathematically explain some properties of the equation and how the SDWave works for smoothing. Then we give two discretization methods, FDM and mixed FEM, of the SDWave and apply it to the wave equation. This numerical experiment reveals that the SDWave is effective for filtering short wavelength components.
• [04162] A quarter century of data from K-NET and KiK-net
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shin Aoi (National Research Institute for Earth Science and Disaster Resilience)
    • Takashi Kunugi (National Research Institute for Earth Science and Disaster Resilience)
    • Wataru Suzuki (National Research Institute for Earth Science and Disaster Resilience)
    • Hiroyuki Fujiwara (National Research Institute for Earth Science and Disaster Resilience)
  • Abstract : Based on the lessons learned from the 1995 Kobe earthquake, the National Research Institute for Earth Science and Disaster Resilience (NIED) has constructed K-NET and KiK-net, nationwide strong-motion observation networks that homogeneously cover the entire country. The strong-motion database obtained from these world's largest strong-motion observation networks contains nearly one million archived records. In this presentation, these observation networks and databases will be introduced and the utilization of the data will be discussed.
• [03553] Optimal Transport in Seismic Wave Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomohisa Okazaki (RIKEN)
  • Abstract : An appropriate measure of the similarity between waveforms is crucial for seismic data analysis and modeling. The use of the Wasserstein distance in optimal transport theory has received attention in seismology because it captures time difference of waveforms. This presentation introduces two research directions: (1) converting acceleration envelopes from long to short periods for predicting ground motions caused by scenario earthquakes; (2) the sliced Wasserstein distance between seismograms to efficiently measure the similarity of oscillating seismic signals. These applications support the effectiveness of the Wasserstein distance as a similarity measure of seismic waveforms.

MS [00289] Nonconvex nonlinear programming: Theory and algorithms

room : D501

• [02633] A Stochastic Conjugate Gradient Algorithm with Variance Reduction
  • Format : Talk at Waseda University
  • Author(s) :
    • Caixia Kou ( Beijing University of Posts and Telecommunications)
  • Abstract : Stochastic gradient descent methods are popular for large scale optimization but has slow convergence asymptotically due to the inherent variance. To remedy this problem, we firstly propose a new stochastic conjugate gradient algorithm, called SCGA. Besides, developing a new stochastic gradient estimate of unbiasedness with minimized variance, we also present another two stochastic conjugate gradient algorithms. The convergence theory can be established and experiments show the new algorithms have satisfactory numerical performance.
• [01352] Golden ratio Bregman proximal gradient algorithm for nonconvex optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Xue Gao (Hebei University of Technology)
    • Kai Wang (Nanjing University of Science and Technology)
  • Abstract : We focus on solving the nonconvex nonsmooth minimization problem over abstract constraint set, whose objective function is the sum of a proper lower semicontinuous convex function and a smooth nonconvex function, where the differentiable part is freed from the restrictive assumption of global Lipschitz gradient continuity. We design, analyze and test a golden ratio Bregman proximal gradient algorithm (GBPG). The globally convergence of GBPG is proved and numerical simulations demonstrate its feasibility and effectiveness.
• [02076] On the quadratic termination property of the gradient method
  • Format : Talk at Waseda University
  • Author(s) :
    • Yakui Huang (Hebei University of Technology)
  • Abstract : The gradient method is one of the most popular algorithms in solving large scale unconstrained optimization problems. However, most of existing gradient methods do not enjoy the quadratic termination property. In this talk, we will provide a summary account of recent and new results on how to equip gradient methods with the two-dimensional quadratic termination property. Moreover, a new mechanism for the gradient method to achieve three- and higer- dimensional quadratic termination will be presented.
• [03083] A novel augmented Lagrangian and its application in linear programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Xinwei Liu (Hebei University of Technology)
  • Abstract : We introduce a twice differentiable augmented Lagrangian for optimization with general inequality constraints. Our function is a combination of the augmented Lagrangian and the logarithmic-barrier technique, and is a generalization of the Hestenes-Powell augmented Lagrangian. The associated augmented Lagrangian method is proved to have strong global convergence, the capability of rapidly detecting the possible infeasibility, and linear convergence to the KKT point. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results. The application in linear programming shows its superiority.

MS [00670] Financial Risk Management and Related Topics

room : D502

• [03276] Discrepancy between Regulations and Practice in Initial Margin Calculation
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryosuke Kitani (Hitotsubashi University)
    • Hidetoshi Nakagawa (Hitotsubashi University)
  • Abstract : Counterparty risk remains at issue in OTC derivative transactions. Since it is difficult to calculate the initial margin according to the regulations, it has been calculated in practice using a simplified method "ISDA SIMM". In this study, we derive an approximate formula for some indicators of counterparty risk for a stochastic volatility model and illustrate some numerical analyses to examine the effect of discrepancy between regulations and practice in margin calculation.
• [02781] Last Passage Time and its Applications in Risk Management
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiko Egami (Kyoto University)
    • Rusudan Kevkhishvili (Kyoto University)
  • Abstract : We decompose the Laplace transform of a regular transient diffusion’s last passage time into a simple formula based on Green functions. This result allows us to bypass often hard calculations related to diffusions with switching parameters by reducing the problem to two processes without switching. The last passage time is not a stopping time because it looks into the future path of the process. We demonstrate its application in credit risk and loss-given-default distribution modeling.
• [04631] Construction and sample path properties of Brownian house-moving
  • Format : Talk at Waseda University
  • Author(s) :
    • Kensuke Ishitani (Tokyo Metropolitan University)
  • Abstract : We are currently investigating higher-order chain rules for computing higher-order Greeks of barrier options, and we expect a stochastic process called ``Brownian house-moving'' to play an important role in their computation. Brownian house-moving is a Brownian bridge conditioned to stays between two curves. The purpose of this talk is to construct Brownian house-moving. Also studied are the sample path properties of Brownian house-moving.
• [02599] Stability of High Order Moments: a Risk Management Approach
  • Format : Talk at Waseda University
  • Author(s) :
    • Olivier Arnaud Le Courtois (emlyon business school)
    • Silvia Faroni (emlyon business school)
  • Abstract : Little research has been produced on the statistical reliability of high order moments. This work studies the stability of higher order moments in equity markets. We extend our study to conditional annual higher order moment using different quantiles. Our aim is to identify which moment is more stable over time, which leads to a more reliable assessment of the future market risk and thus to more robust investment and risk management practices.

MS [00612] New models and methods for capacity planning and scheduling

room : D505

• [01483] Joint replenishment combined with machine scheduling: offline and online algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamás Kis (SZTAKI)
    • Peter Gyorgyi (SZTAKI)
    • Timea Tamasi (SZTAKI)
    • Jozsef Bekesi (University of Szeged)
  • Abstract : In this scheduling problem, each job requires a subset of resource types that have to be purchased after the release date of the job and prior to starting the job. The goal is to determine a schedule along with the purchasing dates and quantities for each resource type to minimize the sum of purchasing costs plus a scheduling criterion. Complexity results and online algorithms will be presented for different special cases of the problem.
• [01552] Sequential testing in batches with resource constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Fan Yang (Shanghai Normal University)
    • Ben Hermans (ORTEC)
    • Nicolas ZUFFEREY (University of Geneva)
    • Roel Leus (KU Leuven)
  • Abstract : We consider the problem of determining the state of a system through costly tests of its components, where components can be tested simultaneously in batches to exploit economies of scale. This problem is a generalization of the classical sequential testing problem and it has applications in various settings, including machine maintenance, disease diagnosis, and new product development. We prove that the problem is strongly NP-hard, and several models and algorithms are proposed for it.
• [00764] A flow-based formulation for parallel machine scheduling using decision diagrams
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Kowalczyk (KU Leuven)
    • Roel Leus (KU Leuven)
    • Christopher Hojny (Eindhoven University of Technology)
    • Stefan Ropke (Technical University of Denmark)
  • Abstract : We present a new flow-based formulation for identical parallel machine scheduling, which is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally non-uniform, periods. We develop a branch-and-price framework that solves several instances from the literature for the first time. We compare the new formulation with the time-indexed and arc-time-indexed formulation.
• [00808] Parallel Machine Scheduling Under Uncertainty: Models and Exact Algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Guopeng Song (National University of Defense Technology)
    • Roel Leus (KU Leuven)
  • Abstract : We study parallel machine scheduling for makespan minimization with uncertain job processing times. To incorporate uncertainty and generate solutions that are insensitive to unfolding information, three different modeling paradigms are adopted: a robust model, a chance-constrained model, and a distributionally robust chance-constrained model. We focus on devising generic solution methods that can efficiently handle these different models. We compare the solutions from the different models for scheduling under uncertainty and report the general lessons learned.

contributed talk: CT177

room : D514

[01434] Pointwise adaptive finite element method for the elliptic obstacle problem

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
• Type : Contributed Talk
• Abstract : In this talk, I will discuss pointwise a posteriori error analysis of a finite element method for the obstacle problem. The reliability and the efficiency of the proposed a posteriori error estimator will be discussed. In the analysis, sign property of Lagrange multipliers, Green's function estimates and the barrier functions play a crucial role. The construction of the barrier functions is based on appropriate corrections of the conforming part of the solution obtained via an enriching operator. The use of the continuous maximum principle guarantees the validity of the analysis without mesh restrictions but shape regularity. Numerical results will be presented to illustrate the performance of a posteriori error estimator.
• Classification : 65N15, 65N30
• Format : Talk at Waseda University
• Author(s) :
  • Kamana Porwal (Indian Institute of Technology Delhi, New Delhi)

[00857] An ecological study of mathematical model on intermittent phytoplankton distribution

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
• Type : Contributed Talk
• Abstract : A microscale ecological study is done using the closure approach to understand the impact of productivity controlled by geographical and seasonal variations on the intermittency of phytoplankton. Parameters are estimated from the nature of productivity and spread of phytoplankton density during field observation done at four different locations of Tokyo Bay. The model validation shows that our results are in good agreement with the field observation and succeeded in explaining the intermittent phytoplankton distribution.
• Classification : 92-10, 92D40, Mathematical Biology
• Format : Talk at Waseda University
• Author(s) :
  • Sandip Banerjee (Indian Institute of Technology Roorkee)
  • Arpita Mondal (Indian Institute of Technology Roorkee)

[01340] Mathematical finance without probability

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
• Type : Contributed Talk
• Abstract : We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
• Classification : 91G99, 91-10, Mathematical finance in continuous-time, model uncertainty
• Format : Talk at Waseda University
• Author(s) :
  • Henry Chiu (Imperial College London)

[01804] Spatiotemporal dynamics of a predator-prey system with fear effect

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
• Type : Contributed Talk
• Abstract : We studied a mathematical model with fear effect due to predator population. The model is investigated from the viewpoint of stability and bifurcation analysis. We investigate how behavioral modification in prey population due to fear for predators and mutual interference among predator species can create various spatiotemporal pattern formation in population distribution. Numerical simulation demonstrates that the fear effect in a diffusive predator-prey system with mutual interference may exhibit complicated dynamics.
• Classification : 92B05, 92B20, 65L05, 37D05, 03C45
• Format : Online Talk on Zoom
• Author(s) :
  • Subhas Khajanchi (Presidency University Kolkata)

[01542] Bipartite synchronization of complex dynamical networks under hybrid-triggered control

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D514
• Type : Contributed Talk
• Abstract : The bipartite synchronization problem for multi-weighted complex dynamical networks subject to random coupling delays and external disturbances is investigated. For this, a hybrid-triggered control is incorporated, which in addition, is effective in the reduction of network resource usage guaranteeing the system’s performance. And, the external disturbances are attenuated under extended passivity performance. Moreover, the conditions for ensuring the requisite synchronization of undertaken networks are derived. A numerical example is illustrated to validate the results obtained.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Author(s) :
  • Birundha Devi Nallamuthu (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

contributed talk: CT185

room : D515

[00429] Mathematical Theory to Maximize Enzymatic Activity Under Thermodynamic Constraints

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Understanding the relationship between enzymatic activity is critical not only for bioengineering, but also for rationalizing enzyme optimization in nature. Here, we applied the Arrhenius and Bronsted-Evans-Polanyi equations to the Michaelis-Menten model of enzyme catalysis, and show that enzymatic activity is maximized when the binding affinity between the enzyme and the substrate (Km) is equal to the substrate concentration.
• Classification : 92C45
• Format : Talk at Waseda University
• Author(s) :
  • Hideshi Ooka (RIKEN)
  • Yoko Chiba (RIKEN)
  • Ryuhei Nakamura (RIKEN)

[01110] Patient-specific simulation of veno-venous Extra Corporeal Membrane Oxygenation (ECMO)

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Veno-Venous ECMO is a well-established procedure used in Intensive Care Units for patients with pulmonary failure. The patient blood is drained via a cannula in the inferior vena cava, oxygenated and reinserted via another cannula in the superior vena cava. Still, its efficacy is very limited, mainly due to recirculation between the two cannulas. In this talk we present a patient-specific, CFD-based computational model to assess the efficacy of the procedure and quantify recirculation.
• Classification : 92C50, 92C35, 65ZXX, 92CXX
• Format : Talk at Waseda University
• Author(s) :
  • Massimiliano Leoni (RICAM)
  • Johannes Szasz (Kepler University Klinikum)
  • Jens Meier (Kepler University Klinikum)
  • Luca Gerardo Giorda (Johannes Kepler University Linz)

[02454] Cellular gradient flow structure connects single-cell-level rules and population-level dynamics

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : In multicellular systems, single-cell behaviors should be coordinated consistently with the overall population dynamics and biological functions. We show that the generalized gradient flow modeling of the cellular population dynamics naturally connects them and reproduces well-known properties of cells. We also demonstrate the gradient flow structure in a standard model of the T-cell immune response. This theoretical framework works as a basis for understanding multicellular dynamics and functions.
• Classification : 92C37, 92D25, 49S05
• Format : Talk at Waseda University
• Author(s) :
  • Shuhei A Horiguchi (The University of Tokyo)
  • Tetsuya J Kobayashi (The University of Tokyo)

[00464] Predicting the role of poroelastic coatings for cell therapies via an asymptotic approach

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Cell therapies are a promising alternative for treating liver disease. Encapsulation modulates the mechanical cues inflicted on a cell, which can increase engraftment at the injury site. We model an individual, hydrogel-coated stem cell translating axially along a fluid-filled channel due to a Stokes flow, obtaining semi-analytic solutions in the limit of a stiff coating. We conduct a parametric study to predict the role of coatings and discuss implications for biological cells.
• Classification : 92C37, Poroelasticity, Fluid-structure interaction, asymptotics
• Format : Talk at Waseda University
• Author(s) :
  • Simon Mark Finney (University of Oxford)
  • Sarah Louise Waters (University of Oxford)
  • Andreas Muench (University of Oxford)
  • Matthew Gregory Hennessy (University of Bristol)

[01171] The role of the autoregulation mechanism in hypertension and hypotension in humans

• Session Time & Room : 1C (Aug.21, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : We present a nonlinear model for the propagation of the pressure and flow velocity waves in the human cardiovascular system, including deep learning tools with available physiological data. This model is used for understanding the system-level dynamics of the pressure and flow rates. This time-domain analysis is best to describe time-dependent controls, collectively known as the autoregulation mechanism. We discuss an application of our model to the study of the hypertension and hypotension.
• Classification : 92C35, 76Z05, 68T07, 49N90
• Author(s) :
  • Radu C Cascaval (University of Colorado Colorado Springs)

MS [00524] Lie Symmetries, Solutions and Conservation laws of nonlinear differential equations

room : A201

• [02723] Conservation laws and variational structure of damped nonlinear wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Almudena P. Márquez (University of Cadiz)
    • Stephen Anco (Brock University)
    • Tamara M. Garrido (University of Cadiz)
    • María L. Gandarias (University of Cadiz)
  • Abstract : All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted much attention in analysis. The conservation laws describe generalized momentum and boost momentum, conformal momentum, generalized energy, dilational energy, and light-cone energies. Both the conformal momentum and dilational energy have no counterparts for nonlinear undamped wave equations in one dimension. All of the conservation laws are obtainable through Noether’s theorem, which is applicable because the damping term can be transformed into a time-dependent self-interaction term by a change of dependent variable. For several of the conservation laws, the corresponding variational symmetries have a novel form which is different than any of the well known variation symmetries admitted by nonlinear undamped wave equations in one dimension.
• [03330] Constructing mass-conserving cnoidal wave solutions for the KdV equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Carel Petrus Olivier (North-West University)
    • Frank Verheest (Universiteit Gent)
  • Abstract : Nonlinear periodic travelling wave solutions of the Korteweg-deVries (KdV) equation in the form of cnoidal wave solutions are investigated. The general cnoidal wave solution does not ensure that the mass of the undisturbed medium is conserved. In this paper, a framework is provided to construct mass-conserving cnoidal wave solutions., and the resulting solutions are analyzed. It is shown that these solutions are consistent with linear solutions in the small amplitude limit.
• [04290] Conservation laws and symmetries of a Generalized Drinfeld-Sokolov system
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamara M. Garrido (University of Cadiz)
    • Rafael De La Rosa (University of Cadiz)
    • Elena Recio (University of Cadiz)
    • Almudena P. Márquez (University of Cadiz)
  • Abstract : The generalized Drinfeld-Sokolov system is a widely-used model that describes wave phenomena in various contexts. Many properties of this system, such as Hamiltonian formulations and integrability, have been extensively studied, and exact solutions have been derived for specific cases. In this paper, we apply the direct method of multipliers to obtain all low-order local conservation laws of the system. These laws correspond to physical quantities that remain constant over time, such as energy and momentum, and we provide a physical interpretation for each of them. Additionally, we investigate the Lie point symmetries and first-order symmetries of the system. Through the point symmetries and constructing the optimal systems of one-dimensional subalgebras, we are able to reduce the system of partial differential equations to ordinary differential systems.
• [02959] Lie symmetry analysis of flow and pressure inside horizontal chamber
  • Format : Talk at Waseda University
  • Author(s) :
    • Tanki Motsepa (University of Mpumalanga)
    • Modisawatsona Lucas Lekoko (North-West University)
    • Gabriel Magalakwe (North-West University)
  • Abstract : Exact solutions improve industrial processes by giving operators greater grasp of how systems operate. The study aims to find exact momentum and pressure solutions during the unsteady filtration process. Lie symmetry analysis is used to transform a system of PDEs representing the case study into solvable ODEs. The ODEs are then solved to obtain velocity and pressure solutions. Effects of parameters resulting from the dynamics are examined to identify the parameters that yield maximum outflow.

MS [01063] Challenges in biomathematical modeling and control

room : A206

• [05271] Analyzing infectious disease dynamics: the challenge of non-stationarity
  • Author(s) :
    • Bernard Cazelles (IBENS CNRS INSERM)
  • Abstract : The spread of disease through human populations is complex. The characteristics of disease propagation evolve with time, as a result of a multitude of environmental and anthropic factors, including social distancing. This non-stationarity is a key factor in the complexity of disease propagation. In the absence of appropriate external data sources, to correctly describe disease propagation, I propose a flexible methodology, based on stochastic models for disease dynamics, and on Brownian processes for parameter evolution. Using such a diffusion process has the advantage of not requiring a specific mathematical function for the parameter dynamics. Coupled with Bayesian inference using particle MCMC, this approach allows us to reconstruct both the time evolution of some key parameters of an epidemiological dynamic and its incidence. I will demonstrate the efficiency of this methodology on toy epidemiological models where the parameters and the observation process are known, and also on more complex epidemics, such as flu, dengue and COVID-19.
• [05319] Models of mosquito population control strategies for fighting against arboviruse
  • Author(s) :
    • Michel Duprez (Inria)
    • Luis Almeida (Inria)
    • Yves Dumont (CIRAD - University of Pretoria)
    • yannick Privat (Université de Strasbourg)
    • Nicolas Vauchelet (Université Paris 13)
  • Abstract : In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, a technique consist in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique). This talk is devoted to studying the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing the dynamic of a mosquitoes population, we will study the control problem and introduce the cost function standing for sterile insect technique. In a second step, we will consider a model with several patchs modeling the spatial repartition of the population. Then, we will establish some properties of these two optimal control problems. Finally, we will illustrate our results with numerical simulations.

MS [00592] Optimization and Inverse Problems

room : A207

• [03137] Sparsity-promoting regularization for inverse problems via statistical learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Ratti (University of Bologna)
    • Giovanni S Alberti (University of Genoa)
    • Ernesto De Vito (University of Genoa)
    • Tapio Helin (Lappeenranta-Lahti University of Technology)
    • Matti Lassas (University of Helsinki)
    • Matteo Santacesaria (University of Genoa)
  • Abstract : In this talk, I will discuss a strategy, based on statistical learning, to design variational regularization functionals for ill-posed linear inverse problems. The proposed approach first restricts the choice to a parametric class of functionals and then searches for the optimal regularizer inside it, combining model-based and data-driven information. I will first recap the main results in the case of generalized Tikhonov functionals, and then focus on a class of sparsity-promotion regularizers.
• [03391] Online Optimization for Dynamic Electrical Impedance Tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Jyrki Jauhiainen (University of Helsinki)
    • Tuomo Valkonen (Escuela Politécnica Nacional)
    • Neil Dizon (University of Helsinki)
  • Abstract : Online optimization generally studies the convergence of optimization methods as more data is introduced into the problem; think of deep learning as more training samples become available. We adapt the idea to dynamic inverse problems that naturally evolve in time. We introduce an improved primal-dual online method specifically suited to these problems, and demonstrate its performance on dynamic monitoring of electrical impedance tomography.
• [03177] Primal-Dual Methods with Adjoint Mismatch
  • Format : Talk at Waseda University
  • Author(s) :
    • Felix Schneppe (Technische Universität Braunschweig)
  • Abstract : Primal-dual algorithms are widespread methods to solve saddle-point problems of the form $\min_x \max_y G(x) + \langle Ax, y \rangle - F^*(y).$ However, in practical applications like computed tomography the adjoint operator is often replaced by a computationally more efficient approximation. This leads to an adjoint mismatch in the algorithm. In this talk, we analyse the convergence of different primal-dual algorithms and prove conditions, under which the existence of a solution can still be guaranteed.
• [02036] Material decomposition in multi-energy X-Ray tomography with Inner Product Regularizer
  • Format : Online Talk on Zoom
  • Author(s) :
    • Salla Maaria Latva-Äijö (University of Helsinki)
  • Abstract : Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two or more distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material present. Further, the same number of X-ray energies are chosen so that there is a clear difference in the spectral dependence of the attenuation coefficients of the materials. A novel regularizer is presented for the inverse problem of reconstructing separate tomographic images for the two materials. A combination of two things, (a) non-negativity constraint, and (b) penalty term containing the inner product between the two material images, promotes the presence of at most one material in a given pixel. A preconditioned interior point method is derived for the minimization of the regularization functional. Numerical tests with digital phantoms suggest that the new algorithm outperforms the baseline method, Joint Total Variation regularization, in terms of correctly material-characterized pixels. While the method is tested only in a two-dimensional setting with two materials and two energies, the approach readily generalizes to three dimensions and more materials. The number of materials just needs to match the number of energies used in imaging.

contributed talk: CT194

room : A208

MS [00815] Recent trends in continuous optimization

room : A502

• [03738] Recent developments in multiobjective fast iterative shrinkage-thresholding algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Ellen Hidemi Fukuda (Kyoto University)
  • Abstract : In this talk, we will present an overview of multiobjective proximal gradient methods, that solve problems of the type $\textrm{min} \, f(x)+g(x)$, where $f \colon \Re^n \to \Re^m$ is continuously differentiable and $g \colon \Re^n \to (\Re\cup\{+\infty\})^m$ is closed, proper and convex. We will also discuss their accelerated versions, including the multiobjective fast iterative shrinkage-thresholding algorithm (FISTA), monotone FISTA, and restarting FISTA. We will show the associated convergence results and some numerical experiments.
• [04395] Adaptive Gradient-Based Method for Convex Optimization Problems Under Error Bounds
  • Format : Talk at Waseda University
  • Author(s) :
    • Masaru Ito (Nihon University)
  • Abstract : First-order methods for smooth convex optimization problems is a fundamental methodology for large-scale optimization arising in machine learning. We present an adaptive first-order method to find an approximate solution in terms of small gradient norm that does not require the problem dependent parameters and automatically accelerates under error bound condition like strong convexity. The iteration complexity to find an approximate solution is shown to be optimal.
• [03739] Accelerated distributed proximal conjugate gradient methods for multi-agent constrained optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Gebrie Anteneh Getachew (Debre Berhan University)
    • Stefan Volkwein (University of Konstanz)
  • Abstract : We introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M number of smooth and M number of non-smooth functions over the common fixed points of M number of nonlinear mappings. Exploiting the special properties of the cost component function of the objective function and the nonlinear mapping of the constraint problem of each agent, a new inertial accelerated incremental and parallel computing distributed algorithms will be presented based on the combinations of computations of proximal, conjugate gradient and Halpern methods. Some numerical experiments and comparisons are given to illustrate our results.
• [03850] Extensions of Constant Rank Qualification Constrains condition to Nonlinear Conic Programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Hector Ramirez (Universidad de Chile)
  • Abstract : We present new constraint qualification conditions for nonlinear conic programming that extend some of the constant rank-type conditions from nonlinear programming. Specifically, we propose a general and geometric approach, based on the study of the faces of the cone, for defining a new extension of this condition to the conic context. We then compare these new conditions with some of the existing ones, including the nondegeneracy condition, Robinson’s constraint qualification, and the metric subregularity constraint qualification. The main advantage of the latter is that we are able to recast the strong second-order properties of the constant rank condition in a conic context. In particular, we obtain a second-order necessary optimality condition that is stronger than the classical one obtained under Robinson’s constraint qualification, in the sense that it holds for every Lagrange multiplier, even though our condition is independent of Robinson’s condition.

MS [00172] On application of principle curvature distribution in local differential geometry

room : A508

• [04166] Fullerene and discrete principal curvature
  • Format : Talk at Waseda University
  • Author(s) :
    • Shigeki Matsutani (Kanazawa University)
    • Yusuke Noda (Okayama Prefectural University)
  • Abstract : Due to geometrical investigations of the carbon configurations of the first principle computations, the novel symmetry in the fullerenes, i.e., the pre-constant discrete principal curvature (pCDPC) structure, was recently found. In this talk, we show the symmetry mainly on the C60 polymers and related fullerenes from geometrical viewpoints.
• [03759] Interplay between topology-induced geometry and the electronic properties of nanocarbon materials
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Onoe (Nagoya University)
  • Abstract : The quantum mechanics in curved surface has been studied in 1950s and predicted that the electron behaviors are affected by Gaussian and average curvatures theoretically in 1980s. We have first demonstrated the quantum mechanics in submanihold experimentally using one-dimensional periodic uneven structured C60 polymer formed by electron-beam irradiation of C60 film.
• [04350] On discrete constant principal curvature surfaces
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuta Ogata (Kyoto Sangyo University)
  • Abstract : In this talk, we will study the discrete surface theory on a full 3-ary oriented tree and introduce the notion of discrete principal curvatures on them. In order to investigate the geometric meaning of discrete principal curvatures, we will also define a discrete analog of curvature lines on discrete surfaces, called weak-curvature lines. At the end of the talk, we also show some examples of discrete constant principal curvature surfaces.
• [04368] Surface parametrization for manufacturing by principal curvature integral
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yutaro Kabata (Nagasaki University)
  • Abstract : The choice of coordinates is crucial in the theory of curves and surfaces. In this presentation, we discuss the appropriate way to choose coordinates for curves and surfaces from a manufacturing perspective. Specifically, we define coordinates obtained from the integration of curvature for curves and principal curvatures for surfaces, and present results related to the stratification of curves and surfaces obtained from these coordinates.

MS [00761] Recent Advances on quadrature methods for integral equations and their applications

room : A510

• [04432] A High-Order Close Evaluation Scheme of Helmholtz Layer Potentials in 3D
  • Format : Talk at Waseda University
  • Author(s) :
    • Hai Zhu (Flatiron Institute)
    • Shidong Jiang (Flatiron Institute)
  • Abstract : We present an efficient high-order discretization scheme for the evaluation of the Helmholtz layer potentials on smooth surfaces in three dimensions. The scheme is panel based and applies an analytical surface to line integral conversion on each panel to evaluate single layer, double layer, adjoint double layer, and hypersingular potentials accurately. A new basis approximation scheme tailed for Helmholtz kernels is proposed. Both nearly singular and singular cases are supported via the same recursive framework.
• [05076] Corrected trapezoidal rules for boundary integral methods on non-parametrized surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Olof Runborg (KTH Royal Institute of Technology)
    • Richard Tsai (The University of Texas at Austin)
    • Yimin Zhong (Auburn University )
    • Federico Izzo (KTH Royal Institute of Technology)
  • Abstract : We present higher-order quadratures for a family of boundary integral operators with application to the linearized Poisson-Boltzmann equation. Using the Implicit Boundary Integral formulation, surface point singularities in a layer potential extend along the surface normal lines. In this volumetric setting, we use the trapezoidal rule, and develop higher-order quadratures by correcting it in nodes close to the singularity line with weights dependent on the singularity type and geometrical information extracted from the non-parametrized surface.
• [03610] Quadrature errors for layer potentials near surfaces with spherical topology
  • Format : Talk at Waseda University
  • Author(s) :
    • Chiara Sorgentone (Sapienza, Università di Roma)
    • Anna-Karin Tornberg (KTH Royal Institute of Technology)
  • Abstract : Numerical simulations often involve 3D objects with spherical topology, e.g. rigid particles, drops, vesicles. When the underlying numerical method is based on boundary integral equations, standard quadrature rules can yield large errors in computing the layer potentials if the distance between the surfaces is too small and the associated integrals become nearly singular. We will present numerical and analytical approaches to efficiently evaluate the quadrature error estimates for these situations.
• [04811] Special quadrature via line extrapolation, with application to Stokes flow
  • Format : Online Talk on Zoom
  • Author(s) :
    • Joar Bagge (KTH Royal Institute of Technology)
    • Anna-Karin Tornberg (KTH Royal Institute of Technology)
  • Abstract : In integral equations, special quadrature methods are needed to perform singular or nearly singular integration. We consider one such method, sometimes called the "Hedgehog method", based on extrapolation (or interpolation) along a line. Different strategies for selecting the placement of sampling points along the line are investigated. We consider extrapolation using polynomials or rational functions. The resulting methods are compared with quadrature by expansion (QBX) in the context of Stokes flow containing rigid rodlike particles.

MS [00779] Advances in numerical methods for evolutionary PDEs and applications

room : A511

• [05243] Implicit-explicit time integration for thermal radiative transfer and radiation hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Ben Scott Southworth (Los Alamos National Laboratory)
  • Abstract : Thermal radiative transfer (TRT) is an extremely stiff high-dimensional partial-integro-differential equation, which requires partitioned integration when coupled to hydrodynamics. I introduce an approximation of TRT that captures both stiff asymptotic limits, and IMEX framework requiring only one transport-sweep per timestep. I then discuss nonlinear coupling to hydrodynamics, which is complicated via equation-of-state relations. We derive a temperature closure and framework for semi-implicit-explicit integration of radiation hydrodynamics, demonstrating excellent convergence on stiff radiative shock problems.
• [03444] Semi-implicit numerical methods for level set equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Nikola Gajdošová (Slovak University of Technology in Bratislava)
    • Katarína Lacková (Slovak University of Technology in Bratislava)
    • Peter Frolkovič (Slovak University of Technology in Bratislava)
  • Abstract : We present semi-implicit higher order numerical methods to solve nonlinear level set equations for evolving interfaces. We introduce up to third order accurate unconditionally stable numerical schemes to solve advection by external velocity and speed in normal direction, and, eventually, regularized by a small curvature term. The methods have fully upwinded stencil in its implicit part so efficient algebraic solvers like fast sweeping methods can be applied.
• [05021] Efficient implicit methods for the Euler equations in Lagrangian coordinates
  • Format : Talk at Waseda University
  • Author(s) :
    • Simone Chiocchetti (University of Stuttgart)
    • Giovanni Russo (University of Catania)
    • Sebastiano Boscarino (University of Catania)
  • Abstract : In this talk, we introduce a novel implicit numerical scheme for the multimaterial Euler equations in Lagrangian coordinates. The method takes advantage of the remarkable structure of the governing equations in Lagrangian coordinates, which admits a single scalar wave equation for the pressure field, generating a symmetric positive definite system of linear equations. At the same time, contacts are resolved exactly, due to the Lagrangian nature of the method, even without a Riemann solver.
• [03910] High-order semi-implicit schemes for evolutionary partial differential equations with higher order derivatives
  • Format : Talk at Waseda University
  • Author(s) :
    • Sebastiano Boscarino (University of Catania, Italy)
  • Abstract : The aim of this work is to apply a semi-implicit (SI) strategy in an implicit-explicit (IMEX) Runge-Kutta (RK) setting introduced in (S. Boscarino- F. Filbet, G. Russo, JSC 2016) to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives. This strategy gives a great flexibility to treat these equations, and allows the construction of simple linearly implicit schemes without any Newton’s iteration. Furthermore, the SI IMEX- RK schemes so designed does not need any severe time step restriction that usually one has using explicit methods for the stability, i.e. ∆t = O(∆t^k) for the k-th (k ≥ 2) order PDEs. For the space discretization, this strategy is combined with finite differ- ence schemes. We illustrate the effectiveness of the schemes with many applications to dissipative, dispersive and biharmonic-type equations. Numerical experiments show that the proposed schemes are stable and can achieve optimal orders of accuracy.

MS [00641] Emerging Collaborations: Mathematical Views of Modelling Biological Scales

room : A512

• [01865] A Multiscale, Interdisciplinary Approach to Blood Clot Degradation
  • Format : Talk at Waseda University
  • Author(s) :
    • Brittany Bannish (University of Central Oklahoma)
    • Nathan Hudson (East Carolina University)
    • Valerie Tutwiler (Rutgers University)
  • Abstract : Blood clots are critical to prevent bleeding, but complications arise when clots are not degraded effectively. We present a stochastic model of clot degradation that includes structural and biochemical details from the single fiber to full clot scales. We show that modeling in tandem with laboratory experimentation yields physiological insights that were impossible with models or experiments alone. We also discuss the need for future models that include mechanical forces.
• [01970] Explorations of DNA Knot Shadows
  • Format : Talk at Waseda University
  • Author(s) :
    • Candice Price (Smith College)
  • Abstract : A core question in knot theory is: How do we identify whether two knots are equivalent under a specific set of operations? Knot theory deals not only with the curious variations in the underlying topological structure, e.g. strands, loops, choice of operations of knots, but also with invariants, e.g. Alexander, Jones, link homologies. Knot theory has been used in various fields of mathematics and has become an essential resource for understanding the topology and the geometry of DNA. In this presentation, we will describe and explore our work to interpret 2-dimensional projections of knots, called knot shadows.
• [02104] A mathematical approach to understanding reproductive health disparities at the intersection of ovulatory and metabolic dysfunction
  • Format : Talk at Waseda University
  • Author(s) :
    • Erica J Graham (Bryn Mawr College)
  • Abstract : Endocrine physiology is a complex system of crosstalk between hormones in various tissues. Reproductive hormone dysregulation may disrupt ovulation and may be exacerbated by metabolic abnormalities. Racial and ethnic disparities are also prevalent at the intersection of metabolic and ovarian dysfunction. Here we introduce a mathematical model of the human ovulatory cycle and consider mechanisms of disruption to characterize ovulatory phenotypes. We then examine how health disparities might influence--or be influenced by--model-based phenotypes.
• [02133] Harmonic Analysis on Simplicial Simplexes: How far could we take it?
  • Format : Talk at Waseda University
  • Author(s) :
    • Karamatou Yacoubou Djima (Wellesley College)
  • Abstract : Networks’ emergence as an ideal setting for studying complex systems brought enormous interest in extending powerful harmonic analysis (HA) tools from Euclidean spaces to graphs. Most efforts focused on the graph Laplacian’s eigendecomposition, producing results such as the graph Fourier transform. Recently, the same endeavor moved to higher-order network structures—simplicial simplexes. We survey classical Fourier analysis and its graph extensions before presenting new developments and challenges of HA on simplicial complexes based on the Hodge Laplacian.

MS [00309] Population Dynamics in Biology and Medicine

room : A601

• [01291] Exploring the effects of the latent eggs on the efficacy of Wolbachia-carrying release technique
  • Format : Talk at Waseda University
  • Author(s) :
    • Claudia Pio Ferreira (Unesp)
  • Abstract : I will present an ordinary differential system that takes into account the interaction of two populations of mosquito, infected and uninfected with wolbachia. Each population will be split in egg, latent egg, larva and adult stage, but for the infected population no transition to larvae coming through latent egg is possible. Therefore, we will explore the contribution of uninfected eggs coming from the latent stage to the efficacy of wolbachia-aedes release.
• [01943] Mathematical models for practical application of the Sterile Insect Technique
  • Format : Talk at Waseda University
  • Author(s) :
    • Yves Dumont (CIRAD - University of Pretoria)
  • Abstract : Sterile Insect Technique-SIT is an autocidal control method used against Pests and Vectors. While conceptually very simple, it can be difficult to set up in the field. That is why, it is sometimes successful, and sometimes not. We show that modeling, analysis and simulations can be helpful to limit the risk of failure in SIT feasability programs. We present some results obtained against Aedes albopictus and Bactrocera dorsalis in Réunion island, a French overseas department.
• [01092] A generalized next generation method for the effective reproduction number
  • Format : Talk at Waseda University
  • Author(s) :
    • Suani Tavares Rubim de Pinho (Universidade Federal da Bahia)
    • Daniel Cardoso Pereira Jorge (Universidade Estadual Paulista)
    • Juliane Fonseca Oliveira (CIDACS - Fundação Oswaldo Cruz)
    • José Garcia Vivas Miranda (Universidade Federal da Bahia)
    • Roberto Fernandes Silva Andrade (Universidade Federal da Bahia)
  • Abstract : The effective reproduction number $R(t)$ plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual. In this work, we present a generalization of next generation method, leading to expressions of $R(t)$ and generation interval distributions, within and between model sub-compartments, provided by an arbitrary compartmental model and by incidence data. Ref: Jorge, DCP et al. (2022). R. Soc. Open Sci. 9, 220005.
• [03871] Modelling human behavioural change during the outbreak of emerging infectious disease
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryosuke Omori (Hokkaido University)
  • Abstract : Disease dynamics like SARS-CoV-2 is difficult to describe by mathematical modelling. One of reasons is lack of knowledge of behavioral change due to the difficulty of measuring individual decision. To solve this problem, we defined index for the mobility avoidance in response to epidemic measured using accommodation reservation data and decision timing for behavioral change can be quantified. Using this index, we revealed general patterns in host behavioral change dynamics in response to SARS-CoV-2 outbreaks.