MS and CT list / Aug. 21, 17:40-19:20.

MS [00795] Topological data analysis and machine learning

room : G301

• [05456] GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Soham Mukherjee (PhD Student)
    • Tamal Krishna Dey (Purdue University)
  • Abstract : $1$-parameter persistent homology, a cornerstone in Topological Data Analysis (TDA), studies the evolution of topological features such as connected components and cycles hidden in data. It has been applied to enhance the representation power of deep learning models, such as Graph Neural Networks (GNNs). To enrich the representations of topological features, here we propose to study $2$-parameter persistence modules induced by bi-filtration functions. In order to incorporate these representations into machine learning models, we introduce a novel vector representation called Generalized Rank Invariant Landscape (GRIL) for $2$-parameter persistence modules. We show that this vector representation is $1$-Lipschitz stable and differentiable with respect to underlying filtration functions and can be easily integrated into machine learning models to augment encoding topological features. We present an algorithm to compute the vector representation efficiently. We also test our methods on synthetic and benchmark graph datasets, and compare the results with previous vector representations of $1$-parameter and $2$-parameter persistence modules.
• [05457] Topological Classification of Zero Sum Games
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Strang (University of Chicago)
  • Abstract : Zero-sum two-player games are widely used to model competitive interactions in biology, economics, and reinforcement learning. Unlike classical game theory, which focuses on optima, empirical game theory studies the structure of games and decision problems via observations of play by a population. We study a classification scheme for games based on their topology after embedding into a latent space. Using observed interactions, we infer the spectrum of the payout function when treated as the kernel of an integral operator. The eigenfunctions of the operator can be used to embed agents. The embedded agents form a scatter cloud whose topology provides a natural framework for classifying games. We study the classification of a series of randomly generated extensive form games and decision problems.
• [05458] Topological Embedding of Brain Networks for Differentiating Temporal Lobe Epilepsy
  • Format : Talk at Waseda University
  • Author(s) :
    • Moo K Chung (University of Wisconsin-Madison)
  • Abstract : In this study, we approach the discrimination of functional brain networks in temporal lobe epilepsy patients from those of healthy controls through persistent homology. Starting with a weighted graph, we perform a graph filtration, yielding the birth-death decomposition. This process allows us to uniquely decompose each graph into two subgraphs characterized by 0D and 1D topology. The 0D subgraph arises from the birth of connected components, whereas the 1D subgraph manifests through the death of 1-cycles during the filtration. The distinguishing features of each graph are thus represented by the sorted birth and death values. To compare multiple weighted graphs, we propose a topological version of multidimensional scaling, which embeds these graphs into a 2D plane. This technique offers potential insights for resting-state functional magnetic resonance imaging (rs-fMRI) studies, particularly in distinguishing the functional brain networks associated with temporal lobe epilepsy. This presentation draws upon the findings from the paper available on arXiv:2302.06673.
• [05459] Barcodes and Kernels for multiparameter persistence
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mathieu Carrière (Centre Inria d'Université Côte d'Azur)
  • Abstract : Multiparameter persistence is a generalization of persistent homology that allows for more than a single filtration function. Such constructions arise naturally when considering data with outliers or variations in density, time-varying data, or functional data. In single-parameter persistence, the barcode is equivalent to the “rank invariant”: the function that associates the rank of the corresponding linear map to every pair of comparable points. However, nearly all of the tools developed in persistent homology are based on the barcode. This is because it is a concise and geometric descriptor that lends well to data analysis and visualization. Therefore, it is crucial, and perhaps imperative, to construct a generalized barcode to work with the rank-invariant for multiparameter persistence efficiently. Perhaps surprisingly, recent work has shown that if we allow the elements of the barcode to be signed intervals, then such a generalization is possible. I will discuss how one can use homological algebra to obtain a signed barcode in a stable manner. Furthermore, I will discuss how signed barcodes can be used in machine learning pipelines and report on recent computational results obtained using generalizations of the so-called sliced Wasserstein kernel to such signed barcodes.

contributed talk: CT008

room : G304

[00770] Rellich eigendecomposition of paraHermitian matrices, with applications

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : Let $H(z)$ be paraHermitian, that is, analytic and Hermitian on the unit circle $S^1$. We prove that $H(z)=U(z)D(z)U(z)^P$ where, for all $z \in S^1$, $U(z)$ is unitary, $U(z)^P=U(z)^*$, and $D(z)$ is real diagonal; moreover, $U(z), D(z)$ are analytic in $w=z^{1/N}$ for some positive integer $N$, and $U(z)^P$ is the paraHermitian conjugate of $U(z)$. We discuss the implications on the svd of an $S^1$-analytic matrix and the sign characteristics of unimodular eigenvalues of $*$-palindromic matrix polynomials.
• Classification : 15A23, 15A18, 15A54, 15B57
• Format : Talk at Waseda University
• Author(s) :
  • Vanni Noferini (Aalto University)
  • Giovanni Barbarino (Aalto University)

[00430] Nearest singular pencil via Riemannian optimization

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : The problem of finding the nearest complex $($real$)$ singular pencil can be cast as a minimization problem over the manifold $U(n) \times U(n)$ $\left( O(n) \times O(n) \right)$ via the generalized Schur form. This novel perspective yields a competitive numerical method by pairing it with an algorithm capable of doing optimization on a Riemannian manifold.
• Classification : 15A22
• Format : Talk at Waseda University
• Author(s) :
  • Lauri Nyman (Aalto University)

[02200] Structured Distances to Nearest Singular Matrix Pencil

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : We consider the structured distance to singularity for a given regular matrix pencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb{C}^{n,n})^2$. This includes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic, T-palindromic, and dissipative Hamiltonian pencils. We derive explicit computable formulas for the distance to the nearest structured pencil $(A-\Delta_A)+s(E-\Delta_E)$ such that $A-\Delta_A$ and $E-\Delta_E$ have a common null vector. We then obtain a family of computable lower bounds for the unstructured and structured distances to singularity.
• Classification : 15A18, 15A22, 65K05
• Format : Talk at Waseda University
• Author(s) :
  • Anshul Prajapati (Indian Institute of Technology Delhi)
  • Punit Sharma (Indian Institute of Technology Delhi)

[01156] Row completion of polynomial matrices

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : Perturbation problems arise frequently in applications, as in structural changes of the dynamics of a system or in pole placement problems in control theory. Perturbation problems of matrices are closely related to completion problems. We present a solution to the row-completion problem of a polynomial matrix, prescribing the eigenstructure of the resulting matrix and maintaining the degree.
• Classification : 15A22, 15A83
• Author(s) :
  • Agustzane Amparan (Universidad del País Vasco, UPV/EHU)
  • Itziar Baragaña (Universidad del País Vasco, UPV/EHU)
  • Silvia Marcaida (Universidad del País Vasco, UPV/EHU)
  • Alicia Roca (Universitat Politècnica de València )

[00757] Effect of electrostatic forces and moments on cracked electrostrictive dielectrics

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : Going beyond the scope of solely mechanical considerations, fracture mechanics of smart dielectrics is additionally concerned with the implications of electric fields on crack tip loading. In this work, the oftentimes neglected electric body and surface forces as well as body couples stemming from the Maxwell stress tensor are studied in the context of a crack in an infinite electrostrictive dielectric by exploiting holomorphic potentials and Cauchy's integral formulae within the framework of complex analysis.
• Classification : 30E20, 30E25, 74A35, 74R10, 78A30
• Format : Talk at Waseda University
• Author(s) :
  • Lennart Behlen (University of Kassel)
  • Daniel Wallenta (University of Kassel)
  • Andreas Ricoeur (University of Kassel)

MS [02396] Recent Advances on Polynomial System Solving

room : G305

contributed talk: CT016

room : G401

[00551] Network suppression of the pathogen spread within the healthcare system

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : We consider an impulsive-differential-equation system, based on SIS model, to describe the spread of pathogens in healthcare systems accounting for patient mobility. We propose sufficient conditions guaranteeing network suppression of infection and an algorithm to indicate hospitals prone to high bacteria prevalence and ultimately to ensure the stability of a disease-free state. As an illustration, we present a model of hospital-acquired multidrug-resistant bacteria transmission based on hospital admission records provided by a German insurance company.
• Classification : 34A37, 65P40, 92D30
• Format : Talk at Waseda University
• Author(s) :
  • Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
  • Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
  • Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw and Institute of High Pressure Physics, Polish Academy of Sciences)

[01010] Superconvergent Scheme for a System of Green Fredholm Integral Equations

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : In this study, we consider a system of second kind linear Fredholm integral equations with Green’s type kernel function. We propose a piecewise polynomial based Galerkin and iterated Galerkin methods to solve the integral model. We carry out the convergence and error analysis for the proposed methods and establish the superconvergence results for iterated Galerkin method. The theoretical results are supported by numerical tests.
• Classification : 34A12, 45F15
• Format : Talk at Waseda University
• Author(s) :
  • Rakesh Kumar (Indian Institute of Technology, Kanpur (India))
  • Kapil Kant (Indian Institute of Technology, Kanpur (India))
  • B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))

[00501] Efficient numerical method for simulation of plasma

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Understanding the dynamics of plasma is crucial in many concurrent applications. Those include astrophysics, space discovery, and designing fusion reactors. Numerical methods are a great tool for this purpose. In this talk, an efficient numerical method based on Galerkin approximations is presented. The method has high accuracy, capability of capturing shocks and turbulence, and consistency with thermodynamics. We show several interesting numerical simulations to demonstrate those properties.
• Classification : 34A45
• Format : Talk at Waseda University
• Author(s) :
  • Tuan Anh Dao (Uppsala University)

[00968] Modelling pathogen spreading in a network of hospitals

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : I will introduce an ODE model describing the spread of multidrug-resistant bacteria in a hospital network. I will present the mathematical properties of the model solutions, including the global stability of steady states. Based on simulations for real-life data, I will describe how the parameters affect the process dynamics at both network and hospital levels. Finally, the relations to other types of models describing similar processes will be discussed.
• Classification : 34Axx, 34Cxx, 34D23, 92D30
• Format : Talk at Waseda University
• Author(s) :
  • Agata Lonc (University of Warsaw)
  • Monika Joanna Piotrowska (Institute of Applied Mrsaathematics and Mechanics, University of Waw)
  • Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)

[00728] Descriptions of distribution function and hyperfunction using discretization

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Nonlinear systems with singular solutions, such as vortices and vortex sequences, can be mathematically described using the distribution function (δ function). However, it is difficult to numerically analyze the singular solution. In this study, we have considered approaches to discretize the distribution function and discussed the usefulness of introducing it into numerical analysis. Furthermore, we have carried out some examples of applications to discrete distribution functions and Sato’s hyperfunction.　
• Classification : 32A45, 46F15, 46F30, 46T30, 65E05
• Format : Talk at Waseda University
• Author(s) :
  • Yuya Taki (Graduate School of Science and Engineering, SOKA University)
  • Yoshio Ishii (Faculty of Science and Engineering, SOKA University)

contributed talk: CT021

room : G402

[02352] Analysis of a model of Dengue fever transmission

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : In our study, we consider a model formulation of a dengue fever transmission including delay terms. The next-generation matrix techniques have been used for deriving the basic reproduction number for the spread of infectious disease. Nondimensionalisation has been carried out and equilibrium points have been obtained. Then stability analysis of the delay model has been investigated. Numerical simulations have been shown for the specific parameters and the effect of the time delays has been observed.
• Classification : 34D20, 37G15, 92D25, 92-10, 34K20
• Format : Talk at Waseda University
• Author(s) :
  • Burcu Gürbüz (Johannes Gutenberg-University Mainz)
  • Aytül Gökçe (Ordu University)
  • Segun Isaac Oke (Ohio University, USA)
  • Michael O. Adeniyi (Lagos State University of Science and Technology)
  • Mayowa M. Ojo (Thermo Fisher Scientific)

[02521] Asymptotic tracking of a point cloud moving on Riemannian manifolds

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : We present two Cucker-Smale type models for the asymptotic tracking of a point cloud moving on complete, connected, and smooth Riemannian manifolds. For each model, we provide a sufficient framework in terms of a moving target point cloud, system parameters, and initial data. In the proposed framework, we show asymptotic flocking, collision avoidance, and asymptotic tracking to a given point cloud. The main result is a joint work with Hyunjin Ahn, Seung-Yeal Ha and Jaeyoung Yoon.
• Classification : 34D05, 34H05, 70F10, 70G60, 92D25
• Format : Talk at Waseda University
• Author(s) :
  • Hyunjin Ahn (Myongji University)
  • Junhyeok Byeon (Seoul National University)
  • Seung-Yeal Ha (Seoul National University)
  • Jaeyoung Yoon (Seoul National University)

[01041] Dynamical Behaviours of a Stochastic Leptospirosis Model with Saturated Incidence Rate

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : Leptospirosis is a zoonotic bacterial disease that is endemic and having high incidence rate in tropical and subtropical regions especially after flooding or heavy rainfall. The objective is to investigate the asymptotic behaviour of a stochastic Leptospirosis model with saturated incidence rate in terms of basic reproduction number using Lyapunov functions. As a first step, a biologically well-posed model perturbed by multiplicative Gaussian noise will be proposed. The existence of a stationary distribution and the ergodicity of solutions of the proposed model will also be established.
• Classification : 34D05, 34K50, 60H10, 60J65
• Format : Talk at Waseda University
• Author(s) :
  • SELSHA S (Research Scholar, Govt College Chittur)

[02289] HIV Community Transmission: A Multi-strain Modelling Approach

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : In this study, we proposed a two-strain model comprising drug-sensitive and drug-resistant strains for the dynamics of Human Immunodeficiency Virus (HIV) spread in a community. A treatment compartment is included in the modelling framework by considering drug adherence. We introduced various time delays for different phase transitions of the disease to track down the effect of its chronicity. A comprehensive stability and bifurcation analysis reveal the importance of treatment availability and drug adherence.
• Classification : 34D05, 34D20, 92D25, 92D30
• Format : Online Talk on Zoom
• Author(s) :
  • Ashish Poonia (Indian Institute of Technology Guwahati)
  • Siddhartha Pratim Chakrabarty (Indian Institute of Technology Guwahati)

[01393] Generalized Mittag-Leffler Functions and Its Rational Approximations with Real Distinct Poles

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : Mittag-Leffler functions are indispensable in the theory of fractional calculus and many other applications in engineering. However, their computational complexities have made them difficult to deal with numerically. A real distinct pole rational approximation of the two-parameter Mittag-Leffler function is proposed. Under some mild conditions, this approximation is proven and empirically shown to be L-Acceptable. These approximations are especially useful in developing efficient and accurate numerical schemes for partial differential equations of fractional order. Some applications are presented, such as complementary error function and solution of fractional differential equations.
• Classification : 33B10, 41A20, 65L05
• Author(s) :
  • Olaniyi Samuel Iyiola (Clarkson University)

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

room : G404

• [04635] Asymptotic classification of forced stochastic systems with memory
  • Format : Talk at Waseda University
  • Author(s) :
    • John A Appleby (Dublin City University)
    • Emmet Lawless (Dublin City University)
  • Abstract : Linear stochastic functional differential equations are among the simplest stochastic systems that possess path-dependence. In recent work, the authors have characterised the asymptotic behaviour, including rates of convergence to equilibria, of solutions of such systems which are not externally forced. In this work, we are able to characterise the asymptotic behaviour of state-independent forcing terms which guarantee specified types of asymptotic rates of decay, growth and fluctuation size, of solutions.
• [04851] Asymptotic analysis of stochastic functional differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Emmet Lawless (Dublin City University)
    • John Appleby (Dublin City University)
  • Abstract : In this talk we are concerned with the asymptotic behaviour of the mean square of scalar stochastic functional differential equations with finite delay. We are primarily interested in providing characterisations of various types of mean square stability and discussing the robustness of solutions under perturbations. Additionally, we highlight how our methods of proof can be utilised to make progress in understanding the mean square behaviour of equations of Volterra type.
• [03977] An order-one adaptive scheme for the strong approximation of stochastic systems with jumps.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Conall Kelly (University College Cork)
    • Gabriel Lord (Radboud University)
    • Fandi Sun (Heriot-Watt University)
  • Abstract : Consider a system of SDEs with coefficients that are locally Lipschitz and together satisfy a montone condition. It is known that the explicit Milstein scheme on a uniform mesh fails to converge here. We construct an adaptive mesh to ensure order-one convergence that reduces the stepsize as solutions approach the boundary of a sphere, and modify it for systems additionally perturbed by Poisson jumps. We demonstrate our scheme in the modelling of telomere length dynamics.
• [02373] Mathematical Model of Hepatitis B Virus Combination Treatment
  • Format : Online Talk on Zoom
  • Author(s) :
    • Irina Volinsky (Ariel University, Israel)
  • Abstract : HBV has a high mortality rate with respect to other common known diseases. The commonly used cure for chronic HBV cases is the fusion of interferon and analogous nucleoside methods. The addition of IL-2 therapy proposed in this article. This method was validated to be highly effective. This model will take into account the response of the immune system of the patient and will use immune therapy as a support.

MS [00982] Partial Differential Equations in Fluid Dynamics

room : G405

• [04434] Hyperbolic Cattaneo-Approximation of the compressible Navier-Stokes-Fourier system
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiang Xu (Nanjing University of Aeronautics and Astronautics)
  • Abstract : We will talk about the Cattaneo-Chistov approximation of the compressible non-isentropic Navier-Stokes system in whole space. First, we establish a global well-posedness of the Navier-Stokes-Cattaneo-Christov system uniformly with respect to the relaxation parameter. Then we justify the strong convergence of the solution toward that of the compressible Navier-Stokes system, and the explicit convergence rates are also exhibited.
• [04767] Local regularity conditions on initial data for local energy solutions of the incompressible Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Hideyuki Miura (Tokyo institute of technology)
    • Kyungkeun Kang (Yonsei university)
    • Tai-Peng Tsai (University of British Columbia)
  • Abstract : We study the regular sets of local energy solutions to the Navier-Stokes equations in terms of conditions on the initial data. It is shown that if a weighted L2 norm of the initial data is finite, then all local energy solutions are regular in a region confined by space-time hypersurfaces determined by the weight. This result refines and generalizes Theorems C and D of Caffarelli, Kohn and Nirenberg (1982).
• [04554] Sharp non-uniqueness of weak solutions to viscous fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Yachun Li (Shanghai Jiao Tong University)
    • Zirong Zeng (Shanghai Jiao Tong University)
    • Deng Zhang (Shanghai Jiao Tong University)
    • Peng Qu (Fudan University)
  • Abstract : In this talk, I will present our recent results about non-uniqueness of weak solutions to some viscous fluid models. For incompressible Navier-Stokes equations , we proved the sharp non-uniqueness of weak solutions at two endpoints of the Ladyžhenskaya-Prodi-Serrin (LPS) criteria even in hyper-viscous regime. For MHD equations, we prove the sharp non-uniqueness near one endpoint of the LPS condition. Furthermore, the strong vanishing viscosity and resistivity result is obtained, it yields the failure of Taylor’s conjecture along some sequence of weak solutions. For hypo-viscous compressible Navier-Stokes equations, we prove that there exist infinitely many different weak solutions with the same initial data. This provides the first non-uniqueness result of weak solutions to viscous compressible fluid. Our proof are based on the spatial-temporal intermittent convex integration scheme. These are joint works with Yachun Li, Peng Qu and Deng Zhang.
• [05340] On controllability of the incompressible MHD system
  • Format : Talk at Waseda University
  • Author(s) :
    • Yaguang Wang (Shanghai Jiao Tong University)
  • Abstract : In this talk, we shall introduce our recent study on the controllability of the initial boundary value problem for the incompressible magnetohydrodynamic systems. For the two-dimensional ideal incompressible MHD system, we obtained the global exact controllability by using the return method, and for the two- and three-dimensional viscous MHD systems with coupled Navier slip boundary condition, we deduced the global approximate controllability. This is a joint work with Manuel Rissel.

MS [00085] Singular Problems in Mechanics

room : G406

• [00203] On Kirchhoff-Love plates with thin elastic junction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexander Khludnev (Lavrentyev Institute of Hydrodynamics of RAS)
  • Abstract : The talk concerns an equilibrium problem for two elastic plates connected by a thin junction (bridge) in a case of Neumann boundary conditions, which provide a non-coercivity for the problem. An existence of solutions is proved. Passages to limits are justified with respect to the rigidity parameter of the junction. In particular, the rigidity parameter tends to infinity and to zero. Limit models are investigated.
• [00235] Optimal Location Problem for Heterogeneous Bodies with Separate and Joined Rigid Inclusions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Niurgun Lazarev (North Eastern Federal University)
  • Abstract : Nonlinear mathematical models describing an equilibrium state of heterogeneous bodies which may come into contact with a fixed non-deformable obstacle are investigated. A possible mechanical interaction of the body and the obstacle is described with the help of the Signorini-type non-penetration condition. We suppose that the heterogeneous bodies consist of an elastic matrix and one or two built-in volume (bulk) rigid inclusions. One of the inclusions can vary its location along a given curve. Considering a location parameter as a control parameter, we formulate an optimal control problem with a cost functional specified by an arbitrary continuous functional on the solution space. Assuming that the location parameter varies in a given closed interval, the solvability of the optimal control problem is established. Furthermore, it is shown that the equilibrium problem for the heterogeneous body with joined two inclusions can be considered as a limiting problem for the family of equilibrium problems for heterogeneous bodies with two separate inclusions.
• [00210] Multiscale analysis of stationary thermoelastic vibrations of a composite material
  • Format : Online Talk on Zoom
  • Author(s) :
    • Evgeny Rudoy (Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences)
  • Abstract : The stationary vibrations problem is studied for a planar thermoelastic body incorporating thin inclusions. This problem contains two small positive, which describe the thickness of an individual inclusion and the distance between two neighboring inclusions. Relying on the variational formulation, by means of methods of asymptotic analysis, we investigate the behavior of solutions as parameters tend to zero. We construct models corresponding to limit cases. The work is supported by Russian Scientific Foundation (№ 22-21-00627).
• [00207] An impulsive pseudoparabolic equation with an infinitesimal transition layer
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sergey Alexandrovich Sazhenkov (Altay State University, Barnaul)
  • Abstract : We study the two-dimensional Cauchy problem for the non-instantaneous impulsive pseudoparabolic equation. Such equations arise in filtration theory, thermodynamics, etc. We rigorously justify the passage to the instantaneous impulsive equation and show that, as the duration of the impulse tends to zero, the infinitesimal transition layer is formed, which inherits the profile of the original non-instantaneous impulsive impact. This is a joint work with Dr. Ivan Kuznetsov of the Lavrentyev Institute of Hydrodynamics, Russia.

MS [00656] Multiscale Pattern Formation

room : G501

• [01917] Symmetry-Breaking for a Compartmental-Reaction Diffusion System
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Ward (University of British Columbia)
  • Abstract : We investigate pattern formation for a 2D PDE-ODE bulk-cell model, where two bulk   diffusing species are coupled to nonlinear intracellular reactions  that are confined within a   disjoint collection of small circular compartments within the domain. The bulk species are coupled to the spatially segregated intracellular reactions   through Robin conditions across the cell boundaries. For this compartmental-reaction   diffusion system, symmetry-breaking bifurcations,   regulated by a membrane binding rate ratio, occur even when the   bulk species have equal diffusivities.
• [01765] Bayesian Model Selection of PDEs for Pattern Formation
  • Format : Talk at Waseda University
  • Author(s) :
    • Natsuhiko Yoshinaga (Tohoku University)
    • Satoru Tokuda (Kyushu University)
  • Abstract : Partial differential equations (PDEs) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying their formation. PDE models often rely on the pre-request knowledge of physical laws and developing a model to reproduce a desired pattern remains difficult. We propose a method to estimate the best PDE from one snapshot of an objective pattern under the stationary state. We apply our method to complex patterns, such as quasi-crystals.
• [02979] Spectral Stability of Far-from-Equilibrium Planar Periodic Patterns
  • Format : Online Talk on Zoom
  • Author(s) :
    • Björn de Rijk (Karlsruhe Institute of Technology)
  • Abstract : We consider the existence and spectral stability of far-from-equilibrium planar periodic patterns in reaction-diffusion-advection systems. The planar periodic traveling waves are constructed by bifurcating from one-dimensional wave trains undergoing a transverse short-wave destabilization. The selected wavenumber matrix and velocity vector at bifurcation are fully determined by the wavenumber, velocity and critical Bloch modes of the underlying wave train. Our spectral analysis of the planar periodic pattern yields an expansion of the critical spectral surface touching the origin due to translational invariance in both spatial directions. In particular, such an expansion allows for an explicit verification of the spectral stability conditions implying nonlinear stability of the planar periodic pattern against spatially localized perturbations. This is joint work with Miguel Rodrigues (Université de Rennes 1, France).
• [01867] Fronts in the wake of a slow parameter ramp
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ryan Goh (Boston University)
    • Tasso Kaper (Boston University)
    • Arnd Scheel (University of Minnesota)
    • Theodore Vo (Monash University)
  • Abstract : We discuss front solutions in the presence of a parameter ramp which slowly varies in space, rigidly propagates in time, and moderates the (in)stability of a spatially-homogeneous equilibrium, nucleating a traveling wave in its wake. For moving ramps, the front location is governed by a slow passage between convective and absolute instability; a projectivized fold. For stationary ramps, fronts are governed by slow-passage through a pitchfork and a connecting solution of the Painléve-II equation.

MS [00550] Multi-scale analysis in random media and applications

room : G502

• [04699] Recent advances in quantitative stochastic homogenisation of nonlinear models
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolas Clozeau (Institute of science and technology Austria)
    • Antoine Gloria (Sorbonne Université)
    • Mathias Schäffner (Uni Halle)
    • Julian Fischer (Institute of science and technology Austria)
    • Antonio Agresti (Institute of science and technology Austria)
  • Abstract : I will present recent advances on the quantitative homogenisation of stochastic nonlinear models. First, I will discuss the case of convex variational models described by its Euler-Lagrange equation, taking the form of a nonlinear elliptic equation in divergence form with monotone and random coefficients. I will present the quantitative homogenisation theory in current development with Antoine Gloria and Mathias Schäffner, aiming at describing the oscillations and fluctuations of solutions at the microscopic scale as well as the large-scale regularity theory of the random nonlinear operator. Second, I will discuss the case of non-convex variational models of Griffith type in fracture mechanics and a quantitative result concerning the convergence of the cell formula recently obtained in collaboration with Julian Fischer and Antonio Agresti.
• [04559] Quantitative Homogenization for Nondivergence Form Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jessica Lin (McGill University)
  • Abstract : In this talk, I will first give an overview of stochastic homogenization for nondivergence form equations (from the PDE perspective) and quenched invariance principles for nonreversible diffusion processes (from the probability perspective). I will then present various quantitative stochastic homogenization results and discuss challenges specific to the homogenization of nondivergence form equations. This talk is based on joint work with Scott Armstrong (NYU) and Benjamin Fehrman (Oxford).
• [04584] Quantitative homogenization of elliptic system with periodic and high contrast coefficients
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenjia Jing (Tsinghua University)
    • Xin Fu (Tsinghua University)
  • Abstract : We present several results about the quantitative estimates of the homogenization of elliptic systems in high contrast periodic media. The periodically distributed high contrast parts have physical parameters that are either extremely large or extremely small compared to those in the background. We develop a method that is somewhat unified and can treat both types of high contrast limits. We obtain quantitative convergence rates with proper correctors, uniform Lipschitz regularity for the solutions of the heterogeneous equations and, as an application, a quantitative description of the spectral convergence for the double-porosity problem. We also discuss possible extensions of the method to some other systems, e.g., linear elasticity, with richer high contrast structures.

MS [02561] Mathematical Puzzles and Games in Theoretical Computer Science

room : G601

• [05095] Generalized Jankens
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiro Ito (University of Electro-Communications)
  • Abstract : Janken or rock-paper-scissors, which is a very simple game and it is usually used as a coin-toss in Japan, originated in China, and many variants are seen throughout the world. A variant of janken can be represented by an asymmetric digraph, where a vertex corresponds a sign and an arc (x,y) means sign x defeats sign y. However, not all asymmetric digraphs define useful janken variants, i.e., some janken variants may include a useless sign, which is strictly inferior than another sign in any case. We call a janken variant efficient if it contains no such a useless sign. We also introduced a measure of amusement of janken variants. We show the results of our mathematical research on janken variants.
• [05219] Tilings and unfoldings
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefan Langerman (Université libre de Bruxelles)
  • Abstract : A tiling is a covering of the plane with copies of a geometric shape (tiles) without gaps or overlaps. A tiler is a shape that tiles the plane. An unfolding is obtained by cutting along the surface of a polyhedron through all its vertices, and opening all the dihedral angles between adjacent faces to obtain a single flat non-overlapping geometric shape. In this talk, I will explore connections between these fascinating concepts, highlight some recent results and mention several still unsolved algorithmic problems,
• [05433] A Hardness Framework for Games and Puzzles: Motion Planning through Gadgets
  • Format : Talk at Waseda University
  • Author(s) :
    • Erik D. Demaine (Massachusetts Institute of Technology)
  • Abstract : Many games and puzzles, especially video games, involve one or more characters moving through a changeable environment, like Mario in Super Mario Bros. We describe a powerful framework for proving hardness of such games by characterizing which "gadgets" it suffices to build in the game. A gadget is a local piece of environment with limited traversals, some of which change local state, which in turn change available traversals, similar to a finite automaton. We prove that very simple gadgets suffice to prove NP-hardness, PSPACE-hardness, or EXPTIME-hardness. This framework enables many hardness proofs, old and new, to be distilled down to a single diagram of a single gadget, resulting in new or simplified hardness proofs for games such as Super Mario Bros., Mario Kart, Pokémon, Lemmings, Rush Hour, and Chess. It also opens up a rich study of gadgets themselves, including which gadgets can "simulate" which others, where a "simulation" is a graph representing a reduction algorithm.
• [05443] Map Folding
  • Format : Talk at Waseda University
  • Author(s) :
    • Yushi Uno (Osaka Metropolitan University)
  • Abstract : Origami (paper folding) is not only a traditional Japanese entertainment, but also an interesting research topic in both engineering and computer science. One of the special cases of paper folding is map folding, and it has interesting open problems. In this talk, we will introduce the map folding problem and show their latest research results.

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

room : G602

• [04224] Deterministic Particle Approximation for aggregation-diffusion equations: entropy solutions, gradient flows, graph.
  • Format : Talk at Waseda University
  • Author(s) :
    • Simone Fagioli (University of L'Aquila)
  • Abstract : We investigate the existence of weak type solutions for a class of aggregation–diffusion PDEs with nonlinear mobility obtained as deterministic large particle limit of a suitable nonlocal versions of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. At the same time, we expose a rigorous gradient flow structure for this class of equations in terms of an Energy-Dissipation balance, which we obtain via the asymptotic convergence of functionals. The well-posedness is also investigated for aggregation/diffusion equation modeling the evolution of opinion formation on an evolving graph.
• [03893] Non-local PDEs on graphs
  • Format : Online Talk on Zoom
  • Author(s) :
    • André Schlichting (University of Münster)
  • Abstract : This talk reviews some recent results on nonlocal PDEs describing the evolution of a density on discrete graph structures. These structures can arise from applications in the data science field, or they can also be obtained by a numerical discretization of a continuum problem. We also show how those equations are linked to their continuous counterpart in suitable local limits.

MS [00559] DNB Theory and its Applications

room : G605

• [05640] DNB based network fluctuation and application to biology and medicine
  • Format : Talk at Waseda University
  • Author(s) :
    • Luonan Chen (Chinese Academy of Sciences)
  • Abstract : I will talk about the recent progress on the DNB methods as well as the applications to biology and medicine. By exploring the original DNB concept, i.e. critical collective fluctuation (CCF) of the observed variables, we developed a network flow entropy, which can quantify the CCF so as to detect the tipping point before the critical transition from one stable equilibrium to another. The applications include the tipping points of various diseases.

MS [00529] Numerical approximation of geophysical flows

room : G606

• [01506] Monotonicity-preserving interpolation in multilevel schemes for balance laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Antonio Baeza (University of Valencia, Spain)
    • Rosa Donat (University of Valencia)
    • Anna Martínez-Gavara (University of Valencia)
  • Abstract : This work deals with the problem of developing cost-effective multilevel schemes for balance laws, in particular for the shallow water equations in 1D and 2D. We focus on the application of monotonicity-preserving interpolatory techniques as a tool for the recursive computation of the numerical divergence in the different grids, which is a key step on multilevel schemes. Numerical tests confirm that this technique leads to a more robust multilevel code while improving its efficiency.
• [01433] Entropy-stable, positivity-preserving and well-balanced Godunov-type schemes for multidimensional shallow-water system
  • Format : Talk at Waseda University
  • Author(s) :
    • Agnes Chan (CEA Cesta - Université de Bordeaux)
    • Gérard Gallice (CEA Cesta)
    • Raphaël Loubère (Université de Bordeaux)
    • Pierre-Henri Maire (CEA Cesta)
    • Alessia Del Grosso (CEA Cesta - Université de Bordeaux)
  • Abstract : An entropy stable, positivity preserving Godunov-type scheme for multidimensional hyperbolic systems of conservation laws on unstructured grids was presented by Gallice et al. in 2022. A specific feature of their Riemann solver is coupling all cells in the vicinity of the current one, making their solver no longer 1D across one edge. We extend their work to handle source terms, specifically for shallow water equations. The scheme we obtain is well-balanced in 1D and 2D.
• [01511] Numerical solution of a system of conservation laws with discontinuous flux modelling flotation with sedimentation
  • Format : Talk at Waseda University
  • Author(s) :
    • Raimund Bürger (Universidad de Concepción)
    • Stefan Diehl (Lund University)
    • Carmen Marti Raga (Universitat de València)
    • Yolanda Vásquez (Universidad de Concepción)
  • Abstract : Froth flotation is a unit operation used in mineral processing to separate valuable mineral particles from worthless gangue particles in finely ground ores. In this talk, we will present a model for froth flotation, including the drainage of liquid that occurs at the top of the column. We will detail the construction of steady-state solutions and present some results that show the ability of the model to capture steady operation of the flotation device.
• [01508] Implicit and IMEX Lagrange Projection schemes for Ripa model
  • Format : Talk at Waseda University
  • Author(s) :
    • Celia Caballero Cárdenas (Universidad de Málaga)
    • Manuel Jesús Castro Díaz (Universidad de Málaga)
    • Tomas Morales de Luna (Universidad de Málaga)
    • María Luz Muñoz-Ruiz (Universidad de Málaga)
  • Abstract : We consider the one-dimensional system of shallow equations with horizontal temperature gradients, i.e., the Ripa system. We present a numerical approximation of this system based on a Lagrange-Projection type finite volume scheme. We shall consider fully implicit and implicit-explicit versions of the scheme for the Lagrangian step, while the Projection step will always be done explicitly. Several numerical experiments are included in order to illustrate the good behavior of the proposed schemes.

MS [00268] Neumann—Poincaré Operator, Layer Potential Theory, Plasmonics and Related Topics

room : G701

• [03110] Homogenization and the spectrum of the Neumann Poincaré operator
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Bonnetier (Institut Fourier, Université Grenoble Alpes)
  • Abstract : Resonances of metallic nano-particles has been an active topic of investigation in the last decade, as this phenomenon allows localization of strong electro-magnetic fields in very small regions of space, an interesting feature for many applications. Asymptotically as the size of the particles tends to 0, the resonant frequencies are related to the spectral properties of the Neumann-Poincaré operator (NP). In this talk, we discuss the spectrum of that integral operator, when one considers a periodic distribution of inclusions made of metamaterials in a dielectric background medium. The underlying question, is what can happen when many resonant particles interact ? We show that under the assumptions that the inclusions are fully embedded in the periodicity cells, the spectra $\sigma_\varepsilon$ of the NP operators for a collection of period $\varepsilon$ converge to a limiting set composed of 2 parts : the union of the Bloch spectra of NP operators defined over periodicity cells with quasi-periodic boundary conditions and a boundary spectrum associated with eigenfunctions which spend a not too small part of their energy near the boundary. This is joint work with Charles Dapogny and Faouzi Triki.
• [00406] From condensed matter theory to sub-wavelength physics
  • Format : Talk at Waseda University
  • Author(s) :
    • Habib Ammari (ETH Zurich)
  • Abstract : The ability to manipulate and control waves at scales much smaller than their wavelengths is revolutionizing nanotechnology. The speaker will present a mathematical framework for this emerging field of physics and elucidate its duality with condensed matter theory.
• [00777] Eigenvalues of zero order pseudodifferential operators and applications to Neumann-Poincare
  • Format : Online Talk on Zoom
  • Author(s) :
    • Grigori Rozenblioum (Chalmers University of Technology)
  • Abstract : The NP operator for 3D elasticity is a zero order pseudodifferential operator, polynomially compact for a homogeneous material . For such operators we study behavior of eigenvalues converging to the points of essential spectrum and find their relation with the geometry of the body. For a nonhomogeneous material the essential spectrum fills intervals, we study eigenvalues converging to the tips of the essential spectrum.

MS [00108] Recent Advances on Kinetic and Related Equations

room : G702

• [01835] Mixture estimate in fractional sense
  • Format : Talk at Waseda University
  • Author(s) :
    • Kung-Chien Wu (National Cheng Kung University)
  • Abstract : In this talk, we consider the Boltzmann equation with angular-cutoff for very soft potential case. We prove a regularization mechanism that transfers the microscopic velocity regularity to macroscopic space regularity in the fractional sense. A precise pointwise estimate of the fractional derivative of collision kernel, and a connection between velocity derivative and space derivative in the fractional sense are exploited to overcome the high singularity for very soft potential case.
• [03301] Dynamical behaviors in stochastic kinetic flocking models
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiongtao Zhang (Wuhan University)
  • Abstract : We will introduce some recent works on the stochastic flocking models. We are interested in the case when the noise is multiplicative and the flocking interaction vanishes at the far field. We will show rigorous proof of mean-field limit (weak or strong) and the emergence of flocking (conditional or unconditional) under various assumptions.
• [04712] Kinetic study of a gas undergoing resonant collisions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Salvarani (DVRC &University of Pavia)
    • Laurent Boudin (Sorbonne Université)
    • Thomas Borsoni (Sorbonne Université)
    • Julien Mathiaud (CEA & Université de Bordeaux)
    • Alex Rossi (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : We study a kinetic model for a gas undergoing résonant collision. After proving the main properties of the model, we study the compactness of the corresponding linearized Boltzmann operator.

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

room : G703

• [04796] Turbulent solutions of fluid equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexey Cheskidov (University of Illinois at Chicago)
  • Abstract : In the past couple of decades, mathematical fluid dynamics has been highlighted by numerous constructions of solutions to fluid equations that exhibit pathological or wild behavior. These include the loss of the energy balance, non-uniqueness, singularity formation, and dissipation anomaly. Interesting from the mathematical point of view, providing counterexamples to various well-posedness results in supercritical spaces, such constructions are becoming more and more relevant from the physical point of view as well. Indeed, a fundamental physical property of turbulent flows is the existence of the energy cascade. Conjectured by Kolmogorov, it has been observed both experimentally and numerically, but had been difficult to produce analytically. In this talk I will overview new developments in discovering not only pathological mathematically, but also physically realistic solutions of fluid equations.
• [03868] A localized maximum principle and its application to the critical SQG on bounded domain
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsukasa Iwabuchi (Tohoku University)
  • Abstract : We discuss a spectral localization technique for the Dirichlet Laplacian on smooth bounded domain to deal with the fractional Laplacian of the derivative order one and commutator estimates in the framework of Besov spaces. It corresponds to a generalization of the analysis by the dyadic decomposition of the frequency through the Fourier transform in the Euclidean space. As an application, we show the existence of global solutions of the surface quasi-geostrophic equation with the critical dissipation for small initial data.
• [03232] Speeding up Langevin Dynamics by Mixing
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuanyuan Feng (East China Normal University)
    • Gautam Iyer (Carnegie Mellon University)
    • Alexei Novikov (Penn State University)
    • Alexander Christie (Penn State University)
  • Abstract : We add a drift to the Langevin dynamics (without changing the stationary distribution) and obtain quantitative estimates on the mixing time. We show that an exponentially mixing drift can be rescaled to make the mixing time of the Langevin system arbitrarily small.
• [04760] On intermittent strong Onsager conjecture
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hyunju Kwon (ETH Zurich)
  • Abstract : Smooth solutions to the incompressible 3D Euler equations, which are spatially periodic, are known to conserve kinetic energy in every local region. Turbulent flows, however, exhibit anomalous dissipation of kinetic energy, indicating the existence of a weak solution to the Euler equations with dissipation of kinetic energy in some region, but no creation of energy everywhere in the domain. This motivates the strong Onsager conjecture, which combines the original Onsager conjecture with the local energy inequality. In this talk, I will discuss the flexibility side of the $L^3$-based strong Onsager conjecture, adapting to the intermittent nature of turbulence, and introduce a wavelet-based convex integration scheme. The talk is based on a joint work with Matt Novack and Vikram Giri.

MS [02578] Interfaces and Mixing – Conservation Laws and Boundary Value Problems

room : G704

• [05008] Generalized Ideal Momentum Jet Model for Non-Circular Nozzle Geometries in Turbulent Pressure-Atomized Liquid Jets: Theoretical and Experimental Comparison
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fermin Franco-Medrano (Autonomous University of Baja California)
  • Abstract : We propose a generalized mathematical model for turbulent pressure-atomized liquid jets with non-circular nozzles and compare to experimental data. We obtain analytical expressions for the locally homogeneous two-phase flow properties as a function of gauge pressure, nozzle dimensions, and fluid densities. Interestingly, we find that the equations describing elliptical and rectangular nozzles are generalizations of those for circular nozzles. Strong correlation is observed between the experimental data and our model function for the elliptical nozzle jet velocity.
• [03716] Front Tracking Simulations of reshocked Richtmyer-Meshkov Instability
  • Format : Talk at Waseda University
  • Author(s) :
    • Tulin Kaman (University of Arkansas)
    • Ryan Holley (University of Arkansas)
  • Abstract : In this talk, we present an increasingly accurate and robust front tracking method for the numerical simulations of re-shocked Richtmyer-Meshkov Instability (RMI) of an air/SF6 interface. The front-tracking with the weighted essentially non-oscillatory (WENO) schemes are compared with Collins and Jacob (2002) shock tube experiments. We study the effects of high-resolution high-order WENO simulations on the fine detail complex vortex roll-up structures and perform verification and validation studies to achieve good agreement between simulations and experiments.
• [05070] A novel data analysis method for Rayleigh-Taylor mixing
  • Format : Talk at Waseda University
  • Author(s) :
    • Kurt Christian Williams (The University of Western Australia)
    • Snezhana Abarzhi (University of Western Australia)
  • Abstract : A recent data analysis method has shed new light on the isotropy and dynamics of Rayleigh-Taylor mixing; the late-stage behavior of two fluids accelerated against their density gradient. In this talk, we elaborate this data analysis method, which employs Whittle estimates based on a new goodness-of-fit test statistic generated from Monte-Carlo methods. Employing a fitting function from isotropic turbulence, the method finds the isotropy of Rayleigh-Taylor mixing and captures a broad dynamic range.
• [03994] Nonlinear interaction of two nonuniform vortex interfaces and large vorticity amplification
  • Format : Talk at Waseda University
  • Author(s) :
    • Katsunobu Nishihara (Osaka University)
    • Chihiro Matsuoka (Osaka Metropolitan University)
  • Abstract : Vortex dynamics is an important research subject for geophysics, engineering and plasma physics. The nonlinear interaction of two nonuniform vortex interfaces with density stratification is investigated using the vortex sheet model. When a strong vortex sheet approaches a weaker vortex sheet with opposite-signed vorticity, a locally peaked secondary vorticity is induced on the latter sheet. This emerging secondary vorticity results in a remarkable vorticity amplification on the stronger sheet, forming pseudo vortex pairs.

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

room : G709

• [03217] The passive symmetries of machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Soledad Villar (Johns Hopkins University)
  • Abstract : Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one possible representation to another. These are the passive symmetries; they include coordinate freedom, gauge symmetry and units covariance, all of which have led to important results in physics. Our goal is to understand the implications of passive symmetries for machine learning: Which passive symmetries play a role (e.g., permutation symmetry in graph neural networks)? What are dos and don'ts in machine learning practice? We assay conditions under which passive symmetries can be implemented as group equivariances. We also discuss links to causal modeling, and argue that the implementation of passive symmetries is particularly valuable when the goal of the learning problem is to generalize out of sample.
• [03186] Graphons in Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Luana Ruiz (Johns Hopkins University)
  • Abstract : Graph neural networks are successful at learning representations from graph data but suffer from limitations in large graphs. Yet, large graphs can be identified as being similar to each other in the sense that they share structural properties. Indeed, graphs can be grouped in families converging to a common graph limit--- the graphon. In this talk, I discuss how graphons can be used to lay the theoretical foundations for machine learning on large-scale graphs.
• [03178] Graphon Analysis of Graph Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Ron Levie (Technion - Israel Institute of Technology)
  • Abstract : In recent years, graph neural networks have led to ground-breaking achievements in the applied sciences and industry. These achievements pose exciting theoretical challenges: can the success of graph neural networks (GNNs) be grounded in solid mathematical frameworks? In this talk, I will show how to define GNN input domains using graphon analysis, and how such domains lead to a universal analysis of GNNs, with generalization bounds and approximation theorems.
• [03202] Graph Neural Networks on Large Random Graphs: Convergence, Stability, Universality
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolas Keriven (CNRS, IRISA)
  • Abstract : In this talk, we will discuss some theoretical properties of GNNs on large graphs. We assume that the graphs are generated with classical models of random graphs. We characterize the convergence of GNNs as the number of nodes grows. We study their stability to small deformations of the underlying model, a crucial property in traditional CNNs. Finally, we study their approximation power, and show how some recent GNNs are more powerful than others.

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

room : G801

MS [01037] From interacting particles to social dynamics: modelling and analysis of agent-based systems

room : G802

• [04502] Feedback loops in opinion dynamics of agent-based and mean-field models
  • Format : Talk at Waseda University
  • Author(s) :
    • Natasa Conrad (Zuse Institute Berlin)
    • Ana Djurdjevac (Freie Universität Berlin)
    • Jonas Koeppl (Weierstraß-Institut Berlin)
  • Abstract : We present a new mathematical model for co-evolving opinion and social dynamics within a group of mobile, interacting agents. Agents’ movements are governed by their social position and opinions of others, and opinion dynamics are affected by their proximity and opinion similarity. We investigate the behaviour of this ABM in different regimes, study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a PDE.
• [03486] Bounded Confidence Models of Opinion Dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Benjamin Goddard (University of Edinburgh)
    • Grigorios Pavliotis (Imperial College London)
  • Abstract : Bounded confidence models postulate that people only take into account the opinions of others if they are already sufficiently close in 'opinion space' (i.e., they somewhat agree). I will introduce agent-based, ODE, SDE, and PDE models, before focusing on the (nonlocal, nonlinear) PDE case. The main results concern the complex dynamics that arise; the presence of 'phase transitions' under varying parameters; the importance of boundary conditions; and the introduction of 'radicals' with unchanging opinions.
• [04255] Open systems of interacting particles: a probabilistic and multiscale framework
  • Format : Talk at Waseda University
  • Author(s) :
    • Mauricio del Razo (Freie Universität Berlin)
  • Abstract : Open systems are ubiquitous in nature and can be found in a variety of applications, such as chemical reactions, biological processes and even social dynamics. In this talk, we will introduce a comprehensive probabilistic framework for open systems of interacting particles. We will further discuss how our framework can be used to systematically construct consistent multiscale models and simulation schemes by examining how the framework scales up in different limiting regimes, such as system size and large population.
• [04762] Branching and coalescing particles in a singular environemnt
  • Format : Talk at Waseda University
  • Author(s) :
    • Tommaso-Cornelis Rosati (University of Warwick)
  • Abstract : In this talk we analyse how the presence of a random, highly irregular, environment can influence the evolution of particle systems. We study the fluctuations of branching particles in a white-in-space environment, leading to a rough super-process. Further, we describe the scaling limit of a system of Brownian motions driven by a singular drift by means of the so-called Brownian castle. Joint works with N. Perkowski and (in progress) M. Hairer and G. Cannizzaro.

MS [02616] Recent Developments in Applied Inverse Problems

room : G808

• [03045] Source Reconstruction from Partial Boundary Data in Radiative Transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Kamran Sadiq (Johann Radon Institute for Computational and Applied Mathematics (RICAM))
  • Abstract : This talk concerns the source reconstruction problem in a transport problem through an absorbing and scattering medium from boundary measurement data on an arc of the boundary. The method, specific to two dimensional domains, relies on Bukgheim’s theory of A-analytic maps and it is joint work with A. Tamasan (UCF) and H. Fujiwara (Kyoto U).
• [03961] Numerical challenges to optical tomography by the stationary radiative transport equation
  • Format : Talk at Waseda University
  • Author(s) :
    • I-Kun Chen (National Taiwan University)
    • Hiroshi Fujiwara (Kyoto University)
    • Daisuke Kawagoe (Kyoto University)
  • Abstract : We discuss quantitative feasibility of optical tomography based on the stationary radiative transport equation which is a mathematical model of particle migration with absorption and scattering by medium. The key idea is the use of discontinuity of its solution induced by a proper boundary condition and discontinuous Galerkin methods. Numerical examples are exhibit to show a possibility of reconstruction of the attenuation coefficient without a priori information on the scattering kernel.
• [04301] Inversion of the momenta X-ray transform of symmetric tensor fields in the plane.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexandru Tamasan (University of Central Florida)
    • Kamran Sadiq (Johann Radon Institute for Computational and Applied Mathematics (RICAM))
    • David Omogbhe (University of Vienna)
    • Hiroshi Fujiwara (Kyoto University)
  • Abstract : The X-ray transform of symmetric tensor fields recovers the tensor field only up to a potential field. In 1994, V. Sharafutdinov showed that augmenting the X-ray data with several momentum $X$-ray transforms establishes uniqueness, with a most recent work (2022) showing stability of the inversion. In this talk, I will present a first reconstruction method, which stably recovers sufficiently smooth symmetric tensor fields compactly supported in the plane. The method is based on the extension of Bukhgeim's theory to a system of A-analytic maps. This is joint work with H. Fujiwara, D. Omogbhe and K. Sadiq.

MS [01935] Advances in Inverse Problems and Imaging

room : G809

• [03733] Increasing stability in the linearized inverse Schrodinger potential problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuai Lu (Fudan University)
  • Abstract : Inverse Schrodinger potential problem concerns about the recovery of a potential function in the Schrodinger equation in a bounded domain throught the DtN map. In this talk, we introduce the linearized DtN map, and prove a stability estimate with explicit dependence on wavenumbers. This is an increasing stability result, in the sense that the logarithmic stable term decays when wavenumber increases. The talk is based on joint works with Victor Isakov (Wichita), Mikko Salo (Jyvaskyla), Boxi Xu (SUFE) and Sen Zou (Fudan).
• [03422] High-order boundary integral equation solvers for layered-medium scattering problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Tao Yin (Chinese Academy of Sciences)
  • Abstract : This talk will present our recent works on the fast and highly accurate boundary integral equation (BIE) methods, including the windowed Green function (WGF) method and perfectly-matched-layer (PML) BIE method, for solving the acoustic and elastic wave scattering problems in both two- and three-dimensional layered-medium. 1) The WGF method utilize the free-space fundamental solution to derive the BIEs on the whole unbounded surface which requires to be truncated in practical computing. Based on the solutions due to the scattering by flat surface, a correction strategy is introduced to ensure uniform accuracy for all incident angles. 2) For the half-space and two layered-medium case, the original scattering problem can be truncated onto a bounded domain by the PML. Assuming the vanishing of the scattered field on the PML boundary, BIEs on local defects are derived only in terms of using the PML-transformed free-space Green's function. For the considered two methods, a high-order Chebyshev-based rectangular-polar singular-integration solver is used in numerical implementation. Numerical experiments for both two- and three-dimensional problems are carried out to demonstrate the accuracy and efficiency of the proposed solvers. Potential applications to the inverse problems of reconstructing unbounded surfaces will also be discussed.
• [04333] An inverse boundary value problem for a nonlinear elastic wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jian Zhai (Fudan University)
  • Abstract : We consider an inverse boundary value problem for a nonlinear model of elastic waves. We show that all the material parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric conditions. The proof is based on the construction of Gaussian beam solutions.
• [03434] Inverse random scattering problems for stochastic wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianliang Li (Hunan Normal University)
    • Peijun Li (Purdue University)
    • Xu Wang (Chinese Academy of Sciences)
  • Abstract : Inverse random scattering problems with a random source or potential will be introduced for time-harmonic wave equations. The unknown random source or potential is assumed to be a generalized isotropic Gaussian random field. With information of the data observed in a bounded domain, the strength of the random source or potential is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band almost surely.

MS [00593] Advances in Nonlinear Dynamics

room : F308

• [04300] Optimal linear response for expanding circle maps
  • Author(s) :
    • Gary Froyland (UNSW Sydney)
    • Stefano Galatolo (University of Pisa)
  • Abstract : We consider the problem of optimal linear response for deterministic expanding maps of the circle. To each infinitesimal perturbation of a circle map we consider the response of the expectation of an observation function, and the response of isolated spectral points of the transfer operator. Under mild conditions on the set of feasible perturbations we show there is a unique optimal perturbation. We derive expressions for the unique optimum, and devise a Fourier-based computational scheme.
• [04937] Finite element approximated manifolds for PDEs by the parameterization method
  • Author(s) :
    • Jorge Gonzalez (Georgia Tech)
    • Jason Desmond Mireles James (Florida Atlantic University)
    • Necibe Tuncer (Florida Atlantic University)
  • Abstract : The computation of invariant manifolds for PDEs is significantly challenging over irregular high dimensional domains where the classical Fourier methods are not applicable. This work presents a new framework of interest for practical applications that combines the parameterization method with the classical finite element method. We implement the method for a variety of examples having both polynomial and non-polynomial nonlinearities, on non-convex and not necessarily simply connected polygonal domains.
• [05240] Dynamics of a Hill four-body problem with oblate bodies
  • Author(s) :
    • Wai Ting Lam (Florida Atlantic University)
  • Abstract : Consider a restricted four body problem with three oblate massive bodies, which are assumed to move in a plane under their mutual gravity, and an infinitestimal fourth body to move in the 3-dimensional space under the gravitational influence of the three heavy bodies, but without affecting them. By performing Hill approximation, we study the dynamics and properties of the infinitesimal body in a neighborhood of the smaller body.
• [05259] Parametrisation method for large finite element models of engineering structures
  • Author(s) :
    • Alessandra Vizzaccaro (University of Exeter)
    • Andrea Opreni (Politecnico di Milano)
    • Giorgio Gobat (Politecnico di Milano)
    • Attilio Alberto Frangi (Politecnico di Milano)
    • Cyril Touze' (ENSTA Paris )
  • Abstract : In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced order dynamics on the manifold. The focus of hte talk is on engineering structures, whose spectrum around the fixed point is usually composed of complex conjugate pair of eigenvalues with always negative but small real part. This gives rise to rich dynamical behaviour such as internal resonances, parametric resonances, and superharmonic resonances. The accuracy of the reduction on the slow invariant manifold will be shown on selected examples.

contributed talk: CT057

room : F309

[01924] Mixed Leader-Follower Dynamics

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
• Type : Contributed Talk
• Abstract : The original Leader-Follower (LF) model partitions all agents whose opinion is a number in $[-1,1]$ to a follower group, a leader group with a positive target opinion in $[0,1]$ and a leader group with a negative target opinion in $[-1,0]$. A leader group agent has a constant degree to its target and mixes it with the average opinion of its group neighbors at each update. A follower has a constant degree to the average opinion of the opinion neighbors of each leader group and mixes it with the average opinion of its group neighbors at each update. In this paper, we consider a variant of the LF model, namely the mixed model, in which the degrees can vary over time, the opinions can be high dimensional, and the number of leader groups can be more than two. We investigate circumstances under which all agents achieve a consensus. In particular, a few leaders can dominate the whole population.
• Classification : 37N99, 05C50, 91C20, 93D50, 94C15
• Format : Talk at Waseda University
• Author(s) :
  • Hsin-Lun Li (National Sun Yat-Sen university )
  • Hsin-Lun Li (National Sun Yat-Sen university )

[00995] Convergence of a Normal Map-Based Prox-SGD Method for Stochastic Composite Optimization

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
• Type : Contributed Talk
• Abstract : In this talk, we present a novel stochastic normal map-based algorithm (nor-SGD) for nonconvex composite-type optimization problems and discuss its asymptotic convergence properties. We first analyze the global convergence behavior of nor-SGD and show that every accumulation point of the generated sequence of iterates is a stationary point almost surely and in an expectation sense. The obtained results hold under standard assumptions and extend the more limited convergence guarantees of nonconvex prox-SGD. In addition, based on the Kurdyka-Lojasiewicz (KL) framework and utilizing an adaptive time window mechanism, we establish almost sure convergence of the iterates and derive convergence rates that depend on the KL exponent and the step size dynamics. The techniques studied in this work can be potentially applied to other families of stochastic and simulation-based algorithms.
• Classification : 90C06, 90C15, 90C26
• Format : Talk at Waseda University
• Author(s) :
  • Andre Milzarek (The Chinese University of Hong Kong, Shenzhen)
  • Junwen Qiu (The Chinese University of Hong Kong, Shenzhen)

[02116] Generalized Polyak Step Size for First Order Optimization with Momentum

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
• Type : Contributed Talk
• Abstract : This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.
• Classification : 90C15, 65K05, 90C06
• Format : Online Talk on Zoom
• Author(s) :
  • Xiaoyu Wang (Hong Kong University of Science and Technology)
  • Mikael Johansson (KTH Royal Institute of Technology)
  • Tong Zhang (Hong Kong University of Science and Technology)

[00403] Exact Penalization at Stationary Points of Sparse Constrained Problem

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
• Type : Contributed Talk
• Abstract : Nonconvex sparse optimization problems with the trimmed l1 norm or truncated nuclear norm, which is a penalty function of cardinality or rank constraint, have been actively studied. A unified framework that includes all the existing trimmed l1-penalized problems is introduced. We show that under mild conditions, any d-stationary point of the penalized problem satisfies the corresponding constraint. Our result is superior to almost all existing results, especially from the viewpoint of practice.
• Classification : 90C06, 90C26, 90C30, 90C46, 90C90
• Author(s) :
  • Shotaro Yagishita (Chuo University)
  • Jun-ya Gotoh (Chuo University)

[01157] The boundary domain integral method for boundary value problems with variable coefficients

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
• Type : Contributed Talk
• Abstract : The boundary domain integral equation method is an important tool to formulate (in terms of integral operators) boundary value problems with variable coefficients. Although the theory of boundary domain integral equations has been largely developed, there is a lack of results in numerical implementations. The aim of this talk is to enumerate the different boundary domain formulations for several boundary conditions and present discretizations of the integral equation systems and comparisons between the numerical behavior of the approximated solutions.
• Classification : 31B10, 65Rxx, boundary domain integral methods
• Author(s) :
  • Nahuel Domingo Caruso (National University of Rosario - CIFASIS-CONICET)
  • Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain))

MS [00297] Wave scattering problems: numerical methods with applications

room : F310

• [02173] Fast butterfly compressed Hadamard-Babich integrators for Helmholtz equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianliang Qian (Michigan State University)
    • Yang Liu (Lawrence Berkeley National Laboratory)
  • Abstract : We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. The proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction {on a state-the-art supercomputer at Lawrence Berkeley National Laboratory}.
• [03005] Inverse wave-number dependent source problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Guanghui Hu (Nankai University, Tianjin, China)
  • Abstract : We consider an inverse problem for imaging the support of a wave-number-dependent source function. The source function is given by the Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a necessary and sufficient criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction.
• [04115] The PML-method for a scattering problem for a local perturbation of an open periodic waveguide
  • Format : Talk at Waseda University
  • Author(s) :
    • Andreas Kirsch (Karlsruher Institut für Technologie)
    • Ruming Zhang (Technische Universität Berlin)
  • Abstract : In this talk, we study the convergence of the PML method to approximate wave propagating in an open periodic waveguide. Different from the scattering problem with periodic surfaces, the existence of propagating modes makes things challenging. We apply a complex contour integral method to deal with the difficulty. Finally an exponential convergence of the PML method is proved.
• [03704] A PML method for signal-propagation problems in axon
  • Format : Talk at Waseda University
  • Author(s) :
    • Xue Jiang (Beijing University of Technology)
    • maohui lyu (Chinese Academy of Sciences)
    • Tao Yin (Chinese Academy of Sciences)
    • Weiying Zheng (Chinese Academy of Sciences)
  • Abstract : This talk concerns the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. We derive a two-dimensional neural-signaling model in cylindrical coordinates from the time-harmonic Maxwell's equations. The well-posedness of model is established. Using the PML method, we propose an approximate problem. The well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution are established.

MS [00063] Recent Advances on Nonlocal Interaction Models

room : F311

• [04295] Patterns in block copolymers
  • Format : Talk at Waseda University
  • Author(s) :
    • Stan Alama (McMaster University)
    • Lia Bronsard (McMaster University)
    • Xin Yang Lu (Lakehead University)
    • Chong Wang (Washington and Lee University)
  • Abstract : We study a nonlocal isoperimetric problem for several interacting phase domains which consists of a local interface energy and of a longer-range Coulomb interaction energy. We consider global minimizers on the two-dimensional torus, in a limit in which some of the species have vanishingly small mass. Depending on the relative strengths of the coefficients we may see different structures for the global minimizers. This represents work with S. Alama, X. Lu, and C. Wang.

MS [00336] Recent advances in Optimization methods with applications

room : F312

• [02720] HABITAT LOSS AND COOPERATIVE HUNTING ON A THREE-SPECIES TROPHIC SYSTEM
  • Format : Talk at Waseda University
  • Author(s) :
    • Jorge Duarte (Instituto Superior de Engenharia de Lisboa)
    • Cristina Januário (Instituto Superior de Engenharia de Lisboa)
    • Nuno Martins (Instituto Superior Tecnico)
  • Abstract : Changes in ecosystems progress at a rapid pace mainly due to the climate crisis and human-induced perturbations. Researchers have used mathematical models to understand how species respond to these changes in habitat in order to ultimately forecast species extinctions and develop efficient conservation strategies. Our work highlights the fragility of predators hunting cooperatively under the loss of habitat.
• [02816] Modeling of impulsive perturbations by generalized fractional differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Snehana Hristova (Plovdiv University)
  • Abstract : The main aim is to emphasize on the statement of the impulsive perturbations in fractional differential equations. It will be considered two types of impulses- instantaneous impulses and non-instantaneous ones. To be more general we will consider the generalized proportional fractional derivatives of both Caputo type and Riemann-Liouville type in differential equations. Some existence results as well as stability properties of the solutions will be presented.
• [02710] Necessary conditions to optimize functionals involving a generalized fractional derivative
  • Format : Talk at Waseda University
  • Author(s) :
    • Ricardo Almeida (University of Aveiro)
  • Abstract : In this work we combine two ideas: fractional derivatives of variable order and fractional derivatives depending on another function. With such operators, we develop a variational problem theory by presenting necessary conditions of optimization. The fundamental problem will be addressed, proving an Euler-Lagrange equation, and then other versions will be considered such as the isoperimetric problem or the Herglotz problem. An integration by parts formula is also proven. To end, we provide a numerical tool to solve fractional problems dealing with such fractional derivatives. The main idea is to approach the fractional derivative by an expansion formula in terms of integer order derivatives and then rewrite the fractional problema as a classical one.
• [02725] Herglotz’s Variational Problem involving distributed-order fractional derivatives with arbitrary kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Natália Martins (University of Aveiro)
  • Abstract : In this talk we extend the study of fractional variational problems of Herglotz type for the case where the Lagrangian function depends on distributed-order fractional derivatives with arbitrary smooth kernels, the endpoints conditions, and a real parameter. The fact that the Lagrangian depends on the boundary conditions and an arbitrary parameter is not an artificial generalization, as this formulation is important in many problems, such as in physics and economics.

contributed talk: CT068

room : F401

[00281] Simulation of the mechanical behaviour of steel-concrete-steel structures including concrete voids

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : Numerical tools, including finite element simulations, are considered to investigate the effect of initial voids inside concrete on the mechanical behavior of steel-concrete composite structures in compression. A refined numerical strategy is first defined, including a particular care on the relations between each structural component. Due to high computational cost, progressive numerical simplifications are then discussed to conclude in the most acceptable simplified hypothesis. A parametric study is finally launched and perspectives are discussed.
• Classification : 74-10, 74S05, 74R05, simulation, damage models, structural behaviour
• Format : Talk at Waseda University
• Author(s) :
  • Ludovic JASON (Université Paris-Saclay, CEA, Service d'Études Mécaniques et Thermiques)

[02286] Partially Observable Stochastic Control with Memory Limitation and Mean-Field Approach

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : In this presentation, we describe the difficulties with partially observable stochastic control, POSC, and then propose memory-limited POSC, ML-POSC, to solve them. POSC does not consider memory limitation, which hampers the applications to actual controllers. Furthermore, POSC needs to solve a functional differential equation, which is intractable even numerically. In contrast, ML-POSC explicitly formulates limited memories of controllers. Additionally, ML-POSC reduces a functional differential equation to a partial differential equation by the mean-field control technique.
• Classification : 49N30, 49N80, 49K45, 93E20
• Format : Talk at Waseda University
• Author(s) :
  • Takehiro Tottori (The University of Tokyo)
  • Tetsuya J. Kobayashi (The University of Tokyo)

[01025] EXISTENCE OF OPTIMAL CONTROL FOR TIME VARYING STOCHASTIC DIFFERENTIAL EQUATIONS

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : The work deals with the control problem for linear stochastic time varying system driven by square integrable stochastic process with zero mean and continuous sample paths. The cost functional is considered to be quadratic in the system state and the control. The completion of squares technique is used to establish the existence of optimal control under the family of non-adapted admissible control.
• Classification : 49N05, 49N10, 93C05, 93C40
• Format : Online Talk on Zoom
• Author(s) :
  • Murugan Suvinthra (Bharathiar University)

[01032] Memory event-triggered finite-time fault control for neural networks system

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : By wielding METS, this topic explores finite-time issue for neural networks comprise to actuator failures and deception attack. By engaging Lyapunov function and integral inequality technique, sufficient conditions in the structure of linear matrix inequality assures the asymptotic mean-square finite-time boundedness of the considered model. Ultimately, the capability of the proposed control design is demonstrated through two numerical examples.
• Classification : 93-XX
• Format : Online Talk on Zoom
• Author(s) :
  • Karthick SA (National Tsing Hua University)
  • Bor-Sen Chen (National Tsing Hua University)

[01416] Autonomous controllers for a Swarm of UAVs

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : Self-organization patterns emerge in biological swarms' due to collective interactions from their individuals. This paper presents a set of novel autonomous controllers of the individuals of a swarm of planar unmanned aerial vehicles for the MPC problem. The stabilizing continuous nonlinear controllers of the UAVs gives rise to diverse pattern formation due to the communication that occurs amongst an individual and its neighbors. The controllers' effectiveness is illustrated through computer and numerical simulations.
• Classification : 93-XX, 93-10, 93Dxx, 93D05
• Format : Talk at Waseda University
• Author(s) :
  • Sandeep Ameet Kumar (School of Information Technology, Engineering, Mathematics and Physics, The University of the South Pacific)

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

room : F402

• [03554] Solving Discrete Subproblems of a Trust-Region Algorithm for MIOCP
  • Format : Talk at Waseda University
  • Author(s) :
    • Marvin Severitt (TU Dortmund University)
    • Paul Manns (TU Dortmund University)
  • Abstract : We consider a trust-region algorithm for the solution of control problems, where the control input is an integer-valued function and is regularized with a total variation term in the objective. A class of integer linear programs arises as discretizations of the trust-region subproblems. We discuss how, in the one-dimensional case, the discretized subproblems can be solved with a graph-based approach and how the information obtained can be used for the two-dimensional case.
• [03555] Regularization and outer approximation for optimal control problems in BV
  • Format : Talk at Waseda University
  • Author(s) :
    • Annika Müller (TU Dortmund University)
    • Christian Meyer (TU Dortmund University)
  • Abstract : We consider optimal control problems with a constraint on the TV-seminorm of the control. We replace the TV-seminorm by a regularized version and solve the resulting optimization problems with an outer approximation algorithm. We prove convergence of the algorithm to the globally optimal solutions, which in turn converge to the optimal solution to the original problem as the regularization parameter vanishes.
• [03256] On integer optimal control problems with total variation regularization
  • Format : Talk at Waseda University
  • Author(s) :
    • Jonas Marko (BTU Cottbus-Senftenberg)
    • Gerd Wachsmuth (BTU Cottbus-Senftenberg)
  • Abstract : We investigate integer optimal control problems of the form $$ \text{Minimize}\quad F(u) + \beta \text{TV}(u)\quad \text{s.t.}\quad u(t)\in\{\nu_1,\dots,\nu_d\}\subset\mathbb{Z}\text{ for a.a. }t\in(0,T)$$ with $\beta>0$. The contribution $F$ is assumed to be differentiable and could e.g. realize the tracking of the state given by an ODE or PDE dependent on $u$. We show local optimality conditions of first and second order as well as non-local optimality conditions. Also, we will calculate numerical solutions exemplary on two specific control problems.
• [04006] Non-uniform Grid Refinement for the Combinatorial Integral Approximation
  • Format : Talk at Waseda University
  • Author(s) :
    • Christoph Hansknecht (TU Clausthal)
    • Paul Manns (TU Dortmund University)
  • Abstract : We examine mixed-integer optimal control problems (MIOCP) with a discrete-valued control variable distributed on a two-dimensional domain. We compute integral controls by rounding fractional ones according to the combinatorial integral approximation (CIA) framework with switching costs modeling total variation. The rounding problem becomes computationally challenging in two dimensions, leading us to examine both heuristic and exact solution approaches, reducing the number of problem variables based on non-uniform grid refinements.

MS [01167] Recent development in mean field control and learning

room : F403

• [04658] Actor-critic learning for mean-field control in continuous time
  • Format : Talk at Waseda University
  • Author(s) :
    • HUYEN PHAM (Université Paris Cité )
    • Noufel Frikha (Université Paris 1)
    • Maximilien Germain (Morgan Stanley )
    • Mathieu Laurière (NYU Shanghai)
    • Xuanye Song (Université Paris Cité)
  • Abstract : We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function, which is amenable to actor-critic type algorithms, where the value functions and the policies are learnt alternately based on observation samples of the state and model-free estimation of the population state distribution, either by offline or online learning.
• [04674] Mean-field singular control problem: regularitiy and related mean-field reflected diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Jodi Dianetti (Bielefeld University)
    • Xin Guo (UC Berkeley)
    • Jiacheng Zhang (UC Berkeley)
    • Huyên Pham (Université Paris Cité )
  • Abstract : We study a class of mean-field control problems with singular controls. Such a model represents the limit of the control problems in which a controller can adjust, through a bounded variation process, an underlying diffusion, which in turn affects an n-particle system. Adopting appropriate notions of convexities, we are able to establish the regularity of the value function of the problem and to show the existence of the optimal control. The regularity of the value function allows to characterize the solution of the problem in terms of a related mean-field Skorokhod problem. This consists in keeping the optimally controlled state process in a region prescribed by the derivative of the value function, by using the optimal control in order to reflect the state at its boundary.
• [04752] A non-asymptotic perspective on mean field control
  • Format : Talk at Waseda University
  • Author(s) :
    • Lane Chun Yeung (Columbia University)
    • Daniel Lacker (Columbia University)
    • Sumit Mukherjee (Columbia University)
  • Abstract : We study a class of stochastic control problems in which a large number of players cooperatively choose their drifts to maximize an expected reward minus a quadratic running cost. For a broad class of potentially asymmetric rewards, we show that there exist approximately optimal controls which are decentralized, in the sense that each player's control depends only on its own state and not the states of the other players.
• [05079] Signature SDEs with jumps and their tractability properties
  • Format : Talk at Waseda University
  • Author(s) :
    • Christa Cuchiero (University of Vienna)
    • Francesca Primavera (University of Vienna)
    • Sara Svaluto Ferro (University of Verona)
  • Abstract : Signature-based models have recently entered the field of Mathematical Finance. Relying on recent advances on the signature of càdlàg paths, we introduce here a generic class of jump-diffusion models via so-called signature SDEs with jumps. We elaborate on their tractability properties and show that the signature-based models for asset prices proposed so far can be embedded in this framework. As a special case, we focus on jump-diffusions with entire characteristics, leading to a far-reaching extension of the class of polynomial processes.

MS [00966] Theoretical and computational advances in measure transport

room : F411

• [05484] Neural Optimal Transport for Single-Cell Biology
  • Format : Online Talk on Zoom
  • Author(s) :
    • Charlotte Bunne (ETH Zurich)
  • Abstract : To accurately predict the responses of a patient’s tumor cells to a cancer drug, it is vital to recover the underlying population dynamics and fate decisions of single cells. However, measuring molecular properties of single cells requires destroying them. As a result, a cell population can only be monitored with sequential snapshots, obtained by sampling a few particles that are sacrificed in exchange for measurements. In order to reconstruct individual cell fate trajectories, as well as the overall dynamics, one needs to re-align these unpaired snapshots, in order to guess for each cell what it might have become at the next step. Optimal transport theory can provide such maps, and reconstruct these incremental changes in cell states over time. This celebrated theory provides the mathematical link that unifies the several contributions to model cellular dynamics that we present here: Inference from data of an energy potential best able to describe the evolution of differentiation processes (Bunne et al., 2022), building on the Jordan-Kinderlehrer-Otto (JKO) flow; recovery of differential equations modeling the stochastic transitions between cell fates in developmental processes (Bunne et al., 2023) through Schrödinger bridges; as well as zero-sum game theory models parameterizing distribution shifts upon interventions, which we employ to model heterogeneous responses of tumor cells to cancer drugs (Bunne et al., 2022, 2023).
• [04473] Tensor train approximation of deep transport maps for Bayesian inverse problems.
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiangang Cui (Monash University)
    • Sergey Dolgov (University of Bath)
    • Robert Scheichl (Heidelberg University)
    • Olivier Zahm (Universite Grenoble Alpes, Inria)
  • Abstract : We develop a deep transport map for sampling concentrated distributions defined by an unnormalised density function. We approximate the target distribution as the pushforward of a reference distribution under a composition of transport maps formed by tensor-train approximations of bridging densities. We propose two bridging strategies: tempering the target density, and smoothing of an indicator function with a sigmoids. The latter opens the door to efficient computation of rare event probabilities in Bayesian inference problems.
• [04231] Tensor-train methods for sequential state and parameter learning in state-space models
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiangang Cui (Monash University)
    • Yiran Zhao (Monash University)
  • Abstract : We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor-train (TT) decompositions, we propose new sequential learning methods for joint parameter and state estimation under the Bayesian framework. Our key innovation is the introduction of scalable function approximation tools such as TT for recursively learning the sequentially updated posterior distributions. The function approximation perspective of our methods offers tractable error analysis and potentially alleviates the particle degeneracy faced by many particle-based methods. In addition to the new insights into algorithmic design, our methods complement conventional particle-based methods. Our TT-based approximations naturally define conditional Knothe-Rosenblatt (KR) rearrangements that lead to filtering, smoothing, and path estimation accompanying our sequential learning algorithms, which open the door to removing potential approximation bias. We also explore several preconditioning techniques based on either linear or nonlinear KR rearrangements to enhance the approximation power of TT for practical problems. We demonstrate the efficacy and efficiency of our proposed methods on several state-space models, in which our methods achieve state-of-the-art estimation accuracy and computational performance.
• [05065] Accelerated Interacting Particle Transport for Bayesian Inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • Martin Eigel (WIAS)
    • Robert Gruhlke (FU Berlin)
    • David Sommer (WIAS)
  • Abstract : Ensemble methods have become ubiquitous for solving Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS) and Affine Invariant Langevin Dynamics (ALDI) rely on many evaluations of the forward model, which we try to improve. First, adaptive ensemble enrichment strategies are discussed. Second, analytical consistency guarantees of the ensemble enrichment for linear forward models are presented. Third, a homotopy formalism for involved distributions is introduced.

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

room : F412

MS [00967] Stochastic Dynamical Systems and Applications in Data Science

room : E502

• [02126] Understanding the diffusion models by conditional expectations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yubin Lu (Illinois Institute of Technology)
  • Abstract : We provide several mathematical analyses of the diffusion model in machine learning. The drift term of the backwards sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion. The training process aims to find such a drift function by minimizing the mean-squared residue related to the conditional expectation. We derive a new target function and associated loss and illustrate the theoretical findings with several numerical examples.
• [02127] Early-warning indicator of transition time for noise-induced critical transition of Atlantic Meridional Overturning Circulation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yayun Zheng (Jiangsu University)
  • Abstract : We develop an effective and general early-warning indicator for critical transition. The indicator of most probable transition time based on the critical tube is proposed by Onsager-Machlup method based on a critical tube probability. The approach is applied to investigate the abrupt transition from the strong to the weak mode in a thermohaline circulation model. The indicator of the most probable transition time can provide important insights for predicting future abrupt climate transitions.
• [02128] Solving the Non-local Fokker-Planck Equations by Physics-informed Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Senbao Jiang (Illinois Institute of Technology)
    • Xiaofan Li (Illinois Institute of Technology)
  • Abstract : We present trapz-PiNNs, incorporated with a modified trapezoidal rule recently developed for accurately evaluating fractional Laplacian and solve the space-fractional Fokker-Planck equations in 2D/3D. We demonstrate trapz-PiNNs have high expressive power through predicting solution with low $L^2$ relative error by a variety of numerical examples. The trapz-PiNN is able to solve PDEs with fractional Laplacian with arbitrary $0<\alpha< (0, 2)$ and on rectangular domains. It could be generalized into higher dimensions or other bounded domains.
• [02119] Neural stochastic differential equations for time series forecasting
  • Author(s) :
    • Luxuan Yang (Huazhong University of Science and Technology)
    • Ting Gao (Huazhong University of Science and Technology)
  • Abstract : We propose a model called Lévy induced stochastic differential equation network, which explores compounded stochastic differential equations with alpha-stable Lévy motion to model complex time series data and solve the prediction problem through neural network approximation. We theoretically prove that the convergence of the numerical solution and apply the algorithm to real financial time series data. We provide various evaluation metrics and find the accuracy increases through the use of non-Gaussian Lévy processes.

MS [00754] Regularization models and sampling algorithms in statistics and inverse problems

room : E503

• [03567] Efficient Bernoulli Factory MCMC
  • Format : Talk at Waseda University
  • Author(s) :
    • Dootika Vats (Indian Institute of Technology Kanpur)
    • Flávio Gonçalves (Universidade Federal de Minas Gerais)
    • Krzysztof Łatuszyński (University of Warwick)
    • Gareth Roberts (University of Warwick)
  • Abstract : Accept-reject based Markov chain Monte Carlo (MCMC) algorithms have traditionally utilised acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian posteriors with unknown functional forms. We introduce a new family of MCMC acceptance probabilities that has the distinguishing feature of not being a function of the ratio of the target density at the two points. We present a stable Bernoulli factory that generates events within this class of acceptance probabilities. The efficiency of our methods rely on obtaining reasonable local upper or lower bounds on the target density and we present an application of MCMC on constrained spaces where this is reasonable.
• [03753] Sampling of Student's t and stable priors for edge-preserving Bayesian inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • Felipe Uribe (Lappeenranta-Lahti University of Technology)
  • Abstract : The identification of sharp features in the solution is a critical aspect of many large-scale Bayesian inverse problems. Markov random field (MRF) priors based on heavy-tailed distributions have proven effective in achieving piecewise constant behavior. This study reexamines the use of Student's t and alpha stable MRFs in this context. To facilitate computation of the resulting posterior distribution, we propose a scale mixture formulation of the MRF priors. This formulation has the advantage of expressing the prior as a conditionally Gaussian distribution that depends on auxiliary hyperparameters. We discuss a Gibbs sampler to solve the hierarchical formulation of the Bayesian inverse problem. The approach is illustrated using applications from imaging science.
• [04286] Comparison of pseudo-marginal Markov chains via weak Poincaré inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • Andi Qi Wang (University of Warwick)
    • Christophe Andrieu (University of Bristol)
    • Anthony Lee (University of Bristol)
    • Sam Power (University of Bristol)
  • Abstract : I will discuss the use of a certain class of functional inequalities known as weak Poincaré inequalities to bound convergence of Markov chains to equilibrium. This enables the straightforward and transparent derivation of subgeometric convergence bounds for methods such pseudo-marginal MCMC methods for intractable likelihoods, which have been used extensively in the context of Bayesian Inverse Problems.
• [04985] CUQIpy: Computational Uncertainty Quantification for Inverse Problems in Python
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolai André Brogaard Riis (Technical University of Denmark)
  • Abstract : We present CUQIpy, a versatile open-source Python package for computational uncertainty quantification (UQ) in inverse problems using a Bayesian framework. This talk highlights CUQIpy's high-level modeling framework with concise syntax, enabling intuitive problem specification, and showcasing its efficient sampling strategies, automatic sampler selection, and test problem library. Designed to handle large-scale problems and support various probability distributions, CUQIpy streamlines the UQ process, serving as a powerful tool for a diverse set of inverse problems.

MS [01098] Elucidating theoretical biology and deep learning by algebraic statistics and topology

room : E504

• [04921] Judging unlearnability from structures of deep neural networks for low dimensional inputs
  • Format : Talk at Waseda University
  • Author(s) :
    • Keiji Miura (Kwansei Gakuin University)
  • Abstract : Zhang, Naitzat and Lim (2019) showed that a feedforward ReLU neural network is equivalent to a tropical rational map. Here we visualize the shapes of deep neural network functions by using the tropical algebra and judge its unlearnability of complicated boundaries. Especially, the limitation can be naturally interpreted by the tropical factorization of polynomials for the cases of one-dimensional input.
• [04805] Hit and Run Sampling from the Space of Phylogenetic Trees
  • Format : Talk at Waseda University
  • Author(s) :
    • David Barnhill (Naval Postgraduate School)
    • Ruriko Yoshida (Naval Postgraduate School)
    • Keiji Miura (Kwansei Gakuin University)
  • Abstract : In this presentation we introduce a Markov Chain Monte Carlo (MCMC) Hit and Run (HAR) uniform sampler over a tropically convex space of ultrametrics. This is particularly important because by sampling from the space of ultrametrics, we are sampling from the space of phylogenetic trees, or tree space. This has wide ranging implications to statistical inference relating to drawing inference about the tree space. Specifically, we show how this HAR sampler can be employed to sample over the space of ultrametrics in order to non-parametrically estimate the phylogenetic tree distribution using what we call tropical density estimator (TDE) with the tropical metric. We compare the results of the TDE using the tropical metric against often used density estimation methods using the Billera-Holmes-Vogtman metric to show that TDE is more accurate and computationally less expensive.
• [04960] Approximate Computation of Vanishing Ideals
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Kera (Chiba University)
  • Abstract : The vanishing ideal of points is the set of all polynomials that vanish over the points. The approximate computation of generators has been developed at the intersection of computer algebra and machine learning in the last decade. Computer-algebraic algorithms have a rich theoretical background, whereas machine learning-oriented algorithms are designed for applications such as classification at the cost of some theoretical properties. This talk reviews the development of approximate computation of vanishing ideals.

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

room : E505

• [04693] Machine-learning-based spectral methods for partial differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Panos Stinis (Pacific Northwest National Laboratory)
    • Saad Qadeer (Pacific Northwest National Laboratory)
    • Brek Meuris (University of Washington)
  • Abstract : We use deep neural operators to identify custom-made basis functions for constructing spectral methods for partial differential equations. The custom-made basis functions are studied both for their approximation capability and used to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.
• [03852] Optimal control for fractional order equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Glusa (Sandia National Laboratories)
  • Abstract : We consider adjoint-based optimization for control problems involving fractional-order state equations, applied to the inference of kernel parameters. We will discuss optimality conditions, error estimates and techniques to efficiently explore the parameter space and approximate gradients.
• [04163] Multi-Resolution and FVM inspired Neural Network (MuRFiV-Net) for PDE prediction
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin-Yang Liu (University of Notre Dame)
    • Jian-Xun Wang (University of Notre Dame)
  • Abstract : Predicting physical processes requires modeling complex spatiotemporal dynamics. Traditional numerical methods are expensive in many-query tasks, while data-driven neural networks face issues of high training costs and poor generalizability. Physics-informed deep learning (PiDL) combines numerical methods and deep learning, offering a promising approach to overcome these limitations. This work proposes MuRFiV-Net, a novel PiDL architecture based on a multi-resolution mesh and finite volume method. The merit of MuRFiV-Net is demonstrated on several PDE-governed dynamic systems.

MS [02169] Recent advances on numerical methods for stochastic ordinary differential equations

room : E506

• [03230] Deterministic implicit two-step Milstein methods for stochastic differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongjiong Tian (Shanghai Normal University)
    • Quanwei Ren (Henan University of Technology)
    • Tianhai Tian (Monash University)
  • Abstract : We propose a class of deterministic implicit two-step Milstein methods for solving Itô stochastic differential equations. Theoretical analysis is conducted for the convergence and stability properties of the proposed methods. We derive sufficient conditions such that these methods have the mean-square(M-S) convergence of order one, as well as sufficient and necessary conditions for linear M-S stability of the implicit two-step Milstein methods. Stability analysis shows that our proposed implicit two-step Milstein methods have much better stability property than those of the corresponding two-step explicit or semi-implicit Milstein methods. Numerical results are presented to confirm our theoretical analysis results.
• [03262] A Positivity Preserving Lamperti Transformed Euler-Maruyama Method for Solving the Stochastic Lotka-Volterra Competition Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Yan Li (Southeast university)
    • Wanrong Cao (Southeast University)
  • Abstract : A new positivity preserving numerical scheme is presented for a class of d-dimensional stochastic Lotka-Volterra competitive models, which are characterized by super-linear coefficients and positive solutions. The scheme, dubbed the Lamperti transformed Euler-Maruyama method, approximates the exact solution by integrating a Lamperti-type transformation with an explicit Euler-Maruyama method that has the benefit of being explicit and straightforward to implement. Even though the coefficients of the transformed models grow exponentially and do not satisfy the general monotonicity condition, based on the exponential integrability of the solution, it is proved that the proposed numerical method is of 1/2-order strong convergence. In particular, when matrix A of the model is a diagonal matrix, the first-order strong convergence is also obtained. Without any step size constraints, the method can preserve long-time dynamical properties such as extinction and pth moment exponential asymptotic stability. Numerical examples are given to support our theoretical conclusions.
• [03158] Numerical methods for stochastic singular initial value problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nan Deng (Southeast University)
    • Wanrong Cao (Southeast University)
    • Guofei Pang (Southeast University)
  • Abstract : In this work, we investigate the strong convergence of the Euler-Maruyama method for second-order stochastic singular initial value problems with additive white noise. The singularity at the origin brings a big challenge that the classical framework for stochastic differential equations and numerical schemes cannot work.  By converting the problem to a first-order stochastic singular differential system, the existence and uniqueness of the exact solution is studied. Moreover, under some suitable assumptions,  it is proved that the Euler-Maruyama scheme is of $(1/2-\epsilon)$ order convergence in mean-square sense, where $\epsilon$ is an arbitrary small positive number, which is different from the consensus that the Euler-Maruyama method is  convergent with first order in strong sense when solving stochastic differential equations with additive white noise. While,  it is found that if the diffusion coefficient vanishes at the origin, the convergent order in mean-square sense will be raised to $1-\epsilon$. Our theoretical findings are well verified by numerical examples.
• [03037] Convergence rate in L^p sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shuaibin Gao (Shanghai Normal University)
    • Qian Guo (Shanghai Normal University)
    • Junhao Hu (South-Central University For Nationalities)
    • Chenggui Yuan (Swansea University)
  • Abstract : This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in $\mathcal{L}^p$ sense are shown. Then the tamed Euler-Maruyama scheme to the corresponding particle system is established and the convergence rate in $\mathcal{L}^p$ sense is obtained. Furthermore, combining these two results gives the convergence error between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding.

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

room : E507

• [01560] A totally C^2 quartic splines defined on mixed macro-structures
  • Format : Online Talk on Zoom
  • Author(s) :
    • Salah Eddargani (University of Rome "Tor Vergata")
    • Domingo Barrera (University of Granada)
    • María José Ibáñez (University of Granada)
  • Abstract : This work deals with the construction of normalized B-splines of degree four and C^2 smooth everywhere on triangulations endowed with mixed splits. The main splits involved herein are Powell-Sabin (6-), and Modified Morgan-Scott (10-) splits. With the help of Marsden identity, a family of C^2 quartic quasi-interpolation splines of optimal orders has been provided.
• [01502] Construction of quadratic and cubic orthogonal wB-spline wavelets
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mohamed Ajeddar (MISI Laboratory, Faculty of Sciences and Technology, University Hassan First, Settat, Morocco.)
  • Abstract : The definition and basic properties of $\omega$B-splines, frequently used as primal scaling functions, are introduced, as well as their refinement equation. Then, a method for constructing orthogonal wavelets using $\mathcal{C}^1$ and $\mathcal{C}^2$ $\omega$B-splines is presented.
• [01492] Algebraic Hyperbolic spline interpolation by means of integral values.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mohammed Oraiche (Department of Mathematics, University Hassan First, Settat, Morocco. )
  • Abstract : In this paper, a cubic Hermite spline interpolating scheme reproducing both linear polynomials and hyperbolic functions is considered. The interpolating scheme is mainly defined by means of integral values over the subintervals of a partition of the function to be approximated, rather than the function and its first derivative values. The scheme provided is $C^2$ everywhere and yields optimal order. We provide some numerical tests to illustrate the good performance of the novel approximation scheme.

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

room : E508

• [01317] Selecting Regularization Parameters for Nuclear Norm Type Minimization Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Raymond Honfu Chan (City University of Hong Kong)
    • Kexin Li (Hunan Normal University)
    • Hongwei Li (Captial Normal University)
    • Youwei Wen (Hunan Normal University)
  • Abstract : The reconstruction of low-rank matrix from its noisy observation is a constrained nuclear norm minimization problem, where the constraint bound $\eta$ can be estimated from the noise variance. Its solution can be obtained by the singular value thresholding operator where the thresholding parameter $\lambda$ is the same as the regularization parameter. We derive a closed-form solution for $\lambda$ in terms of $\eta$ which allows us to automatically choose $\lambda$ by the discrepancy principle.
• [01895] A nonconvexly regularized least squares approach for sparsity aware estimation
  • Format : Talk at Waseda University
  • Author(s) :
    • Masao Yamagishi (Tokyo Institute of Technology)
    • Isao Yamada (Tokyo Institute of Technology)
  • Abstract : We present basic ideas and applications of a nonconvexly regularized least squares model ((\text{LiGME model})), which can achieve its overall convexity through strategic tuning of a matrix-valued parameter called the Generalized Moreau Enhancement ((\text{GME})) matrix. The LiGME model can exploit sparsity in a linearly transformed domain. Recent related advancements will also be introduced briefly.
• [02058] Separable Quaternion Matrix Factorization
  • Author(s) :
    • Junjun Pan (The University of Hong Kong)
    • Michael Ng (The University of Hong Kong)
  • Abstract : This presentation proposes a separable low-rank quaternion linear mixed model for polarized signals. The corresponding problem is called Separable Quaternion Matrix Factorization (SQMF). We discussed some properties of matrices that SQMF can decompose. We propose a heuristic algorithm called the quaternion successive projection algorithm to determine the source matrix. To compute the activation matrix, we use the block coordinate descent algorithm. Polarization and spectro-polarimetric images are tested to verify the model's effectiveness.
• [01543] GMRES methods for tomographic reconstruction with an unmatched back projector
  • Format : Talk at Waseda University
  • Author(s) :
    • Ken Hayami (Professor Emeritus, National Institute of Informatics/The Graduate University for Advanced Studies (SOKENDAI))
    • Per Christian Hansen (Technical University of Denmark)
    • Keiichi Morikuni (University of Tsukuba)
  • Abstract : Unmatched pairs of forward and back projectors are common in X-ray CT computations due to the need for fast algorithms that best utilize the computer hardware. We propose using preconditioned GMRES, namely, AB-, BA- GMRES, to handle the unmatched normal equations. They are simple to implement and rely only on available forward and back projectors. Numerical experiments show that they exhibit a desired semi-convergence behavior and are suited for large-scale CT reconstruction problems with noisy data.

MS [00488] Eigenvector-Dependent Nonlinear Eigenvalue Problems: Theory, Algorithms and Applications

room : E603

• [03905] A Self-Consistent-Field Iteration for OCCA
  • Format : Talk at Waseda University
  • Author(s) :
    • Leihong Zhang (Soochow University)
    • Li Wang (University of Texas at Arlington)
    • Zhaojun Bai (University of California, Davis)
    • Rencang Li (University of Texas at Arlington)
  • Abstract : In this talk, we propose an efficient algorithm for solving the orthogonal canonical correlation analysis (OCCA). Within an alternating optimization scheme, a customized self-consistent-field (SCF) iteration for a core trace-fractional sub-maximization over orthogonality constraint is devised and analyzed. The SCF iteration is further extended to deal with the multi-view OCCA. Experiments on real-world applications of multi-view learning will be reported.
• [04633] Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoying Dai (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk, we will introduce our study on the energy minimization model arising in the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We investigate the invariance of the energy functional and the existence of the minimizer of the ensemble Kohn-Sham model. We propose an adaptive two- parameter step size strategy and the corresponding preconditioned conjugate gradient methods to solve the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence for the gradients of the energy functional produced by our algorithms. Numerical experiments show that our algorithms are efficient, especially for large scale metallic systems. In particular, our algorithms produce convergent numerical approximations for some metallic systems, for which the traditional self-consistent field iterations fail to converge. This is a joint work with Dr. Bin Yang and Prof. Aihui Zhou.
• [05119] Convergence of SCF Iteration for Eigenvector-dependent Nonlinear Eigenvalue Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ding Lu (University of Kentucky)
  • Abstract : The self-consistent field (SCF) iteration is a widely used method for solving eigenvector-dependent nonlinear eigenvalue problems (NEPv). Despite its simplicity, SCF is prone to slow convergence and can even fail to converge entirely. Extensive research has been devoted to analyzing the algorithm's convergence, and in this talk, we will share new insights on the local convergence analysis of SCF. First, for NEPv with a unitarily-invariant coefficient matrix, we will establish a precise estimation of the local convergence factor of SCF. This estimation enables us to prove the convergence of a level-shift scheme, which can help address the convergence issues of SCF. Second, for a class of NEPv without the unitary invariance property, we will show how to transform the problem into a unitarily invariant NEPv locally at the eigenbasis of interest. We will then establish the convergence rate of SCF based on this transformed problem. This work is a joint effort with Zhaojun Bai and Ren-Cang Li.
• [04225] Geometric inexact Newton method for generalized singular values
  • Format : Online Talk on Zoom
  • Author(s) :
    • Weiwei Xu (Nanjing University of Information Science and Technology)
    • Michael K. Ng (The University of Hong Kong)
    • Zhengjian Bai (Xiamen University)
  • Abstract : We give new model formulations for computing arbitrary generalized singular value of a Grassmann matrix pair or a real matrix pair, where we need to solve matrix optimization problems with unitary constraints or orthogonal constraints. We propose a geometric inexact Newton-CG method for solving these optimization problems. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method for the complex case. We illustrate its effectiveness by some numerical examples.

MS [02527] AI for Healthcare and Medicine

room : E604

• [03888] Causal inference and machine learning on distributed data
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuji Kawamata (Center for Artificial Intelligence Research, University of Tsukuba)
    • Ryoki Motai (Graduate School of Science and Technology, University of Tsukuba)
    • Yukihiko Okada (Center for Artificial Intelligence Research, University of Tsukuba)
    • Akira Imakura (Center for Artificial Intelligence Research, University of Tsukuba)
    • Tetsuya Sakurai (Center for Artificial Intelligence Research, University of Tsukuba)
  • Abstract : Utilizing distributed data allows for more reliable estimation of conditional average treatment effects. However, it is difficult to share data owing to privacy concerns. To address this issue, we proposed Data Collaboration Double Machine Learning (DC-DML), which can address horizontally and vertically distributed data and provide point and interval estimation. In experiments using synthetic data, we found that DC-DML could lead to more accurate estimation results than when using distributed data individually.
• [05313] Precision Preventive Medicine in Sub-Healthy Population
  • Format : Talk at Waseda University
  • Author(s) :
    • Han-Mo Chiu (National Taiwan University Hospital)
    • Hung-Ju Lin (National Taiwan University Hospital)
  • Abstract : Preventing the onset or progression of non-communicable diseases in sub-health population tremendously impact the population health and the related cost and both primary and secondary prevention play pivotal roles in this aspect. The State-of-the-art digital health and artificial intelligence technologies have been applied widely in the healthcare sector, and are anticipated to play a more proactive role in preventive medicine in terms of risk stratification, adopting clinical, genomic, or metagenomic information, and leveraging lifestyle modification.
• [03660] Medical AI, Biosensors and Privacy
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Kimura (University of Tsukuba)
  • Abstract : As Medical AI is expected to improve health care, there is also a concern regarding collecting personal data via AI devices, including biosensors. Advanced biosensors could read and collect inner physiological, emotional, and sensitive conditions. However, patients cannot control their private information collected with biosensors and, once they become data belonging to a hospital or data collection company, cannot have access to their private information. The associated ethical issues are examined.
• [05312] HeaortaNet: AI for Quantifying Heart Structures on Non-Contrast CT Images
  • Format : Talk at Waseda University
  • Author(s) :
    • Wen-Jeng Lee (Department of Medical Imaging, National Taiwan University Hospital)
  • Abstract : HeaortaNet is an AI model developed by TW-CVAI for the segmentation of pericardium/aorta and calcium/fat quantification on non-contrast chest CT images. This talk introduces the technology, benefits, and real-world applications of CT data from Taiwan's National Health Insurance Administration. Our research aims to enhance patient care by providing an effective tool for identifying and measuring heart disease, ultimately leading to better treatment and outcomes.

MS [00622] Inverse Problems and Imaging

room : E605

• [03917] A paraxial approach for the inverse problem of vibroacoustic imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Teresa Rauscher (University of Klagenfurt)
  • Abstract : Vibroacoustography by means of ultrasound is an imaging method that was developed to achieve higher resolutions while avoiding the drawbacks of scattering and stronger attenuation. High frequency waves that show a strongly preferred direction of propagation are sent into the medium. Therefore, we make use of a paraxial approach to arrive at a system of PDEs that involve space dependent parameters. In this talk, we will deal with the modeling and inverse problem for vibroacoustography.
• [05513] Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Clason (University of Graz)
    • Stanislav Mazurenko (Masaryk University)
    • Tuomo Valkonen (EPN, Quito and University of Helsinki)
  • Abstract : We demonstrate that non-convex non-smooth optimization problems like the Potts segmentation model can be written in terms of generalized conjugates of convex functionals, which can be solved by a conceptually straightforward extension of the primal–dual proximal splitting method of Chambolle and Pock. We show convergence and illustrate these theoretical results numerically on the aforementioned example problem.

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

room : E606

• [03591] The Behaviors of Rupture Solutions for a Class of Elliptic MEMS Equations
  • Author(s) :
    • Yanyan Zhang (East China Normal University)
  • Abstract : We will talk about the rupture solutions of a semilinear elliptic equation $$\Delta u=\frac{\lambda |x|^{\alpha}}{u^p},\quad x\in\mathbb{R}^2\backslash\{0\},u(0)=0,\lambda>0,p>0,\alpha>-2,$$ which derived from fields such as Micro-Electro-Mechanical System(MEMS). The remarkable feature of MEMS equations is the singularity of nonlinear terms. In this talk, we will firstly analysis the classification of all possible singularities at $x=0$ for rupture solutions $u(x)$. In particular, we show that for some $(\alpha,p)$, $u(x)$ admits only the isotropic singularity at $x=0$, and otherwise $u(x)$ may admit the anisotropic singularity at $x=0$. Secondly, global solutions in $\mathbb{R}^2\backslash\{0\}$(their existence and their behavior near $x=\infty$ as well as near $x=0$) are also studied. These results contribute to providing theoretical basis for the design and application of MEMS devices. This is a joint work with Y.J. Guo, F. Zhou and Qing Li.

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

room : E701

contributed talk: CT102

room : E702

[00032] A geometrically preservative semi-adaptive method for the numerical solution of Kawarada equations

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : This presentation concerns the numerical stability and geometric preservations of the numerical solution of Kawarada equation problems. The nonlinear partial differential equations exhibit strong quenching types of singularities that represent a number of key characteristics from industrial and multi-physical applications. A second order semi-adaptive implicit finite difference method will be constructed and investigated. We shall begin with a detailed mathematical analysis of the stability without freezing singular source terms of Kawarada equations in this talk. Preservation features of the solution vector sequences will then be studied. Realistic orders of the convergence will be given via generalized Milne's devices. Finally, computer simulations will be carried out to demonstrate the effectiveness of the theoretical analysis and conclusions.
• Classification : 65M06, 65M12, 65M50, 68U01, 65D18
• Format : Talk at Waseda University
• Author(s) :
  • Qin Sheng (Baylor University)

[00314] The Orthogonal Spline Collocation Method for Parabolic Problems with Interfaces

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : The parabolic problems with interfaces are solved using a method in which orthogonal spline collocation (OSC) is employed for the spatial discretization and the Crank–Nicolson method for the time-stepping. The derivation of the method is described in detail for the case in which cubic monomial basis functions are used in the development of the OSC discretization. The results of extensive numerical experiments involving examples from the literature are presented.
• Classification : 65M06, 65M22, 65M55, 65M70, 35K05
• Format : Talk at Waseda University
• Author(s) :
  • Danumjaya Palla (BITS-Pilani KK Birla Goa Campus)
  • Santosh Kumar Bhal (Centurion University of Technology and Management)
  • Graeme Fairweather (Mathematical Reviews, American Mathematical Society)

[00328] Schrödinger map and Multifractality

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : In this talk, we will explore the richness of the Schrödinger map equation by discussing some recent results on its evolution in both hyperbolic and Euclidean geometrical settings. In the latter case, the equivalent form of the equation describes the motion of a vortex filament, e.g., smoke rings, tornadoes, etc. With numerical, theoretical techniques, we will show that when the filament curve initially has corners, its evolution and the trajectory of its corners exhibit multifractality.
• Classification : 65M06, 28A80, 11L05, 65M20, 35Q55, Mathematical physics, Numerical methods, Schrödinger-type equtaions, Hyperbolic space
• Format : Talk at Waseda University
• Author(s) :
  • Sandeep Kumar (CUNEF University)
  • Luis Vega (Basque Center for Applied Mathematics)
  • Francisco de la Hoz (The University of the Basque Country)

[00104] High order approximation of Caputo-Prabhakar derivative and its application in solving time fractional Advection-Diffusion equation

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : This work aims to devise a high-order numerical scheme to approximate the CaputoPrabhakar derivative of order 0 < α < 1, using an rth degree Lagrange interpolation polynomial, where $3\leq r\in\mathbb{Z^{+}}.$. This numerical scheme can be thought of as an extension of the presented schemes for the approximation of the Caputo-Prabhakar derivative in our previous work \cite{r1}. Further, we adopt the proposed scheme to solve a time-fractional Advection-Diffusion equation with the Dirichlet boundary condition. It is shown that the method is unconditionally stable, uniquely solvable, and convergent with convergence order, $ O(\tau^{r+1-\alpha}, h^{2}), $ where τ and h are the step sizes in the temporal and spatial directions, respectively. Without loss of generality, obtained results are supported by numerical examples for r = 4, 5. \bibitem{r1} Deeksha Singh, Farheen Sultana, and Rajesh K Pandey, Approximation of Caputo Prabhakar derivative with application in solving time fractional advection-diffusion equation, International Journal for Numerical Methods in Fluids. $94(7)(2022)$, pp. 896-919.
• Classification : 65M06, 65M12, Numerical approximation of fractional derivative and its application
• Format : Talk at Waseda University
• Author(s) :
  • DEEKSHA SINGH (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi)
  • Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi)

[00111] A convergent numerical method for time-fractional reaction-diffusion equation

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : This paper design and analyze a robust finite difference scheme for solving a time-fractional reaction-diffusion equation with smooth and non-smooth solutions. The solution of this equation exhibits a weak singularity at the initial time $\mathrm{t}=0$. So we use graded temporal mesh in order to handle the singularity. We discretize the space variable using a cubic polynomial spline difference scheme. Further, the stability and convergence for both the smooth and non-smooth solutions are analyzed separately.
• Classification : 65M06, 65M12
• Format : Online Talk on Zoom
• Author(s) :
  • Anshima Singh (Indian Institute of Technology (BHU) Varanasi)

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

room : E703

• [01407] Nonlinear Preconditioning Strategies Based on Residual Learning for PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Li Luo (University of Macau)
    • Xiao-Chuan Cai (University of Macau)
  • Abstract : We present nonlinearly preconditioned inexact Newton methods for solving highly nonlinear system of algebraic equations from the discretization of PDEs. From a large number of numerical experiments, we observe that when the inexact Newton stagnates or fails to converge, the space of residuals often contains a subspace that is difficult to resolve by Newton iteration. We introduce a learning technique to identify this subspace and then improve the convergence.
• [02019] ENO schemes with adaptive order for solving hyperbolic conservation laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Hua Shen (University of Electronic Science and Technology of China)
  • Abstract : We present a class of ENO schemes with adaptive order for solving hyperbolic conservation laws. The proposed schemes select the optimal polynomial from several candidates that are reconstructed on stencils of unequal sizes by using a novel strategy. In this way, the schemes give high-order accuracy whenever the data is smooth but avoid the Gibbs phenomenon at discontinuities.
• [03281] Energy stable schemes for gradient flows based on the DVD method
  • Format : Talk at Waseda University
  • Author(s) :
    • Jizu Huang (Academy of mathematics and systems science, Chinese academy sciences)
  • Abstract : In this talk, we propose a new framework to construct energy stable scheme for gradient flows based on the discrete variational derivative method. Combined with the Runge--Kutta process, we can build an arbitrary high-order and unconditionally energy stable scheme based on the discrete variational derivative method. The new energy stable scheme is implicit and leads to a large sparse nonlinear algebraic system at each time step, which can be efficiently solved by using an inexact Newton type algorithm. To avoid solving nonlinear algebraic systems, we then present a relaxed discrete variational derivative method, which can construct linear unconditionally second-order energy stable schemes. Several numerical simulations are performed to investigate the efficiency, stability, and accuracy of the newly proposed schemes.
• [01460] Scalable multilevel preconditioners for hybrid-DG discretizations of nonlinear cell-by-cell cardiac models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ngoc Mai Monica Huynh (University of Pavia)
  • Abstract : We present theoretical and numerical results for a scalable and quasi-optimal BDDC preconditioner for Discontinuous Galerkin discretizations of cardiac cell-by-cell models in order to approximate the discontinuous nature of cellular networks. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells/subdomains without influencing the overall discontinuity of the global solution.

contributed talk: CT108

room : E704

[00816] Ultraspherical spectral methods for time-dependent problems

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
• Type : Contributed Talk
• Abstract : Spectral methods solve elliptic partial differential equations (PDEs) numerically. Their main advantage is spectral convergence, i.e., error decays exponentially when the solution is analytic. We present numerical schemes for solving some time-dependent linear PDEs utilizing the ultraspherical spectral method in space and time, thus portraying overall spectral convergence. Moreover, they lead to sparse and well-conditioned linear systems. We compare their performance with existing spectral schemes and explore their parallelization in time.
• Classification : 65M70, 65L05, 35K20, 35L20, 41A10
• Format : Talk at Waseda University
• Author(s) :
  • Avleen Kaur (University of Saskatchewan)
  • S, H. Lui (University of Manitoba)

[00663] Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
• Type : Contributed Talk
• Abstract : In this talk, we first provide a brief introduction to quantum computing from a mathematical perspective. No prior knowledge of quantum computing is necessary. We then introduce a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d of the PDE and the reciprocal of the prescribed accuracy ε and so demonstrate that our quantum Monte Carlo algorithm does not suffer from the curse of dimensionality. This talk is based on a joint work with Yongming Li.
• Classification : 65M75, 91G20, Deep Learning method for nonlinear PDEs
• Format : Talk at Waseda University
• Author(s) :
  • Ariel Neufeld (NTU Singapore)
  • Philipp Schmocker (NTU Singapore)
  • Sizhou Wu (NTU Singapore)

[00934] Slab LU, a sparse direct solver for heterogeneous architectures

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
• Type : Contributed Talk
• Abstract : This talk describes a scalable sparse direct solver for linear systems that arise from the discretization of elliptic PDEs in 2D or 3D. The scheme uses a decomposition of the domain into thin subdomains, or ``slabs''. The general framework is easier to optimize for modern heterogeneous architectures than than traditional multi-frontal schemes. Crucial to the scalability, are novel randomized algorithms that recover structure from matrix-free samples and reduce the dimensionality of large dense matrices.
• Classification : 65M70, 65M55, 65M22, 65M06
• Format : Talk at Waseda University
• Author(s) :
  • Anna Yesypenko (University of Texas at Austin)
  • Per-Gunnar Martinsson (University of Texas at Austin)

[01117] Non-Linear Study of Interaction of Viscous Fingering Instability and Chemical Reaction

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
• Type : Contributed Talk
• Abstract : We investigate a chemically reactive front A+B→C involving the radial miscible displacement in porous media. It is a non-linear phenomenon that is mathematically modeled by Darcy’s law coupled with convection-reaction-diffusion equations. A chemical reaction may result in a change in the viscosity profile, which may lead to the interfacial instability known as viscous fingering, which occurs when a low-viscosity fluid displaces a high-viscosity fluid in a porous medium. The instability enhances the fluid mixing.
• Classification : 76Exx, 76Sxx, 76Vxx
• Format : Talk at Waseda University
• Author(s) :
  • Priya Verma (Indian Institute of Technology Ropar)
  • Manoranjan Mishra (Indian Institute of Technology Ropar)

MS [00194] Recent Progress of Computational Electromagnetics

room : E705

• [03979] Application of POD to solve non linear magnetoquasistatic FE problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stephane Clenet (AMValorArts et Métiers Science and Technology)
    • Thomas Henneron (University of Lille)
    • Theo Delagnes (EdF R&D)
  • Abstract : The Finite Element (FE) method is widely used to build accurate models of electrical devices but leads to the solution of large scale equation systems. To overcome this issue, model order reduction methods, like Proper Orthogonal Decomposition (POD), can significantly reduce the size of the equation system. In the presentation, the principles of POD method will be presented and how it can be applied to reduce FE model of non linear magnetoquasistatics problems. Application examples (transformers, electrical machines….) are given to illustrate the effectiveness of the POD method and also its limitations.
• [04030] BDD-DIAG Preconditioner of the Interface Problem for Magnetostatic Domain Decomposition Analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hiroshi Kanayama (Japan Women's University)
    • Masao Ogino (Daido University)
    • Shin-ichiro Sugimoto (Hachinohe Institute of Technology)
    • Kaworu Yodo (Insight Inc.)
  • Abstract : An iterative domain decomposition method is proposed for numerical analysis of 3-Dimensional linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the Preconditioned Conjugate Gradient procedure and the Hierarchical Domain Decomposition Method which is adopted in parallel computing. Our previously employed preconditioner was the Neumann-Neumann preconditioner. Numerical results showed that the method was only effective for smaller problems. In this paper, we consider its improvement with the Balancing Domain Decomposition DIAGonal scaling (BDD-DIAG) preconditioner.
• [04666] Reduced Order Modeling of a Cage Induction Motor with Skewed Rotor Slots
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yasuhito Takahashi (Doshisha University)
    • Koji Fujiwara (Doshisha University)
    • Kengo Sugahara (Kindai University)
    • Tetsuji Matsuo (Kyoto University)
  • Abstract : A method for deriving a reduced-order model of cage induction motors with skewed rotor slots is investigated based on the multiport Cauer ladder network method. The features of the several formulations for the skewed rotor are discussed, in which the continuity of the bar currents and the space harmonics included in the air-gap flux density waveform are treated differently. The effectiveness of the developed methods is verified from the viewpoints of computational accuracy and cost.
• [05040] Introducing extended finite element approaches in eddy currents analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Shingo Hiruma (Kyoto University)
  • Abstract : In recent years, the evaluation of eddy current losses caused by harmonic components in power supplies has become increasingly important. However, the conventional finite element method requires the conductor region to be divided into fine elements, which results in high computational cost. In this study, we apply the extended finite element approach to high-frequency eddy current analysis and show that accurate analysis can be performed with low computational cost.

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

room : E708

• [04140] Cardiac hemodynamics simulations with fluid-structure interaction and reduced valve modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Miguel A. Fernández (Inria)
    • Oscar Ruz (Inria)
    • Jérôme Diaz (Inria)
    • Marina Vidrascu (Inria)
    • Philippe Moireau (Inria)
    • Dominique Chapelle (Inria)
  • Abstract : The development of efficient physiological simulations of the complete FSI phenomena involved in the heart is a challenging problem. We investigate an hybrid approach which combines FSI in the myocardium with a reduced modeling of the valves. A loosely coupled treatment of the interface coupling facilitates the treatment of the isovolumetric phases. The benefits of the proposed approach are investigated and compared with kinematic uncoupling in simulations of the left heart hemodynamics.
• [03773] Parametric Fluid-structure interaction solvers for haemodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Damiano Lombardi (Inria Paris)
    • Sébastien Riffaud (Inria Paris)
    • Miguel A. Fernández (Inria Paris)
  • Abstract : Data assimilation and uncertainty quantification are essential tasks in numerous realistic applications. They involve a prohibitive computational burden. The goal of the present work is to propose and investigate efficient parametric solvers for Partial Differential Equations describing fluid-structure interaction. The solvers consider parameters as extra variables and enable applications such as parameter estimation and uncertainty quantification. Several formulations will be discussed and numerical experiments will be presented to assess the properties of the methods.
• [04521] Towards developing high-speed cardiac mechanics simulations using a neural network finite element approach
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael S Sacks (University of Texas at Austin)
    • Shruti Motiwale (University of Texas at Austin)
  • Abstract : We have developed a neural network finite element (NNFE) approach for cardiac simulations, which is a physics-based method using a neural network to solve the parametric map and finite elements to define the problem domain. Cardiac simulations were performed to predict the P-V responses of a simulated left ventricle, accounting for active contraction and transmural fiber distributions. Results demonstrate the first application of the NNFE approach at the organ level within clinically relevant timeframes.
• [05099] Modeling Cardiac Fluid-Structure Interaction in the Human Heart
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marshall Davey (University of North Carolina at Chapel Hill)
    • Charles Puelz (Baylor College of Medicine)
    • Simone Rossi (University of North Carolina at Chapel Hill)
    • Margaret Anne Smith (University of North Carolina at Chapel Hill)
    • David R. Wells (University of North Carolina at Chapel Hill)
    • Boyce E. Griffith (University of North Carolina at Chapel Hill)
  • Abstract : Cardiac fluid-structure fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. This talk will detail methods and models for simulating cardiac fluid-structure interaction in a comprehensive, image-based model of the human heart. The talk will highlight key methodological approaches to developing the model along with simulation results demonstrating its ability to generate physiologic outputs, including realistic pressure-volume loops.

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

room : E709

• [03431] Structure-preserving methods for Boltzmann continuous slowing down equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Vincent Bosboom (University of Twente)
    • Herbert Egger (Johannes Kepler Universität)
    • Matthias Schlottbom (University of Twente)
  • Abstract : We discuss the linearized Boltzmann equation (LBE) describing the transport of particles under the influence of the Lorentz force and (inelastic) scattering. For this purpose, we consider the equation in the continuous slowing down approximation (CSDA). We present a high-order discretization of the equation based on a mixed finite element $P_N$ approximation that preserves the energy-conserving/dissipating nature of the different physical processes. Additionally, we provide stability estimates of our discretization and present some numerical examples.
• [03359] Positivity-preserving high-order DG method for weakly compressible two-phase flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Fan Zhang (University of Science and Technology Beijing)
  • Abstract : This work focuses on the development of a high-order DG method for solving a three-equation model of weakly compressible two-phase flows. A novel WENO limiter and a positivity-preserving limiter are designed and applied in the numerical simulations. Moreover, we prove that the proposed method satisfies the uniform-pressure-velocity criterion which is a necessary condition for maintaining an oscillation-free phase interface.

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

room : E710

• [03598] Virtual element methods for Biot--Kirchhoff poroelasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Rekha Mallappa Khot (Monash University)
    • David Mora (Universidad del B\'io-B\'io)
    • Ricardo Ruiz Baier (Monash University)
  • Abstract : We propose and analyse conforming and nonconforming virtual element formulations for the coupling of solid and fluid phases in deformable porous plates. The governing equations consist of one fourth-order equation for the transverse displacement of the middle surface coupled with a second-order equation for the pressure head relative to the solid. The discretisation supports arbitrary polynomial degrees on general polygonal meshes and we design companion operators with orthogonal properties and best-approximation estimate. We derive both a priori and a posteriori error estimates in appropriate norms, and these error bounds are robust with respect to the main model parameters. A few computational examples illustrate the properties of the numerical methods.
• [04832] Analyzing Multi-Dimensional Time-Dependent Solute Transport Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Marius Zeinhofer (Simula Research Laboratory)
    • Rami Masri (Simula Research Laboratory)
    • Miroslav Kuchta (Simula Research Laboratory)
    • Marie Elisabeth Rognes (Simula Research Laboratory)
  • Abstract : We derive and analyze 3D-1D time dependent solute transport models for convection, diffusion, and exchange in and around pulsating vascular and perivascular networks from their 3D-3D counterpart. These models are applicable e.g. for transport in vascularized tissue and brain perivascular spaces. We discuss existence and uniqueness questions, quantify the modelling error, discuss finite element discretizations and present numerical results. Technical key challenges are controlling constants in classical numerical analysis tools, such as Poincaré's inequality.
• [03951] Unfitted finite element methods for PDEs with dynamic interfaces and boundaries
  • Format : Talk at Waseda University
  • Author(s) :
    • Santiago Badia (Monash University)
    • Hridya Dilip (Monash University)
    • Francesc Verdugo (Vrije Universiteit Amsterdam)
    • Pere Antoni Martorell (Universitat Politecnica de Catalunya)
  • Abstract : In this presentation, we will present recent advances in the numerical approximation of PDEs with moving interfaces/boundaries using unfitted finite element methods. We will describe the numerical discretisation of transient problems using unfitted finite elements that are robust with respect to the small cut cell problems. We will design these algorithms for transient problems, e.g., by defining space-time discrete extension operators. We will propose two different ways to design space-time unfitted methods. One approach is a pure space-time formulation, in which our geometries are considered in 4D (for a 3D problem in space). This approach is suitable, e.g., for problems in which the geometry is described via level sets. For complex geometrical representations in terms of oriented surface meshes, we propose a geometrical discretisation framework (for 3D in space) that provides all the quadrature rules needed to integrate our numerical methods on unfitted meshes. The extension of this 3D algorithm to 4D is a challenge. We propose another space-time approach that solves the problem in the time-varying domain by using an extrusion of the 3D problem and a geometrical map. This way, one does not require 4D geometrical algorithms. In time, we consider discontinuous Galerkin spaces. The integration of inter-slab jump terms involves two functions on each side of the interface that are defined on different meshes (the background mesh and the mapped background mesh). In order to exactly compute these integrals, we propose to use intersection algorithms.
• [05346] A two-way coupled Stokes-Biot-transport model
  • Format : Talk at Waseda University
  • Author(s) :
    • Sergio Caucao (Catolica University Concepcion)
    • Xing Wang (University of Pittsburgh)
    • Ivan Yotov (University of Pittsburgh)
  • Abstract : We study mathematical and computational modeling for coupled fluid-poroelastic structure interaction with transport. The model is two-way coupled and nonlinear, with the velocity driving the transport and the concentration affecting the fluid viscosity. We use a Galerkin method, energy estimates, compactness arguments, and fixed point theory to establish well-posedness of the model. We study the finite element approximation of the model and obtain solvability, stability, and error estimates. Computational experiments are conducted to illustrate the theoretical convergence rates and the performance of the method for modeling physical flow and transport phenomena.

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

room : E711

• [05142] Arbitrary order DG-DGLM method for hyperbolic systems of multi-dimensional conservation laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Mi-Young Kim (Inha University)
  • Abstract : An arbitrary order discontinuous Galerkin method with Lagrange multiplier in space and time is proposed to approximate the solution to hyperbolic systems of multi-dimensional conservation laws. Weak formulation is derived through the definition of weak divergence. Weak solution on the edge is characterized as the average of the solutions on the elements sharing the edge. Stability of the approximate solution is proved in a broken $L_2(L_2)$ norm. Error estimates of $O(h^r + k_n^q)$ with $P_r(E)$ and $P_q(J_n)$ elements $(r, q > 1 + d/2)$ are then derived in a broken $L_2(L_2)$ norm, where $h$ and $k_n$ are the maximum diameters of the elements and the time step of $J_n,$ respectively, $J_n$ is the time interval, and $d$ is the dimension of the spatial domain. Some numerical examples are presented.
• [04537] Implementation and Application of Virtual Element Method in FEALPy
  • Format : Talk at Waseda University
  • Author(s) :
    • Huayi Wei
    • HUAYI WEI (Xiangtan University )
  • Abstract : The virtual element method is a novel numerical solution technique for PDEs. It can be considered an extension of the finite element method to polygonal or polyhedral meshes. Due to its novelty, the program implementation of this method differs significantly from that of the traditional finite element method. Unfortunately, there are relatively few open-source program implementations available. FEALPy is an open-source numerical solution algorithm library for PDEs. It is built entirely on Python's basic scientific computing module and provides rich mesh data structures, meshes adaptive algorithms, and partial differential equation numerical discrete algorithms. This report primarily focuses on the design and implementation of the virtual element method in FEALPy, along with several typical application examples.
• [05586] Convergence of an AWG method for indefinite time-harmonic Maxwell equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yingying Xie (Guangzhou University)
    • Liuqiang Zhong (South China Normal University)
    • Ming Tang (South China Normal University)
  • Abstract : In this talk, an adaptive weak Galerkin (AWG) method for indefinite time-harmonic Maxwell equations is studied. Firstly, a residual type a posteriori error estimator is presented and analyzed. Then, a quasi-orthogonality is presented by introducing interpolator operators. And the convergence of AWG algorithm is also proved. Finally, some numerical experiments is provided to support the theoretical results.
• [04955] High order stable generalized finite element method for interface problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Qinghui Zhang (Harbin Institute of Technology, Shenzhen)
  • Abstract : Generalized or Extended Finite Element Methods (GFEM/XFEM) of degree 1 (linear elements) for interface problems have been reported in the literature; they (i) yield optimal order of convergence in energy norm, i.e., O(h), (ii) are stable in a sense that conditioning is not worse than that of the standard FEM, and (iii) are robust in that the conditioning does not deteriorate as interface curves are close to boundaries of underlying elements. However, higher order GFEM/XFEM with the properties (i)-(iii) have not been successfully addressed yet. Various enrichment schemes for GFEM/XFEM based on D or DP_k (D is a distance function or the absolute value of level set function, and P_k is the polynomial basis of degree k) have been reported to obtain higher order convergence, but they are not stable or robust in general; in fact, they even may not yield the optimal orders of convergence. In this talk, we propose a stable GFEM/XFEM of degree 2 (SGFEM2) for the interface problems, where we use the enrichment scheme based on D{1, x, y}, instead of D or D{1,x, y, x^2, xy, y^2} in the literature. We prove that the SGFEM2 yields the optimal order of convergence, i.e., O(h^2), for the interface problems with curved (smooth) interfaces. A local principal component analysis technique is proposed, which ensures that the SGFEM2 is stable and robust. Numerical experiments for straight and curved interfaces have been presented to illuminate these properties.

MS [00840] Efficient and scalable solvers and algorithms for multiscale phenomena

room : E802

• [03815] Overlapping Schwarz methods for Isogeometric analysis based on generalized B-splines
  • Format : Talk at Waseda University
  • Author(s) :
    • Durkbin Cho (Dongguk University)
  • Abstract : Isogeometric analysis (IGA) is an innovative numerical methodology for the solution of partial differential equations (PDEs), introduced by Hughes, that potentially allows for a direct connection with CAD, thus providing a much easier and exact representation of the computational domain in a wide range of applications. Generalized B-splines (GB-splines) are a special class of Tchebycheff B-splines that are smooth piecewise function with sections in more general spaces. GB-splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation. They have been proposed as an attractive tool in isogeometric analysis. Since then, isogeometric analysis based on GB-splines have been studied. In this talk, we present overlapping Schwarz preconditioners for {\sf elliptic} and {\sf biharmonic} problems discretized with isogeometric analysis based on GB-splines. An h-analysis of the proposed preconditioners shows an optimal convergence rate bound. Numerical results in two- and three-dimensional tests confirm our theory and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters.
• [03711] Higher Order Time Integration for EMI Cardiac Electrophysiology Simulations with Nested Subset Selection and BDDC Preconditioning
  • Format : Talk at Waseda University
  • Author(s) :
    • Fatemeh Chegini (Zuse Institute Berlin(ZIB))
    • Martin Weiser (Zuse Institute Berlin(ZIB))
  • Abstract : Cardiac electrophysiology simulations call for adaptive methods due to locality of solution features. Traditional mesh refinement and coarsening approaches incur significant overheads. We investigate a novel approach using nested subset selection for algebraic degrees of freedom in hierarchical spectral deferred correction methods. This enables multi-rate integration with minimal overhead, and reduces the computational cost significantly. We also propose a novel domain decomposition preconditioner of BDDC type for cell-by-cell electrophysiology models and show numerical results.
• [03593] Adaptive BDDC preconditioners for 3D divergence free virtual element discretizations of the Stokes equations.
  • Format : Talk at Waseda University
  • Author(s) :
    • Tommaso Bevilacqua (University of Milan)
    • Franco Dassi (University of Milano-Bicocca)
    • Stefano Zampini (King Abdullah University of Science and Tecnology, )
    • Simone Scacchi (University of Milan)
  • Abstract : The balancing domain decomposition by constraints (BDDC) preconditioners are domain decomposition methods based on the subdivision of the computational domain of a partial differential equation (PDE) into non-overlapping subdomains. We apply BDDC to solve PDEs discretized by Virtual Element Methods (VEM) proving scalability and quasi-optimality of the algorithm. Numerical results with adaptively generated coarse spaces confirm the method's robustness in the presence of large jumps in the viscosity and with high-order VEM discretizations.
• [03487] Efficient solvers for models of personalized whole heart electromechanics
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthias Gsell (Medical University of Graz)
    • Christop Augustin (Medical University of Graz)
    • Karli Gillette (Medical University of Graz)
    • Alexander Jung (Medical University of Graz)
    • Gernot Plank (Medical University of Graz)
  • Abstract : Anatomically accurate computer models of four-chamber electromechanics, which are able to replicate electromechanical function of an individual patient’s heart show high potential for both clinical and industrial applications such as diagnostics, treatment optimization and device development. Methodology used to obtain a first fully mechanistic whole-heart electromechanics models with non-invasively personalized electrophysiology and calibrated mechanical and vascular function will be presented. We demonstrate goodness of fit of the calibrated model, and validation against common physiological principles.

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

room : E803

• [04912] Evaluation of various arithmetic for linear algebra on GPU and FPGA
  • Format : Talk at Waseda University
  • Author(s) :
    • Naohito Nakasato (University of Aizu)
  • Abstract : We present the evaluation of various non-standard floating-point (FP) arithmetic for linear algebra. We accelerate matrix multiplication in 128-bit FP arithmetic on both GPU and FPGA. Also we evaluate other FP format such as POSIT and reduced precision FP arithmetic. We discuss the energy efficiency and the numerica accuracy of the non-standard FP arithmetic on GPUs and FPGA accelerators for dense matrices.
• [05094] Using quad-precision numbers for preconditioner of domain decomposition method
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Kawai (Toyo University)
    • Masao Ogino (Daido University)
    • Ryuji Shioya (Toyo University)
  • Abstract : Domain decomposition method with BDD preconditioner is one of the effective parallelization methods for the finite element method. Coarse grid correction in BDD handles a medium-sized linear system, which could be bottleneck in parallel environment. To accelerate this step, the inverse approach is adopted. It replaces foward and back substitution to parallel matrix vector multiplication. Double-double is utilized to preserve the accuracy of the inverse matrix.

MS [00455] Recent Development of Theory and Algorithms of Scientific Machine Learning

room : E804

• [05474] Monte Carlo neural networks: Stochastic gradient descent learns random variables
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sebastian Becker (ETH Zurich)
    • Arnulf Jentzen (The Chinese University of Hong Kong, Shenzhen & University of Münster)
    • Marvin Müller (2Xideas Switzerland AG)
    • Philippe von Wurstemberger (ETH Zurich & The Chinese University of Hong Kong, Shenzhen)
  • Abstract : In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. Here we introduce a new approximation strategy for such parametric approximation problems where we employ stochastic gradient descent not to train parameters of standard neural networks (NNs) but instead to learn random variables appearing in Monte Carlo approximations. The proposed approach achieves in the tested examples much high approximation precisions than standard NNs.
• [01329] Deep adaptive basis Galerkin method for evolution equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yiqi Gu (University of Electronic Science and Technology of China)
    • Michael K. NG (The University of Hong Kong)
  • Abstract : We study deep neural networks (DNNs) for solving high-dimensional evolution equations. Unlike other existing methods (e.g., the least square method) that simultaneously deal with time and space variables, we propose a deep adaptive basis approximation structure. On the one hand, orthogonal polynomials are employed to form the temporal basis to achieve high accuracy in time. On the other hand, DNNs are employed to form the adaptive spatial basis for high dimensions in space.
• [01635] Identifying reaction channels via reinforcement learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Senwei Liang (Lawrence Berkeley Laboratory)
  • Abstract : Reactive trajectories between metastable states are rare yet important in studying reactions. This talk introduces a new method to identify the reaction channels where reactive trajectories occur frequently via reinforcement learning (RL). The action function in RL learns to seek the connective configurations based on reward from simulation. We characterize the reactive channels by data points sampled by shooting from the located connective configurations. These data points bridge stable states and cover most transition regions of interest, enabling us to study reaction mechanism on narrowed regions rather than entire configuration space.
• [03340] Finite Expression Methods for Discovering Pyhsical Laws from Data
  • Format : Online Talk on Zoom
  • Author(s) :
    • chunmei wang (University of Florida)
  • Abstract : The speaker will present the finite expression method (FEX) for discovering the governing equations of data. By design, FEX can provide physically meaningful and interpretable formulas for physical laws compared to black-box deep learning methods. FEX only requires a small number of predefined operators to automatically generate a large class of mathematical formulas. Therefore, compared to existing symbolic approaches, FEX enjoys favorable memory cost and can discover a larger range of governing equations while other methods fail, as shown by extensive numerical tests.

MS [00153] Recent Advances on Inverse Analysis

room : E811

• [01421] Tidal current estimation based on the extended Kalman filter FEM
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahiko Kurahashi (Nagaoka University of Technology)
  • Abstract : In this presentation, some numerical results of tidal current estimation analysis for Tokyo bay model will be shown. The shallow water equation is introduced as the governing equation, and the discretized equation is employed as the system equation in the extended Kalman filter FEM. Numerical results will be compared with the result based on the normal Kalman filter FEM, and the superiority of extended Kalman filter FEM will be shown.
• [01427] Optimal shape design of auxetic structures with periodicity
  • Format : Talk at Waseda University
  • Author(s) :
    • Jin-Xing Shi (Komatsu University)
  • Abstract : Auxetic structures indicate structures with negative Poisson’s ratio. To achieve their best auxetic performance, in this work, optimal shape design of periodic auxetic structures is performed for identification of the negative Poisson’s ratio based on a gradient-based shape optimization method and the homogenization method. Numerical design examples are given to confirm the validity and efficiency of the proposed optimization approach. The present work aims to help design auxetic structures in industrial applications.
• [01428] Density-based topology optimization using a modified optimality criteria method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Masayuki Kishida (National Institute of Technology (KOSEN), Gifu College)
    • Takahiko Kurahashi (Nagaoka University of Technology)
  • Abstract : In this study, we present the density-based topology optimization for minimizing equivalent stress using our developed modified optimality criteria method. The method is an update method for density that incorporates the concepts of Newton's method for the conventional optimality criteria method. The number of arbitrary constants required for topology optimization can be reduced by using our proposed method. In this presentation, p-norm is employed for the performance function and several numerical results will be presented.
• [03034] Shape Design Problems Considering Fluid-Structure-Interactive Fields
  • Format : Talk at Waseda University
  • Author(s) :
    • Eiji Katamine (National Institute of Technology, Gifu College)
    • Yashushi Yoshida (Gifu University)
  • Abstract : This paper presents numerical solution to a shape design of stationary fluid-structure-interactive fields. The minimization problem for total dissipation energy in the viscous flow field and the mean compliance minimization problem in order to achieve stiffness maximization in the structural field are considered for the shape optimization. Numerical analysis program for the shape design is developed by using FreeFEM, and the validity of proposed method is confirmed by results of 2D numerical analyses.

MS [00211] Mathematics of Geometric Deep Learning

room : E812

• [05341] Scattering Message Passing
  • Author(s) :
    • Yuanhong Jiang (Shanghai JiaoTong University)
  • Abstract : Graph neural network (GNN) with message Passing scheme provides an elegant way to process graph data. However, the stability, oversmoothing and oversquashing problems commonly exist in current GNN models. We propose the message passing scheme with scattering transform which is proved theoretically to solve the above problems. In the numerical experiments, the scattering message passing has been validated to be effective compared to SOTA GNN models.
• [05231] Ridgelet Transforms of Neural Network on Manifolds and Hilbert Spaces
  • Author(s) :
    • Sho Sonoda (RIKEN AIP)
  • Abstract : Ridgelet transform is a pseudo-inverse operator of neural networks. Namely, given a function $f \in L^2(\mathbb{R}^m)$, the ridgelet transform $R[f]$ describes how the network parameters should be distributed for the network to represent $f$. In this talk, I will explain a systematic scheme to derive the ridgelet transform by turning the network into a Fourier expression. As applications, we extend the scheme to networks on manifolds $G/K$ and Hilbert spaces $H$, and derive their associated ridgelet transforms.
• [03588] Geometric Diffusion Generative model for protein sequence design
  • Author(s) :
    • Kai Yi (UNSW)
  • Abstract : Propose a new approach to protein sequence design using a diffusion generative model in geometric. This approach has the potential to improve protein properties and has implications for biotechnology and medicine. The method outperforms state-of-the-art methods on benchmark datasets.
• [04999] On oversquashing and expressivity: can GNNs mix variables?
  • Author(s) :
    • Francesco Di Giovanni (University of Cambridge)
  • Abstract : I discuss how Message Passing Neural Networks (MPNNs) model mixing among features in a graph. As a consequence of this approach, I show that MPNNs may need as many layers as the (largest) commute time to model strong mixing of distant nodes in a graph. This allows to derive a measure for over-squashing and to clarify how the latter limits the expressivity of MPNNs to learn functions with long-range interactions.

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

room : E817 -> A715 (changed)

• [02853] Almost Sure Error Bounds for Data Assimilation in Dissipative Systems with Unbounded Observation Noise
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tobias Kuna (Universita dell'Aquila)
    • Jochen Broecker (University of Reading)
    • Lea Oljaca (sustainable investment research)
  • Abstract : Data assimilation is widely used technique, in particular, in the geophysical community. It aims at inferring information of a model by combining incomplete and noisy observations with imperfect models even for very large models and often on the fly in real time. This methods have been extensively studied for a plethora of models, assimilation methods and error terms. In this talk, I will concentrate on how one can treat unbounded noise in the observations not only in expectation, but actually I will present a technique to obtain an a.s. bound. More specifically, we prove that the error is bounded by a finite and stationary processes. We use the simple replacement data assimilation scheme by Hayden, Olson and Titi, see [1] with observations discrete in time, including but not limited to 2D Navier-Stokes equation. The method should extend to more general algorithms like described in [2], as its estimates are based on absorbing and squeezing properties generalizing [3]. The content of the talk was published in [4]. [1] K. Hayden, E. Olson, and E. S. Titi, Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations, Phys. D, 240 (2011), pp. 1416–1425 [2] D. Sanz-Alonso and A. M. Stuart, Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems, SIAM/ASA J. Uncertain. Quantif., 3 (2015), pp. 1200–1220, [3] C. E. A. Brett, K. F. Lam, K. J. H. Law, D. S. McCormick, M. R. Scott, and A. M. Stuart, Accuracy and stability of filters for dissipative PDEs, Phys. D, 245 (2013), pp. 34–45, [4] L. Oljača, J. Bröcker and T. Kuna, Almost sure error bounds for data assimilation in dissipative systems with unbounded observation noise, IAM J. Appl. Dyn. Syst., 17(4) (2018) pp. 2882--2914.
• [04934] Challenges in high dimensional nonlinear filtering
  • Format : Talk at Waseda University
  • Author(s) :
    • Jana de Wiljes (Uni Potsdam)
  • Abstract : The seamless integration of large data sets into computational models is one of the central challenges for the mathematical sciences of the 21st century. Despite the fact that the underlying assumptions do not hold for many applications, Gaussian approximative filters are considered state of the art as they have been successfully implemented for highly nonlinear settings with large dimensional state spaces. Moreover several recent studies have been devoted to showing accuracy of such filters in terms of tracking ability for nonlinear evolution models and we will present one of these results given in the form of distinct bounds for certain filter variants. While the robustness of such Gaussian approximative filters is undeniable there has been considerable aspiration to design filters that can achieve even higher levels of accuracy while maintaining an appropriate level of robustness and stability. Here we will discuss a family of such filters that do not require a parametrization of the posterior distribution and can be combined with traditional Gaussian filters via a likelihood split.
• [02745] Particle Filters for Data Assimilation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dan Crisan (Imperial College London )
  • Abstract : I will present the latest developments of on-going work on the application of particle filters to develop high dimensional data assimilation methodologies.
• [04884] A novel regularity criterion for the 3D Navier-Stokes equations based on finitely many observations.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Animikh Biswas (University of Maryland Baltimore County)
    • Abhishek Balakrishna (University of Maryland Baltimore County)
  • Abstract : We present a novel regularity criterion for the 3D Navier-Stokes equations (NSE) based on finitely many modal, nodal or volume element observations of the velocity field. The proof is based on a data assimilation algorithm utilizing a Newtonian relaxation scheme (nudging) motivated by feedback-control. The observations, which may be either modal, nodal or volume elements, are obtained from a weak solution of the 3D NSE and are collected almost everywhere in time over a finite grid. The regularity criterion we propose follows from our data assimilation algorithm and is hence intimately connected to the notion of determining functionals (modes, nodes and volumeelements). To the best of our knowledge, all existing regularity criteria require knowing the solutionof the 3D NSE almost everywhere in space. Our regularity criterion is fundamentally different fromany preexisting regularity criterion as it is based on finitely many observations (modes, nodes andvolume elements). We further prove that the regularity criterion we propose is both a necessaryand sufficient condition for regularity. Thus our result can be viewed as a natural generalizationof the notion of determining modes, nodes and volume elements as well as the asymptotic trackingproperty of the nudging algorithm for the 2D NSE to the 3D setting.

MS [00479] Advances in clinically-driven AI image reconstruction and processing

room : E818

• [05254] The impact of model-based ML driven CT reconstruction on tumor segmentation and clinical diagnosis
  • Format : Talk at Waseda University
  • Author(s) :
    • Ander Biguri (University of Cambridge)
    • Carola-Bibiane Schönlieb (University of Cambridge)
    • Lorena Escudero (University of Cambridge)
  • Abstract : Machine learning has recently found success in tomographic image reconstruction, particularly CT. This work explores its impact on image quality, but most importantly, how (or if) that image quality translates to clinically relevant parameters, in this case radiomics. The evaluation of the reconstruction quality thus is moved from image quality metrics like SSIM or PSNR to clinically relevant metrics like predictive power of radiomics based tumour analysis.
• [03919] Bringing research advances in imaging sciences into the clinic
  • Format : Talk at Waseda University
  • Author(s) :
    • Ozan Öktem (KTH Royal Institute of Technology)
    • Lorena Escudero (University of Cambridge)
    • Thomas Buddenkotte (Jung Diagnostics GmbH)
    • Cathal McCague (University of Cambridge)
    • Carola-Bibiane Schönlieb (University of Cambridge)
    • Evis Sala (University of Cambridge)
  • Abstract : The talk will survey both scientific and practical challenges associated with making state-of-the-art deep learning methods available to clinicians. It will showcase these challenges in an ambitious setting where one seeks to use an end-to-end deep learning based approach for joint reconstruction and downstream post-processing task, the latter being specific for a clinical use case.
• [02867] Spectral Normalisation of Depthwise Separable Convolutions for Medical Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Christina Runkel (University of Cambridge)
    • Christian Etmann (University of Cambridge)
    • Michael Moeller (University of Siegen)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : An increasing number of models require the control of the spectral norm of convolutional layers of a neural network. While there is an abundance of methods for estimating and enforcing upper bounds on those during training, they are typically costly in either memory or time. In this talk, we introduce a very simple method for spectral normalisation of depthwise separable convolutions, which introduces negligible computational and memory overhead - allowing to control spectral norms for practical relevant applications like medical imaging.
• [05266] Mice PET/CT Dataset Augmentation using a 3D Single Image GAN
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jeremy Kim (Stanford University)
    • Jonathan Fisher (Stanford University)
    • Craig Levin (Stanford University)
  • Abstract : In this study, we applied GANs for 3D mice PET/CT data augmentation; these synthetic mice will be used in deep learning (DL) based preclinical research. The lack of available datasets makes it difficult for researchers to apply DL to solve tasks that involve small-animal datasets, such as emission-based attenuation correction for small-animals PET/MR. We applied the Single-Image GAN (SinGAN) Framework to generate multiple realistic synthetic PET/CT scans of mice from a limited number of examples.

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

room : E819

• [03812] Periodic and homo/heteroclinic solutions of the restricted three-body problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Mitsuru Shibayama (Kyoto University)
  • Abstract : The restricted three-body problem is an important research area that deals with significant issues in celestial mechanics, such as analyzing asteroid movement behavior and orbit design for space probes. We aim to show the existence of periodic and heteroclinic orbits in the planar circular R3BP. To find these orbits, we adopt a variational approach and symmetry.
• [04714] Existence of transit orbits in the restricted three-body problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Taiga Kurokawa (Kyoto University)
    • Mitsuru Shibayama (Kyoto University)
  • Abstract : We discuss the existence of transit orbits with fixed energy in the planar circular restricted three-body problem. In 2005, Moeckel provided sufficient conditions for the existence of transit orbits using the Maupertuis functional. In this talk, we give another sufficient condition using the Lagrange functional. This is joint work with Mitsuru Shibayama.
• [03894] regularizable collinear periodic solutions in the n-body problem with arbitrary masses
  • Format : Talk at Waseda University
  • Author(s) :
    • Guowei Yu (Nankai University)
  • Abstract : For n-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the Schubart orbit, when n=3.
• [03430] Braids and periodic solutions of the planar N-body problem
  • Format : Talk at Waseda University
  • Author(s) :
    • EIKO KIN (Osaka University)
    • Yuika Kajihara (Kyoto University)
    • Mitsuru Shibayama (Kyoto University)
  • Abstract : Periodic solutions of the planar N-body problem determine braids through the trajectory of N bodies. Braids fall into three types: periodic, reducible and pseudo-Anosov. The last type is significant for the study of dynamical systems. In this talk I discuss a family of braid types obtained from periodic solutions, simple choreographies of the chain types by Guowei Yu and multiple choreographic solutions of the planar 2n-body problem by Shibayama.

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

room : E820

MS [00666] Simulations and Algorithms for Materials Sciences

room : D101

MS [00062] Analysis and computation of vortical flows

room : D102

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

room : D401

• [00786] Extending the Gibbon-Fokas-Doering stagnation-point-type ansatz to finite-energy initial conditions: A solution to the Navier-Stokes Millennium Prize Problem?
  • Format : Talk at Waseda University
  • Author(s) :
    • Miguel David Bustamante (University College Dublin)
  • Abstract : The stagnation-point-type solution to the 3D incompressible Navier-Stokes equations found in {Gibbon, Fokas and Doering, (Physica \, D) $\bf 132$, 497 {1999}} produced an infinite family of solutions to the 3D incompressible Euler equations that blow up in a finite time. There is an exact formula for the singularity time as a functional of the initial conditions {Constantin, (Int. \, Math.\, Res.\, Not.) $\bf 2000$, 455 {2000}; Mulungye, Lucas and Bustamante, (J.\, Fluid\, Mech.) $\bf 771$, 468 {2015}; ___ , (J.\, Fluid\, Mech.) $\bf 788$, R3 {2016}}, and the solutions to this and related models are best understood in terms of infinitesimal Lie symmetries {Bustamante, (Phil.\, Trans.\, R.\, Soc.\, A) $\bf 380$, 20210050 {2022}}. The main drawback of these solutions, $\textit{from the viewpoint of the Clay Millennium Prize}$, is that the velocity field depends linearly on the out-of-plane spatial coordinate, and thus the initial condition has infinite energy. In this talk, I will present a way to extend these solutions in order to have an arbitrary dependence on the out-of-plane coordinate, allowing in principle for finite-energy solutions. This extension seems to break the infinitesimal Lie symmetry structure inherent to the previous infinite-energy solutions, so a statement regarding finite-time blowup is not yet available analytically in the finite-energy case. However, the extension allows for a novel numerical attempt at the finite-energy solution, via a hierarchy of systems of coupled 2D partial differential equations, which are much easier to handle than a full 3D problem. I will present results and prospects, and discuss potential applications to real-life experiments.
• [04968] Singularity detection via regularization: Blow-up criteria for 3D Euler and related equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Adam Larios (University of Nebraska-Lincoln)
    • Edriss Titi (Texas A&M University)
    • Isabel Safarik (University of Nebraska-Lincoln)
  • Abstract : The 3D Euler-Voigt equations can be thought of as a regularization of the 3D Euler equations in the sense that they are globally well-posed, and the solutions approximate the solutions to the 3D Euler equations. We describe a blow-up criterion for the 3D incompressible Euler equations based on inviscid Voigt regularization. Therefore, the blow-up criterion allows one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the “better-behaved” 3D Euler-Voigt equations. Analytical and computational results will be discussed. We will also discuss a applications to Navier-Stokes and a recent Voigt-type regularization and blow-up criterion based on the Velocity-Vorticity formulation of the 3D Navier-Stokes equations.
• [02897] Thermalisation in finite-dimensional, inviscid equations of hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Samriddhi Sankar Ray (International Centre for Theoretical Sciences, Tata Institute of Fundamental Research (ICTS-TIFR))
    • Sugan D. Murugan (International Centre for Theoretical Sciences, Tata Institute of Fundamental Research (ICTS-TIFR))
  • Abstract : The question of thermalisation of classical systems with many degrees of freedom is a fundamentally important one in statistical physics. There are several examples of such systems, with explicitly broken integrability, which thermalise. A slightly different class of such systems which are even less understood are the finite-dimensional (Galerkin-truncated) equations of ideal hydrodynamics. The long time solutions of these equations thermalise---characterised by a Gibbs distribution of the velocity field and kinetic energy equipartition amongst its (finite) Fourier modes---by virtue of a phase-space and energy conservation and a simple application of Liouville's theorem. While this property has been long known, the precise mechanisms which trigger such states have only been discovered recently. In this talk we discuss this mechanism and show how there could be ways to prevent the onset of thermalisation and provide a way to tackle the important questions of finite-time blow-up and weak solutions numerically.
• [00758] How advection delays singularity formation in the Navier-Stokes equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Koji Ohkitani (RIMS, Kyoto University)
  • Abstract : We numerically study the Navier-Stokes equations modified by depleting advection. In the inviscid case some solutions blow up in finite time when advection is discarded, Constantin 1986. We use a pair of orthogonally offset vortex tubes as initial data. We show that: 1) blowup persists even with viscosity when advection is discarded, and 2) the time of breakdown increases logarithmically as we reinstate advection, consistent with the regularity of the Navier-Stokes equations.

MS [00118] On mathematical modeling and simulation of droplets

room : D402

• [02884] Capillary rebound of droplets impacting onto a liquid bath
  • Format : Talk at Waseda University
  • Author(s) :
    • Radu Cimpeanu (University of Warwick)
    • Luke F.L. Alventosa (Brown University)
    • Daniel M. Harris (Brown University)
  • Abstract : We study millimetric drops impacting onto the free surface of a quiescent bath, a canonical scenario which provides excellent opportunities to co-develop experimental, analytical and computational techniques in a rich multi-scale context. We find that increases in gravitational forces or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. The inertio-capillary limit defines an upper bound on the coefficient of restitution, depending only on the Weber number.
• [01510] Motion of Liquid Droplets in Gas Channels
  • Format : Talk at Waseda University
  • Author(s) :
    • Marina Chugunova (Claremont Graduate University )
  • Abstract : Understanding of liquid droplets dynamics in gas channels is critical for improvement of performance and durability of the catalysts made of a dense porous material. We derive a mathematical model to study how different surface properties and operating conditions affect the dynamics of liquid droplets. We present multiple numerical simulations of a single droplet dynamics for different sizes of droplets and different choices of contact angles. We show the influence of an air flow to a thin liquid film and analyze traveling wave type solutions. Joint work with A. Nadim, Y Ruan, and R Taranets
• [02886] On the immersed boundary method in simulating liquid-gas interfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Pejman Sanaei (Georgia State University)
    • Michael Y. Li (New York University)
    • Daniel Chin (New York Universty)
    • Charles Puelz (Baylor College of Medicine)
  • Abstract : In this work, we use the immersed boundary method with four extensions to simulate a moving liquid-gas interface on a solid surface. We first define a moving contact line model and implements a static-dynamic friction condition at the immersed solid boundary. The dynamic contact angle is endogenous instead of prescribed, and the solid boundary can be non-stationary with respect to time. Second, we simulate both a surface tension force and a Young’s force with one general equation that does not involve estimating local curvature. In the third extension, we splice liquid-gas interfaces to handle topological changes, such as the coalescence and separation of liquid droplets or gas bubbles. Finally, we re-sample liquid-gas interface markers to ensure a near-uniform distribution without exerting artificial forces. We demonstrate empirical convergence of our methods on non-trivial examples and apply them to several benchmark cases, including a slipping droplet on a wall and a rising bubble.

MS [01933] Fluid-structure interactions in Stokes flows

room : D403

• [02866] Soft magnetic microrobots move more efficiently with a flat tire
  • Format : Talk at Waseda University
  • Author(s) :
    • Brennan Sprinkle (Colorado School of Mines)
    • Yan Gao (Colorado School of Mines)
    • David Marr (Colorado School of Mines)
    • Ning Wu (Colorado School of Mines)
  • Abstract : I'll discuss the rolling of active Pickering emulsions - small droplets (~10-100 um) covered in smaller (~1um) active particles that can be rolled along a surface by an external, AC magnetic field. Curiously, these droplets roll much faster and more efficiently when they have a larger area of contact with the confining surface. I'll describe experiments done by collaborators to validate this behavior and numerical simulations that I developed to quantify it.
• [05297] Bacterial swarming above surfaces with friction
  • Format : Talk at Waseda University
  • Author(s) :
    • Enkeleida Lushi (New Jersey Institute of Technology)
  • Abstract : We present a mathematical model and numerical simulations for the collective dynamics of swimming bacteria above surfaces with and without friction. The bacteria are modeled as self-propelling force-dipole ellipsoids that interact with each-other and the surface through hydrodynamics and direct collisions. The conditions for when the surface friction is sufficient to render an individual swimmer immobile are determined, as well as the swimmer density needed to collectively generate fluid flow disturbances that are strong enough to help regain mobility. Analysis of the characteristics of the emerging collective dynamics reveals a phase diagram of qualitatively distinct regimes for varying swimmer shape and population densities. Lastly, we compare our findings with recent experimental results of swarming Bacillus subtilis mutants.

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

room : D404

• [04664] On some contact angle problems in fluid dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mathias Wilke (Martin-Luther-University Halle-Wittenberg)
  • Abstract : In this talk, we consider some contact angle problems for the dynamic of fluids and discuss several topics such as existence and uniqueness of solutions as well as their qualitative behaviour.
• [00258] The relativistic Euler equations with a physical vacuum boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Marcelo Mendes Disconzi (Vanderbilt University)
  • Abstract : We consider the relativistic Euler equations with a physical vacuum boundary and an equation of state $p(\varrho)=\varrho^\gamma$, $\gamma > 1$. We establish the following results. i. local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and continuous dependence on the data; ii. low regularity solutions: our uniqueness result holds at the level of Lipschitz velocity and density, while our rough solutions, obtained as unique limits of smooth solutions, have regularity only a half derivative above scaling; iii. stability: our uniqueness in fact follows from a more general result, namely, we show that a certain nonlinear functional that tracks the distance between two solutions, in part by measuring the distance between their respective boundaries, is propagated by the flow; iv. we establish sharp, essentially scale invariant energy estimates for solutions; v. we establish a sharp continuation criterion, at the level of scaling, showing that solutions can be continued as long as the velocity is in $L^1_t Lip_x$ and a suitable weighted version of the density is at the same regularity level. This is joint work with Mihaela Ifrim and Daniel Tataru.

contributed talk: CT152

room : D405

[01192] Application of MUSIC Algorithm in Microwave Imaging Without Switching Device

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : Although the MUltiple SIgnal Classification (MUSIC) algorithm has demonstrated suitability as a microwave imaging technique for identifying unknown anomalies, there is a fundamental limit that it requires a switching device to be used which permits a dipole antenna for signal transmission and reception. In this contribution, we design a MUSIC-type imaging function and explore its mathematical structure. Considering the investigated structure, we confirm that the imaging performance is highly dependent on the antenna arrangement and suggest an optimal antenna arrangement to improve the imaging performance. Simulation results with real-data are displayed to support the theoretical result.
• Classification : 78A46
• Format : Talk at Waseda University
• Author(s) :
  • Won-Kwang Park (Kookmin University)

[00780] Mathematical Modelling of Bidirectional Transport System

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : One of the major issues in real life is evolving vehicular traffic. Recently the totally asymmetric simple exclusion process (TASEP) has been utilized to investigate transport systems. We present a novel generalized two-lane TASEP model with bidirectional movement under a new kind of symmetric coupling between lanes to gain insight into the evolutionary traffic dynamics. We employ the mean-field theory to solve the system theoretically and validate theoretical outcomes through extensively performed Monte Carlo Simulations.
• Classification : 82DXX, 82-10, 82M20, 82M60, 82M31, Non-equilibrium Statistical Mechanics, Mathematical Modelling and Simulation, Partial Differential Equations, Stochastic Processes
• Format : Talk at Waseda University
• Author(s) :
  • Atul Kumar Verma (NIT Trichy, India)

[00678] Monitoring distributed strains on solid surfaces by electrical impedance tomography

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : Measuring strains induced by loads on structural elements is a key component of structural health monitoring $(\text{SHM})$. Current methods are mostly based on localized measurements and offer limited information on distributed strain. We present results on distributed strain monitoring based on electrical impedance tomography $(\text{EIT})$ imaging of a painted, elastic surface coating. The method can extract information on the surface strain field by solving the EIT inverse problem based on measured data.
• Classification : 78A46, 78A55, 74Bxx
• Format : Talk at Waseda University
• Author(s) :
  • Mikko Räsänen (University of Eastern Finland)
  • Aku Seppänen (University of Eastern Finland)
  • Moe Pour-Ghaz (North Carolina State University)
  • Jari Kaipio (University of Eastern Finland)

[01391] Defect reconstruction in waveguides using resonant frequencies

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : This talk aims at introducing a new multi-frequency method to reconstruct width defects in waveguides. Different inverse methods already exist, but those methods are not using some frequencies, called resonant frequencies, where propagation equations are known to be ill-conditioned. Since waves seem very sensible to defects at these particular frequencies, we exploit them instead. Given partial wavefield measurements, we reconstruct slowly varying width defects in a stable way and provide numerical comparisons with existing methods.
• Classification : 78A46, 35B34
• Format : Talk at Waseda University
• Author(s) :
  • Angèle Niclas (CMAP - École Polytechnique )

[02580] Topological-sensitivity framework for detecting perfectly-conducting buried objects in layered media

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : Identification of the location of a scattering object from its recorded scattering signature is one of the inverse problems that finds many applications in non-destructive testing. A typical application is a detection and removal of buried land mines. The underlying problem is linked to the discovery of buried objects in a two-layered medium. We present a topological derivatives-based algorithm for detecting a perfectly conducting object in the lower layer of a two-layer unbounded 3D background medium using electromagnetic plane waves. Since the underlying problem is highly ill-posed, most of the existing methods that are qualitative turn out to be quite sensitive to unavoidable medium and measurement noises. Our focus is on designing a direct algorithm based on the topological derivative of an L2-discrepancy function. We perform a rigorous analysis of the proposed algorithm and debate its localization and stability features regarding random medium and measurement noises.
• Classification : 78A46, 65J20, Inverse scattering, Maxwell’s equations, Electromagnetic imaging, Topological derivative, Localization, Resolution analysis, Stability analysis, Medium noise, Measurement noise.
• Format : Talk at Waseda University
• Author(s) :
  • Aibike Nagyz (Nazarbayev University)
  • Abdul Wahab (Nazarbayev University)

MS [00915] The mathematics of quantum interaction models

room : D407

• [03466] On the Weyl spectral counting function of certain semiregular global systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alberto Parmeggiani (University of Bologna)
  • Abstract : In this talk I will be discussing some recent work with Marcello Malagutti about the spectral asymptotics of certain global semiregular pseudodifferential systems. The class considered here contains important models such as the Jaynes-Cummings system, which is fundamental in Quantum Optics, but also models of geometric differential complexes over $\mathbb{R}^n$. We give the asymptotics of the Weyl spectral counting functions in terms of the principal, semiprincipal and subprincipal symbols of the system, along with (time permitting) quasi-clustering properties of the spectrum.
• [03916] On The Spectral Zeta Function Of Second Order Semiregular Non-Commutative Harmonic Oscillators
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marcello Malagutti (University of Bologna)
  • Abstract : In this talk we give a meromorphic continuation of the spectral zeta function for semiregular Non-Commutative Harmonic Oscillators (NCHO). By “semiregular system” we mean a pseudodifferential systems with a step $−j$ in the homogeneity of the $j$th-term in the asymptotic expansion of the symbol. As an application of our results, we first compute the meromorphic continuation of the Jaynes-Cummings (JC) model spectral zeta function. Then we compute the spectral zeta function of the JC generalization to a 3-level atom in a cavity. For both of them we show that it has only one pole in 1.

MS [00893] Higher Order-type Optimization Methods for Machine Learning

room : D501

• [03305] An efficient skipping BFGS algorithm with nice Hessian correction properties
  • Author(s) :
    • Yu-Hong Dai (AMSS)
  • Abstract : An efficient skipping BFGS algorithm is designed with nice Hessian correction properties. We analyze the skipping method from the perspective of improving quasi-Newton equations by operators and derive stronger quadratic termination properties. Global convergence and superlinear convergence results are established under classical assumptions. Numerical experiments illustrate the efficiency of the proposed method compared with the standard BFGS method.
• [02797] An Overview of Stochastic Quasi-Newton Methods for Large-Scale Machine Learning
  • Author(s) :
    • Tiande Guo (University of Chinese Academy of Sciences)
    • Yan Liu (Naikai University)
    • Congying Han (University of Chinese Academy of Sciences)
  • Abstract : Numerous intriguing optimization problems arise as a result of the advancement of machine learning. Second-order algorithms have their typical advantages in dealing with highly nonlinear and ill-conditioning problems. This paper provides a review on recent developments in stochastic variants of quasi-Newton methods, which construct the Hessian approximations using only gradient information. We concentrate on BFGS-based methods in stochastic settings and highlight the algorithmic improvements that enable the algorithm to work in various scenarios. Future research on stochastic quasi-Newton methods should focus on enhancing its applicability, lowering the computational and storage costs, and improving the convergence rate.
• [02795] Riemannian Natural Gradient Methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Zaiwen Wen (Peking University)
    • Jiang Hu (The Chinese University of Hong Kong)
    • Ruicheng Ao (Peking University)
    • Anthony Man-Cho So (The Chinese University of Hong Kong)
    • Minghan Yang (Peking University)
  • Abstract : In this talk, we present a Riemannian natural gradient method for large-scale optimization problems on Riemannian manifolds. Such problems arise in various machine learning and signal processing applications. The notion of Fisher information matrix is extended from the Euclidean setting. We establish the almost-sure global convergence and local convergence of our proposed method under standard assumptions. Numerical experiments on applications arising from machine learning demonstrate the advantages of the proposed method over state-of-the-art ones.
• [04755] Newton-PMR: Newton Subspace Methods with Complexity Guarantees for Non-convex Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Yang Liu (University of Oxford)
    • Andre Milzarek (The Chinese University of HThe Chinese University of Hong Kong, Shenzhenong Kong, Shenzhen)
    • Fred Roosta (the University of Queensland)
  • Abstract : Recently, Newton-MR methods have been introduced for solving nonconvex unconstrained smooth optimization problems. Leveraging the inherent ability of the minimum residual (MINRES) inner solver to detect directions of nonpositive curvature (NPC), Newton-MR variants enjoy a variety of optimal complexity guarantees. However, the application of these methods to modern high-dimensional problems remains challenging. To address this, we present novel variants that incorporate certain dimensionality reduction techniques. In particular, our proposed methods are based on recent results that have shown that preconditioning MINRES with a positive semi-definite but singular preconditioner is in fact equivalent to solving a low-dimensional problem whose dimension corresponds to the nullity of the preconditioning matrix. Utilizing these dimensionality reduction properties of preconditioned MINRES, we present novel variants of Newton-MR, called Newton-PMR, which can be readily applied to high-dimensional problems, while achieving desirable complexity guarantees.

MS [00441] Intersection between financial economics and optimal control

room : D502

• [05612] Asset Pricing with Misallocation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yan Ji (HKUST)
  • Abstract : We develop an endogenous growth model with heterogeneous firms facing financial frictions, in which misallocation emerges explicitly as a crucial state variable. In equilibrium, misallocation endogenously generates long-run uncertainty about economic growth by distorting innovation decisions, leading to significant welfare losses and risk premia in capital markets. Macroeconomic shocks that affect misallocation are likely to have overly persistent effects on aggregate growth. Using an empirical misallocation measure motivated by the model, we find evidence showing that misallocation captures low-frequency variations in both aggregate growth and stock returns. Empirically, a two-factor model with market and misallocation factors prices size, book-to-market, momentum, and bond portfolios with an $R$-squared and a mean absolute pricing error close to the Fama-French three-factor model.
• [03797] An optimal consumption and investment problem for general factor models : Epstein-Zin recursive utility case.
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroaki Hata (Hitotsubashi University)
  • Abstract : We consider an optimal consumption and investment problem with Epstein-Zin recursive utility on the finite time horizon. The returns and volatilities of the assets depend on nonlinearly on the factor processes modeled as diffusion process. The problem becomes a standard control problem. We derive the Hamilton-Jacobi-Bellman (HJB) equation and study its solutions. Under some conditions we construct a suitable pair of sub- and super-solution. And, we prove the existence and uniqueness of solution for this HJB equation. Finally, we show the verification theorem.
• [05413] Patience is a virture: optimal investment in the presence of limit order book
  • Format : Talk at Waseda University
  • Author(s) :
    • Nan Chen (The Chinese University of Hong Kong)
    • Qiheng Ding (The Chinese University of Hong Kong)
    • Chen Yang (The Chinese University of Hong Kong)
  • Abstract : We study an optimal investment problem of a CARA investor trading in a market operated with a limit order book (LOB). The model synergizes three key features of market microstructure: the bid-ask spread, the market depth, and a finite market resilience. Under a Bachelier process for the dynamic of the fundamental value of the asset, we manage to develop explicit characterization through a system of variational inequalities on the investor’s optimal trading strategy. A patience index is derived to highlight the importance of trading timing in reconciling several competing goals such as achieving the current optimal risk exposure, incorporating the trading signals about the future, and minimizing trading impact costs.
• [05411] Why is Cash U-Shape in Firm Size?
  • Format : Talk at Waseda University
  • Author(s) :
    • Hao Xing (Boston University)
    • Ali Kakhbod (UC Berkeley)
    • Anders Max Reppen (Boston University Questrom School of Business)
    • Tarik Umar (Rice University)
  • Abstract : Cash holdings are U-shaped in firm size. To rationalize this finding, we develop a model of firm dynamics with costly financing allowing for heterogeneous size} Cash is U-shaped in firm size because of decreasing returns to scale and hedging incentives. When a firm is small, cash decreases with size because investment opportunities are better resulting in more aggressive investing. Investing slows as the firm grows, and eventually, cash increases with firm size to hedge larger-scale cash flow shocks. Our model likewise explains why in the data issuance amounts (payout rates) are U-shaped (hump-shaped) in firm size.

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

room : D505

• [03681] A hybrid algorithm of integrated container truck scheduling problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenchao Wei
    • Yanrong Zhang (Beijing Jiaotong University)
  • Abstract : This article establishes an inland container transportation network that includes inland container depots (ICDs) and studies the dispatching problem of container empty containers and trucks in the network. A mixed integer programming model is proposed to tackle the scheduling problem together with ICD locations. To solve the proposed problem, we develop a hybrid algorithm combining large neighborhood search in a fix-and-optimize framework and a tabu search algorithm.
• [05024] Compact formulations for parallel machine scheduling with conflicts
  • Format : Talk at Waseda University
  • Author(s) :
    • Phablo Moura (KU Leuven)
    • Roel Leus (KU Leuven)
    • Hande Yaman (KU Leuven)
  • Abstract : Parallel machine scheduling with conflicts consists in, given a set of jobs $V$ with known processing times, a set of identical machines $M$, and an undirected graph $(V,E)$, finding a mapping from $V$ to $M$ such that pairs of jobs in $E$ are assigned to different machines, and the maximum completion time (makespan) is minimized. We present compact MILP formulations, introduce classes of valid inequalities, and report on preliminary computational experiments
• [01311] Project scheduling under various resource constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicklas Klein (University of Bern)
    • Mario Gnägi (University of Bern)
    • Norbert Trautmann (University of Bern)
  • Abstract : The execution of a project often requires two types of resources: renewable resources representing, e.g., staff members or equipment; and production and consumption resources representing, e.g., the project budget. We present a mixed-integer linear programming formulation for scheduling such a project which significantly outperforms state-of-the-art models from the literature.

MS [00574] Recent Progress on Stochastic Analysis, Control, and their Applications

room : D514

• [03662] On the weak stability and stabilization of McKean-Vlasov stochastic differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Zhu (University of Wisconsin-Milwaukee)
  • Abstract : This work focuses on weak stability and stabilization of a class of McKean-Vlasov stochastic differential equations (SDEs). First, under suitable conditions on the coefficients of the SDE, we derive explicit quantitative contraction rates for the convergence in Wasserstein distances of McKean-Vlasov SDEs using the coupling method. The contraction results are then used to prove a propagation of chaos uniformly in time, which provides quantitative bounds on convergence rate of interacting particle systems, and establishes exponential ergodicity for McKean-Vlasov SDEs. Finally we consider the question of stabilizing in the weak sense an arbitrary McKean-Vlasov SDE using suitable feedback controls with delays.
• [05067] Limit Theorems for Distribution Dependent Jump Processes with Random Switching
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fubao Xi (Beijing Institute of Technology)
    • Chao Zhu (University of Wisconsin-Milwaukee)
  • Abstract : We consider distribution dependent jump processes with random switching, where the switching processes may have a countably infinite state space. By virtue of the martingale approach, we first establish the existence and uniqueness theorem of the underlying processes for a special Markovian switching case. Using a martingale function, we then transfer the existence and uniqueness result onto the general state-dependent switching case. Moreover, we establish two limit theorems for the processes with mean field interactions.
• [03342] From the optimal singular stochastic control to the optimal stopping for regime-switching processes
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jinghai Shao (Tianjin University)
    • Taoran Tian (Tianjin University)
  • Abstract : This work generalizes the connection between optimal singular control and optimal stopping problem for regime-switching processes. Via optimal singular control, the optimal stopping time and the continuation region are characterized. Moreover, we prove the existence of optimal singular stochastic control for a finite horizon singular control problem with the cost function containing the terminal cost. We prove it directly by the compactification method. Such a problem was left open in Haussmann and Suo (SICON, 1995).

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

room : A201

• [03451] Lie group analysis of the nonlinear 3D KP-BBM equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jonathan Lebogang Bodibe (North-West University, Mafikeng Campus)
    • Chaudry Masood Khalique (North-West University, South Africa)
  • Abstract : In this talk, we present Lie group analysis of the nonlinear (3+1)-dimensional Kadomtsev Petviashvili Benjamin Bona Mahony equation. We find exact solutions of the equation using Lie symmetry method together with Kudryashov's and (G’/G)-expansion methods. Moreover, we derive the conservation laws for the equation using the multiplier and Ibragimov’s methods.

MS [01063] Challenges in biomathematical modeling and control

room : A206

MS [00616] Continuous optimization: theoretical and algorithmic trends

room : A207

• [03840] Constant rank constraint qualification for nonlinear second-order cone programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Gabriel Haeser (University of Sao Paulo)
  • Abstract : We revisit the classical notions of nondegeneracy and Robinson's condition in the context of nonlinear second-order cone programming. For an m-dimensional second-order cone, instead of stating nondegeneracy at the vertex as the linear independence of m derivative vectors, we do it in terms of several statements of linear independence of two derivative vectors. This allows embedding the structure of the second-order cone into the formulation of the conditions, providing weaker variants and applications.
• [03851] Strong global convergence properties of an Augmented Lagrangian method for symmetric cones
  • Format : Talk at Waseda University
  • Author(s) :
    • Daiana Oliveira dos Santos (UNIFESP)
  • Abstract : Sequential optimality conditions have played a major role in proving stronger global convergence results for numerical algorithms used in nonlinear programming. Several extensions have been described in conic contexts, leading to many open questions. In this talk, we will present new sequential optimality conditions for nonlinear symmetric cone programming. Stronger results are obtained by exploiting the rich algebraic structure of the problem.
• [02990] On enhanced KKT optimality conditions for smooth nonlinear optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Roberto Andreani (State University of Campinas/ UNICAMP)
  • Abstract : The Fritz-John and Karush-Kuhn-Tucker (KKT) conditions are crucial for finding minimizers in constrained optimization. They have been augmented with extra necessary conditions since the 1970s, with the enhanced KKT stationarity being one of them. This work focuses on enhanced KKT stationarity for smooth nonlinear programming and analyzes improved multipliers with quasi-normality. The results have implications for sequential optimality conditions and complementarity constraints in multi-objective problems.

MS [01081] New Trends in Education of Applied Mathematics, Industry, Technology and Knowledge Transfer

room : A208

• [04341] How the last few years have reshaped teaching First-Year mathematics
  • Format : Talk at Waseda University
  • Author(s) :
    • Joshua Jordan Capel (UNSW, School of Mathematics and Statistics)
  • Abstract : In this talk we will discuss how the past few years have reshaped the teaching of mathematics in the School of Mathematics and Statistics, UNSW (University of New South Wales) Sydney, Australia. We will discuss how the in-term and end-of-term assessment have been re-designed to scaffold student learning throughout term and test understanding instead of just rewarding rote learning and computing. We will also discuss how this style has been embraced or challenged by university administrators and accreditation bodies, and speculate on what future challenges await us.
• [02936] Applied Mathematics curriculum in the 21 st century
  • Format : Talk at Waseda University
  • Author(s) :
    • Beatriz Rumbos (Instituto Tecnológico Autónomo de México)
  • Abstract : Throughout history, Mathematics has made it possible for humans to cope and understand their surroundings and to make our lives more predictable. In the 20th century, mathematical models became indispensable tools for the development of almost every discipline; thus, promoting the creation of Applied Mathematics degrees at universities worldwide. The essence of an Applied Mathematics undergraduate program is to endow the student with the knowledge and analytical skills, needed to model and solve problems arising in a diversity of fields. The complexity of modern societies, the boom of the knowledge economy, the pace of technological change and the increasing social responsibility of modern youth, call for a major overhaul in the Applied Mathematics curricula and its teaching methods. In this talk I shall address the actions that we have taken at ITAM in order to address these challenges.
• [04591] Experiencing Mathematics: Compute. Intuit. Imagine. Create.
  • Format : Talk at Waseda University
  • Author(s) :
    • Amrik Sen (Plaksha University )
  • Abstract : If the next generation of engineering and science students are to be trained with the skills required to address contemporary societal and environmental challenges then both the curriculum and pedagogy of mathematics needs to be re-visited. I propose that training students to use computer technology to do mathematics and incorporating experiential projects as an immersive learning technique will foster intuition and imagination necessary to anchor abstract conceptual learnings to practical applications.
• [01931] An innovative experience in a Computer Engineering programme
  • Format : Talk at Waseda University
  • Author(s) :
    • M. Teresa T. Monteiro (Centre Algoritmi, Systems and Production Department,University of Minho)
    • Gabriel Hornink (Educational Media Laboratory, Department of Biochemistry, Institute of Biomedical Sciences, Federal University of Alfenas)
    • Flávia Vieira (Centro de Investigação em Educação (CIEd), Institute of Education, University of Minho, Braga)
  • Abstract : The talk reports an innovative learner-centred experience developed with 146 graduate students in the course “Numerical Methods and NonLinear Optimization” in a Computer Engineering programme at the University of Minho, Portugal. Students developed collaborative MATLAB projects by applying a course topic to a real-world phenomenon. Project analysis and students’ perceptions collected through a survey showed that they became pro-active learners and developed their ability to formulate, analyse and solve problems from a multidisciplinary perspective.

MS [00815] Recent trends in continuous optimization

room : A502

• [01619] Generalized Levenberg-Marquardt method with oracle complexity bound and local convergence
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoki Marumo (University of Tokyo)
    • Akiko Takeda (University of Tokyo)
    • Takayuki Okuno (Seikei University)
  • Abstract : The generalized Levenberg–Marquardt, abbreviated as LM, method has been developed for minimizing the sum of a possibly nonsmooth convex function and a smooth composite function. In this talk, we propose a new generalized LM method with three theoretical guarantees: iteration complexity bound, oracle complexity bound, and local convergence under a Holderian growth condition. These theoretical guarantees are achieved by use of an accelerated gradient method for solving convex subproblems.
• [04603] Line search methods for nonconvex optimization in deep learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuki Tsukada (Meiji University)
    • Hideaki Iiduka (Meiji University)
  • Abstract : Stochastic gradient descent (SGD) using line search methods achieves high accuracies for several classification tasks in deep learning. Moreover, it can find optimal parameters for deep neural network models by using nonconvex optimization. This talk experimentally investigates the convergence speed of SGD using line search methods with several batch sizes. Our results indicate that the smaller the batch size is, the smaller the stochastic first-order oracle complexity becomes.
• [01615] Proximal structured quasi-Newton method for nonlinear least squares with nonsmooth regularizer
  • Format : Talk at Waseda University
  • Author(s) :
    • Shummin Nakayama (The University of Electro-Communications)
    • Yasushi Narushima (Keio University)
    • Hiroshi Yabe (Tokyo University of Science)
  • Abstract : We consider composite minimization problems whose objective function is the sum of a nonlinear least squares formed smooth function and a nonsmooth regularizer. Structured quasi-Newton methods are efficient for solving nonlinear least squares problems and proximal Newton-type methods are efficient for composite minimization problems. In this talk, combining the above two methods, we propose a proximal structured quasi-Newton-type method. Finally, we present some numerical experiments to investigate the efficiency of the proposed method.
• [03538] Newton-type proximal gradient method for multi-objective optimization with composite D.C. functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasushi Narushima (Keio University)
    • Antoine J.V. Vadès (Keio University)
    • Hiroshi Ben (Keio University)
  • Abstract : In this talk, we propose a Newton-type proximal gradient method for multi-objective optimization whose objective functions are the sum of a continuously differentiable function and a Difference of Convex (D.C.) function. The proposed method is an extension of Newton-type proximal gradient methods for single-objective optimization. We give an algorithm of the proposed method with the Armijo-type line search and show its global convergence. Finally, we present some numerical results for comparison with the existing methods.

MS [02545] Challenges and Recent Advances in Phylogenetics

room : A508

• [04778] Log-concave density estimation on tree space
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Takazawa (The University of Tokyo)
    • Tomonari Sei (The University of Tokyo)
  • Abstract : A probability density is log-concave if its logarithm is concave. In recent decades, the maximum likelihood estimation method for log-concave densities has been developed in Euclidean spaces. In this talk, we introduce a generalization of this estimator to the space of phylogenetic trees. We provide a sufficient condition for the existence of the estimator, present the estimation algorithm, and discuss some challenges in the computation.
• [03260] Tropical Logistic Regression Model on Space of Phylogenetic Trees
  • Format : Talk at Waseda University
  • Author(s) :
    • Ruriko Yoshida (Naval Postgraduate School)
    • George Aliatimis (University of Lancaster)
    • Burak Boyaci (University of Lancaster)
    • James Grant (University of Lancaster)
  • Abstract : In recent years, tropical geometry has found applications in statistical learning over the space of phylogenetic trees. In this talk, we propose an analogue of the logistic regression model in the setting of tropical geometry. Our proposed method is to classify gene trees over the space of ultrametrics, a tropical linear space. The generalization errors of our model is discussed. Experiment results with simulated and empirical data show our model works well.
• [04319] From phylogenetics to semigroups, through set partitions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andrew Francis (Western Sydney University)
  • Abstract : We show that the set of all phylogenetic trees and forests are in correspondence with the set of all partitions of finite sets, extending Diaconis and Holmes (1998). This correspondence can be further extended to phylogenetic networks through a class of covers of finite sets. Partitions of finite sets can be represented as diagrams in a partition monoid, leading to applications of semigroups in phylogenetics. Joint work with Peter Jarvis and with Mike Steel.
• [04284] Learning from phylogenies to uncover evolutionary dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Olivier GASCUEL (CNRS - Institut de Systématique, Evolution, Biodiversité (ISYEB))
  • Abstract : I will describe the work done in my group to estimate the parameters of models used in phylodynamics and macroevolution studies. In particular, we use neural networks combined with simulations to learn to predict the parameters of these models. This involves both adequate representations of phylogenies and the use of appropriate neural architectures. The results compare favourably with the state of the art, with extremely fast methods for analyzing very large trees.

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

room : A510

• [02383] Is polynomial interpolation in the monomial basis unstable?
  • Format : Talk at Waseda University
  • Author(s) :
    • Zewen Shen (University of Toronto)
    • Kirill Serkh (University of Toronto)
  • Abstract : Polynomial interpolation in the monomial basis is a key step in a number of popular quadrature methods for integral equations. We will show that, despite its ill-conditioning, the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the Vandermonde matrix has a condition number smaller than the reciprocal of machine epsilon. We will also explore some applications of our analysis.
• [04278] A new boundary integral equation solver for problems in exteriors of open arcs
  • Format : Talk at Waseda University
  • Author(s) :
    • Abinand Gopal (Yale University)
    • Shidong Jiang (Flatiron Institute )
    • Vladimir Rokhlin (Yale University)
  • Abstract : When solving a constant-coefficient elliptic PDE, it is often convenient to first reformulate the problem as a boundary integral equation. This is usually done by representing the solution as an unknown density function times a kernel function integrated over the boundary of the domain. The choice of kernel is usually dictated by the boundary conditions and made such that the resulting equation for the density is a second kind Fredholm integral equation. However, when the problem is posed on the exterior of an arc in 2D or a surface in 3D, this becomes more complicated and the usual single layer and double layer representations run into difficulties. In this talk, we present a new solver for this regime. We use a representation based on the composition of standard layer potential with a hypersingular operator and compute the kernel of the composite operator directly. We then solve the resulting linear system with a direct solver.
• [04717] Density interpolation methods for volume integral operators
  • Format : Talk at Waseda University
  • Author(s) :
    • Carlos Perez-Arancibia (University of Twente)
    • Thomas G. Anderson (Rice University)
    • Luiz M. Faria (INRIA/ENSTA Paris)
    • Marc Bonnet (CNRS/ENSTA Paris)
  • Abstract : This talk outlines a novel class of high-order methods for the efficient numerical evaluation of volume potentials (VPs) defined by volume integrals over complex geometries. Inspired by the Density Interpolation Method (DIM) for boundary integral operators, the proposed methodology leverages Green’s third identity and a local polynomial interpolation of the density function to recast a given VP as a linear combination of surface-layer potentials and a volume integral with a regularized (bounded or smoother) integrand. The layer potentials can be accurately and efficiently evaluated inside and outside the integration domain using existing methods (e.g. DIM), while the regularized volume integral can be accurately evaluated by applying elementary quadrature rules to integrate over structured or unstructured domain decompositions without local numerical treatment at and around the kernel singularity. The proposed methodology is flexible, easy to implement, and fully compatible with well-established fast algorithms such as the Fast Multipole Method and H-matrices, enabling VP evaluations to achieve linearithmic computational complexity. To demonstrate the merits of the proposed methodology, we applied it to the Nyström discretization of the Lippmann-Schwinger volume integral equation for frequency-domain Helmholtz scattering problems in piecewise-smooth variable media.
• [05303] Recursive product integration schemes for volume potentials on irregular domains
  • Format : Online Talk on Zoom
  • Author(s) :
    • shravan veerapaneni
    • Hai Zhu (Flatiron Institute)
  • Abstract : We will discuss a new volume potential evaluation scheme for Gaussian and Laplace kernel in complex domains. The volume integral is computed by applying Green's theorem to convert these smooth or singular domain integrals on a volume mesh to a set of line integrals on the boundary skeleton of the volume mesh. This new approach allows easier integral-equation based solver implementation in complex domains, with much fewer restrictions on leaf level box refinement.

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

room : A511

• [03846] Efficient simulation of high-dimensional kinetic equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Lukas Einkemmer (University of Innsbruck)
  • Abstract : Solving high-dimensional kinetic equations (such as the Vlasov equation or the Boltzmann equations) numerically is extremely challenging. Methods that discretize phase space suffer from the exponential growth of the number of degrees of freedom, the so-called curse of dimensionality, while Monte Carlo methods converge slowly and suffer from numerical noise. In addition, standard complexity reduction techniques (such as sparse grids) usually perform rather poorly due to the lack of smoothness for such problems. Dynamical low-rank techniques approximate the dynamics by a set of lower-dimensional objects. For those low-rank factors, partial differential equations are derived that can then be solved numerically. We will show that such dynamical low-rank approximations work well for a range of kinetic equations due to their capacity to handle non-smooth solutions and the fact that in many situations important physical limit regimes are represented very efficiently by such an approximation (e.g. fluid or diffusive limits).
• [04978] A conservative semi-Lagrangian method for inhomogeneous Boltzmann equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Seung Yeon Cho (Gyeongsang National University)
    • Sebastiano Boscarino (University of Catania)
    • Giovanni Russo (University of Catania)
  • Abstract : In this work, we propose a conservative semi-Lagrangian method for the Boltzmann equation. Semi-Lagrangian approach enables us to avoid CFL-type restrictions on the time step. High order in time is obtained by Runge-Kutta or Adams-Bashforth methods. High order in space is obtained by a high order conservative reconstruction which also prevents spurious oscillations. The fast spectral method with L2-correction guarantees spectral accuracy and conservation. Numerical results confirm the accuracy and efficiency of the methods.
• [03164] Asymptotic preserving and uniformly unconditionally stable schemes for kinetic transport equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Guoliang Zhang ( Shanghai Jiaotong University)
  • Abstract : In this talk, we will give uniformly unconditionally stable finite difference schemes for kinetic transport equations in the diffusive scaling. The schemes are based on a coupling of macroscopic and microscopic equations, by utilizing a backward semi-Lagrangian approach for transport part, and implicit method for the diffusive part. The schemes can be shown to be asymptotic preserving in the diffusive limit. Uniformly unconditional stabilities are verified by Fourier analysis. Numerical experiments will demonstrate their good performances.
• [04700] High order structure preserving schemes for MHD flows in all sonic Mach numbers
  • Format : Talk at Waseda University
  • Author(s) :
    • Tao Xiong (Xiamen University)
  • Abstract : In this work, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number $\varepsilon$ ranging from $0$ to $\mathcal{O}(1)$. High-order accuracy in time is obtained by SI implicit-explicit Runge–Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.

MS [00643] Stochastic modeling in cell biology

room : A512

• [04558] Intracellular Transport Across Scales
  • Format : Talk at Waseda University
  • Author(s) :
    • Keisha Cook (Clemson University)
    • Scott A. McKinley (Tulane University)
  • Abstract : Biological systems are traditionally studied as isolated processes (e.g. regulatory pathways, motor protein dynamics, transport of organelles, etc.). Although more recent approaches have been developed to study whole cell dynamics, integrating knowledge across biological levels remains largely unexplored. In experimental processes, we assume that the state of the system is unknown until we sample it. Many scales are necessary to quantify the dynamics of different processes. These may include a magnitude of measurements, multiple detection intensities, or variation in the magnitude of observations. The interconnection between scales, where events happening at one scale are directly influencing events occurring at other scales, can be accomplished using mathematical tools for integration to connect and predict complex biological outcomes. In this work we focus on building inference methods to study the complexity of the cytoskeleton from one scale to another.
• [02757] Inferring RNA Dynamic Rates from Spatial Stochastic Snapshots
  • Format : Talk at Waseda University
  • Author(s) :
    • Christopher Edward Miles (University of California, Irvine)
  • Abstract : There are unresolved mysteries about the dynamics of RNA splicing, an important molecular process in the genetic machinery. These mysteries remain because the obtainable data for this process are not time series, but rather static spatial images of cells with stochastic particles. From a modeling perspective, this creates a challenge of finding the right mathematical description that respects the stochasticity of individual particles but remains computationally tractable. I'll share our approach to constructing a spatial Cox process with intensity governed by a reaction-diffusion PDE. We can do inference on this process with experimental images by employing variational Bayesian inference. Several outstanding issues remain about how to combine classical and modern statistical/data-science approaches with more exotic mechanistic models in biology. This work is in collaboration with the Ding lab of Biomedical Engineering at UCI.
• [02952] Centrosome Movement and Clustering During Mitosis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sarah Olson (Worcester Polytechnic Institute)
    • Amity Manning (Worcester Polytechnic Institute)
  • Abstract : While much work has been done to understand the roles of the key molecular components of the mitotic spindle during cell division, identifying the consequences of force perturbations in the spindle remains a challenge. In particular, cells with extra centrosomes may undergo a bipolar or multipolar division. We combine experimental approaches with computational modeling to define a role for cortical dynein in centrosome clustering, allowing for a bipolar division in cells with extra centrosomes.
• [01821] Stochastic model of nuclear size control in S. pombe
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xuesong Bai (Brandeis University)
    • Thomas Fai (Brandeis University)
  • Abstract : The size of the nucleus scales robustly with cell size so that the nuclear-to-cell size—the N/C ratio—is maintained during growth in many cell types. To address the fundamental question of how cells maintain the size of their organelles despite the constant turnover of proteins and biomolecules, we consider a model based on osmotic force balance predicts a stable nuclear-to-cell size ratio, in good agreement with experiments on the fission yeast Schizosaccharomyces pombe. We model the synthesis of macromolecules during growth using chemical kinetics and demonstrate how the N/C ratio is maintained in homeostasis. We compare the variance in the N/C ratio predicted by the model to that observed experimentally.

MS [00309] Population Dynamics in Biology and Medicine

room : A601

• [04326] Population Dynamics in Biology and Medicine
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunmi Lee (Kyung Hee University )
  • Abstract : The rapid spread of COVID-19 worldwide has highlighted the importance of non-pharmaceutical interventions. Policies that limit gatherings and enforce social distancing help to mitigate the spread of the disease, but also negatively impact the economy. Consequently, policymakers face the dilemma of whether to slow the outbreak by imposing strict rules or reduce the economic burden. This paper presents a novel framework for designing intervention policies based on deep reinforcement learning. The social distancing policies used by the South Korean government and their effects on the national economy are surveyed and integrated into a newly designed multi-patch epidemic model. The mobility between each pair of 17 patches (South Korean regions) is reconstructed using official data. The proximity policy optimization algorithm is adopted to optimize the policy model. The reward function incorporates the outbreak and economic loss, with an additional control variable that helps policymakers to determine the desired equilibrium between disease outbreak and economic recession. Our results highlight region-specific social distancing interventions compromising the dilemma between epidemic costs and economic costs.

MS [00082] Development in fractional diffusion equations: models and methods

room : A618

• [00162] Solution of a fractional Stefan problem using a Landau transformation
  • Format : Talk at Waseda University
  • Author(s) :
    • Vaughan Richard Voller (University of Minnesota)
  • Abstract : The Stefan problem, tracking the motion of a heat conduction driven melt interface, is the classical moving boundary problem. A means of obtaining a solution for such problems is through the use of a variable transformation --- the Landau transformation --- immobilizing the melt interface. Here we apply this technique for the approximate solution of a fractional Stefan problem where the integer time derivative, in the governing diffusion equation, is replaced with a fractional derivative.
• [00166] Fractional diffusion as an intermediate asymptotic regime
  • Format : Talk at Waseda University
  • Author(s) :
    • Gianni Pagnini (BCAM - Basque Center for Applied Mathematics)
    • Paolo Paradisi (ISTI-CNR, Pisa)
    • Silvia Vitali (Eurecat Centre Tecnològic de Catalunya Barcellona )
  • Abstract : A continuous-time random walk driven by two different Markovian hopping-trap mechanisms is investigated and it is shown that paradigmatic features of anomalous diffusion are met. More precisely, anomalous diffusion results from a process that goes through the action of two co-existing Markovian mechanisms acting with different statistical frequency, and the probability of occurrence of this switch between the two Markovian settings originates and fully characterizes the anomalous diffusion. In fact, ensemble and single-particle observables of this model have been studied and they match the main characteristics of anomalous diffusion as they are typically measured in living systems. In particular, the celebrated transition of the walker’s distribution from exponential to stretched-exponential and finally to Gaussian distribution is displayed by including also the Brownian yet non-Gaussian interval. Moreover, the model dynamically provides the power-law exponent of the mean-square displacement as a function of the probability of switching between the two Markovian states, namely the fractional order. Hence, fractional diffusion emerges as an intermediate asymptotic regime. Finally, within the present approach, fractional diffusion can be interpreted as a mathematical method for bridging two co-existing equilibrium states in a disordered medium. This talk is based on: Vitali S, Paradisi P and Pagnini 2022 J. Phys. A: Math. Theor. 55 224012
• [02596] Dissipativity of the energy functional in time-fractional gradient flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Marvin Fritz (Johann Radon Institute for Computational and Applied Mathematics (RICAM))
  • Abstract : In this talk, the monotonicity of the energy functional of time-fractional gradient flows is investigated. It is still unknown whether the energy is dissipating in a timely manner. This characteristic is critical for integer-order gradient flows, and many numerical systems utilize it. We suggest an energy functional that incorporates the solution's history, which is reasonable given that time-fractional partial differential equations are nonlocal in time and feature a natural memory effect. On the basis of this new energy, we demonstrate that a time-fractional gradient flow is equivalent to an integer-order flow. In addition, this connection guarantees the dissipative nature of the augmented energy and permits the development of numerical schemes.