MS and CT list / Aug. 25, 10:40-12:20.

MS [00283] Recent developments in mathematical imaging and modeling in magnetic particle imaging

room : G301

• [04792] A Flexible Approach to Model-Based Reconstruction in Magnetic Particle Imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas März (Hochschule Darmstadt)
  • Abstract : In Magnetic Particle Imaging (MPI) images are usually reconstructed using a system matrix obtained via a time-consuming calibration procedure. Our approach employs a mathematical model based on the MPI signal encoding and its analytical properties. We present our two-stage algorithm: First stage: we estimate components of the MPI Core Operator by using a variational formulation. Second stage: the image is reconstructed by regularized deconvolution while fitting the results of the first stage. We demonstrate the performance of our algorithm with simulated data.
• [04806] Reconstruction of Dynamic Concentrations with Sequential Subspace Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Marius Nitzsche (University of Stuttgart)
  • Abstract : Magnetic particle imaging faces challenges in dealing with dynamics, which often results in motion artifacts and lower quality reconstructions due to limited averaging. Standard algorithms cannot produce high-quality images under these circumstances. To address these issues, we utilize the Regularized Sequential Subspace Optimization (Resesop) algorithm, which can account for model imperfections caused by motion without requiring strong prior information. We demonstrate the effectiveness of Resesop on both simulated and real dynamic MPI data.
• [04730] Joint motion estimation and image reconstruction for dynamic MPI
  • Format : Talk at Waseda University
  • Author(s) :
    • Christina Brandt (Universität Hamburg)
    • Lena Zdun (Universität Hamburg)
  • Abstract : Potential applications of MPI include highly dynamic tasks as blood flow imaging and instrument tracking during inteventions. In this talk, we propose to tackle the additional challenges caused by the dynamics by a joint image reconstruction and motion estimation approach. We combine a multi-scale motion estimation algorithm with a stochastic primal-dual algorithm for image reconstruction. Convincing numerical results are achieved on in-vitro and in-vivo data using motion models matching the specific application.

MS [00575] Factors and Cycles

room : G302

• [02338] On cycles and factors in graphs with large degree sum
  • Format : Talk at Waseda University
  • Author(s) :
    • Takamasa Yashima (Seikei University)
  • Abstract : Numerous researchers have conducted investigations into a Hamiltonian cycle and related objects in both general graphs and bipartite graphs. In this talk, we will focus on two specific topics related to this field. The first topic concerns the problem of finding a spanning subgraph, also known as a factor, that satisfies certain degree constraints. The second topic concerns the problem of finding a Hamiltonian cycle containing a pre-specified set of independent edges, or a matching.
• [02275] Toughness and forbidden subgraphs for graphs to be hamiltonian
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiro Sanka (Keio University)
  • Abstract : We say that a graph $G$ is $t$-tough if for each vertex cut $S \subset V(G)$, the number of components of $G-S$ does not exceed $\frac{|S|}{t}$. In 1973, Chvátal has conjectured that there exists a constant $t_0$ such that every $t_0$-tough graph is hamiltonian. In this talk, we discuss some results on Chvátal's conjecture in $R$-free graphs for some graph $R$. In particular, we will present hamiltonicity of $2K_2$-free graphs and $(K_2 \cup kK_1)$-free graphs.
• [02216] Recent progress on distance matching extension in graphs on surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Fujisawa (Keio University)
  • Abstract : A graph $G$ is said to be distance $d$ matchable if, for any matching $M$ of $G$ in which edges are pairwise at least distance $d$ apart, there exists a perfect matching of $G$ which contains $M$. If we choose a class of graphs $A$ and an integer $d$ appropriately, then we may observe a phenomenon that every graph in $A$ is distance $d$ matchable. In this talk recent results concerning this phenomenon is introduced.
• [02696] Eigenvalues and factors in regular graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Suil Oh (SUNY Korea)
  • Abstract : In this talk, we investigate spectral conditions for an (r-regular) graph G to guarantee the existence of a certain factor.

MS [00652] Recent Advances in Quasi-Monte Carlo Methods and Related Topics

room : G304

• [04989] The fast reduced QMC matrix-vector product
  • Format : Talk at Waseda University
  • Author(s) :
    • Josef Dick (UNSW)
    • Adrian Ebert (JKU Linz)
    • Lukas Herrmann (RICAM Linz)
    • Peter Kritzer (RICAM Linz)
    • Marcello Longo (ETH Zurich)
  • Abstract : We study the approximation of integrals of the form $\int_D f(\boldsymbol{x}^\top A) \,d \mu(\boldsymbol{x})$, where $A$ is a matrix, by quasi-Monte Carlo (QMC) rules $N^{-1} \sum_{k=0}^{N-1} f(\boldsymbol{x}_k^\top A)$. We are interested in cases where the main computational cost in computing the approximation arises from the computation of $\boldsymbol{x}_k^\top A$. We design QMC rules for which the computation of $\boldsymbol{x}_k^\top A$, $k = 0, 1, \ldots, N-1$ can be done in a fast way.
• [05066] Recent Advances on discrepancy and WCE of constructible point sets on spheres
  • Format : Talk at Waseda University
  • Author(s) :
    • Johann S. Brauchart (Graz University of Technology)
  • Abstract : We discuss bounds for the $L_2$-discrepancy and worst-case error for equal-weight quasi Monte Carlo rules (and compare them with optimal bounds) for constructible $N$-point sets that arise from mapping rational lattice points in the plane to the sphere using an area preserving Lambert transformation. Our standard examples are spherical Fibonacci point configurations defined by a Fibonacci lattice in the unit square. This is joint work with Josef Dick (UNSW) and Yuan Xu (University of Oregon).
• [03448] Quasi-Monte Carlo approach to Bayesian optimal experimental design
  • Format : Talk at Waseda University
  • Author(s) :
    • Vesa Kaarnioja (Free University of Berlin)
  • Abstract : The goal in Bayesian optimal experimental design (OED) is to maximize the expected information gain for the reconstruction of unknown quantities given a limited budget for collecting measurement data. Quasi-Monte Carlo (QMC) methods have been demonstrated to be effective for numerical treatment of partial differential equations (PDEs) involving input uncertainties in recent years. In this talk, we derive tailored QMC cubature rules to reduce the computational burden in Bayesian OED problems governed by PDEs.
• [04877] Density estimation by Monte Carlo and quasi-Monte Carlo
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre L'Ecuyer (University of Montreal)
  • Abstract : Estimating the density of a continuous random variable X has been studied extensively in settings where n independent observations of X are given a priori. Popular methods include histograms and kernel density estimators. These methods have bias and their mean square error converges at a slower rate than the usual O(1/n) rate. In this talk, we consider the situation where the observations are generated by Monte Carlo simulation from a model. Unbiased estimators and better convergence rates can then be obtained, sometimes much better than O(1/n). We show how this can be achieved, using techniques such as conditional Monte Carlo, likelihood ratio methods for derivative estimation, and randomized quasi-Monte Carlo. Theoretical and empirical results will be given. This is based on joint work with Amal Ben Abdellah and Florian Puchhammer.

MS [00505] Structured matrices with applications in sciences and engineering

room : G305

• [02264] Reciprocal Matrices, Ranking and the Relationship with Social Choice
  • Format : Online Talk on Zoom
  • Author(s) :
    • Charles R Johnson (William and Mary)
  • Abstract : There is a close connection between the use of efficient vectors for reciprocal (pairwise comparison) matrices, used in business project ranking schemes, and social choice/voting rules from political science and economics. However, the two seem not to have been discussed together before. We explore this connection, as well as advance the theory of reciprocal matrices. In addition, there seem to be natural connections with other parts of economic theory.
• [01723] A matrix approach to the study of efficient vectors in priority setting methodology
  • Format : Talk at Waseda University
  • Author(s) :
    • Susana Furtado (Faculdade de Economia do Porto and CEAFEL)
    • Charles Johnson (College of William and Mary)
  • Abstract : The Analytic Hierarchy Process is a much discussed method in ranking business alternatives based on empirical and judgemental information. Here we use a matrix approach to study the key component of efficient vectors for a reciprocal matrix of pairwise comparisons. In particular, we give new efficient vectors for a reciprocal matrix, which we compare numerically with other known efficient vectors.
• [00811] Singular matrices whose Moore-Penrose inverse is tridiagonal.
  • Format : Talk at Waseda University
  • Author(s) :
    • Maria Isabel Bueno Cachadina (University of California Santa Barbara)
    • Susana Borges Furtado (Faculdade de Economia do Porto and CEAFEL)
  • Abstract : A variety of characterizations of nonsingular matrices whose inverse is tridiagonal (irreducible or not) have been widely investigated in the literature. One well-known such characterization is stated in terms of semiseparable matrices. In this talk, we consider singular matrices $A$ and give necessary and sufficient conditions for the Moore-Penrose inverse of $A$ to be tridiagonal. Our approach is based on bordering techniques, as given by Bapat and Zheng (2003). In addition, we obtain necessary conditions on $A$ analogous to the semiseparability conditions in the nonsingular case, though in the singular case they are not sufficient, as illustrated with examples. We apply our results to give an explicit description of all the $3\times3$ real singular matrices and $3\times3$ Hermitian matrices whose Moore-Penrose inverse is irreducible and tridiagonal.
• [03060] Spectral geometric mean versus geometric mean by generalized Kantorovich constant
  • Format : Talk at Waseda University
  • Author(s) :
    • Shigeru Furuichi (Nihon University)
  • Abstract : In this talk, we give two different operator inequalities between the weighted spectral geometric mean and the weighted geometric mean. We also study the mathematical properties for the generalized Kantorovich constant. Applying the obtained inequalities on the generalized Kantorovich constant, we give the ordering of two inequalities between the weighted spectral geometric mean and the weighted geometric mean. In addition, we give some inequalities such as Ando type inequality, Kantorovich type inequality, and Ando-Hiai type inequality with the weighted spectral geometric mean and the generalized Kantorovich constant.

MS [00484] Matrix Analysis and Applications

room : G306

• [01222] Some new results on matrix and tensor equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qing-Wen Wang (Shanghai University, China)
  • Abstract : In this talk, we mainly introduce some new developments of matrix and tensor equations over the quaternion algebra.
• [01920] Matrix inequalities and properties of means on positive definite matrices
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luyining Gan (University of Nevada Reno)
  • Abstract : In this talk, we will introduce the study of the relations between the weighted metric geometric mean, the weighted spectral geometric mean and the weighted Wasserstein mean of the positive definite matrices in terms of (weak) log-majorization relation. In addition, we will also introduce some new properties of means, like geodesic property and tolerance relation.
• [05621] How to chesk D-stability: a simple determinantal test
  • Format : Online Talk on Zoom
  • Author(s) :
    • Volha Y. Kushel (Shanghai University)
  • Abstract : The concept of matrix $D$-stability, introduced in 1958 by Arrow and McManus is of major importance due to the variety of its applications. However, characterization of matrix $D$-stability for dimensions $n > 4$ is considered as a hard open problem. In this talk, we propose a simple way for testing matrix $D$-stability, in terms of the inequalities between principal minors of a matrix. The conditions are just sufficient but they allow to test matrices of an arbitrary size n, are easy to verify and can be used for the analysis of parameter-dependent models.

contributed talk: CT019

room : G401

[00018] Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G401
• Type : Contributed Talk
• Abstract : We study the diffusive generalized logistic problem with constant yield harvesting: \begin{equation*} \left \{ \begin{array}{ll} u^{\prime \prime }(x)+\lambda g(u)-\mu =0, & -10$. We prove that, for any fixed $\mu >0,$ on the $(\lambda ,\left \Vert u\right \Vert _{\infty })$-plane, the bifurcation diagram consists of a $\subset $-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying $\mu >0.$
• Classification : 34B18, 74G35
• Format : Talk at Waseda University
• Author(s) :
  • Shin-Hwa Wang (National Tsing Hua University, TAIWAN)
  • Kuo-Chih Hung (National Chin-Yi University of Technology, Taiwan)
  • Yiu-Nam Suen (National Tsing Hua University, TAIWAN)

[01883] An application to the generalized logistic growth model

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G401
• Type : Contributed Talk
• Abstract : We study the bifurcation curves for a Dirichlet problem with geometrically concave nonlinearity. We give an application to the generalized logistic growth model. There are totally six qualitatively bifurcation curves.
• Classification : 34B18, 74G35
• Format : Talk at Waseda University
• Author(s) :
  • Kuo-Chih Hung (National Chin-Yi University of Technology)
  • Kuo-Chih Hung (National Chin-Yi University of Technology)

[01163] An infinite class of shocks for compressible Euler

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G401
• Type : Contributed Talk
• Abstract : We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion.
• Classification : 35L67, 35Q31, 76N15, 76L05
• Format : Talk at Waseda University
• Author(s) :
  • Calum Rickard (University of California, Davis)
  • Sameer Iyer (University of California, Davis)
  • Steve Shkoller (University of California, Davis)
  • Vlad Vicol (New York University)

MS [02017] Recent progress in theory and applications of time-delay systems

room : G402

• [04818] Delay induced self-sustained oscillations in the Nonlinear Noisy Leaky Integrate and Fire model for networks of neurons.
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre Roux (Mathematical Institute, University of Oxford)
  • Abstract : The emergence of patterned activity in a neural networks is a key process in human and animal brains. However, since they often arise from the interplay between a large number of cells, these mechanisms are very difficult to encompass whithout the use of simple, consistent and self-contained mathematical models. In this talk, I will present a time-delayed nonlinear partial differential equation, the so-called Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model. In a recent work, my collaborators Kota Ikeda, Delphine Salort, Didier Smets and myself have obtained some new results and insights about the emergence and the shape of periodic self-sustained oscillations in this model. In particular, we have found and studied a simplified version of the problem in the form of a delayed differential equation.
• [04601] Global stability of multi-cell reaction systems with arbitrary time delays
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirokazu Komatsu (National Institute of Technology Toyota College)
  • Abstract : In the present talk, we consider the stability of multi-cell chemical reaction systems with arbitrary time delays for each reaction, in which each intracellular chemical reaction network is weakly reversible and has zero deficiency. By constructing a Lyapunov functional and assuming additional conditions, we can show that any positive solution to the delay differential equation for the system with mass action kinetics globally converges to a positive equilibrium point in the functional state space.
• [04324] Time lag monotonicity-breaking in time-delay systems with impulses
  • Format : Talk at Waseda University
  • Author(s) :
    • Kevin Church (CIBC)
  • Abstract : In this talk, we prove that the solution manifold concept for differential equations with state-dependent delay (DE-SDD) has no "topologically generic" analogue for DE-SDD with impulses. Precisely, the existence of a semiflow is conditional on monotonicity of the time lag. We demonstrate pathologies that occur in the monotonicity-breaking case, which in some instances lead to dynamical behaviour completely different from what is possible in DE-SDD or impulsive differential equations with constant delays.
• [03244] Mode Selection Rules for multi-Delay Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Kin'ya Takahashi (Kyushu Institute of Technology)
    • Taizo Kobayashi (Kyushu University )
  • Abstract : We investigate mode selection rules at the first bifurcation for a two-delay system. Selected modes are sensitively changed with the ratio of two delay times, but obey a definite selection rule if the strengths of two delays are fixed. When the strength of the short delay takes negative values, different types of mode selection rules are observed. We explore the underlying mechanism of the change of mode selection rules in the singular perturbation limit.

MS [01140] Modelling and simulation of electro-chemo-mechanical processes in batteries and fuel cells

room : G404

• [01934] Li-Ion battery kinetics model validation of NMC 111 and Graphite
  • Format : Talk at Waseda University
  • Author(s) :
    • Robert Morasch (Technical University of Munich)
    • Bharatkumar Suthar (Indian Institute of Technology Bombay)
    • Hubert Gasteiger (Technical University of Munich)
  • Abstract : Understanding Li-Ion battery fundamentals is an important aspect when modelling Li-Ion batteries. The Doyle-Fuller-Newman model is often used as mathematical basis for such models, but rarely validated. Here we present an in-depth analysis of the kinetic behavior of NMC 111 and graphite using Electrochemical Impedance Spectroscopy. Measurements on thin electrodes allow an easy distinction of the kinetic resistance for either electrode without the influence of transport resistances.
• [04354] Fluid–electrochemical-stress-coupled Simulation Method for SOFC Degradation Prediction
  • Format : Talk at Waseda University
  • Author(s) :
    • Mayu Muramatsu (Keio University)
    • Masami Sato (Tohoku University)
    • Reika Nomura (Tohoku University)
    • Kenjiro Terada (Tohoku University)
    • Yashiro Keiji (Tohoku University)
    • Tatsuya Kawada (Tohoku University)
    • Harumi Yokokawa (The University of Tokyo)
  • Abstract : To predict the mechanical degradation of solid oxide fuel cells (SOFCs) during operation, we have developed an analysis system for their electro-chemo-mechanical phenomena by incorporating general-purpose finite element analysis software. This simulation system also takes into account the effects of gas and heat distributions, also calculated by commercial software.
• [02306] Modeling and State Estimation of Lithium-Ion Batteries under Long-Term Degradation Conditions in Aerospace Application
  • Format : Talk at Waseda University
  • Author(s) :
    • Linda Juliane Bolay (German Aerospace Center (DLR))
    • Tobias Schmitt (German Aerospace Center (DLR))
    • Simon Hein (German Aerospace Center (DLR))
    • Omar Mendoza-Hernandez (Japan Aerospace Exploration Agency (JAXA))
    • Eiji Hosono (National Institute of Advanced Industrial Science and Technology (AIST))
    • Daisuke Asakura (, National Institute of Advanced Industrial Science and Technology (AIST))
    • Koichi Kinoshita (, National Institute of Advanced Industrial Science and Technology (AIST))
    • Hirofumi Matsuda (, National Institute of Advanced Industrial Science and Technology (AIST))
    • Minoru Umeda (Nagaoka University of Technology)
    • Yoshitsugu Sone (Japan Aerospace Exploration Agency (JAXA))
    • Arnulf Latz (German Aerospace Center (DLR))
    • Birger Horstmann (German Aerospace Center (DLR))
  • Abstract : The performance and durability of Li-ion batteries is impacted by various degradation mechanisms such as SEI growth. Here, we address the modeling and simulation of the batteries of the Japanese satellite REIMEI. We simulate SEI growth in a P2D and microstructure-resolved framework. The simulations are validated with in-flight data from JAXA. Furthermore, a multi-time-scale filter algorithm is applied to estimate the inner states of the battery by making use of the battery in-flight data.
• [02922] Simulation of Chemo-Mechanically Coupled Battery Active Particles with Mechanical Constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Raphael Schoof (Karlsruhe Institute of Technology)
    • Giuseppe Fabian Castelli (Karlsruhe Institute of Technology)
    • Willy Dörfler (Karlsruhe Institute of Technology)
  • Abstract : During charging and discharging of lithium-ion batteries, large mechanical stresses can occur due to phase-separation or limited swelling area. A chemo-mechanically coupled model for cycling battery active particles with mechanical constraints is used to investigate the stress development within representative active particles. The combination of the primal-dual active set algorithm, interpreted as semismooth Newton method, and a spatial and temporal adaptive algorithm allows the efficient two- and three-dimensional numerical simulation and computationally intensive parameter regimes.

MS [00084] Asymptotic approaches to multi-scale PDEs in mathematical physics

room : G405

• [04992] Relative entropy and application to asymptotic limits for bipolar Euler-Poisson systems.
  • Format : Talk at Waseda University
  • Author(s) :
    • Athanasios Tzavaras (King Abdullah University of Science and Technology (KAUST))
    • Nuno Alves (King Abdullah University of Science and Technology (KAUST))
  • Abstract : The relative entropy method has been a very effective tool for describing asymptotic limit problems in mechanics and mathematical physics. A formalism for Hamiltonian systems can be easily extended to the system of bipolar Euler-Maxwell equations. We will describe here various results on asymptotic limits from bipolar Euler Poisson to models that are used for the description of plasmas, or (when combined with high-friction limits) to semi-conductors (joint work with Nuno Alves).
• [04461] From compressible euler equation to porous media
  • Format : Talk at Waseda University
  • Author(s) :
    • Piotr Gwiazda (Institute of Mathematics of Polish Academy of Sciences)
  • Abstract : We consider a combined system of Euler, Euler–Korteweg and Euler–Poisson equations. We show the existence of dissipative measure-valued solutions in the cases of repulsive and attractive potential in Euler–Poisson system. Furthermore we show that the strong solutions to the Cahn–Hillard–Keller–Segel system are a high-friction limit of the dissipative measure-valued solutions to Euler–Korteweg–Poisson equations.
• [03337] On the asymptotic dynamics of point vortices for the lake equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Lars Eric Hientzsch (Bielefeld University)
    • Christophe Lacave (University Grenoble Alpes)
    • Evelyne Miot (University Grenoble Alpes)
  • Abstract : The lake equations describe the evolution of the vertically averaged velocity field of an incompressible inviscid 3D fluid in a domain with spatially varying topography (depth). We derive the asymptotic dynamics of point vortices for the lake equations with positive depth, when the vorticity is initially sharply concentrated around $N$ points. More precisely, we show that the vorticity remains concentrated in suitable sense around $N$ points for all times, and that the trajectories follow the level lines of the depth function. This is joint work with Christophe Lacave and Evelyne Miot (Université Grenoble Alpes).
• [03190] Strong Convergence of Vorticity in the Viscosity Limit
  • Format : Talk at Waseda University
  • Author(s) :
    • Emil Wiedemann (Universität Erlangen-Nürnberg)
  • Abstract : Consider the 2D incompressible Navier-Stokes equations with initial vorticity in $L^p$ ($1

MS [00545] Waves in complex and multiscale media

room : G406

• [03757] Effective waves in random particulate media: introduction and numerical validation
  • Format : Talk at Waseda University
  • Author(s) :
    • ARTUR LEWIS GOWER (University of Sheffield)
    • Stuart Hawkins (Macquarie University)
    • Gerhard Kristensson (Lund University)
  • Abstract : Describing how waves scattering between a large set of particles is challenging. There are accurate numerical methods, but they lack intuition and can be slow. Effective theory is a method to replace the particles with a homogeneous media which leads to greater intuition and is quick to calculate. One drawback is often that effective theory is only accurate for long wavelengths. In this talk, I will show how we overcame the challenges to extend effective theory for a large range of wavelengths (0 < k a < 2) and material properties (particle type and volume fractions) for waves in a random particulate material.
• [04234] Scattered wavefield in the stochastic homogenization regime
  • Format : Talk at Waseda University
  • Author(s) :
    • Laure Giovangigli (ENSTA Paris)
    • Quentin Goepfert (ENSTA Paris)
    • Pierre Millien (Institut Langevin, ESPCI)
    • Josselin Garnier (Ecole Polytechnique)
  • Abstract : This work aims at modelling and studying the propagation and diffusion of ultrasounds in complex multi-scale media such as biological tissues or composite materials. We consider in the free space a homogeneous bounded medium in which lie randomly distributed inhomogeneities that are small compared to the wavelength. In order to characterize the response of this medium to an incident plane wave, we perform an asymptotic expansion of the scattered wave with respect to the size of the inhomogeneities using stochastic homogenisation techniques. The difficulties lie in the transmission conditions at the boundary of the medium. We derive quantitative error estimates given that the random distribution of inhomogeneities verifies mixing properties. Finally we present numerical simulations to illustrate and validate our results.
• [04262] Waves on Graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Gregor Tanner (University of Nottingham)
    • Stephen C Creagh (University of Nottingham)
    • Cerian Brewer (University of Nottingham)
  • Abstract : We consider the wave dynamics on networks or graphs carrying both propagating and evanescent modes on each edge. This is an extension of quantum graph theory and occurs naturally when considering networks of plates or beams with different mode types (flexural, longitudinal and shear waves) propagating on each connecting structure. The local vertex scattering matrices and the global transfer operator are no longer unitary with interesting consequences for secular equations and the Weyl law.
• [04615] Designing large-scale acoustic scattering systems using structural optimization and multiple scattering theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Kei Matsushima (The University of Tokyo)
    • Takayuki Yamada (The University of Tokyo)
  • Abstract : In this talk, we present a numerical scheme for designing large-scale acoustic scattering systems based on a multiple scattering theory and shape/topology optimization. We first solve exterior Helmholtz problems using the T-matrix method. This formulation allows us to evaluate a design sensitivity of multiple scattering systems using the adjoint variable method. We will demonstrate that the proposed scheme can design an omnidirectional acoustic cloak.

MS [00316] Dynamics of patterns and traveling waves arising from reaction-diffusion systems

room : G501

• [03601] Cross-diffusion derived from predator-prey models with two behavioral states in predators
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirofumi Izuhara (University of Miyazaki)
    • Masato Iida (University of Miyazaki)
    • Ryusuke Kon (University of Miyazaki)
  • Abstract : Cross-diffusion may be an important driving force of pattern formation in population models. Recently, a relation between cross-diffusion and reaction-diffusion systems has been revealed from the mathematical modeling point of view. In this talk, we derive a predator-prey model with cross-diffusion from a simple reaction-diffusion system with two behavioral states in the predator population and examine whether cross-diffusion can induce spatial patterns in predator-prey models.
• [00453] Weak entire solutions of reaction–interface systems
  • Format : Talk at Waseda University
  • Author(s) :
    • YANYU CHEN (National Taiwan University)
  • Abstract : In this talk, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which are called reaction–interface systems. All weak entire solutions originating from finitely many excited intervals are completely characterized. For weak entire solutions originating from infinitely many excited intervals, periodic wave trains and time periodic solutions are discussed.
• [03042] Pulse bifurcations in a three-component FitzHugh-Nagumo system
  • Format : Talk at Waseda University
  • Author(s) :
    • Kei Nishi (Kyoto Sangyo University)
  • Abstract : Pulse dynamics in a three-component FitzHugh-Nagumo system in one dimensional space is considered. The system admits a pulse solution of bistable type, which exhibits a variety of interface dynamics, not observed for the two-component FitzHugh-Nagumo system. In order to analytically investigate the mechanism for the pulse behavior, we apply the multiple scales method to the original reaction-diffusion system, and derive finite-dimensional ordinary differential equations which describe the motions of the pulse interfaces. The reduced ODEs enable us to reveal the global bifurcation structures of the pulse solutions, and to clarify the mechanism behind the variety of the pulse dynamics from a view point of bifurcation theory.
• [05009] The Motion of Weakly Interacting Waves for Reaction-Diffusion Equations in a Cylinder
  • Format : Talk at Waseda University
  • Author(s) :
    • Chih-Chiang Huang (National Chung Cheng University )
    • Shin-Ichiro Ei (Hokkaido University)
  • Abstract : In the talk, I am going to introduce the well-known results of the weakly interaction of two waves in a real line, for the Allen-Cahn equation, the FitzHugh-Nagumo system and competition-diffusion systems. Next, I would like to discuss such an interaction for reaction-diffusion equations with a triple-well potential in a cylinder. In this case, we can construct a stable traveling wave which is made up by two repulsive fronts. Based on a perturbation theory, the wave profile and wave speed can be characterized by a small parameter. This work is joint with Prof. Shin-Ichiro Ei.

contributed talk: CT033

room : G502

[00132] Incompatibility-governed deformations: a new approach to Elastoplasticity

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G502
• Type : Contributed Talk
• Abstract : We present theoretical as well as numerical results concerning a novel approach to model elasto-plastic phenomena in deformable solids based on a decomposition of the total deformation tensor into a compatible (i.e., a symmetric gradient) and an incompatible part at each point of the domain. The incompatible part aims to model the part of the deformation due to dislocation movement that eventually is responsible for the creation of plastic regions. This is a joint work with Samuel Amstutz (Ecole Polytechnique de Palaiseau, France).
• Classification : 35J48, 49S05, 74C05, 74G99, 80A17
• Format : Talk at Waseda University
• Author(s) :
  • Nicolas Van Goethem (Universidade de Lisboa )

[01203] Existence and regularity results for nonlinear elliptic equations with degenerate coercivity

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G502
• Type : Contributed Talk
• Abstract : In this research we drive the existence and regularity results for solutions of some nonlinear degenerate Dirichlet problems containing two lower order terms, the fi rst is a nonlinear convection term satisfying an optimal growth conditions and without any hypothesis of coercivity and the second is a zero order perturbation term, which called the hardy potential, that creates an obstruction to the existence of a solution. Not also that for right hand side, it is assumed that to be an L^m-function with m⩾1.
• Classification : 35J60, 35K65, 35J70
• Format : Online Talk on Zoom
• Author(s) :
  • Fessel Achhoud (MISI Laboratory Hassan First University of Settat)
  • Abdelkader Bouajaja (MISI Laboratory Hassan First University of Settat)

[02424] Nonlinear fractional elliptic systems : Theory and Numerics

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @G502
• Type : Contributed Talk
• Abstract : In this talk, we focus on a class of elliptic systems with gradient source terms, governed by the fractional Laplacian $(-\Delta)^s$ of order $0
• Classification : 35J66, 35K57, 65N30, 35-00, 65-00
• Format : Online Talk on Zoom
• Author(s) :
  • Maha Daoud (Hassan II University of Casablanca)

MS [00220] Reaction-Diffusion Systems and Applications in life Sciences

room : G601

• [01711] Propagation dynamics of the Fisher-KPP nonlocal diffusion equation with free boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Yihong Du (University of New England)
  • Abstract : Propagation has been modelled by reaction-diffusion equations since the pioneering works of Fisher and Kolmogorov-Peterovski-Piskunov (KPP). Much new developments have been achieved in the past several decades on the modelling of propagation, with traveling wave and related solutions playing a central role. In this talk, I will report some recent results obtained with several collaborators on the Fisher-KPP equation with free boundary and "nonlocal diffusion", where the diffusion operator is given by a convolution integral instead of the traditional Laplacian operator. A key feature of this nonlocal equation is that the propagation may or may not be determined by traveling wave solutions. There is a threshold condition on the kernel function in the diffusion operator which determines whether the propagation rate is linear or superlinear in time, also known as accelerated spreading in the latter case, where the rate of spreading is not determined by traveling waves. For some typical kernel functions, sharp spreading rates will be presented.
• [03297] propagation phenomena of fractional diffusion equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Xing Liang (University of Science and Technology of China)
  • Abstract : In this talk, I will introduce our works on the propagation phenomena of fractional diffusion equations. The first part is about KPP-type equations in almost periodic media. We will show the existence of exponential speeds of propagation and a counterintuitive conclusion that faster diffusion yields slower propagation. The second part is about bistable and multi-stable equation in periodic media. We will show the existence of the traveling terrace and when the traveling terrace becomes a traveling wave.
• [02984] Sharp traveling waves for degenerate equations with time-delay: Fisher-KPP equations and Burgers equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Ming Mei (McGill University & Champlain College)
  • Abstract : In this talk, we are concerned with the degenerate diffusion equations with time-delay. The typical examples include Fisher-KPP equations and Burgers equations. The main issue is to investigate the structure of traveling waves, which are the sharp traveling waves with oscillations. The sharpness is caused by the degeneracy of diffusion, and oscillation is caused by the large time-delay.
• [03485] Accelerating propagation in a nonlocal model with periodic time delay
  • Format : Talk at Waseda University
  • Author(s) :
    • Jian Fang (Harbin Institute of Technology)
  • Abstract : In this talk, we investigate the accelerating propagation dynamics of a nonlocal population model with periodic time delay, which may arise from the study of stage-structured invasive species subject to seasonal successions. After establishing the fundamental solution of related linear equation, we obtain a sharp estimate for the solution level set.

MS [00135] Nonlinear PDEs and related diffusion phenomena

room : G602

• [03273] First order fully nonlinear nonlocal evolution equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Kagaya (Muroran Institute of Technology)
    • Qing Liu (Okinawa Institute of Science and Technology)
    • Hiroyoshi Mitake (University of Tokyo)
  • Abstract : This talk is concerned with geometric motion of a closed surface whose normal velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of first order nonlocal evolution equations in the framework of viscosity solution theory. We prove the uniqueness of solutions by establishing a comparison principle. Our existence result is based on careful analysis on parallel surfaces and an optimal control interpretation. We also mention several properties of the solution such as quasiconvexity preserving, fattening phenomenon and large time behavior.
• [02461] The generalized porous medium equation on graphs: Existence and uniqueness of solutions with l^1 data
  • Format : Talk at Waseda University
  • Author(s) :
    • Davide Bianchi (Harbin Institute of Technology (Shenzhen))
  • Abstract : We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node measure.
• [03236] Global regularity estimates for the Poisson equation on complete manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Ludovico Marini (University of Milano-Bicocca (soon at Fukuoka University))
    • Stefano Meda (University of Milano-Bicocca)
    • Stefano Pigola (University of Milano-Bicocca)
    • Giona Veronelli (University of Milano-Bicocca)
  • Abstract : In this talk, we investigate the validity of first and second-order, global $L^p$ estimates for the solutions of the Poisson equation. While these estimates always hold on $\mathbb{R}^n$, on complete non-compact manifolds their validity is strongly influenced by the large-scale geometry. I will present some positive results and discuss the sharpness of certain assumptions through counterexamples. This is a joint work with Stefano Meda, Stefano Pigola and Giona Veronelli of the University of Milano-Bicocca.
• [03203] Radial solutions to a semilinear equation on Riemannian models
  • Format : Talk at Waseda University
  • Author(s) :
    • Elvise Berchio (Politecnico di Torino)
    • Alberto Ferrero (Università del Piemonte Orientale)
    • Debdip Ganguly (Indian Institute of Technology Delhi)
    • Prasun Roychowdhury (National Center for Theoretical Sciences)
  • Abstract : We provide a classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation $\Delta_g u=e^u$ on Riemannian models. Our assumptions include Riemannian manifolds with sectional curvatures bounded or unbounded from below. As it is well-known in the Euclidean case, intersection and stability properties are influenced by the dimension; here the analysis highlights properties of solutions that cannot be observed in the flat case.

MS [00176] Hyperbolic PDEs modelling non-Newtonian fluid flows

room : G605

• [00332] Well-posedness and asymtotic behavior for hyperbolized compressible Navier-Stokes equations
  • Author(s) :
    • Yuxi Hu (China University of Mining and Technology, Beijing)
  • Abstract : We consider the non-isentropic compressible Navier-Stokes equations (CNS) for which the heat conduction of Fourier's law is replaced by Cattaneo's law and the classical Newtonian flow is replaced by a revised Maxwell flow. We shall present our recent results on global well-posedness, finite time blow-up and asymptotic behaviour of solutions. Some quality behaviour of solutions are shown to be changed, i.e., Global existence VS blowup in finite time, between the classical CNS and the studied hyperbolized model, although the solutions of two system are quite close to each other for small relaxation parameter.
• [00503] Structure preserving finite element schemes for a non-Newtonian flow
  • Author(s) :
    • Gabriel R. Barrenechea (University of Strathclyde, Glasgow, UK)
    • Tristan Pryer (University of Bath)
    • Emmanuil Georgoulis (Heriot-Watt University)
  • Abstract : We propose a finite element discretisation of a three-dimensional non-Newtonian flow whose dynamics are described by an Upper Convected Maxwell model. The scheme preserves structure in the sense that the velocity is divergence-free and the overall discretisation is energy consistent with the underlying problem. We investigate the problem's complexity and devise relevant timestepping strategies for effcient solution realisation. We showcase the method with several numerical experiments, confirm the theory and demonstrate the efficiency of the scheme.
• [00918] Temporal discretisation of non-Newtonian fluid flows
  • Author(s) :
    • Ben Ashby (Heriot-Watt University, Edinburgh, UK)
    • Tristan Pryer (University of Bath)
    • Gabriel Barrenechea (University of Strathclyde, Glasgow)
    • Emmanuil Georgoulis (Heriot-Watt University, UK & National Technical University of Athens, Greece)
  • Abstract : Choice of discretisation of the constitutive law for the stress in a non-Newtonian fluid is crucial for the success of any numerical method. We propose a new methodology for temporal discretisations of some non-Newtonian flows with the aim of preserving flow structure. We show that for models where both differential and integral constitutive laws are available, such as Oldroyd-B, a correspondence can be found between discretisations of both.
• [04850] New symmetric-hyperbolic PDEs for viscoelastic fluid flows
  • Author(s) :
    • Sébastien Julien Boyaval (Ecole des Ponts ParisTech)
  • Abstract : Many Partial Differential Equations (PDEs) have been proposed to model viscoelastic flows, in between fluids and solids. Seminal hyperbolic PDEs with stress relaxation have been proposed by Maxwell in 1867 to ensure propagation of 1D shear waves at finite-speed while capturing the viscosity of real fluid continua. But actual computations of multi-dimensional viscoelastic flows using Maxwell's PDEs have remained limited, at least without additional diffusion that blurs the hyperbolic character of Maxwell's PDEs. We propose a new system of PDEs to model 3D viscoelastic flows of Maxwell fluids. Our system, quasilinear and symmetric-hyperbolic, unequivocally models smooth flows on small times, while ensuring propagation of waves at finite-speed. Our system rigorously unifies fluid models with elastodynamics for compressible solids, and it can be extended for applications in environmental hydraulics (shallow-water flows) or materials engineering (non-isothermal flows).

MS [02613] Advances in Variational and Hemivariational Inequalities: Modeling, Analysis, and Applications

room : G606

• [04082] Recent Advances on Partial Differential Variational Inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • zhenhai Liu (guangxi minzu university)
  • Abstract : In this talk, we consider a partial differential complex system obtained by mixing an evolution partial differential equation and a variational inequality. This kind of problems may be regarded as a special feedback control problem. Firstly, we give our research motivation and examples. Then, based on the theory of semigroups, Filippov implicit function lemma and fixed point theory for set-valued mappings, we show several existence results of solutions to the mentioned problem. Finally we point out some problems for the further research.
• [03283] Optimal contol for variational inequalities of obstacle type
  • Format : Talk at Waseda University
  • Author(s) :
    • Zijia Peng (Guangxi Minzu University)
  • Abstract : This talk is concerned with optimal control of obstacle problems whose weak formulations are nonlinear variational inequalities. Under appropriate assumptions, existence of optimal solutions is proved. Moreover, the necessary optimality conditions of first order are derived by regularization techniques.
• [03248] Approximation techniques for solving hemivariational inequalities arising from contact mechanics
  • Format : Talk at Waseda University
  • Author(s) :
    • Li Zhibao (Central South University)
  • Abstract : Frictional contact phenomena are common in various industrial processes and engineering applications, and they can be described by variational or hemivariational inequalities. Most of these inequality problems lack analytical solutions. Hence, developing effective numerical methods to solve these inequalities is important. Hemivariational inequality is a useful tool to study nonlinear boundary value problems with nonsmooth and nonconvex functionals. With finite element discretization, HVIs become nonconvex optimization problems. In this talk, I will present some numerical methods based on approximation techniques to solve the nonconvex optimization problem for the hemivariational inequality arising from the frictional contact mechanics problem. These methods include the smooth quadratic regularization method, as well as the first and second order approximation methods for the nonconvex functions. I will also evaluate and compare these methods using numerical experiments at the end.
• [03265] A virtual element method for a quasistatic frictional contact problem
  • Format : Talk at Waseda University
  • Author(s) :
    • fang feng (East China Normal University )
    • Weimin Han (University of Iowa)
    • Jianguo Huang (Shanghai Jiao Tong University)
  • Abstract : We consider the numerical solution of an abstract quasistatic variational inequality arising in the study of quasistatic physical processes. The temporal discretization is carried out by the backward difference method, while the spatial discretization is based on the virtual element method. A general framework is provided and a quasistatic contact problem is studied and the optimal order error estimates are derived for the lowest-order virtual element method.

MS [00086] Recent advances in the theory of rogue waves: stability and universality of wave pattern formation

room : G701

• [05527] Universal rogue wave patterns and their connections with special polynomials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jianke Yang (University of Vermont)
  • Abstract : Rogue wave patterns in integrable systems are investigated. We show that universal rogue patterns of various types appear in integrable systems when one of the internal parameters in bilinear expressions of rogue waves gets large, and these universal rogue patterns can be predicted asymptotically by root structures of certain special polynomials, such as the Yablonskii–Vorob’ev polynomial hierarchy and the Okamoto polynomial hierarchies. This is joint work with Dr. Bo Yang of Ningbo University.
• [05532] Determinant formula for Rogue waves and the binomial theorem
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasuhiro Ohta (Kobe University)
  • Abstract : The rogue wave solutions for integrable systems are often given by the determinant formula for tau functions explicitly. The determinant expression is related with the binomial theorem of rational type. We report an observation about the bilinear structure for the tau functions derived through the binomial theorem.
• [05549] Two-dimensional rogue waves generated by resonance collision
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jingsong He (Shenzhen University)
  • Abstract : It is one of important topics to construct rogue waves in two-dimensional integrable systems. In recent years, we have obtained two kinds of rogue wave in few two-dimensional integrable systems by Hirota method. The generating mechanism of them is the resonant collision between different nonlinear waves. In this talk, two kinds of rogue wave of the Davey–Stewartson I equation are discussed with details by analytical and graphic ways. The main results have been published in two papers: Journal of Nonlinear Science 31(2021) 67 and Letters in Mathematical Physics112(2022)75, co-authored with Jiguang Rao, Athanassios S. Fokas, Yi Cheng.

MS [00215] Mathematical Advances in the nonlinear PDEs from physics

room : G702

• [03959] Polynomial tail solutions for Boltzmann equation in the whole space
  • Format : Talk at Waseda University
  • Author(s) :
    • Renjun Duan (The Chinese University of Hong Kong)
  • Abstract : We are concerned with the Cauchy problem on the Boltzmann equation in the whole space. The goal is to construct global-in-time bounded mild solutions near Maxwellians with the perturbation admitting a polynomial tail in large velocities. The main difficulty to be overcome in case of the whole space is the polynomial time decay of solutions which is much slower than the exponential rate in contrast with the torus case.
• [02793] Analytic regularization effect for the spatially inhomogeneous Boltzmann equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei-Xi LI (Wuhan University)
  • Abstract : We verify in this work the spatially inhomogeneous Boltzmann equation with strong angular singularity will admit the analytic smoothing effect, just like its diffusive models such as the Landau and Fokker-Planck equations. To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role in the proof
• [04010] Dispersive limit of kinetic models for collisional plasma
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhu Zhang (The Hong Kong Polytechnic University)
    • Tong Yang (The Hong Kong Polytechnic University)
  • Abstract : The motion of charged particles can be described by the Vlasov-Poisson-Boltzmann (VPB) system. Compared to the classical Boltzmann equation for dilute gases, solutions to VPB are expected to have dispersive behavior because of the dispersion mechanism on the dynamics of plasma in different scales of physical interest. By a formal spectrum analysis, we can observe asymptotic relations between VPB and some limiting dispersive equations in a suitable regime. Then we justify that the propagation of non-linear ions-acoustic waves are governed by the KdV equation. This is a joint work with T. Yang.
• [04067] Wave propogation and stabilization in the Boussinesq-Burgers system
  • Format : Talk at Waseda University
  • Author(s) :
    • Xianpeng Hu (City University of Hong Kong)
    • Anita Yang (The Chinese University of Hong Kong)
  • Abstract : In this talk, we will present the existence and stability of traveling wave solutions of the Boussinesq–Burgers system describing the propagation of bores. Assuming the fluid is weakly dispersive, we establish the existence of three different wave profiles by the geometric singular perturbation theory alongside phase plane analysis. We further employ the method of weighted energy estimates to prove the nonlinear asymptotic stability of the traveling wave solutions against small perturbations. The technique of taking antiderivative is utilized to integrate perturbation functions because of the conservative structure of the Boussinesq–Burgers system. Using a change of variable to deal with the dispersion term, we perform numerical simulations for the Boussinesq–Burgers system to showcase the generation and propagation of various wave profiles in both weak and strong dispersions. The numerical simulations not only confirm our analytical results, but also illustrate that the Boussinesq–Burgers system can generate numerous propagating wave profiles depending on the profiles of initial data and the intensity of fluid dispersion, where in particular the propagation of bores can be generated from the system in the case of strong dispersion. The talk is based on a recent joint work with Prof. Zhian Wang and Prof. Kun Zhao.

MS [01152] Recent trends in the mathematical theory for incompressible fluids

room : G703

• [03363] Uniform in gravity estimates for 2D water waves
  • Format : Talk at Waseda University
  • Author(s) :
    • Siddhant Agrawal (ICMAT)
  • Abstract : We consider the 2D gravity water waves equation on an infinite domain. We prove a local wellposedness result which allows interfaces with corners and cusps as initial data, such that the time of existence of solutions is uniform even as the gravity parameter $g \to 0$. As an application of the new energy estimate, we prove a blow up result for the water waves model where the fluid is homeomorphic to the disc.
• [04740] Invariant KAM tori around annular vortex patches for 2D Euler equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Zineb Hassainia (NYUAD)
    • Taoufik Hmidi (New York University Abu Dhabi)
    • Emeric Roulley (SISSA International School for Advanced Studies)
  • Abstract : We shall discuss the emergence of quasi periodic vortex patch solutions with one hole for the 2D-Euler equations. We prove the existence of such structures close to any annular vortex patch provided that its modulus belongs to a Cantor set with almost full Lebesgue measure. The proof is based on Nash-Moser implicit function theorems and KAM theory.
• [03663] Euler and Navier-Stokes equations. Quasi-periodic solutions and inviscid limit
  • Format : Talk at Waseda University
  • Author(s) :
    • RICCARDO MONTALTO (University of Milan)
  • Abstract : In this talk I will discuss some recent results on Euler and Navier Stokes equations concerning the construction of quasi-periodic solutions. In particular, I will focus on the construction of vanishing viscosity quasi-periodic solutions for the Navier-Stokes equation in the inviscid limit. The key step of the analysis is to implement Normal Form techniques which allow to prove sharp estimates (uniform in time) w.r. to the viscosity.
• [04625] Reducibility of a class of quasi-linear wave equation on the torus
  • Format : Talk at Waseda University
  • Author(s) :
    • Shulamit Terracina (Università degli Studi di Milano)
  • Abstract : We discuss the reducibility of a linear wave equation on the torus perturbed by a pseudo-differential potential of order 2 depending quasi-periodically on time. Under suitable conditions on the frequency vector, we develop a general strategy, combining Egorov theory with straightening of vector fields, to reduce to constant coefficients a class of weakly dispersive operators. Finally, we discuss generalizations to operators arising from the linearization of fluid models such as pure gravity Water Waves.

MS [00674] Modern numerical methods for PDE-constrained optimization and control

room : G704

• [03637] Recent Developments in Preconditioning for PDE-Constrained Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • John Pearson (University of Edinburgh)
  • Abstract : In this talk, we survey some recent research into numerical linear algebra for PDE-constrained optimization problems. In particular, we consider preconditioned iterative methods for the robust solution of resulting linear(ized) systems. Having provided some motivation for the construction of effective preconditioners, we briefly summarise some solution strategies devised by the speaker along with collaborators, for time-dependent problems, fluid flow control systems, and multiple saddle-point systems arising from PDE-constrained optimization.
• [01670] GKBO method for global optimization of non-convex high dimensional functions.
  • Format : Talk at Waseda University
  • Author(s) :
    • Federica Ferrarese (University of Verona and Trento)
  • Abstract : The study of numerical methods for global optimization of non-convex high dimensional functions has attracted a lot of attention in recent years. In this talk, a new efficient numerical method for global optimization inspired to classical algorithms will be presented. Different theoretical and numerical results will be shown comparing this algorithm to the classical ones. Finally, further extensions to localized versions of this algorithm, useful to minimize functions with multiple global minima, will be introduced.
• [01649] Online identification and control of PDEs via RL methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessandro Alla
    • Michele Palladino (Università degli studi dell'Aquila)
    • Agnese Pacifico (Sapienza, Università di Roma)
    • Andrea Pesare (Bending Spoons)
  • Abstract : In this talk we focus on the control of unknown Partial Differential Equations. Our approach is based on the idea to control and identify on the fly. The control, in this work, is computed using the State Dependent Riccati approach whereas the identification of the model on bayesian linear regression. At each iteration we obtain an estimation of the a-priori unknown coefficients of the PDEs based on the observed data and then we compute the control of the correspondent model. We show by numerical evidence the convergence of the method for infinite horizon problems.
• [03371] A statistical POD approach for feedback boundary optimal control in fluid dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luca Saluzzi (Scuola Normale Superiore di Pisa)
    • Sergey Dolgov (University of Bath)
    • Dante Kalise (Imperial College London)
  • Abstract : I consider feedback boundary optimal control problems and their reduction by the means of a Statistical Proper Orthogonal Decomposition, method characterized by the introduction of stochastic terms in the model to enrich the knowledge of the Full Order Model and in the collection of optimal trajectories as snapshots. The HJB equation is then solved by a data-driven Tensor Train Cross and applied to the control of the incompressible Navier-Stokes equation in a backward-step domain.

MS [00981] Various Methods for the Analysis of PDEs

room : G709

• [03982] Carleson's problem for infinitely many fermions
  • Format : Talk at Waseda University
  • Author(s) :
    • Neal Bez (Saitama University)
  • Abstract : Carleson's problem for the free Schrodinger equation is concerned with the minimal level of regularity that guarantees the solution converges to the initial data in an almost everywhere sense as time goes to zero. Here we consider a version of this problem for infinitely many particles.
• [05489] Stabilité results for the Sobolev inequality with computable constants and optimal behaviour
  • Format : Talk at Waseda University
  • Author(s) :
    • Maria J. Esteban (CNRS and University Paris-Dauphine)
  • Abstract : In this talk I will present recent results concerning optimal quantitative stability properties for the Sobolev and logarithmic-Sobolev inequalities with computable constants. The result for the Gaussian version of the logarithmic Sobolev inequality is actually a corollary of the one for Sobolev. This is done, in an optimal manner, by a limiting argument in high dimensions. This work is the result of a collaboration with J. Dolbeault, A. Figalli, R. Frank and M. Loss.
• [05451] Lifespan estimate for classical damped wave equations with some initial data
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazumasa FUJIWARA (Ryukoku university )
    • Vladimir Georgiev (Pisa University)
  • Abstract : The lifespan estimate for the Cauchy problem of the semilinear classical damped wave equation is estimated when the Fourier 0th mode of the initial data is 0. In earlier works, the lifespan was estimated based on the magnitude of the Fourier 0th mode of the initial data. We will explore the lifespan estimate by considering the magnitude of the Fourier 1st and 2nd modes of the initial data instead of the 0th mode.
• [05511] Blow-up for the 1d cubic NLS
  • Format : Talk at Waseda University
  • Author(s) :
    • Luis Vega (BCAM-UPV/EHU)
  • Abstract : We consider the 1D cubic NLS on R and prove a blow-up result for functions that are of borderline regularity, i.e. Hs for any s<−1/2 for the Sobolev scale and FL∞ for the Fourier-Lebesgue scale. This is done by identifying at this regularity a certain functional framework from which solutions exit in finite time. This functional framework allows, after using a pseudo-conformal transformation, to reduce the problem to a large-time study of a periodic Schrödinger equation with non-autonomous cubic nonlinearity. The blow-up result corresponds to an asymptotic completeness result for the new equation. We prove it using Bourgain's method and exploiting the oscillatory nature of the coefficients involved in the time-evolution of the Fourier modes. Finally, as an application we exhibit singular solutions of the binormal flow. More precisely, we give conditions on the curvature and the torsion of an initial smooth curve such that the constructed solutions generate several singularities in finite time. This is a joint work with V. Banica, R. Luca, and N. Tzvetkov

MS [00615] Nonlinear PDEs & Probability

room : G710

• [04215] A mixed-norm estimate of two-particle reduced density matrix of many-body Schrödinger dynamics for deriving Vlasov equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Li Chen (Universität Mannheim)
  • Abstract : We re-examine the combined semi-classical and mean-field limit in the N-body fermionic Schrödinger equation with pure state initial data using the Husimi measure framework. The Husimi measure equation involves three residue types: kinetic, semiclassical, and mean-field. The main result of this paper is to provide better estimates for the kinetic and mean-field residue than those in the authors' previous work. Especially, the estimate for the mean-field residue is shown to be smaller than the semiclassical residue by a mixed-norm estimate of the two-particle reduced density matrix factorization. Based on this estimate, we find that the mean-field residue is of higher order than the semiclassical residue. The talk is based on the joint work with Jinyeop Lee, Matthew Liew, and Yue Li.
• [03911] Hydrodynamic limit equations derived from microscopic interacting particle systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Makiko Sasada (University of Tokyo)
  • Abstract : Hydrodynamic limit provides a rigorous mathematical method to derive the deterministic partial differential equations describing the time evolution of macroscopic parameters, from the stochastic dynamics of a microscopic large scale interacting system. In this talk, by introducing the notion of a class of valid interacting particle systems, and we discuss what kind of equations can be derived from such interacting particle systems.
• [01645] The Vicsek-BGK equation in collective dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Raphael Winter (University of Vienna)
  • Abstract : The Vicsek-BGK equation describes the collective motion of agents with local alignment. It is known that the spatially homogeneous model undergoes a phase transition from disoriented motion to collective motion. In this contribution we give a prove the onset of a phase transition in the spatially inhomogeneous case. Joint work with Sara Merino Aceituno and Christian Schmeiser.
• [03240] Quasilinear SPDEs with rough paths
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexandra Neamtu (University of Konstanz)
    • Antoine Hocquet (Technical University of Berlin)
  • Abstract : We investigate quasilinear parabolic evolution equations driven by a $\gamma$-Hölder rough path, where $\gamma\in(1/3,1/2]$. This includes the Brownian motion and a fractional Brownian motion with Hurst index $H\in(1/3,1/2]$. We explore the mild formulation combining functional analytic techniques with the controlled rough paths approach. We apply our results to the stochastic Landau-Lifshitz-Gilbert equation for which we additionally prove the existence of stochastic flows. This talk is based on a joint work with Antoine Hocquet.

MS [00778] Analysis, Applications, and Advances in Metamaterials and Composites

room : G801

• [04081] Large-scale metasurface design with fast direct solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • Owen Miller (Yale University)
  • Abstract : Metasurfaces offer nanophotonic performance for centimeter-scale optics applications. Yet simulating such large structures is beyond current simulation capabilities. We demonstrate a 2D “fast direct” integral-equation solver that can simulate and design a high-efficiency, high-numerical-aperture metalens that is 20,000 wavelengths in diameter. For a visible wavelength of 500nm, this corresponds to a design diameter of 1cm, achieved with full simulations of Maxwell’s equations.
• [04889] Relaxation of variational principles for bounding the effective operators of composites
  • Format : Talk at Waseda University
  • Author(s) :
    • Aaron Welters (Florida Institute of Technology)
  • Abstract : An approach to the theory of composites is presented that allows a relaxation of the direct and dual minimization principles used to bound effective operators. This is based on representing the effective operator as the Schur complement of a positive semidefinite operator on a Hilbert space having a Hodge decomposition. We show the theory also applies in electric circuit theory for the Dirichlet-to-Neumann map and for the classical effective conductivity on a finite linear graph.
• [04890] Bessmertnyĭ realizations of effective tensors for metamaterial synthesis: conjectures and counterexamples
  • Format : Talk at Waseda University
  • Author(s) :
    • Anthony Dean Stefan (Florida Institute of Technology)
  • Abstract : Effective tensors of isotropic n-phase composites are known to be homogeneous multivariate Herglotz functions. Recently, M. Bessmertnyĭ claimed to characterize any such rational function as being in the Bessmertnyĭ class because each partial Wronskian associated with it has a polynomial sum-of-squares representation. We disprove this claim by providing a counterexample derived from the basis generating polynomial for the Vámos matroid and give a conjecture on the realizability of effective tensors. Joint work with Aaron Welters.

MS [00595] Combinatorial topological dynamics

room : G802

• [05133] Analyzing Network Representations of Dynamical Systems Using Persistent Homology
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elizabeth Munch (Michigan State University)
  • Abstract : Persistent homology, the flagship method of topological data analysis, can be used to provide a quantitative summary of the shape of data. One way to pass data to this method is to start with a finite, discrete metric space (whether or not it arises from a Euclidean embedding) and to study the resulting filtration of the Rips complex. In this talk, we will discuss several available methods for turning a time series into a discrete metric space, including the Takens embedding, and ordinal partition networks. Combined with persistent homology and machine learning methods, we show how this can be used to classify behavior in time series in both synthetic and experimental data.
• [01382] Topological Data Analysis of Spatiotemporal Honeybee Aggregation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elizabeth Bradley (University of Colorado)
    • Chad Topaz (Williams College)
    • Golnar Gharooni Fard (University of Colorado)
    • Varad Deshmukh (University of Colorado)
    • Orit Peleg (University of Colorado)
    • Morgan Byers (University of Colorado)
  • Abstract : We employ topological data analysis to explore honeybee aggregations in the context of trophallaxis: the exchange of food among nestmates. Using synthetic and laboratory data, we build topological summaries called CROCKER plots to capture the shape of the data as a function of both scale and time. Our results show two distinct regimes corresponding to successive dynamical regimes: a dispersed phase before the food is introduced, followed by a food-exchange phase in which clusters form.
• [03128] What does Multivector Fields Theory have to offer?
  • Format : Talk at Waseda University
  • Author(s) :
    • Michał Lipiński (Polish Academy of Sciences)
  • Abstract : The theory of Multivector Fields (MVF) is a generalization of Forman vector fields. It has been continuously developed since 2017. MVF theory is equipped with a number of fundamental dynamical concepts and matures into a useful combinatorial model for classical vector fields. In the talk I will present the general idea of the MVF theory, its suitability for the analysis in the spirit of topological data analysis, and its usefulness in understanding continuous dynamical systems.
• [03410] A Persistence-like Algorithm for Computing Connection Matrices Efficiently
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamal Krishna Dey (Purdue University)
  • Abstract : Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical tools for discrete data. Toward this goal, the classical theory for connection matrices has been adapted to combinatorial frameworks that facilitate computation. We develop an efficient persistence-like algorithm to compute a connection matrix from a given combinatorial (multi) vector field on a simplicial complex. This algorithm requires a single-pass, improving upon a known algorithm that runs an implicit recursion executing two-passes at each level. Overall, the new algorithm is more simple, direct, and efficient than the state-of-the-art. Because of the algorithm's similarity to the persistence algorithm, one may take advantage of various software optimizations from topological data analysis. This is a joint work with Michal Lipinski, Marian Mrozek, and Ryan Slechta

MS [00696] Scientific Machine Learning for Inverse Problems

room : G808

• [03213] Projected variational inference for high-dimensional Bayesian inverse problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Peng Chen (Georgia Institute of Technology)
  • Abstract : In this talk, I will present a class of transport-based projected variational methods to tackle the computational challenges of the curse of dimensionality and unaffordable evaluation cost for high-dimensional Bayesian inverse problems governed by complex models. We project the high-dimensional parameters to intrinsically low-dimensional data-informed subspaces, and employ transport-based variational methods to push samples drawn from the prior to a projected posterior. Moreover, we employ fast surrogate models to approximate the parameter-to-observable map. I will present error bounds for the projected posterior distribution measured in Kullback--Leibler divergence. Numerical experiments will be presented to demonstrate the properties of our methods, including improved accuracy, fast convergence with complexity independent of the parameter dimension and the number of samples, strong parallel scalability in processor cores, and weak data scalability in data dimension.
• [03215] Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lu Lu (University of Pennsylvania)
    • Min Zhu (University of Pennsylvania)
  • Abstract : Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here we address this challenge by using multifidelity learning, i.e., learning from multifidelity data sets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.
• [02629] Surrogate modeling for many-body hydrodynamic interactions via graph neural networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wenxiao Pan (University of Wisconsin-Madison)
  • Abstract : This talk presents a new framework, the hydrodynamic interaction graph neural network (HIGNN), for fast simulation of particulate suspensions. It generalizes the state-of-the-art GNN by 1) introducing higher-order structures in graph and 2) reducing the scaling of its prediction cost down to quasi-linear. The HIGNN, once constructed with low training cost, permits fast predictions of the particles' velocities and is transferable across suspensions of different numbers/concentrations of particles subject to any external forcing.
• [04531] A practical use of neural density estimators for Bayesian experimental design
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rafael orozco (Georgia Institute of Technology)
    • Mathias Louboutin (Georgia Institute of Technology)
    • Felix Herrmann (Georgia Institute of Technology)
  • Abstract : Neural density estimation is a powerful approach for learning conditional distributions, including Bayesian posteriors in inverse problems. While Bayesian statisticians find these methods promising, some practitioners remain skeptical about their practicality compared to deterministic solutions. We present a practical use case that exploits the posterior entropy minimization properties of conditional neural density estimators to identify optimal experimental designs. By utilizing normalizing flows, we demonstrate our technique’s scalability for tackling realistic 2D and 3D inverse problems.

MS [02277] New regularizing algorithms for solving inverse and ill-posed problems

room : G809

MS [00785] Learning Dynamical Systems by Preserving Symmetries, Energies, and Variational Principles

room : F308

• [01395] Symplectic Model Reduction on Quadratic Manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Boris Kramer (University of California San Diego)
  • Abstract : When Hamiltonian models are used for long-term simulation, constraints on CPU hours need to be met. Structure-preserving model reduction for Hamiltonian systems addresses this computational issue by projecting Hamilton’s equations of the full-order model onto linear symplectic subspaces, which can yield inaccurate results for problems with a slowly decaying Kolmogorov n-width. We present symplectic structure-preserving reduced-order modeling of Hamiltonian systems using quadratic manifolds. We demonstrate the proposed method on wave equations in 1-D and 2-D.
• [01373] Identification of variational principles, symmetries, and conservation laws from data
  • Format : Talk at Waseda University
  • Author(s) :
    • Yana Lishkova (University of Oxford)
    • Paul Scherer (University of Cambridge)
    • Steffen Ridderbusch (University of Oxford)
    • Mateja Jamnik (University of Cambridge)
    • Pietro Lio (University of Cambridge)
    • Sina Ober-Blöbaum (Paderborn University)
    • Christian Offen (Paderborn University)
  • Abstract : The identification of equations of motions of dynamical systems from data as well as dynamical properties such as symmetries and conservation laws is an important task in the context of system identification. I will show a framework based on Lie group theory to learn a variational principle governing a dynamical system which can identify variational symmetries and conservation laws along the way. Identified symmetries prove helpful when the learned equations of motions are integrated numerically.
• [01597] Data-driven structure-preserving model reduction for stochastic Hamiltonian systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomasz Tyranowski (Max Planck Institute for Plasma Physics)
  • Abstract : In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and the large number of independent Monte Carlo runs. We also extend the proper symplectic decomposition method to stochastic Hamiltonian systems, both with and without external forcing, and argue that preserving the underlying symplectic or variational structures results in more accurate and stable solutions that conserve energy better than when the non-geometric approach is used. We validate our proposed techniques with numerical experiments for a semi-discretization of the stochastic nonlinear Schrödinger equation and the Kubo oscillator.
• [01793] Learning video models with Lagrangian/Hamiltonian neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Christine Allen-Blanchette (Princeton University)
  • Abstract : The dynamics underlying object and camera motion in a video typically evolve on a low-dimensional manifold with unknown structure and dimension. While prior work has used the Hamiltonian formalism to give a physically meaningful interpretation to this manifold, the problem of discovering the manifold structure and dimension remains unaddressed. We introduce a Hamiltonian neural network for video generation where the structure and dimension of the phase-space are implicitly learned from data. To achieve this we introduce a GAN-based video generation pipeline which embeds a learned transformation from a Gaussian distribution to the phase-space manifold, and captures the underlying dynamics of the video in a Hamiltonian neural network motion model.

MS [02115] Theory and applications of random/non-autonomous dynamical systems Part III

room : F309

• [04171] Arcsine and Darling--Kac laws for piecewise linear random interval maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Kouji Yano (Osaka University)
  • Abstract : We give examples of piecewise linear random interval maps satisfying arcsine and Darling--Kac laws, which are analogous to Thaler's arcsine and Aaronson's Darling--Kac laws for the Boole transformation. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.
• [04000] Generalized uniform laws for occupation times of intermittent maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Toru Sera (Osaka University)
  • Abstract : Interval maps with indifferent fixed points are called intermittent maps. In this talk, we impose the condition that the orbit stays away from indifferent fixed points at the final observation time. Under this condition, we study the scaling limit of occupation times. This talk is based on joint work with Jon. Aaronson (Tel Aviv).
• [04085] Estimates of invariant measures for random maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoki Inoue (Ehime University)
  • Abstract : We consider a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. Especially, we consider random dynamical systems with indifferent fixed points and/or with unbounded derivatives. Under some conditions, such random dynamical systems have absolutely continuous invariant measures. We give some estimates of the absolutely continuous invariant measures.
• [04503] probability and ergodic theory for inner functions
  • Format : Talk at Waseda University
  • Author(s) :
    • jon aaronson (tel aviv university)
    • Kouji Yano (Osaka University)
  • Abstract : An analytic endomorphism of the unit disk is called an inner function if it's boundary limit defines a transformation of the circle - which is necessarily Lebesgue nonsingular. I'll review the ergodic theory of inner functions & present some results recently obtained with Mahendra Nadkarni.

MS [01074] Approximation Theory, Approximation Methods and Applications (ATAMA)

room : F310

• [04256] Approximation Theory, Approximation Methods and Applications: an introduction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stefano De Marchi (University of Padova)
  • Abstract : In this initial talk, I will briefly summarize why we have proposed such a mini-symposium, why approximation theory is still an important research subject for numerical and analytical analysts, and why approximation theory can help industrial applications. I will also outline the main contributions provided by all the speakers invited to this mini-symposium.
• [04857] On the quality of adaptive methods for numerical approximation
  • Format : Talk at Waseda University
  • Author(s) :
    • Leszek Plaskota (University of Warsaw)
  • Abstract : Methods for numerical approximation generally fall into two categories: nonadaptive algorithms and adaptive algorithms. By ‘adaptive’ we mean that in its successive steps the algorithm uses information about the underlying function obtained from the previous steps. If the function possesses some singularities and is otherwise smooth, then adaption is necessary to restore the right convergence rate. For globally smooth functions adaptive algorithms can essentially lower asymptotic constants. We present recent quantitative results on the subject.
• [05019] Monte Carlo approximation of non-autonomous Julia sets
  • Format : Online Talk on Zoom
  • Author(s) :
    • Maciej Klimek (Uppsala University)
  • Abstract : In the the metric space of compact, pluriregular and polynomially convex subsets of $\mathbb{C}^N$, both finite and infinite families of proper polynomial mappings generate a variety of Julia type compact sets, known also as the composite Julia sets. These sets can be interpreted as attractors of generalized iterated function systems. Since stochastic approximation of composite Julia sets is viable, some of those sets can be visualized with the help of Monte Carlo methods.

MS [00746] Variational methods for singularities and concentration on low dimensional sets

room : F312

• [04293] Ginzburg-Landau with Oblique Anchoring and Boojums
  • Format : Talk at Waseda University
  • Author(s) :
    • Lia Bronsard (McMaster University)
    • Stan Alama (McMaster University)
    • Dmitry Golovaty (The University of Akron)
  • Abstract : We study the Ginzburg-Landau functional with oblique angle condition via boundary penalization. We consider the singular limit and for strong anchoring strength, defects will occur in the interior, but for weaker anchoring strength all defects will occur on the boundary. These `boojums'' defects carry a fractional winding number and will occur in ordered pairs along the boundary. For the ``light" boojums, we prove an asymptotic convergence. S. Alama, D. Golovaty, P. Mironescu are collaborators.
• [04158] Dipole removal for discrete energy minimizers
  • Format : Talk at Waseda University
  • Author(s) :
    • Mircea Petrache (Pontificia Catolica Universidad de Chile)
    • Adriana Garroni (University of Rome La Sapienza)
    • Emanuele Spadaro (University of Rome La Sapienza)
  • Abstract : We consider a minimization problem for vector fields in the plane, allowing discrete vortex-like singularities, and we find conditions on the boundary datum on the boundary of a ball, under which the minimum-energy optimizer must have a single interior singularity. A consequence is that the screw dislocation energy minimizers with continuous boundary datum close enough to $u(\theta)=\theta$ will have exactly one charge. The approach passes by a discretized version of the problem of independent interest, connected to the initial problem via the Smirnov decomposition of 1-currents, and proved by a discussion based on the MaxFlow - MinCut theorem. The same strategy may apply to a larger class of problems with integer-degree topological singularities. Extension of the 1-charge result are given for cases where the minimum possible number of interior singularities is larger than 1, and we give counterexamples to further extensions of the result.
• [03999] From Volterra's dislocations to strain-gradient plasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Raz Kupferman (The Hebrew University)
    • Cy Maor (The Hebrew university)
  • Abstract : Dislocations, first classified by Volterra, can be viewed as generated by cut and weld procedures. It is only in the last 15 years that plasticity models have been derived rigorously as limits of models of finitely-many dislocations. In most of these works, the elemental dislocation is modeled as an “admissible” strain field, which is in a sense, a pre-assumed linearization of Volterra's model. I will show how strain gradient plasticity are obtained from Volterra's model.
• [01900] Harmonic dipoles in elasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Duvan Henao (Universidad de O'Higgins)
    • Marco Barchiesi (Università degli Studi di Trieste)
    • Carlos Mora-Corral (Universidad Autónoma de Madrid)
    • Rémy Rodiac (Université Paris Saclay)
  • Abstract : Malý (1993) proved that the relaxation of the neoHookean energy coincides with the neoHookean energy at diffeomorphisms, thus establishing the first existence result for neoHookean materials in 3D. We present some progress on the more explicit understanding of what deformations can fall into the weak closure of regular (injective, orientation-preserving, controlled Jacobian) maps and of the relaxed energy evaluated at deformations with singularities. For the pathological example of Conti & De Lellis (2003) we show that the singular energy is precisely twice the length of the dipole times the area of the bubble across which two portions of the elastic body which were separated in the reference configuration are now in contact in the deformed configuration. This, in turns, coincides with twice the total variation of the singular part of the derivative of the inverse map. We show that in the weak closure all maps have inverses with BV regularity, and in the axisymmetric case establish the Sobolev regularity for the first two components. In this axisymmetric case we obtain, as a lower bound for the singular energy, precise twice the variation of the singular part of the inverse. In the case of map with further SBV regularity for the inverse, we show that the singularities are dipoles, showing that the example of Conti & De Lellis is very generic.

MS [00675] New trends in (optimal) control theory

room : F401

• [01828] Stability of open quantum systems designed by reservoir engineering.
  • Format : Talk at Waseda University
  • Author(s) :
    • Rémi Robin (Laboratoire de Physique de l’école Normale Supérieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Université, PSL Research University)
    • Pierre Rouchon (Laboratoire de Physique de l’école Normale Supérieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Université, PSL Research University)
    • Lev-Arcady Sellem (Laboratoire de Physique de l’Ecole Normale Supérieure, Mines Paris, CNRS, ENS-PSL, Inria, Sorbonne Université, PSL Research University, Paris, France)
  • Abstract : Dynamically protected cat-qubits are an open quantum system that stabilizes a finite dimensional subspace of a quantum harmonic oscillator. Such a process is achieved through reservoir engineering, a method of coupling a high-quality cavity with a dissipative one. In this talk, we will present a new generalized LaSalle's invariance principle to prove the long time convergence of this system towards the finite dimensional subspace of interest.
• [01818] Turnpike phenomena in optimal control
  • Format : Talk at Waseda University
  • Author(s) :
    • Roberto Guglielmi (University of Waterloo)
  • Abstract : We provide a characterization of the exponential turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential stabilizability and detectability. The proof relies on the analysis of the exponential convergence of solutions to the differential Riccati equations to the algebraic counterpart, and on a necessary condition for exponential stabilizability in terms of a closed range test.
• [02571] Stabilization of traffic flow using fixed bottlenecks
  • Format : Talk at Waseda University
  • Author(s) :
    • Thibault Liard (University of Limoges)
  • Abstract : We study the asymptotic behavior of scalar conservation laws with local side constraints. Our aim is to construct a boundary feedback law, based on a sliding mode procedure, which globally stabilizes G-solutions of scalar conservation laws around a given stationary solutions. To that end, we will extend the notion of generalized characteristics to G-solutions. In the context of vehicular traffic, this leads to control the flow of cars at the tolls of a highway to reach a given target function. Thus, some bottlenecks could be created. Simulations using particle methods will be given to illustrate our results.
• [02530] Optimal Boundary Control for the semilinear Transport Equation under Uncertainty: A Turnpike Result
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Schuster (FAU Erlangen-Nuremberg)
    • Noboru Sakamoto (Nanzan University Nagoya)
  • Abstract : We show an integral turnpike result for an optimal Dirichlet boundary control problem with a semilinear transport equation in the sense that if the time horizon goes to infinity, then the dynamic optimal control converges to the corresponding steady state optimal control. Further we show that the integral turnpike result also holds if the initial data and/or the source term is uncertain with respect to a random variable

MS [00023] Recent advances on application driven nonlinear optimization

room : F402

• [01318] A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Zi Xu (Shanghai University)
    • Huiling Zhang (Shanghai University)
    • Guanghui Lan (Georgia Institute of Technology)
  • Abstract : Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this paper, we propose a unified single-loop alternating gradient projection $($AGP$)$ algorithm for solving smooth nonconvex-$($strongly$)$ concave and $($strongly$)$ convex-nonconcave minimax problems. AGP employs simple gradient projection steps for updating the primal and dual variables alternatively at each iteration. We show that it can find an $\varepsilon$-stationary point of the objective function in $O(\varepsilon^{-2})$ $($resp. $O(\varepsilon^{-4})$ $)$ iterations under nonconvex-strongly concave $($resp. nonconvex-concave$)$ setting. Moreover, its gradient complexity to obtain an $\varepsilon$-stationary point of the objective function is bounded by $\mathcal{O}(\varepsilon ^{-2})$ $($resp., $O(\varepsilon^{-4})$$)$ under the strongly convex-nonconcave $($resp., convex-nonconcave$)$ setting. To the best of our knowledge, this is the first time that a simple and unified single-loop algorithm is developed for solving both nonconvex-$($strongly$)$ concave and $($strongly$)$ convex-nonconcave minimax problems. Moreover, the complexity results for solving the latter $($strongly$)$ convex-nonconcave minimax problems have never been obtained before in the literature. Numerical results show the efficiency of the proposed AGP algorithm. Furthermore, we extend the AGP algorithm by presenting a block alternating proximal gradient $($BAPG$)$ algorithm for solving more general multi-block nonsmooth nonconvex-$($strongly$)$ concave and $($strongly$)$ convex-nonconcave minimax problems. We can similarly establish the gradient complexity of the proposed algorithm under these four different settings.
• [01287] Accelerated ADMM-type Methods for Convex and Noncovex Optimization Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianchao Bai (Northwestern Polytechnical University)
  • Abstract : In this talk, several accelerated stochastic and deterministic Alternating Direction Method of Multipliers, abbreviated as ADMM, are presented for solving separable convex optimization problems whose objective function is the sum of a possibly nonsmooth convex function and a smooth function which is an average of many component convex functions. We also show an advanced inexact accelerated ADMM for solving separable nonsmooth and nonconvex optimization problem. The convergence and complexity of these algorithms are discussed briefly, and a number of large-scale examples have verified the effectiveness of our algorithms compared with state-of-the-art first-order methods.
• [01284] On a special discrete phase constrained complex-field optimization problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Cong Sun (Beijing University of Posts and Telecommunications)
  • Abstract : Reconfigurable intelligent surface (RIS) with discrete phase shifts aided wireless communication network is considered. The resource allocation problem of sum rate maximization with power constraints and discrete phase shifts is solved. The complicated objective function is approximated by its upper bound. The difficult orthogonal constraint is penalized to the objective function through Courant penalty function technique. Two algorithms are proposed for the approximated problem based on alternating direction of multipliers method and proximal gradient method, respectively. Simulations show that the two proposed algorithms achieve higher sum rate with significantly lower computational cost than the sate of the art.
• [01368] Stochastic regularized Newton methods for nonlinear equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiani Wang (Chinese Academy of Sciences)
    • Xiao Wang (Peng Cheng Laboratory)
    • Liwei Zhang (Dalian University of Technology)
  • Abstract : In this talk, we study finding zeros of nonlinear equations, whose exact function information is normally expensive to calculate but approximations can be easily accessed via calls to stochastic oracles. Based on inexact line search we propose a stochastic regularised Newton method and investigate its global convergence and local convergence rate. We also propose a variant of algorithm incorporating variance reduction scheme and we establish its sample complexity. We also report some numerical results.

MS [00882] Geometric Shape Generation II: Design

room : F403

• [01784] Construcion of discrete zero mean curvature surfaces in Euclidean and Lorentz-Minkowski spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Masashi Yasumoto (Tokushima University)
  • Abstract : In this talk we first introduce discrete timelike minimal surfaces in Lorentz-Minkowski 3-space. Compared with other dicrete zero mean surfaces, discrete timelike minimal surfaces possess richer mathematical structures. Starting from discrete timelike minimal surfaces, we construct discrete zero mean curvature surfaces in Lorentz-Minkowski 3-space that can have both spacelike and timelike parts. As an application, we construct discrete holomorphhic functions and new discrete minimal surfaces in Euclidean space.
• [01406] Bifurcation of the trajectory shape in self-propelled motions
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Kitahata (Chiba University)
  • Abstract : We consider the motion of a self-propelled particle which is driven by the surface tension gradient originating from the concentration of the chemicals released from the particle itself. First, we discuss the trajectory shape of the particle confined in a circular region. Next, we discuss the bifurcation of the motion for the motion observed in the system with a self-propelled particle and a passive particle.
• [01771] Construction of weaving structures by standard realizations with repulsive interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Eriko Shinkawa
    • Motoko Kotani (Tohoku University)
    • Hisashi Naito (Nagoya University)
  • Abstract : We consider weaving structures. Let T be two sets of threads in 2-dimensional Euclidean space, where all the threads in each set are parallel and assign up/down information at their intersections. To find a suitable configuration of T in 3-dimensional Euclidean space, we take the energy that is given by the standard realization with repulsive interactions introduced by A. Dechant et al. We discuss the existence of energy minimizing configurations, which are called weaving structures.

MS [00888] Geometric Shape Generation I: Structures

room : F411

• [02773] Variational principle for generating discrete surfaces with piecewise constant Gaussian curvatures
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuki Hayashi (Kyoto University)
    • Yoshiki Jikumaru (Kyushu University)
    • Makoto Ohsaki (Kyoto University)
    • Takashi Kagaya (Muroran Institute of Technology)
    • Yohei Yokosuka (Kagoshima University)
  • Abstract : We derive a method to generate triangular meshes with piecewise constant Gaussian curvatures, in which the connection between the patches is G0 continuous. Gaussian curvature flows at interior vertices and those at the internal boundary are derived from the variational principle of the energy functional. The proposed method can generate the shape of the whole surface integrally using the derived flows.
• [02776] Geometric shape generation of hanging membranes
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshiki Jikumaru (Toyo University)
    • Yohei Yokosuka (Kagoshima University)
  • Abstract : In this talk, we present a differential geometric formulation of hanging membranes based on the equilibrium equations in the shell membrane theory and the variational principle. We also propose a geometric shape generation of hanging membranes.
• [05556] Proposal for a temporary structure with a mechanism capable of curved folding
  • Format : Talk at Waseda University
  • Author(s) :
    • Yohei Yokosuka (Kagoshima University)
    • Miyuki Koiso (Kyushu University)
    • Kento Okuda (National Institute of Technology, Sasebo College)
    • Toshio Honma (Kagoshima University)
    • Jun Mitani (University of Tsukuba)
  • Abstract : Temporary housing requires the rapid supply of numerous houses after a disaster. Therefore, it is useful to use architectural structures that utilizes curved folding, which enables the immediate development of a flat board into a three-dimensional structure. In this presentation, a pillow type box that maximizes the inner volume is adopted for the design shape, we demonstrate numerical analysis of rigid folding and scaled models of temporary structures with a mechanism capable of curved folding.
• [05623] Topology of vibrating shapes
  • Format : Talk at Waseda University
  • Author(s) :
    • Konrad Polthier (FU Berlin)
    • Jakub Rondomanski (FU Berlin)
    • Carlos Andres Palma (HU Berlin)
    • José D. Cojal González (HU Berlin)
    • Jürgen P. Rabe (HU Berlin)
  • Abstract : Vibrations of a parameter dependent set of physical shapes exhibit characterizing topological properties. We will discuss the topology of such vibrations based on a carefully selected metric and its holonomy. Overall, the choice of the metric embarks beyond the classical Berry connection. Applications aim at a better understanding of the topology of vibrating crystals.

MS [02408] Recent advances in two-phase flow influenced by thermal fluctuations

room : F412

• [03080] The stochastic Navier-Stokes-Allen-Cahn system with singular potential
  • Format : Talk at Waseda University
  • Author(s) :
    • Andrea Di Primio (Politecnico di Milano)
    • Maurizio Grasselli (Politecnico di Milano)
    • Luca Scarpa (Politecnico di Milano)
  • Abstract : In this talk, I consider the stochastic Navier-Stokes-Allen-Cahn system in a bounded domain of $\mathbb{R}^d$, with $d \in \{2,3\}$, and give some insights on the existence of martingale (in two and three dimensions) and probabilistically-strong solutions (in two dimensions). With respect to its deterministic counterpart, two independent cylindrical stochastic perturbations, which account for thermodynamical effects (e.g., microscopic collisions), are introduced. Moreover, a singular potential is considered, as prescribed by the thermodynamical derivation of the model.
• [03081] On some stochastic phase-field models of Cahn-Hilliard-Cook type with logarithmic potential
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luca Scarpa (Politecnico di Milano)
  • Abstract : We give an overview of some recent results on stochastic phase-field models with logarithmic potential, which cover the celebrated Cahn-Hilliard-Cook equation. Both the conservative and the non-conservative cases are considered, as well as degenerate and non-degenerate mobilities. Well-posedness, regularity, and long-time behaviour of solutions are discussed, with a mention on uniqueness-by-noise. The works presented in the talk are based on joint collaborations with A. Di Primio, Prof. M. Grasselli, and Dr. M. Zanella.

MS [00323] Integrating rough paths into domain applications

room : E501

• [01350] Signatures and Functional Expansions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bruno Dupire (Bloomberg)
    • Valentin Tissot-Daguette (Princeton University)
  • Abstract : Path dependent options can be generated by combinations of signatures. We focus on the case of one asset augmented with time. We construct an incremental basis of signature elements which allows us to write a smooth path dependent payoff as a converging series of signature elements. By recalling the main concepts of Functional Itô Calculus, a natural framework for path-dependence, we draw links between two approximation results, the Taylor expansion and the Wiener chaos decomposition. We also establish the pathwise Intrinsic Expansion and link it to Functional Taylor Expansion.
• [01349] Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Maud Lemercier (University of Oxford)
    • Cristopher Salvi (Imperial College London)
    • Andris Gerasimovics (University of Bath )
  • Abstract : Neural SDEs are a class of physics-inspired neural networks that are particularly well-suited for modelling temporal dynamics. However, they may not be the most appropriate tool to model systems that vary both in space and in time. In this talk, I will present a way to address this issue, leveraging the notion of a mild solution of an SPDE. I will introduce the Neural SPDE model and demonstrate its ability to learn solution operators of PDEs with stochastic forcing from partially observed data.
• [01332] Neural Controlled Differential Equations: The Log-ODE Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Benjamin Walker (University of Oxford)
  • Abstract : Neural controlled differential equations $($NCDEs$)$ are a powerful approach to time-series modelling. Their output is a linear map of a CDE's solution, where the vector field is learnt and the control is a continuous interpolation of the input data. This work demonstrates that NCDEs can achieve start-of-the-art performance on long time-series given two modifications: ensuring the vector field is smooth by bounding its Lip$(2)$-norm, and applying the Log-ODE method to the learnt vector field.
• [01297] Nowcasting with signatures
  • Format : Talk at Waseda University
  • Author(s) :
    • Lingyi Yang (Alan Turing Institute)
    • Samuel Cohen (University of Oxford)
  • Abstract : Nowcasting refers to inference of the recent past, present, or near future. This is common in economics as key indicators, like GDP, are published with significant delays due to data collection/cleansing. The signature, a mathematical object arising from rough analysis, captures geometric properties and handles missing data from complex sampling patterns. We look at nowcasting with regression on signatures and show that this simple model subsumes the popular Kalman filter in theory and performs well in practice.

MS [00672] Efficient inference for large and high-frequency data

room : E502

• [05600] Fast and asymptotically efficient inference for large and high-frequency data
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexandre Brouste (Le Mans Université)
  • Abstract : In this minisymposium, the notion of asymptotically statistical decision is discussed for various models appearing in finance and econometrics. In some applications, the large sample observation scheme is used. Asymptotical efficient statistical decisions and estimations are introduced for time series in econometrics (FARIMA, Threshold AR). For other applications, the data are acquired at high-frequency and in-fill observation scheme is considered. Asymptotical properties for the estimators of the parameters in the solutions of stochastic differential equations with jumps or with singular coefficients or in the rough volatility models in quantitative finance will be presented.
• [05624] On Adaptive Kalman Filtration
  • Format : Talk at Waseda University
  • Author(s) :
    • Yury Kutoyants (Le Mans University )
  • Abstract : We consider a linear partially observed system. The coefficients of this system depend on some unknown parameter. We study the problems of the construction of adaptive Kalman-Bucy filtration equations in the asymptotic of large samples. The properties of the MLE and BE are described. The adaptive filter is constructed in two steps. First we propose a method of moments preliminary estimator. Then this estimator is used for construction of One-step MLE-process. Finally we construct an adaptive recurrent filter.
• [05359] Fast calibration of weak FARIMA models
  • Format : Talk at Waseda University
  • Author(s) :
    • Youssef Esstafa (Le Mans Université )
  • Abstract : In this work, we investigate the asymptotic properties of Le Cam's one-step estimator for weak FARIMA models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator.
• [05613] Fast Inference for Stationary Time Series
  • Format : Talk at Waseda University
  • Author(s) :
    • Samir BEN HARIZ (Le Mans Université)
    • Marius Soltane (Université de Compiègne)
    • Alexandre Brouste (Le Mans Université)
    • Youssef Esstafa (Le Mans Université)
  • Abstract : Stationary processes are widely used to model temporal dependence in various random phenomena including Economy, Finance, Hydrology,... In the Gaussian case, statistical inference for such processes, which is well-known, often relies on the maximum likelihood estimation or its approximation using the Whittle method. The asymptotic variance is then optimal in both cases. However, these methods are generally computationally expensive or even extremely difficult to apply to large samples. We propose an alternative which is computationally fast while keeping the same asymptotic properties both in terms of speed and asymptotic variance. The procedure consists of applying a so-called one-step method to an initial estimator that is easy to implement and satisfies a certain condition on its convergence rate. The process begins by initializing the parameter estimate by a simple and eventually poor estimator. Once the initial estimates are determined, the iteration step begins. Using the score vector and the Fisher Information Matrix, the parameter estimates are updated. The updated estimates are obtained by taking a step proportional to the inverse of the Fisher Information Matrix multiplied by the score vector. The one-step estimation method is called so because it updates the parameter estimates only once per iteration. This makes it computationally efficient and relatively simple to implement compared to other more complex estimation methods. We will start with the simplest case where the process is Gaussian and then generalize this procedure to non-Gaussian processes. We also illustrate the numerical performance of this method through simulations and compare it to classical methods.

MS [00193] Adversarial robustness at the interface of analysis, geometry and statistics

room : E503

• [00265] Distributionally Robust Gaussian Process Regression and Bayesian Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose Blanchet (Stanford)
  • Abstract : We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our formulation seeks the best mean-squared error predictor, in an infinite-dimensional space, against an adversary who chooses the worst-case model in a Wasserstein ball around a nominal infinite-dimensional Bayesian model. The transport cost is chosen to control features such as the degree of roughness of the sample paths that the adversary is allowed to inject. We show that the game has a well-defined value (i.e., strong duality holds in the sense that max-min equals min-max) and that there exists a unique Nash equilibrium which can be computed by a sequence of finite-dimensional approximations. Crucially, the worst-case distribution is itself Gaussian. We explore properties of the Nash equilibrium and the effects of hyperparameters through a set of numerical experiments, demonstrating the versatility of our modeling framework.
• [01932] Adversarial distributional robustness from Wasserstein ascent-descent particle dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Camilo García Trillos (University College London)
    • Nicolas Garcia Trillos (University of Wisconsin Madison)
  • Abstract : We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings. Our algorithms, suggested by ascent-descent dynamics in a projected Wasserstein space, take the form of a system of interacting particles. We show the particle dynamics converge toward mean-field limit equations as the number of particles grows. In turn, the mean-field dynamics converge, as time goes to infinity, to epsilon-Nash equilibria of the original adversarial learning problem. We study, moreover, some advantages found on a nonconvex- strongly concave case -in a sense to be made precise in the talk-. Joint work with Nicolás García Trillos.
• [00273] Optimal Algorithms for Stochastic Nested Composition Optimization with Applications to Robust Training
  • Format : Online Talk on Zoom
  • Author(s) :
    • Krishnakumar Balasubramanian (UC DavisUC Davis)
  • Abstract : Many robust training problems could be cast in the form of optimizing a nested composition of $T$ functions. Examples include distributionally robust optimization, risk-averse learning, robust meta learning, etc. In this talk, I will discuss stochastic optimization algorithms for minimizing nested composition of $T$ functions with and without bi-level structures. Assuming access to noisy evaluations of the functions and their gradients through a stochastic first-order oracle, I will present an algorithm using moving-average stochastic estimates for solving the above problem. We show that the proposed algorithm can achieve a sample complexity of $\mathcal{O}(1/\epsilon^4)$ for converging to an $\epsilon$-stationary point of the problem. To the best of our knowledge, this is the first time that such an online algorithm designed for the (un)constrained multi-level setting, obtains the optimal sample complexity of the smooth single-level setting, under mild assumptions on the stochastic first-order oracle.
• [00274] Convergence of GDA for mean field two-player zero-sum games
  • Format : Talk at Waseda University
  • Author(s) :
    • Yulong Lu (University of Massachusetts Amherst)
  • Abstract : Min-max optimization problems arise from many problems in machine learning ,such as generative modeling and adversarial learning. In general, finding the global Nash-equilibrium of a two-player zero-sum game is difficult when the objective function lacks convexity and concavity assumptions. In this talk, I will introduce a mean-field setting of the game problem and discuss some global convergence results of GDA for finding mixed equilibria on the space of probability measures.

contributed talk: CT089

room : E505

[00694] Large deviation theory-based adaptive importance sampling for rare events in high dimensions

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
• Type : Contributed Talk
• Abstract : I will discuss our proposed method for estimating rare event probabilities for expensive-to-evaluate numerical models in high dimensions. The approach combines ideas from large deviation theory and adaptive importance sampling. Large deviation theory is used to find a good initial biasing distribution and to identify a low-dimensional subspace that is most informative of the rare event probability. We compare the method with a state-of-the-art cross-entropy-based importance sampling scheme.
• Classification : 65C05, 60F10, 62L12, 65F15, 65K10
• Format : Talk at Waseda University
• Author(s) :
  • Shanyin Tong (Columbia University)
  • Georg Stadler (New York University)

[00832] Monte Carlo estimation of equity measures for apportionment problem

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
• Type : Contributed Talk
• Abstract : A Markov chain Monte Carlo method is devised for the computation of several equity measures for the apportionment problem of assembly seats to electoral districts. Seat bias and Gini mean difference is of our primary interest in computing. Generating a random walk in the high-dimensional simplex is the key to our algorithm. It is helpful to estimate the mean and several quantiles of the target statistics.
• Classification : 65C05, 91G60, 60J22
• Format : Talk at Waseda University
• Author(s) :
  • Hozumi Morohosi (National Graduate Institute for Policy Studies)

[01001] Recent developments on low-discrepancy point sets for Markov chain quasi-Monte Carlo

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
• Type : Contributed Talk
• Abstract : We consider the problem of estimating expectations by using Markov chain Monte Carlo methods and improving the accuracy by replacing IID uniform random points with quasi-Monte Carlo (QMC) points. In this talk, we present short-period Tausworthe generators for Markov chain QMC optimized in terms of the $t$-value, which is a criterion of uniformity widely used in the study of QMC methods. In addition, we show the effectiveness in some numerical examples using Gibbs sampling.
• Classification : 65C10, 11K45, 65C05
• Format : Talk at Waseda University
• Author(s) :
  • Shin Harase (Ritsumeikan University)

[00396] A Stochastic Approach for the Computation of Large-Scale Matrix Functions

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
• Type : Contributed Talk
• Abstract : Although many scientific problems can be described in term of functions over matrices, their high computational cost and the lack of parallel and scalable numerical tools propel scientists to seek alternative solutions. In this talk, we will introduce a Monte Carlo method that is capable of computing matrix functions for large-scale datasets and in particular present how it can be used to solve time-fractional differential equations.
• Classification : 65C05, 35R11, 33E12, 60Gxx, 60K50
• Format : Talk at Waseda University
• Author(s) :
  • Nicolas Guidotti (INESC-ID, Instituto Superior Técnico, Lisboa)

[00476] Hierarchical Sampling Techniques and Goal-Oriented Adaptive Finite Element for Elliptic PDE with Lognormal Coefficients

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E505
• Type : Contributed Talk
• Abstract : We propose our Adaptive Multilevel Monte Carlo (AMLMC) method to solve an elliptic partial differential equation with lognormal random input data where the PDE model has geometry-induced singularities. This work combines (MLMC) and the dual-weighted-residual goal-oriented adaptive finite element. Specifically, for a given input coefficient realization and an accuracy level, the (AMLMC) constructs its approximate sample as the ones using the first mesh in the sequence of pre-generated, non-uniform meshes satisfying the sample-dependent bias constraint.
• Classification : 65C05, 65N50, 65N22, 35R60
• Format : Talk at Waseda University
• Author(s) :
  • Joakim Beck (King Abdullah University of Science and Technology)
  • Yang Liu (King Abdullah University of Science and Technology)
  • Erik von Schwerin (King Abdullah University of Science and Technology)
  • Raul Tempone (King Abdullah University of Science and Technology)

MS [01054] Scalable Solvers for Multiphysics Problems

room : E507

• [03836] Co-Design of Modelling and Monolithic Overlapping Schwarz Solvers in Chemo-Mechanics
  • Format : Talk at Waseda University
  • Author(s) :
    • Friederike Röver (TU Bergakademie Freiberg)
    • Bjoern Kiefer (TU Bergakademie Freiberg)
    • Stefan Prüger (TU Bergakademie Freiberg)
    • Oliver Rheinbach (TU Bergakademie Freiberg)
  • Abstract : The focus of this talk is the co-design of the variational formulations arising from model problems in chemo-mechanics and parallel iterative solvers from domain decomposition. We choose the FROSch framework of the Trilinos Software library as a parallel solver. It contains a parallel implementation of the GDSW preconditioner, which allows an algebraic construction. We present results applying FROSch to a fully coupled deformation-diffusion boundary value problem of a swelling hydrogel. For the FE-implementation, we use the deal.II software library and incorporate FROSch as a solver framework.
• [03397] A tensor-preserving domain decomposition preconditioner for high-order implicit methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Jing-Yuan Wang (University of Macau)
    • Yingzhi Liu (University of Macau)
    • Xiao-Chuan Cai (University of Macau)
  • Abstract : We investigate high-order block implicit methods for solving parabolic and unsteady Stokes problems, including the fully implicit Runge-Kutta method as a special case. These methods provide high accuracy with relatively large time step size, but the large, often nonsymmetric, and highly ill-conditioned stiffness matrix limits its practical use. To overcome this, we propose one- and two-level tensor-preserving domain decomposition preconditioners. Numerical experiments show the effectiveness and scalability of this approach for parabolic and Stokes flows.

MS [02178] Efficient computational methods for data matrices: exploiting sparsity and structure

room : E508

• [04733] Structured Matrices in Unsupervised Cross-Validation
  • Format : Talk at Waseda University
  • Author(s) :
    • Srinivas Eswar (Argonne National Laboratory)
  • Abstract : We consider matrix low-rank approximation algorithms in the setting of unsupervised cross-validation. Unlike most structured matrix computations, a cross-validation user has more control of sparsity, with different choices implying different performance trade-offs. For example, controlling the rank of these matrices results in a trade-off between efficiency and cross-validation accuracy. This talk surveys these choices and trade-offs. Additionally, this presentation will also introduce the minisymposium.
• [04283] Randomized Algorithms for Rank Structured Matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Per-Gunnar Martinsson (University of Texas at Austin)
  • Abstract : The talk describes randomized algorithms for computing a data sparse representation of a rank structured matrix (HSS, HODLR, H-matrix, ...). The algorithms are black box in that they interact with the target matrix only through its action on vectors, making them ideal for tasks such as forming Schur complements or matrix matrix multiplication. When the target matrix can be applied in O(N) operations, the compression as a whole typically has linear complexity as well.
• [03473] Scalable Data Analytics using Sparse Matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Giulia Guidi (Cornell University)
  • Abstract : Massively parallel systems are vital for processing large data and play a critical role in data analysis. However, programming high-performance computing systems poses productivity and scalability challenges. Here, we focus here on advances in genome sequencing and the associated flood of genomic data, which present computational challenges and require new approaches. This work demonstrates the feasibility of writing parallel code for irregular genomic computation through sparse matrix abstraction for de novo long-read genome assembly.
• [04632] Structure of Fisher information matrices in deep learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Rio Yokota (Tokyo Institute of Technology)
  • Abstract : Fisher information matrices have many applications in deep learning such as continual learning, generalization metrics, hyperparameter prediction, model sparsification, and optimization. The Fisher information matrix has a Kronecker product structure, which can be exploited to accelerate its computation. This talk will cover the various applications of Fisher information matrices, and its relation to Hessian and Gauss-Newton matrices, along with the theory behind its approximation through Kronecker factorization.

contributed talk: CT097

room : E603

[00835] A shifted LOPBiCG method for solving nonsymmetric shifted linear systems

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
• Type : Contributed Talk
• Abstract : Premature convergence of the seed system can lead to shifted systems being unsolved when applying shifted Krylov subspace methods to solve shifted linear systems. To avoid this, a seed-switching technique may be a method of choice; however, the conventional product-type methods cannot use this technique since it requires the collinear residuals between the seed and shifted systems. We propose a variant of the shifted BiCGStab method so that the technique can be applied.
• Classification : 65Fxx
• Format : Talk at Waseda University
• Author(s) :
  • Ren-Jie Zhao (Nagoya University)
  • Tomohiro Sogabe (Nagoya University)
  • Tomoya Kemmochi (Nagoya University)
  • Shao-Liang Zhang (Nagoya University)

[02053] An efficient preconditioner for the Riemannian trust-region method on the manifold of fixed-rank matrices

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
• Type : Contributed Talk
• Abstract : In 2010, Vandereycken and Vandewalle proposed a preconditioner for the Riemannian trust-region (RTR) method on the manifold of symmetric positive semidefinite matrices of fixed rank. Here, we generalize their work to the manifold of fixed-rank matrices. We use the RTR method with our preconditioner to solve a stiff time-dependent PDE, the Allen--Cahn equation, on the manifold of fixed-rank matrices. Numerical experiments show the efficiency of our preconditioner. This is joint work with Bart Vandereycken.
• Classification : 65F55, 65F45, 65F08, 65L04, 65L05
• Format : Talk at Waseda University
• Author(s) :
  • Marco Sutti (National Center for Theoretical Sciences, Mathematics Division, Taipei, Taiwan)

[00771] New class of Nested Hierarchical matrices and its applications

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
• Type : Contributed Talk
• Abstract : I'll discuss a new class of nested Hierarchical matrices in $2$D (HODLR2D^2). This is based on weak admissibility criteria and the compressions are done using NCA. Using this Hierarchical framework, one can perform matrix-vector product that scales almost linearly; hence, large dense linear systems arising out of $N$ body problems can be solved using iterative solvers with almost linear complexity. Also, I'll discuss its performance over other Hierarchical matrices and applications in solving integral equation and radial basis interpolation.
• Classification : 65F55, 65R20, 65R10, Numerical Linear Algebra
• Format : Talk at Waseda University
• Author(s) :
  • Ritesh Khan (Indian Institute of Technology Madras)
  • Sivaram Ambikasaran (Indian Institute of Technology Madras)

[01179] Applications of a Tiled Monte Carlo Algorithm to the Computation of Matrix Functions

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
• Type : Contributed Talk
• Abstract : We extend our prior work on Monte Carlo algorithms for solving large linear systems to compute other matrix functions such as exponential and logarithm. Our recent algorithm that computes with matrix tiles is shown to guarantee convergence for sufficiently large tiles. We compute matrix functions by summing a polynomial approximation (e.g. Taylor, Chebyshev). We investigate the convergence conditions for each function and optimize the algorithm by adjusting the parameters.
• Classification : 65F60, 65C05
• Format : Talk at Waseda University
• Author(s) :
  • Hyeji Choi (Stony Brook University)

[01226] Health Care: Robotic Dog for Navigation of a Rehabilitation Robot

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
• Type : Contributed Talk
• Abstract : One of the more recent technological advancements is assistive robots, which can improve patient-centered care in the health sector. This paper presents a unique set of continuous nonlinear control laws derived from a Lyapunov-based control scheme for navigation of an assistive robot and a rehabilitation wheelchair robot together modeled as a new autonomous robotic dog and rehabilitation wheelchair system. The computer simulations also present a qualitative analysis of the effectiveness of the control laws.
• Classification : 70B15, 93C85, 93D05, 93C10
• Author(s) :
  • Bibhya Nand Sharma (The University of the South Pacific )
  • Sandeep Kumar (The University of the South Pacific )

MS [00295] Estimation problems over groups

room : E604

• [05122] Vector bundles for alignment and dimensionality reduction
  • Author(s) :
    • Jose Perea (Northeastern University)
    • Luis Scoccola (Northeastern University)
  • Abstract : Vector bundles have rich structure and arise naturally when trying to solve dimensionality reduction and synchronization problems in data science. I will show in this talk how the classical machinery (e.g., classifying maps, characteristic classes, etc) can be adapted to the world of algorithms and noisy data, as well as the insights one can gain.
• [04867] Group-robust metrics
  • Format : Online Talk on Zoom
  • Author(s) :
    • William Leeb (University of Minnesota, Twin Cities)
  • Abstract : This talk will describe a family of metrics between functions. These metrics are provably robust to a large class of perturbations of the inputs, including the group of integral-preserving reparameterizations; they are also robust to additive noise, and can be evaluated rapidly. Their theoretical properties will be illustrated by numerical experiments.

MS [01605] Recent advances in computational methods for kinetic and hyperbolic equations

room : E702

• [03143] A Natural Model Reduction Framework for Kinetic Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Ruo Li (Peking University)
  • Abstract : To investigate a kinetic equation with prescribed low dimensional input data set, the solutions provided by the equation has to be confined in a low dimensional manifold. We propose in this article a natural framework for the model reduction of the kinetic equation with such the setup that an approximate solution manifold with finite dimension is available. The method results in a symmetric hyperbolic system automatically with natural assumptions. As the applications of the framework, we present some interesting cases, some of which gives brand-new models with elegant features. A few essential factors, including conservative quantities and entropy increasing, can be discussed in terms of the properties of the approximate the solution manifold.

contributed talk: CT107

room : E703

[00798] Accelerating Low-Order Matrix-Free Finite Element Methods for Geophysics on GPU Architectures

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
• Type : Contributed Talk
• Abstract : Low-order matrix-free FEMs offer an alternative approach that avoids the need to construct a global stiffness matrix. In this study, we compare the performance of low-order matrix-free FEMs with a sparse-matrix approach on GPU architectures for geophysics applications. Our results show that low-order matrix-free FEMs can significantly accelerate the solution of large linear systems on GPU architectures.
• Classification : 65M60, 86-08, 65F50
• Format : Talk at Waseda University
• Author(s) :
  • Yohann Dudouit (Lawrence Livermore National Lab)
  • Randy Settgast (Lawrence Livermore National Lab)
  • Nicola Castelletto (Lawrence Livermore National Lab)

[00930] Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
• Type : Contributed Talk
• Abstract : The Ericksen--Leslie equations are used to model liquid crystals in their nematic phase. We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept satisfies the weak-strong uniqueness property. We construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.
• Classification : 65M60, 35A35, 35Q35, 76A15
• Format : Talk at Waseda University
• Author(s) :
  • Maximilian Elias Vincenzo Reiter (Technische Universität Berlin)

[00852] Energy stable and positive DG scheme for Keller-Segel equations

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
• Type : Contributed Talk
• Abstract : This work is focused on discretization of the Keller-Segel equations for chemotaxis, a challenging problem due to its convective nature. Specifically, we introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin which is based on the gradient-flow structure of the equations. Also we present some numerical tests in accordance with the aforementioned properties of the discretization, showing a good behaviour in the case of chemotactic collapse, where very steep gradients appear
• Classification : 65M60, 35Q92, 92-10
• Format : Online Talk on Zoom
• Author(s) :
  • J. Rafael Rodríguez-Galván (Universidad de Cádiz)
  • Francisco Guillén-González (Universidad de Sevilla)
  • Daniel Acosta-Soba (Universidad de Cádiz)

[01018] VMS Stablized FEA of M-NS Equations For Nano Thermal Fluid

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E703
• Type : Contributed Talk
• Abstract : In this paper, we present a variable multiscale stabilised finite element metthod for NS equations with thermal transport for hybrid nano fluid flow. In particular algebraic approach of approximating the subscales has been considered and then the stabilization parameters are derived using Fourier analysis. Following that, we have derived an apriori error estimates. Also we have analysed the flow, velocity, pressure and temperature distribution over the bench mark problems viz. Multiply driven cavity flow.
• Classification : 65M60, 65M15, 65M22
• Author(s) :
  • Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)
  • B. V. Rathish Kumar (Indian Institute of Technology, Kanpur)
  • Anil Rathi (Indian Institute of Technology, Kanpur)

MS [00737] Numerical methods for semiconductor devices simulation and the computational lithography

room : E704

MS [00633] Unconventional numerical methods for advection-diffusion PDEs

room : E705

• [04883] Optimization-based, property-preserving algorithm for passive tracer transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Pavel Bochev (Sandia National Laboratories)
    • Kara Peterson (Sandia National Laboratories)
    • Denis Ridzal (Sanda National Laboratories)
  • Abstract : We present a new optimization-based property-preserving algorithm for passive tracer transport. The algorithm utilizes a semi-Lagrangian approach based on incremental remapping of the mass and the total tracer. However, unlike traditional semi-Lagrangian schemes, which remap the density and the tracer mixing ratio through monotone reconstruction or flux correction, we utilize an optimization-based remapping that enforces conservation and local bounds as optimization constraints. In so doing we separate accuracy considerations from preservation of physical properties to obtain a conservative, second-order accurate transport scheme that also has a notion of optimality. Moreover, we prove that the optimization-based algorithm preserves linear relationships between tracer mixing ratios. We illustrate the properties of the new algorithm using a series of standard tracer transport test problems in a plane and on a sphere.
• [04980] Multi-material ALE remap: interface sharpening in a matrix-free computation
  • Format : Talk at Waseda University
  • Author(s) :
    • Vladimir Z Tomov (Lawrence Livermore National Lab)
    • Tzanio Kolev (Lawrence Livermore National Laboratory)
    • Robert Rieben (Lawrence Livermore National Lab)
    • Arturo Vargas (Lawrence Livermore National Lab)
  • Abstract : We propose a new method for remap of material volume fractions, densities, and specific internal energies in the context of compressible ALE hydrodynamics. The remap is based on advection in pseudotime. As the volume fraction method can diffuse materials over many mesh elements, we introduce a sharpening modification on PDE level. We explain the effects of the modification and how it produces results that are still conservative and bounded. The latter involves FCT-type methods. The second major contribution, next to sharpening, is that all remap methods avoid assembly of global matrices. This avoids data motion and provides higher computational efficiency. Performed under the auspices of the U.S. Department of Energy under Contract DE-AC52-07NA27344 (LLNL-ABS-847808)
• [05104] Robust second-order approximation of the compressible Euler Equations with an arbitrary equation of state
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Joseph Tovar (Los Alamos National Laboratory)
    • Bennett Clayton (Texas A&M University)
    • Jean-Luc Guermond (Texas A&M University)
    • Matthias Maier (Texas A&M University)
    • Bojan Popov (Texas A&M University)
  • Abstract : This work is concerned with constructing a robust, high-order approximation of the compressible Euler equations for gas dynamics supplemented with an arbitrary or tabulated equation of state. In particular, we show how to construct a high-order graph-viscosity coefficient using an interpolated entropy pair useful when the equation of state is given by tabulated experimental data. Similarly, we construct an entropy surrogate functional that is used in a convex limiting technique that preserves the invariant domain of the system. Finally, the numerical method is then verified with analytical solutions and then validated with several benchmarks seen in the literature and laboratory experiments.
• [05153] Heuristic Topological Estimation of Reduced Order Model Basis Functions from PDE Solution Snapshots
  • Format : Talk at Waseda University
  • Author(s) :
    • Candace Pauline Diaz (Sandia National Laboratories)
    • Pavel Bochev (Sandia National Laboratories)
    • Denis Ridzal (Sandia National Laboratories)
  • Abstract : Proper Orthogonal Decomposition (POD) is a common approach to obtain reduced basis sets for projection-based model reduction. For some classes of problems, such as hyperbolic Partial Differential Equations (PDEs), POD does not always achieve reasonable order reduction due to the lack of exponential decay of the leading singular values. In this work we investigate persistent homology as an alternative approach for deriving reduced order basis functions that may be particularly parsimonious for such PDEs.

MS [01170] High Performance Multigrid Methods for Large-Scale Applications

room : E708

MS [01077] Recent Advances on Spectral Methods and Applications

room : E709

• [04186] A positive and moment-preserving Fourier spectral method
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhenning Cai (National University of Singapore)
    • Bo Lin (National University of Singapore)
  • Abstract : We present a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method and prove that it maintains spectral accuracy. To solve the optimization problem, we propose an efficient Newton solver that has quadratic convergence rate. Applications to the Boltzmann equation are considered in our numerical tests.
• [03237] Efficient structure-preserving spectral methods for plasma simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhiguo Yang (Shanghai Jiao Tong University)
  • Abstract : In this talk, we present H^1-, H(div) and H(curl)-conforming spectral method with exact preservation of the curl/divergence-free constraints for two typical PDEs arising from plasma simulations. One is the incompressible visco-resistive MHD system and the other one is the Vlasov-Ampere system. Two key ingredients, i.e. exact de Rham complexes and their commuting diagram, and the derivative property of the generalized Jacobi polynomials, are essential for the derivation of the desired basis functions. Besides, we propose a novel efficient solution algorithm based on simultaneous multiple-matrices diagonalisation technique. Ample 2D and 3D numerical examples illustrate both the accuracy and efficiency of the proposed methods.
• [04790] A deep adaptive sampling method for the approximation of PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kejun Tang (Changsha Institute for Computing and Digital Economy, Peking University)
    • Jiayu Zhai (ShanghaiTech University)
    • Xiaoliang Wan (Louisiana State University)
  • Abstract : In this work, we develop an adaptive sampling strategy when approximating the PDE solution with a neural network. Two neural networks will be trained simultaneously through a min-max optimization problem, which is formulated by coupling PINN and the optimal transport. One neural network is used as a surrogate model of the true solution and the other neural network is used to optimize the collocation points in the training set. Numerical experiments will be presented.
• [04098] A variable time-step scheme for Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yana DI (Beijing Normal University)
  • Abstract : In the talk, the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar auxiliary variable (SAV) scheme for Navier-Stokes equation with periodic boundary conditions (${Huang\; and\; Shen, SIAM\; J. Numer. Anal., 2021}$) has been generalized to a variable time-step IMEX-BDF2 SAV scheme. We derive global and local optimal $H^1$ error estimates in 2D and 3D, respectively. An adaptive time-stepping strategy has also been designed and numerical examples will confirm the effectiveness and efficiency of our proposed methods.

MS [00639] Analytical and computational aspects of topological photonics

room : E710

• [05207] Pseudo-magnetism and Landau Levels in strained 2-dimensional photonic crystals
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael I Weinstein (Columbia University)
  • Abstract : The principal use of photonic crystals is to engineer the photonic density of states, which controls light-matter coupling. We show theoretically that a strained 2D honeycomb photonic crystal can generate artificial electromagnetic fields and highly degenerate Landau levels, having high density of states. Since the tight-binding approximation is generally not applicable to photonics, we employ a multiscale analysis of the full continuum 2D Helmholtz wave equation and derive effective Dirac equations with pseudo-magnetic and pseudo-electric potentials for the dynamics of wave-packets. The deformation can be chosen to induce a constant pseudo-magnetic field, for which the effective Hamiltonian has Landau level spectrum. Our numerical simulations of the full continuum wave equations show mildly dispersive Landau levels, which we show can be “flattened" by adjusting the pseudo-electric potential. This theory is joint work with J. Guglielmon and M.C. Rechtsman. The predictions have recently been corroborated in optical experiments, in joint work with M. Barsukova, Z. Zhang, B. Zhen, L. He, F. Grisé, R. McEntaffer, S. Vaidya, J. Guglielmon and M.C. Rechstman
• [05298] Quantized Fractional Thouless Pumping of Solitons
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mikael Rechtsman (Penn State Univ)
  • Abstract : I will present my group’s recent work on the fractional pumping of solitons in photonic Thouless pumps. Specifically, I will show that the displacement (in unit cells) of solitons in Thouless pumps is strictly quantized to the Chern number of the band from which the soliton bifurcates in the low power regime; whereas in the intermediate power regime, nonlinear bifurcations lead to fractional quantization of soliton motion. This fractional quantization can be predicted from multi-band Wannier functions associated with the states of the pump.
• [04812] Topological insulators in semiclassical regime
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexis Drouot (University of Washington)
  • Abstract : I will study a semiclassical Dirac equation that originates in the field of topological insulators. The semiclassical regime allows to make sense of propagating and counter-propagating companion states. We'll derive speed and profile for wavepackets corresponding to topological edge states, and show that the counter-propagating state disperses strongly -- an unusual phenomena in the analysis of coherent states.
• [05311] Topological-cavity surface-emitting laser
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ling Lu (Institute of Physics, CAS)
  • Abstract : Contrary to the perception that the Nobel-winning topological physics has not found useful applications, we show that the textbook design of daily-life semiconductor lasers are equivalent to standard topological models in 1D. By upgrading to the 2D vortex zero mode, we invent the topological-cavity surface-emitting lasers (TCSEL) whose performance far exceeds that of the commercial counterparts. Finally, we demonstrate the monopole cavity in 3D with the optimal single-mode behavior, completing the kink-vortex-monopole trilogy of topological defect modes.

MS [01168] Network based reduced-order models for forward and inverse PDE problems

room : E711

• [02869] Regularized Lippmann-Schwinger-Lanczos Algorithm for Inverse Scattering Problems in the Frequency Domain
  • Format : Talk at Waseda University
  • Author(s) :
    • Justin Baker (University of Utah)
    • Elena Cherkaev (University of Utah)
    • Vladimir Druskin (Worcester Polytechnic Institute)
    • Shari Moskow (Drexel University)
    • Mikhail Zaslavsky (Schlumberger-Doll Research Center)
  • Abstract : Inverse scattering techniques have broad applicability in medical imaging, geophysics, and remote sensing. This talk presents a robust direct reduced order model (ROM) method for solving inverse scattering problems. The approach is based on a Lippmann-Schwinger-Lanczos (LSL) algorithm in the frequency domain with two levels of regularization. Results of numerical experiments for Schrodinger and Helmholtz problems show that the proposed regularization scheme significantly improves the performance of the LSL algorithm, allowing for good reconstructions with noisy data.
• [04821] Can one identify damped Stieltjes string from its spectral function?
  • Format : Talk at Waseda University
  • Author(s) :
    • Vladimir Druskin (WPI)
    • Jörn Zimmerling (Uppsala University)
    • Rob Remis (Delft University University)
  • Abstract : The Stieltjes strings were introduced by Gantmakher and Krein as isomorphic mechanical representations of the Stieltjes spectral functions. However, dissipative strings cannot be uniquely identified for the continuous spectral functions, corresponding to the unbounded domains. Generally, any passive transfer function can be represented as a Stieltjes function, that yields a wide class of equivalent solutions. We analyze constraints leading to the uniqueness for damped problems and numerical implementation in the data-driven ROM framework.
• [04751] Inverse scattering in attenuating media -- a ROM approach
  • Format : Talk at Waseda University
  • Author(s) :
    • Jörn Zimmerling (Uppsala University)
    • Vladimir Druskin (WPI)
    • Rob Remis (TU Delft)
  • Abstract : Inverse scattering problems in attenuating media arise in important applications in biomedical imaging or radar imaging. In inverse scattering the goal is to reconstruct the coefficients of a PDE based on remote measurements of scattered waves. Based on these measurements a reduced-order model can be constructed that goes beyond the typical data fitting. It has a special algebraic structure that allows analogies to finite-difference discretization of PDEs and facilitates efficient solution of the inverse problem.

contributed talk: CT118

room : E802

[00074] Chaos in multidimensional disordered nonlinear lattices

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E802
• Type : Contributed Talk
• Abstract : We study the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We perform an extensive numerical investigation of the dynamics of the considered model revealing (i) the effects of the type of the impurity (heterogeneity) parameter on the systems' transport properties and classify the transport mechanisms of the nonlinear versions of the models into various dynamical regimes. (ii) that for it's nonlineaar version, chaotic transport persists and (iii) chaotic hotspots meander in the region of energy concentration supporting the spreading mechanism of energy.
• Classification : 70K55, 70H07
• Format : Talk at Waseda University
• Author(s) :
  • Bob Senyange (Muni University)

[01141] On tensor-based training of neural networks

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @E802
• Type : Contributed Talk
• Abstract : In this work by resorting to the continuous ‘model’ of a shallow neural network, we present a novel training approach, that is based on a suitable approximate solution of a Fredholm integral equation of the first kind. Here, we concentrate on least-squares collocation, functional tensor networks and alternating ridge regression. Application of the algorithm to some supervised learning tasks is on par with other state-of-the-art approaches.
• Classification : 65R20
• Format : Talk at Waseda University
• Author(s) :
  • Patrick Gelß ( Zuse Institute Berlin)
  • Aizhan Issagali ( Freie Universität Berlin)
  • Ralf Kornhuber (Freie Universität Berlin)

MS [00353] Interpretable constrained tensor decompositions: models, algorithms, efficient implementations and applications

room : E803

• [05162] Speeding up Nonnegative Low-rank Approximations with Parallelism and Randomization.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Koby Hayashi (Georgia Institute of Technology)
  • Abstract : Many algorithms for constrained matrix and tensor factorization follow an alternating updating scheme. In such a scheme, the factor matrices are updated one at a time using some update rule. Computationally many update rules require the same bulk computations. That is the most expensive parts of the computations needed to perform an update are shared between update rules. Using this observation, we design a Framework for Alternating Updating NMF and NTF (FAUN). FAUN defines the bulk computations needed throughout an AU type algorithm allowing us to focus on optimizing these computations for multiple methods. Based on this we implement a distributed, highly parallel code called PLANC which optimizes computation and communication and allows for the use of various updating rules such as Hierarchical Least Squares, Nonnegative Least Squares, ADMM, Nesterov updates, ect… More recently we have explored the use of randomization in FAUN. As in the parallel case we can largely decouple the randomized aspects of the algorithms from the update rules.
• [03142] A probabilistic nonnegative tensor factorization method for tumor microenvironment analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Neriman Tokcan (University of Massachusetts Boston)
  • Abstract : The tumor microenvironment (TME) comprises the intricate environment surrounding cancer cells, such as stromal, immune, and extracellular elements. We have devised a probabilistic non-negative tensor factorization approach to model the TME of Hodgkin Lymphoma. We have also incorporated a statistical pipeline to produce robust and biologically relevant factors. Our methodology will enhance our understanding of the TME by identifying cellular heterogeneity and intrinsic pathways driving tumor growth and immune evasion.
• [03182] Scalable symmetric Tucker tensor decomposition
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ruhui Jin (UW-Madison)
    • Joe Kileel (UT-Austin)
    • Tamara Kolda (MathSci.ai)
    • Rachel Ward (UT-Austin)
  • Abstract : We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is in decomposing higher-order multivariate moments, which has special structure and is important to various data science problems. We advocate for a straightforward projected gradient descent (PGD) method and the higher-order eigenvalue decomposition (HOEVD) approximation as computation schemes. Most importantly, we develop scalable adaptations of the basic PGD and HOEVD methods to decompose sample moment tensors. With the help of implicit and streaming technique, we evade the overhead cost of building and storing the moment tensor. Such reductions make computing the Tucker decomposition realizable for large data instances in high dimensions. Numerical experiments demonstrate the efficiency of the algorithms and the applicability of moment tensor decompositions to real-world datasets. Finally we study the convergence on the Grassmannian manifold and prove that the update sequence derived by the PGD solver achieves first and second-order criticality
• [02021] A tensor factorization model of mulitlayer network interdependence
  • Format : Online Talk on Zoom
  • Author(s) :
    • Izabel Aguiar (Stanford University)
    • Dane Taylor (University at Buffalo the State University of New York)
    • Johan Ugander (Stanford University)
  • Abstract : We use the nonnegative Tucker decomposition (NNTuck) with KL-divergence as an expressive factor model for multilayer networks that naturally generalizes existing methods for stochastic block models of multilayer networks. The NNTuck provides a factor-based perspective on layer dependence, enabling linear-algebraic techniques for analyzing dependence in specific layers. We propose a definition of layer dependence based on a likelihood ratio test and evaluate the NNTuck in synthetic and real-world data.

MS [01218] Challenges in single-cell data science: theory and application

room : E804

• [03512] Geometry-aware high-dimensional vector field reconstruction using Hodge decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazumitsu Maehara (Kyushu University)
  • Abstract : We propose a method based on Hodge decomposition for analyzing high-dimensional and complex molecular dynamics using single-cell omics data. Drawing inspiration from topology and differential geometry, we developed a data-driven vector field reconstruction method that smoothly captures key features of dynamics (e.g., potential, divergence, curl, and Jacobian) with reduced computational costs through appropriate connections and regularization. Our approach has the potential to contribute to biological discoveries and understanding.
• [03922] Reconstructing single cell dynamics on graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianhua Xing (University of Pittsburgh)
  • Abstract : Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. A frontier of research is how to extract dynamical information from the snapshot data. I will first discuss our recently developed dynamo framework (Qiu et al. Cell, 2022), focusing on the underlying mathematical framework. Then I will discuss our recent efforts of reconstructing full dynamical equations using discrete calculus on graphs (Zhang et al. to be submitted).
• [04897] Deep generative models to reveal cellular level dynamics and communication
  • Format : Talk at Waseda University
  • Author(s) :
    • Teppei Shimamura (Tokyo Medical and Dental University)
  • Abstract : In this talk, we present a deep generative model for investigating the dynamic changes and interactions between cells that alter various states during the onset and progression of diseases from single-cell and spatial omics data.

MS [00184] Recent advances in data-driven methods for inverse problems

room : E811

• [03828] Recent advance of diffusion models in inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jong Chul YE (KAIST)
  • Abstract : Recently, diffusion models have been used to solve various inverse problems for medical imaging applications in an unsupervised manner. In this talk, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold.
• [04409] Conditional Image Generation with Score Based Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Jan Pawel Stanczuk (University of Cambridge)
    • Georgios Batzolis (University of Cambridge)
  • Abstract : Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional probability distributions with score-based diffusion models. In particular, we prove results which provide a theoretical justification for one of the most successful estimators of the conditional score. Moreover, we introduce a multi-speed diffusion framework, which leads to a new estimator for the conditional score, performing on par with previous state-of-the-art approaches.
• [01555] Data-Driven Convex Optimization via Mirror Descent
  • Format : Talk at Waseda University
  • Author(s) :
    • Hong Ye Tan (University of Cambridge)
    • Subhadip Mukherjee (University of Bath)
    • Junqi Tang (University of Cambridge)
    • Carola Bibiane Schoenlieb (University of Cambridge)
    • Andreas Hauptmann (University of Oulu)
  • Abstract : Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. We propose a provably approximately convergent learning-to-optimize scheme for convex optimization based on a functional parameterization of the classical mirror descent algorithm. In particular, we model the underlying convex function with an input-convex neural network and derive corresponding convergence rate bounds. We demonstrate improved convergence rates on various convex image processing examples.
• [03784] Multi-Modal Hypergraph Diffusion Network with Dual Prior for Alzheimer Classification
  • Format : Talk at Waseda University
  • Author(s) :
    • Angelica Aviles-Rivero (University of Cambridge)
  • Abstract : The automatic early diagnosis of prodromal stages of Alzhei\-mer's disease is of great relevance for patient treatment to improve quality of life. We address this problem as a multi-modal classification task. Multi-modal data provides richer and complementary information. However, existing techniques only consider lower order relations between the data and single/multi-modal imaging data. In this work, we introduce a novel semi-supervised hypergraph learning framework for Alzheimer’s disease diagnosis. Our framework allows for higher-order relations among multi-modal imaging and non-imaging data whilst requiring a tiny labelled set. Firstly, we introduce a dual embedding strategy for constructing a robust hypergraph that preserves the data semantics. We achieve this by enforcing perturbation invariance at the image and graph levels using a contrastive based mechanism. Secondly, we present a dynamically adjusted hypergraph diffusion model, via a semi-explicit flow, to improve the predictive uncertainty.

MS [00703] Combining machine learning with domain decomposition and multilevel methods

room : E812

• [04378] A Splitting Approach of Multilevel Optimization with an Application to Physics Informed Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Valentin Mercier (Université de Toulouse, IRIT, CERFACS, BRLi)
    • Serge Gratton (Université de Toulouse, INP-ENSEEIHT, IRIT,ANITI)
    • Philippe Toint (Namur Center for Complex Systems (naXys), University of Namur)
    • Elisa Riccietti (Université de Lyon, INRIA, EnsL, UCBL, CNRS)
  • Abstract : We propose a multilevel optimization algorithm, based on coordinate-block descent, to solve nonlinear problems while maintaining the advantages of multilevel methods. We demonstrate its effectiveness in solving complex Poisson problems using neural networks (NN) with PINN's method. We address the unique challenges posed by NNs, such as the F-principle, by employing frequency-aware network architectures. Overall, our approach offers a cost-effective solution for solving complex nonlinear optimization problems using neural networks.
• [04367] Improved Accuracy of Physics-Informed Neural Networks Using a Two-Level Training Approach and Lagrange Multipliers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Deok-Kyu Jang (Kyung Hee University)
    • Kyungsoo Kim (Kyung Hee University)
    • Hyea Hyun Kim (Kyung Hee University)
  • Abstract : In this talk, we introduce efficient techniques to enhance accuracy of Physics-Informed Neural Networks (PINNs) for solving second-order elliptic problems. We first present a two-level training approach incorporating a scaling process to capture high-frequency solution components more effectively at the first training stage, and a post-processing residual training step to resolve the remaining low-frequency components. We also introduce a non-overlapping domain decomposition method for PINNs where we employ Lagrange multipliers to enforce suitable interface conditions and boundary conditions so as to improve the solution accuracy further. We demonstrate the effectiveness of our proposed methods through numerical test examples.

MS [02386] Recent advances on theory and algorithms in deep learning applications

room : E817

• [03329] Generative Models Based Statistical Priors for Compressive Sensing and Medical Imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiulong Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Sparsity is a mathematically elegant tool for reducing the sampling rate for compressive sensing reconstruction and thereby its applications are also extended to many underdetermined imaging systems, such as MRI and CT. However, with the development of deep learning, there are many methods proposed to learn data representation and they are shown to be more efficient in signal and image processing. In order to efficiently and stably solve the under-determined and ill-conditioned inverse problems with fewer measurements, we established compressive sensing reconstruction methods using generative priors which are shown much more efficient than the traditional priors or some other data-driven priors. In this talk, I will introduce some of these methods and present our recent results for MRI reconstruction, phase retrieval, and some other nonlinear inverse problems.
• [03483] Normalizing-flows based design of experiments for failure probability estimation
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongqiao Wang (Central South University)
  • Abstract : Failure probability estimation problem is an crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this setting, reducing the calls of computer model is of essential importance. We formulate the problem of estimating the failure probability with expensive computer models as an sequential experimental design for the limit state (i.e., the failure boundary) and propose a series of efficient adaptive design criteria to solve the design of experiment (DOE). In particular, the proposed method employs the deep neural network (DNN) as the surrogate of limit state function for efficiently reducing the calls of expensive computer experiment. A map from the Gaussian distribution to the posterior approximation of the limit state is learned by the normalizing flows for the ease of experimental design. Three normalizing-flows-based design criteria are proposed in this work for deciding the design locations based on different assumption of generalization error. The accuracy and performance of the proposed method is demonstrated by both theory and practical examples.
• [03477] Unsupervised learning driven by Langevin dynamics and its applications to inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ji Li (Capital Normal University)
  • Abstract : From the Bayesian view, the key component of image restoration is to estimate the posterior distribution. Generally, the sampling from posterior distribution is intractable. To this end, there have been some variational approaches to approximate the posterior distribution using a proxy distribution. In this talk, we first review the Langevin dynamics as an effective sampler for a given distribution. Then we apply it or embed it to the unsupervised learning solution to two image restoration problems with slight modifications.
• [03450] Self-supervised Deep learning Methods in Imaging
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tongyao Pang (National University of Singapore)
  • Abstract : In this talk, I will share our recent research on using self-supervised deep learning techniques for image reconstruction. Deep learning has recently become a powerful tool in image restoration but it requires a large amount of paired training data. Our proposed self-supervised methods alleviate this requirement while still achieving comparable performance to supervised learning. Our methods are designed to find the minimum mean-squared error (MMSE) solution from a Bayesian inference perspective.

MS [02515] Novel deep learning methodologies in Industrial and Applied Mathematics

room : E818

• [05353] Artificial Intelligence for Wind Turbine Predictive Maintenance
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yolanda Vidal (Universitat Politècnica de Catalunya. Jordi Girona 31. 08034. Barcelona. VAT: ESQ0818003F)
  • Abstract : This proposal states a data-driven predictive maintenance (PM) strategy for wind turbines that uses artificial neural networks with Bayesian regularization and Levenberg-Marquardt optimization. The proposed strategy aims to address challenges associated with SCADA data such as high dimensionality, low sampling rate, and unbalanced datasets. The strategy will be validated on real SCADA data from a wind farm consisting of 12 wind turbines and is expected to provide reliable predictions with minimum false alarms and early warnings months in advance. This PM approach can help reduce the levelized cost of energy (LCOE) of wind farms and promote renewable energy as a cost-effective solution to achieve energy independence and combat climate change.
• [03575] Innovative Models for Explainable Artificial Intelligence
  • Format : Online Talk on Zoom
  • Author(s) :
    • Silvia Franchini (National Research Council of Italy)
    • Francesco Prinzi (University of Palermo)
    • Salvatore Vitabile (University of Palermo)
  • Abstract : Traditional data-driven ML approaches show very interesting performance even if their internal mechanisms are very cryptic (black box). However, in some critical contexts, model interpretability is mandatory to explain the learned functionality, becoming even a legal requirement. Among the benefits of reformulating neural networks through the geometric calculus paradigm, geometric interpretability could potentially serve as a characteristic that improves model transparency. This work proposes the use of higher-dimensional neurons to reduce computational complexity while preserving model accuracy.
• [05376] Applications of Quaternion Monogenic Signal ConvNet Layer
  • Format : Online Talk on Zoom
  • Author(s) :
    • E. Ulises Moya-Sanchez (Universidad Autonoma de Guadalajara/Gobierno de Jalisco)
    • Genaro Paredes (Universidad Autonoma de Guadalajara)
    • Sebastian Xambó-Descamps (UPC)
    • Ulises Cortes (BSC)
    • Abraham Sanchez (Gobierno de Jalisco)
  • Abstract : The monogenic ConvNet layer is a quaternion bio-inspired input layer. This layer creates a new geometric feature space using the Fourier transform. This new representation assigns a structural and geometrical interpretation to each image point and allows the detection of local symmetry elements (such as line-like or edge-like). Its main strength is that it behaves robustly under a variety of illumination transforms. In this work we present the design details and characteristics of this layer and consider a number of situations in which it can be applied.
• [05352] Novel deep learning methodologies in Industrial and Applied Mathematics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sebastian Xambó-Descamps (IMTech and BSC)
  • Abstract : This talk, with the same title as the MS, is meant to be the first and it aims at a broad presentation of the most promising novel methodologies in IAM based on deep learning techniques, with a particular attention focused on those pioneered by the MS speakers.

MS [02447] Advances in Diesel Engine Design and Control for Industry 4.0

room : E819

• [03642] XAI Based Fault Diagnosis for Steel Plates Manufacturing
  • Author(s) :
    • Athar Kharal (Center for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahuddin Zakariya University, Multan)
  • Abstract : This work uses Explainable Artificial Intelligence tools to develop a fault diagnosis classifier for steel plates. By incorporating insights from techniques such as Ceteris Paribus, Partial Dependence and Breakdown profiles, IF-THEN rules, and an optimized Random Forest and Association Rule Mining, the methodology sought to achieve a high performance using a single ensemble classifier. The methodology is based on medoids and SMOTE and provides valuable insights for experts in the steel manufacturing industry.
• [04142] Distinguishability of linear control systems
  • Author(s) :
    • Awais Younus (CASPAM, BZU, Multan)
    • Zoubia Dastgeer (CASPAM, BZU, Multan)
  • Abstract : Consideration of the observabilities of linear hybrid descriptor systems implies the distinguishability of these systems to be imperative. We have obtained some results related to the distinguishability of the descriptor systems. Also, we have attained equivalent criteria for input distinguishability of descriptor systems with a regular pencil.
• [04661] Optimizing Flow Parameters in Convergent Diesel Nozzles with Rough Walls
  • Author(s) :
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
    • Ms Saima Zainab (The Women University, Multan)
  • Abstract : Fuel injector nozzle geometry affect the diesel engine spray and combustion characteristics. This paper explores the effects of nozzle geometry parameters, wall roughness parameters and pressure difference on swirl number, mass flow rate, turbulent kinetic energy and vapor volume fraction. Large-eddy simulations and k-𝜔 SST Transient models are used to validate the modelling approach. Response Surface Method and Design of Experiment are used to optimize swirl number, turbulent kinetic energy and their linear combination.
• [04696] In-Cylinder Combustion Investigation Against Some Injection Characteristics
  • Author(s) :
    • Anam Ali (CASPAM BZU Pakistan)
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
  • Abstract : This study investigates the impact of fuel injection timing and spray angle on combustion characteristics of a heavy-duty diesel engine. CFD simulations are carried out by employing appropriate models to represent different physical and chemical processes. These parameters have significant role in engine design for enhanced combustion efficiency and engine performance. Late injection results into relatively smooth burning rates and considerably lower temperature and pressure peaks without significantly compromising the combustion quality and engine power.

contributed talk: CT138

room : D101

[00424] A Hydrodynamic Model for Active Polar Liquid Crystals

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @D101
• Type : Contributed Talk
• Abstract : We present a hydrodynamic model of active polar liquid crystals. We consider sheared active polar liquid crystals, and study dynamics of the polar order and shear rheology of the system. We show that shear may increase or decrease the polarization magnitudes. We derive the apparent viscosity formula showing a regime of negative apparent viscosity and a superfluid behavior for pushers, Our results echo previous results from numerical simulations and experiments.
• Classification : 76A15, 76A05
• Format : Talk at Waseda University
• Author(s) :
  • Zhenlu Cui (Fayetteville State University)

[02242] Metaheuristic based numerical solution and statistical optimization of heat transfer through rotating heat pipe

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @D101
• Type : Contributed Talk
• Abstract : This study presents the numerical solution for heat transfer through a rotating heat pipe filled with hybrid nanofluid Graphene oxide-molybdenum disulphide (GO-MoS2). The developed mathematical model is solved by hybridization of “Particle Swarm Optimization” along with finite difference method. Sensitivity of different parameters on heat transfer is analysed by fitting the full quadric regression model using response surface method. The identified parameters for heat transfer enhancement are nanoparticle concentration, inlet fluid mass and temperature difference.
• Classification : 76A20, 80M20, 65L06, 62P35, 90C31
• Format : Talk at Waseda University
• Author(s) :
  • Ziya Uddin (BML Munjal University, Gurugram)
  • Hamdy Hassan (Egypt-Japan University of Science and technology)
  • Souad Harmand (UPHF)
  • Wubshet Ibrahim (Ambo University)

[02351] THE WELL-POSEDNESS AND DISCONTINUOUS GALERKIN APPROXIMATION FOR THE NON-NEWTONIAN STOKES–DARCY–FORCHHEIMER COUPLING SYSTEM

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @D101
• Type : Contributed Talk
• Abstract : We establish the well-posedness theorem and study discontinuous Galerkin $($DG$)$ approximation for the non-Newtonian Stokes--Darcy--Forchheimer system modeling the free fluid coupled with the porous medium flow with shear/velocity-dependent viscosities. The unique existence is proved by using the theory of nonlinear monotone operator. In particular, we prove a coupled inf-sup condition to show the existence of pressure in $L^2(\Omega_1) \times L^\frac{3}{2}(\Omega_2)$. We also explore the convergence of the Picard iteration for the continuous problem. Moreover, we apply the DG method with $\mathbb{P}_k/\mathbb{P}_{k-1}$ element for numerical discretization and obtain the well-posedness, stability, and error estimate. For the discrete problem, we also investigate the convergence of the Picard iteration. The theoretical results are confirmed by the numerical examples.
• Classification : 76Axx, 76Sxx, 76Dxx, 65Nxx
• Format : Talk at Waseda University
• Author(s) :
  • Jingyan Hu (University of Electronic Science and Technology of China)
  • Guanyu Zhou (University of Electronic Science and Technology of China)

[01624] MHD free Convection of Casson fluid flow in an Inclined Square Cavity with Moving upper wall

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @D101
• Type : Contributed Talk
• Abstract : We have studied the natural convection of Casson fluid in a partially heated, inclined porous square cavity in the presence of external inclined magnetic field and viscous dissipation. In addition to these, it is assumed that the upper wall of the cavity is moving. We have used higher order Galerkin finite element method to solve the system of governing equations. Moreover, a comparative study for effects of various physical parameters has been done.
• Classification : 76A05, 76D05, 76M10, 76S05, 76W05
• Format : Online Talk on Zoom
• Author(s) :
  • Ram Dhan Mahla (University of Rajasthan)
  • Sharad Sinha (University of Rajasthan Jaipur )

MS [02567] Data-driven Computational Mechanics for Structures, Structural Dynamics, and Materials

room : D102

• [03424] Model Order Reduction for Fluid-Structure Interaction Analysis via the Data-driven Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • SiHun Lee (Seoul National University)
    • Sangmin Lee (Seoul National University)
    • Haeseong Cho (Jeonbuk National University)
    • SANGJOON SHIN (Seoul National University)
  • Abstract : Analysis on the multi-disciplinary analysis such as a fluid-structure interaction usually requires huge computational time due to nonlinearity and interpolation. In this research, a completely data-driven model order reduction method is considered that is capable of the parametric estimation regarding fluid-structure interaction analysis. The proposed method first constructs a snapshot matrix that contains various parametric result and then, singular value decomposition (SVD) is conducted. By SVD, proper orthogonal decomposition (POD) modes and coefficients will be gathered, which is interpolated by the machine learning technique.
• [05031] Data-driven Model Reduction Approach for Multiscale Homogenization of Microstructure
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyejin Kim (Jeonbuk National University)
    • Dahan Song (Jeonbuk National University)
    • Seongwoo Cheon (Jeonbuk National University)
    • Haeseong Cho (Jeonbuk National University)
  • Abstract : Given the heterogeneous nature of composite materials at the microscopic level, computational multiscale homogenization can be employed to obtain effective macroscopic material properties. However, it requires significant computational resources for recursive procedures. In this study, an efficient data-driven homogenization method is proposed. Herein, a clustering-based data-driven model reduction and autoencoder are utilized to alleviate high-dimensional data, followed by the application of a recurrent network model to predict the stress field of microstructure from loading conditions.
• [05220] An efficient neural network approximation of entropy solutions
  • Format : Talk at Waseda University
  • Author(s) :
    • Donsub Rim (Washington University in St. Louis)
    • Gerrit Welper (University of Central Florida)
    • Randall J LeVeque (University of Washington)
  • Abstract : We show that a family of neural networks with fixed number of layers and degrees of freedom, can approximate any entropy solution to scalar conservation laws and furthermore, the embedded dynamics in the free parameters is linear regardless of the complexity of the solution.

MS [02426] Mathematics of turbulent transport and coherent structures

room : D401

• [04104] Analysis of transport by coherent structures; overview
  • Format : Talk at Waseda University
  • Author(s) :
    • Kengo Deguchi (Monash University)
  • Abstract : A primary ongoing problem in fluid mechanics is the need to comprehend the large-scale average transport features of turbulent flows. For example, the prediction or improvement of heat/momentum transport is critical in a wide range of applications, but currently it relies on trial and error with massive amounts of experiments/simulations. A natural question arises: can we explain the mechanism of the transport logically based on Navier-Stokes equations? The key to the answer seems to lie in the coherent structures in turbulence, and an overview of recent developments will be given in the talk.
• [04490] Analysis, modeling, and simulation of slow-fast quasilinear dynamical systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Greg Chini (University of New Hampshire)
  • Abstract : We describe a new formalism for quasilinear systems exhibiting slow mean and fast, possibly unstable, linearized fluctuation dynamics. Using ODE and PDE models, we show that a slaving relation for the fluctuation amplitude can be derived by exploiting the tendency for the dynamics to self-organize on a slow marginal-stability manifold. Transient, fully nonlinear bursting events also can be predicted and systematically incorporated into our formalism. We conclude with an application to strongly stratified Kolmogorov flow.
• [04122] Steady coherent states in Rayleigh–Bénard convection
  • Format : Online Talk on Zoom
  • Author(s) :
    • Baole Wen (New York Institute of Technology)
    • David Goluskin (University of Victoria)
    • Gregory Chini (University of New Hampshire)
    • Charles Doering (University of Michigan)
  • Abstract : A central question in Rayleigh--B\'enard convection is how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ as $Ra\to\infty$. Experiments/simulations have yet to rule out either `classical' 1/3 or `ultimate' 1/2 asymptotic scaling. Here we show that certain steady rolls have classical 1/3 scaling and they transport more heat than turbulent experiments/simulations at comparable parameters. If turbulent heat transport continues to be dominated by steady transport asymptotically, it cannot achieve ultimate scaling.
• [04022] Optimal heat transport using branching flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anuj Kumar (University of California Santa Cruz)
  • Abstract : We are interested in the design of forcing in the Navier–Stokes equation such that the resultant flow maximizes the transport of a passive temperature between two differentially heated walls for a given power supply budget. Previous work established that the transport cannot scale faster than 1/3-power of the power supply. Recently, Doering & Tobasco (CPAM’19) constructed self-similar two-dimensional steady branching flows, saturating this upper bound up to a logarithmic correction to scaling. We present a construction of three-dimensional “branching pipe flows” that eliminates the possibility of this logarithmic correction and for which the corresponding passive scalar transport scales as a clean 1/3-power law in power supply. Our flows resemble previous numerical studies of the three-dimensional wall-to-wall problem by Motoki, Kawahara & Shimizu (J. Fluid Mech. vol.851, 2018, p.R4}). However, using an unsteady branching flow construction, it appears that the 1/3 scaling is also optimal in two dimensions. After carefully examining these designs, we extract the underlying physical mechanism that makes the branching flows “efficient.”

MS [01003] Mathematical Modeling and Simulation in Land-Ocean Transition Zones

room : D402

• [05596] An incremental SVD method for integro-differential equations: addressing storage and computational challenges
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yangwen Zhang (University of Louisiana at Lafayette)
    • Gang Chen (Sichuan University)
  • Abstract : At the current stage, it is widely recognized that the numerical solution of integro-differential equations with a memory term depends on all previous time instances. Consequently, the storage requirement increases linearly, while the computational complexity grows quadratically with the number of time steps. This presents a significant challenge for numerical simulations, and to the best of our knowledge, it remains an unresolved issue. In this paper, we present a memory-free algorithm, based on the incremental SVD technique, that exhibits only linear growth in computational complexity as the number of time steps increases. Rigorous error analysis and numerical experiments will be presented to validate our approach.
• [02217] Parameterizing the baroclinic instability with an artificial potential energy term
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qingshan Chen (Clemson University)
  • Abstract : In a numerical model that is under-resolved in the horizontal and/or vertical directions, baroclinic instability is often suppressed, leading to a build-up of layer interface slopes and potential energy that can not be released. In this work, we demonstrate, within the multilayer shallow water model and the Hamiltonian framework, how the baroclinic instability can be parameterized by adding an artificial potential energy term based on the slope of the interior layer interfaces.
• [05568] Boundary layer dynamics of wave-current flows over cylindrical canopies
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Ao Kan (Shanghai Jiao Tong University)
    • Rui Wang (Shanghai Jiao Tong University)
    • Hui Xu (Shanghai Jiao Tong University)
  • Abstract : Interactions of waves and currents with large roughness elements in the coastal ocean play a crucial role in drag generation and energy dissipation, which are quite different from the extensively-investigated smooth wall boundary layer or small-scale roughness. In the framework of high-order spectral/hp element method, the present study focuses on the analysis of implicit large eddy simulations of the combined current-wave flows over arrays of staggered circular cylinders with a diameter and a height of 0.5D. Unlike previous studies, our research examines array units that go beyond individual obstacles, enabling us to explore a wider range of physical mechanisms in turbulence, which consequently increases the computational complexity. By manipulating the wave amplitude, three distinct scenarios were obtained (i.e. pure current, weak wave and strong wave conditions, respectively) to analyze the effects of waves on currents or vice versa. The primary objective of current work is to investigate the energy transport mechanisms between the canopy and non-canopy layers, as well as the characteristics of the population of coherent structures. The dependences of energy budget, large-scale structures, sweeps and ejections are analyzed in detail.

MS [00869] Theory, numerics and data driven methods for fluids

room : D403

• [01423] Parameter analysis in continuous data assimilation for three-dimensional Brinkman-Forchheimer-extended Darcy model
  • Format : Online Talk on Zoom
  • Author(s) :
    • Débora Aparecida Francisco Albanez (Universidade Tecnológica Federal do Parana)
  • Abstract : Analytical results of the long-time behavior of three-dimensional Brinkman-Forchheimer-extended Darcy model in the context that the parameters related to the damping nonlinear term are unknown is presented. We show estimates in $L^2$ and $H^1$ for large-time error between the true solution and the assimilated solution, which is constructed with the unknown damping parameters and observational measurements obtained continuously in time from a continuous data assimilation technique.
• [04819] Boundary layers for a viscous fluid in a corner domain
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anna Mazzucato (Penn State University)
  • Abstract : We study boundary layers for incompressible slightly viscous fluids in a rectangular domain when steady shears are applied to the top and bottom side. We establish the vanishing viscosity limit using various types of correctors. In particular, we introduce suitable corner layer correctors at the corners. This is joint work with Gung-Min Gie (U. Louisville) and James Kelliher (UC Riverside).
• [03465] Numerical schemes for various stochastic models in hydrodynamic
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hakima Bessaih (Florida International University)
  • Abstract : We will introduce space-time numerical schemes for some stochastic models in hydrodynamic. The models include, the stochastic Navier-Stokes equations, the Boussinesq equations and some other models in porous media. We will also discuss various rates of convergences in probability and in mean square.
• [01351] Coupling of free flow and flow in porous media
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoming Wang (Missouri University of Science and Technology and Southern University of Science and Technology)
  • Abstract : We present some recent progress in the study of coupled free flow and porous media flow. In particular, we show that the several competing interface boundary conditions are asymptotically equivalent at the physically importance small Darcy number regime. We also offer a coarse-grained theory in predicting the deep vs shallow convections in the case when heat convection is involved. Effective numerical algorithms will be presented if time permits.

MS [00932] Some recent advances on time-modulated metamaterials

room : D404

• [04433] Modeling Plasmons on Graphene with Time- and Space-Dependent Properties
  • Format : Talk at Waseda University
  • Author(s) :
    • Fadil Santosa (Johns Hopkins University)
    • Tong Shi (University of Minnesota)
  • Abstract : Graphene sheets are two-dimensional materials that are known to support plasmonic modes. The latter are electromagnetic waves which are concentrated near a surface and propagate along it. In graphene, these modes can exist on both sides of surfaces of the 2-D material. It has been shown that graphene sheets are effective in its ability to concentrate light, and for this reason, it is a candidate for photonic devices. In this work, we study graphene sheets which have time- and space-dependent properties. They are modeled as a flat conductive sheet with time- and space-dependent Drude weights. We show that in two dimensions, the governing equations can be reduced to a single 1-D time-dependent integro-partial-differential equation. The equation can be discretized and also solved approximately using perturbation arguments. We demonstrate the accuracy of the approximate solution and also show interesting behavior of the plasmons when the Drude weight is modulated temporarily and spatially.
• [05163] Analytical and FDTD Modelling of EM Wave Interacting with Time-Varying Media
  • Format : Talk at Waseda University
  • Author(s) :
    • Debdeep Sarkar (Indian Institute of Science, Bangalore)
  • Abstract : First, we will focus on quasi-analytical ODE (ordinary differential equations) based methods to analyze velocity modulation imparted on EM (electromagnetic) waves interacting with infinitely extended time-varying medium. Later, we will examine EM wave interaction with finitely extended time-varying media using in-house Finite Difference Time Domain (FDTD) simulation methods. After critical observations on the generated reflection and transmission spectra of signals, we will comment on possible applications in next generation communication and Radar technologies.
• [04583] Using Time-Varying Systems to Challenge Fundamental Limitations in Electromagnetics and Photonics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Monticone (Cornell University)
  • Abstract : Time-varying systems offer opportunities for efficient electromagnetic and photonic devices, potentially surpassing various well-established theoretical limits, such as the Bode-Fano limit, the Chu limit, the Rozanov bound, delay-bandwidth limits, and others. At the same time, the characteristics of the temporal dimension create challenges and constraints that are unique to time-varying systems. In this talk, I will first review these opportunities and limitations, and will then discuss some of our recent research efforts in this area.
• [03155] Energy conserving temporal metasurfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Kshiteej Jayendra Deshmukh (University of Utah)
    • Graeme W Milton (University of Utah)
  • Abstract : Changing the microstructure properties of a space-time metamaterial while a wave is propagating through it, in general requires addition or removal of energy, which can be of exponential form depending on the type of modulation. This limits the realization and application of space-time metamaterials. In this work we present non-linear energy conserving temporal interfaces which address this problem.

MS [00877] Mathematical and Computational Methods for Topological Materials

room : D405

• [03694] Computation of phononic crystals using the PG finite element method
  • Format : Talk at Waseda University
  • Author(s) :
    • Liqun Wang (China University of Petroleum-Beijing)
  • Abstract : Phononic crystals are composite materials with periodic distribution of two or more media. The difficulty of computing the band structure of the phononic crystals lies in capturing the complex geometry and jump conditions effectively on the interface between the scatterer and the matrix. This talk will present the Petrov-Galerkin Finite Element Method for the band structure computation of phononic crystals, and the properties of various materials are also discussed.
• [05337] Conically degenerate spectral points of the periodic Schrödinger operator
  • Format : Talk at Waseda University
  • Author(s) :
    • Yi Zhu (Tsinghua University)
  • Abstract : Conical spectral points on the dispersion bands are the origin of many novel topological phenomena, including various topological phases. I will first review recent mathematical theories on these points, especially Fefferman & Weinstein's results (JAMS 2012) on 2D Dirac points, which paved the way for rigorous justifications of such points. Then I will focus on our recent progress in constructing 3-fold Weyl points at which two energy bands intersect conically with an extra band sandwiched in between. We give the existence of such points in the spectrum of the 3-dimensional Schrödinger operator H = −Δ+V (x) with V (x) being in a large class of periodic potentials. This is the first rigorous result on the existence of 3-fold Weyl points for a broad family of 3D continuous Schrödinger equations. Our result extends Fefferman-Weinstein's pioneering work to higher dimensions and multiplicities.
• [02726] Frozen Gaussian sampling for wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Lihui Chai (Sun Yat-sen University)
    • Ye Feng (Sun Yat-sen University)
    • Zhennan Zhou (Peking University)
  • Abstract : We introduce the frozen Gaussian sampling (FGS) algorithm to solve the wave equation in the high-frequency regime. The FGS algorithm is a Monte Carlo sampling strategy based on the frozen Gaussian approximation, which greatly reduces the computation workload in wave propagation and reconstruction. We propose feasible and detailed procedures to implement the FGS algorithm, and we analyze the error caused by the sampling algorithm with Gaussian initial conditions and WKB initial conditions respectively.

MS [02570] Parameter Estimation, Targeted Observation, and Data Assimilation in Coupled Systems

room : D407

• [04638] Improving Numerical Forecast Skill: Combinational Parameter Optimization and Coupled Data Assimilation
  • Format : Talk at Waseda University
  • Author(s) :
    • Seon Ki Park (Ewha Womans University)
  • Abstract : Numerical weather prediction (NWP) requires coupled modeling and data assimilation, and its forecast skill depends on uncertainties in physical parameterizations and initial conditions. This study illustrates that NWP skill can be improved through optimization of physical parameterizations and data assimilation; the former includes combinational optimization which seeks for the optimal set of parameterizations followed by optimal parameter estimation, whereas the latter develops the coupled data assimilation systems such as the WRF-Noah LSM and the WRF-Chem.
• [05388] Application of the CNOP-PEP method in hydrological ensemble prediction in China to reduce model parameter uncertainties
  • Author(s) :
    • Guodong Sun (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Mu Mu (Fudan University)
  • Abstract : In this talk, a conditional nonlinear optimal parameter perturbation ensemble prediction (CNOP-PEP) method is proposed. The CNOP-PEP method is employed to carry out ensemble prediction of evapotranspiration (ET) over Tibetan Plateau (TP). The numerical results show that ensemble prediction experiments conducted with the CNOP-PEP method exhibit better prediction skills compared to the reference ET over the TP. The prediction skill by employing the CNOP-PEP method is more excellent than those of the traditional methods.
• [05401] The effect of Westerly Wind Burst on ENSO
  • Author(s) :
    • Youmin Tang (University of Northern British Columbia)
  • Abstract : Westerly wind bursts (WWBs), as a semi-stochastic process, play a vital role in El Niño–Southern Oscillation (ENSO). However, current dynamical models have large challenges in the representation of WWBs. In this study, we introduced and developed several WWB parameterization schemes, including a novel scheme developed using the deep learning technique. The effect of these parameterization schemes on ENSO simulation and prediction was comprehensively evaluated and systematically compared using coupled models with varied complexity.
• [04422] Improving Model Uncertainty in Physical Parameterizations: Combinational Optimizations Using Genetic Algorithm in the Coupled Atmosphere-Chemistry Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Ji Won Yoon (Ewha Womans University)
  • Abstract : The Asian dust storm is one of the important air pollution problems in South Korea; thus, it is significant to improve the air quality forecasting skill using a numerical prediction system. In this study, we developed an optimization system by applying the micro-genetic algorithm (μGA) interfaced with the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) to enhance air quality forecasting skills in East Asia. We introduce the results of the combinational optimizations.

MS [00891] Derivative-Free Optimization Theory, Methods, and Software

room : D501

• [03615] Stochastic Average Model Methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Matt Menickelly (Argonne)
    • Stefan M Wild (Lawrence Berkeley National Laboratory)
  • Abstract : We consider finite-sum minimization problems in which the summand functions are computationally expensive, making it undesirable to evaluate all summands on every iteration. We present the idea of stochastic average model methods, which sample component functions according to a probability distribution on component functions that minimizes an upper bound on the variance of the resulting stochastic model. We present promising numerical results on a corresponding extension to the derivative-free model-based trust-region solver POUNDERS.
• [01372] DFO with Transformed Objectives and a Model-based Trust-region Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Pengcheng Xie (Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS))
  • Abstract : Derivative-free optimization, i.e., DFO, is the optimization where the derivative information is unavailable. The least Frobenius norm updating quadratic model is an essential under-determined model for derivative-free trust-region methods. We propose DFO with transformed objectives and give a model-based method with the least Frobenius norm model. We prove the existence and necessary and sufficient condition of model optimality-preserving transformations, and analyze the model, interpolation error and convergence property. Numerical results support our model and method.
• [01341] COBYQA — A Derivative-Free Trust-Region SQP Method for Nonlinearly Constrained Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Tom M. Ragonneau (The Hong Kong Polytechnic University)
    • Zaikun Zhang (The Hong Kong Polytechnic University)
  • Abstract : This talk introduces COBYQA, a derivative-free trust-region SQP method for nonlinear optimization. The method builds trust-region quadratic models using the derivative-free symmetric Broyden update. An important feature of COBYQA is that it always respects bound constraints. COBYQA is competitive with NEWUOA, BOBYQA, and LINCOA while being able to handle more general problems. Most importantly, COBYQA evidently outperforms COBYLA on all types of problems. COBYQA is implemented in Python and is publicly available at https://www.cobyqa.com/.
• [03192] A General Blackbox Optimization Framework for Hyperparameter Optimization in Deep Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Edward Hallé-Hannan (Polytechnique Montréal)
    • Sébastien Le Digabel (Polytechnique Montréal)
    • Charles Audet (Polytechnique Montréal)
  • Abstract : Tuning the hyperparameters of a deep model is a mixed-variable BBO problem with an unfixed structure. For instance, the number of layers (a hyperparameter) affects the number of architectural hyperparameters: meta variables are introduced to model this unfixed structure. Moreover, the hyperparameter optimization problem (HPO) may also simultaneously contain categorical, integer and continuous variables. A mathematical framework, which is compatible with direct search methods and Bayesian optimization, is proposed to tackle and model the HPO.

MS [02376] Recent Advances in Dynamic Games and Control Theory and Their Connection to Data Science

room : D502

• [03672] The Role of Information Structure in Games and Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Quanyan Zhu (New York University)
  • Abstract : The information structure of dynamic multi-agent systems plays a crucial role in determining the observation patterns of states, actions, and payoffs during interactions between agents. Differences in information structure can lead to surprising outcomes in a game. This talk aims to explore the role of information in dynamic games and learning. Specifically, we introduce the concept of the "price of information" and the "price of transparency" to quantify the gain or loss under different information patterns. We will discuss how information affects the strategic learning process, in which agents form beliefs based on their observations and generate policies based on those beliefs. Additionally, we will present how informational design can be used to incentivize agents and achieve the designer's goals at equilibrium in multi-agent systems.
• [02854] Optimal transaction mechanism for dynamic storage management game in smart grid
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasuaki Wasa (Waseda University)
  • Abstract : In this talk, we discuss an optimal transaction mechanism for a dynamic storage management game in smart grids in order to minimize the imbalance penalty charge of the grid in the wholesale electricity market. Our proposed mechanism is inspired by the primal-dual decomposition technique and the contract theory in economics. First, we present that the optimal power charge control profiles of the storage devices constitute a dynamic market equilibrium with a real-time pricing mechanism in a distributed fashion. Under the linear-quadratic dynamic grid model, the optimal design of the reference adjustment to modify the real-time pricing mechanism is analytically derived. The effectiveness of our proposed mechanism is also illustrated and discussed through simulation.
• [02858] Reinforcement Learning Algorithm for Mixed Mean Field Control Games
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jean-Pierre Fouque (University of California Santa Barbara)
  • Abstract : We present a new combined Mean Field Control Game (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between the groups. We propose a reinforcement learning algorithm to approximate the solution of such mixed Mean Field Control Game problems. We test the algorithm on benchmark linear-quadratic specifications for which we have analytic solutions. Joint work with A. Angiuli, N. Detering, Mathieu Laurière, and J. Lin
• [02930] Recent Advances on Fractional Optimal Control Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Moon (Hanyang University)
  • Abstract : In this talk, we study recent results on fractional control problems. We first consider the fractional optimal control problem with terminal and running state constraints in finite dimensions. Then we study the fractional optimal control problem (without state constraints) in infinite dimensions described by fractional evolution equations. For both problems, we obtain the Pontryagin maximum principle, which constitutes the necessary condition for optimality.

MS [01145] High dimensional recent computational approaches in finance and control

room : D505

• [03950] Learning to Simulate Tail-Risk Scenarios
  • Format : Talk at Waseda University
  • Author(s) :
    • Rama Cont (University of Oxford)
    • Mihai Cucuringu (University of Oxford)
    • Renyuan Xu (University of Southern California)
    • Chao Zhang (University of Oxford)
  • Abstract : The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. Scalability to large or heterogeneous portfolios involving multiple asset classes is particularly challenging, as is the accurate representation of tail risk. We propose a novel data-driven approach for the simulation of realistic multi-asset scenarios with a particular focus on the accurate characterization of tail risk for a given class of static and dynamic portfolios selected by the user. By exploiting the joint elicitability property of Value-at-Risk (VaR) and Expected Shortfall (ES), we design a Generative Adversarial Network (GAN) architecture capable of learning to simulate price scenarios that preserve tail risk features for these benchmark trading strategies, leading to consistent estimators for their VaR and ES. From a theoretical perspective, we show that different choices of score functions lead to different optimization landscapes and different complexities in GAN training. In addition, we prove that the generator in our GAN architecture enjoys a universal approximation property under the criteria of tail risk measures. In addition, we prove the bi-level optimization formulation between the generator and the discriminator is equivalent to a max-min game, leading to a more effective and practical formulation for training. From an empirical perspective, we demonstrate the accuracy and scalability of our method via extensive simulation experiments using synthetic and market data. Our results show that, in contrast to other data-driven scenario generators, our proposed scenario simulation method correctly captures tail risk for both static and dynamic portfolios in the input datasets.
• [04737] Learning mappings on Wasserstein space with mean-field neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • HUYEN PHAM (Université Paris Cité )
    • Xavier Warin (EDF)
  • Abstract : We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions. Two classes of neural networks based on bin density and on cylindrical approximation, are proposed to learn these so-called mean-field functions, and are theoretically supported by universal approximation theorems. We perform numerical experiments for training these two mean-field neural networks, and show their accuracy in the generalization error with various test distributions.
• [04743] Neural Optimal Stopping Boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Anders Max Reppen (Boston University Questrom School of Business)
    • Halil Mete Soner (Princeton University)
    • Valentin Tissot-Daguette (Princeton University)
  • Abstract : A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.
• [05236] MFG-OMO: An optimization framework for mean field game
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Guo (UC Berkeley)
  • Abstract : We propos a new mathematical paradigm to analyze discrete-time mean-field games. It removes the contractive and the monotone assumptions and the uniqueness of the Nash equilibrium imposed in existing approaches for mean-field games. We show that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization problem with bounded variables and simple convex constraints, called MF-OMO. This equivalence framework enables finding multiple (and possibly all) Nash equilibrium solutions of mean-field games by standard algorithms. For instance, projected gradient descent is shown to be capable of retrieving all possible Nash equilibrium solutions when there are finitely many of them, with proper initializations. Moreover, analyzing mean-field games with linear rewards and mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. Based on joint work with Anran Hu (University of Oxford) and Junzi Zhang (Amazon).

MS [00589] Computational Biomedical Physics and Mechanics

room : D514

• [01471] A Multi-Scale Approach to Model K+ Permeation Through the KcsA Channel
  • Format : Talk at Waseda University
  • Author(s) :
    • Tzyy-Leng Horng (Feng Chia University)
    • Ren-Shiang Chen (Tunghai University)
    • Maria Vittoria Leonardi (University of Perugia)
    • Fabio Franciolini (University of Perugia)
    • Luigi Catacuzzeno (University of Perugia)
  • Abstract : K+ channels allow a very efficient passage of K+ ions through the membrane while excluding Na+ ions, which is essential for life. The 3D structure of the KcsA K+ channel allows to address many relevant aspects of K+ permeation and selectivity mechanisms at the molecular level. Using a multi-scale approach, we studied the mechanism of K+ permeation through KcsA channels and reproduced the main permeation properties of the KcsA channel found experimentally.
• [02551] Modeling electrohydrodynamic flow through a nanochannel
  • Format : Talk at Waseda University
  • Author(s) :
    • Kumar Saurabh (National Health Research Institutes)
    • Maxim A Solovchuk (National Health Research Institutes)
  • Abstract : Fluid-ion transport through a nanochannel can be described through coupled fourth order-Poisson-Nernst- Planck-Bikerman (4PNPBik) and Navier-Stokes equations. The 4PNPBik model describes ionic and nonionic interactions between particles while accounting for the effect of polarization of the medium, electrostatic correlations, solvation of ions etc. Navier-Stokes equations model the hydrodynamics of the system. Governing equations are discretized using lattice Boltzmann method on GPU. Impact of phenomenon like viscoelectric effect, finite size of particles, velocity slip, non-homogeneous diffusion etc. has been studied.
• [02740] Double diffusion for nanofluid
  • Format : Talk at Waseda University
  • Author(s) :
    • Yende Chou (National Taiwan University)
    • Maxim A Solovchuk (National Health Research Institutes)
    • Wei-Shien Hwang (National Taiwan University)
  • Abstract : In double diffusion problems, fluid is driven by temperature and concentration differences within the flow field. By adding nanoparticles into the fluid to form a nanofluid, heat transfer and mass transfer can be enhanced. This study investigates the effect of volume fraction of nanoparticles on heat and mass transfer in a three-dimensional square cavity. The governing equations for this problem are mass conservation, momentum conservation, energy conservation and mass transfer equations. The finite volume method is applied to discretize these equations. Multigrid method is developed for the solution of flow problem to improve computational efficiency.
• [03003] GPU Computation of High-Intensity Focused Ultrasound Ablation Under Different Pathways
  • Format : Talk at Waseda University
  • Author(s) :
    • Tatiana Filonets (National Taiwan University)
    • Maxim Solovchuk (National Health Research Institutes)
  • Abstract : High-performance computing is important to accelerate the numerical solutions of partial differential equations which are used for modeling high-intensity focused ultrasound and temperature. The nonlinear Westervelt equation was coupled with the bioheat equation to model temperature under ultrasound sonication. CUDA program was developed for GPU to speed up computations. An appropriate scanning pathway can help to ablate a big tumor volume uniformly within a few minutes considering that cavitation can also affect the lesion form.

MS [02370] Recent advances in Ultrasound Biomedical Imaging

room : D515

• [05140] Applications of Spatial Coherence to Ultrasonic Imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • David Pierson Bradway (Duke University)
    • Gregg Trahey (Duke University)
    • Nick Bottenus (University of Colorado Boulder)
    • Will Long (Duke University)
    • James Long (Rice University)
    • Katelyn Flint (Duke University)
    • Matthew Huber (Duke University)
  • Abstract : Conventional pulse-echo ultrasound imaging relies primarily on signals’ relative magnitudes and is limited in its ability to mitigate acoustic clutter and other types of image degradation. Advances in computing power have recently enabled an alternative data analysis method utilizing spatial coherence, a measure of the similarity of the signals received across an ultrasound array. The theory of spatial coherence and applications to diagnostic medical ultrasound imaging will be reviewed.
• [04772] A local space-invariant approximation for DAS Point Spread Function computation
  • Format : Talk at Waseda University
  • Author(s) :
    • Chiara Razzetta (DIMA - Università di Genova)
    • Valentina Candiani (University of Genoa)
    • Federico Benvenuto ( DIMA - Università di Genova)
    • Marco Crocco (Esaote S.p.A.)
  • Abstract : The Delay And Sum (DAS) algorithm is the standard technique for ultrasound image reconstruction, it is usually implemented on the hardware of the ultrasound device and it depends on several parameters set in the machine. This makes it possible to produce real time images but at the same time it is a limitation in studying parameter optimization to obtain better reconstructions. In this talk, we propose an approximation of the computation of the DAS algorithm by decomposing it into a sum of space-invariant operators by means of a partition of the unity. This approximation allows parameter optimization algorithms to be applied to the DAS in order to increase the resolution of the reconstruction.
• [03464] Design and 3-D medical applications of 2-D ultrasound sparse arrays
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessandro Ramalli (University of Florence)
  • Abstract : The talk will report on the design methods that are currently used for the development of 2-D sparse arrays. Sample implementations of 2-D sparse arrays based on piezoelectric and capacitive micromachined ultrasonic transducer technologies will be presented. Finally, images and videos of (real-time) 2-D sparse array applications to 3-D flow imaging, super-resolution imaging, and high frame rate imaging will be shown.
• [04653] Recent advances in array and sequence design for 3D and high frame rate medical ultrasound imaging
  • Format : Online Talk on Zoom
  • Author(s) :
    • Herve Liebgott (Université Lyon 1)
  • Abstract : Medical ultrasound imaging has been based for years on the transmission of short pulses inside a thin beam. While the beam sweeps over the whole medium, images are reconstructed by beamforming the raw radio-frequency signals. Following the emergence of compressed sensing, faster acquisition concepts based on coded excitations have been suggested. This talk will present some challenges raised by such approaches e.g. choice of the codes, the array, decoding, and image reconstruction algorithm, …

contributed talk: CT188

room : A201

[00944] Modelling of healthcare-acquired infection spread in regional healthcare systems

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A201
• Type : Contributed Talk
• Abstract : A network-compartmental model for simulation of healthcare-associated infection spread in healthcare systems is presented. The model accounts for transmission of the pathogen by inter-hospital patient transfers and colonized patients' readmission. Estimates for basic reproduction number per hospital-community pairs are calculated for multidrug-resistant Enterobacteriaceae for selected German regions. Inter-hospital transfer network is created from anonymized German health-insurance datasets. By numerical simulations, we examine interventions to reduce spread of the pathogen within the healthcare network.
• Classification : 92D30, 62P10
• Format : Talk at Waseda University
• Author(s) :
  • Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw)
  • Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
  • Agata Lonc (Institute of Applied Mathematics and Mechanics, University of Warsaw)
  • Johannes Horn (Institute for Medical Epidemiology, Biometrics, and Informatics, Interdisciplinary Center for Health Sciences, Medical Faculty of the Martin Luther University Halle-Wittenberg, Halle (Saale))
  • Rafael Mikolajczyk (Institute for Medical Epidemiology, Biometrics, and Informatics, Interdisciplinary Center for Health Sciences, Medical Faculty of the Martin Luther University Halle-Wittenberg, Halle (Saale))
  • André Karch (Institute of Epidemiology and Social Medicine, University of Münster)
  • Paweł Brachaczek (University of Warsaw)
  • Mirjam Kretzschmar (University Medical Center Utrecht, Utrecht University)

[01913] Mathematical modeling, analysis, and simulation of the Epidemic Dynamics with Stochastic Perturbations: A case study of COVID-19 in Bogotá

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A201
• Type : Contributed Talk
• Abstract : We study the basic reproduction number for the epidemic models with stochastic perturbations in transmission rates and social behavior to analyze the dynamics of the COVID-19 pandemic in Bogotá, Colombia. We also consider the effect of vaccination as a control measure. We present the stability conditions and illustrate the simulation results for the proposed model. Finally, we present a computational experiment and validate the model by performing statistical analysis for the actual data.
• Classification : 92D30, 92BXX, 60H30
• Format : Talk at Waseda University
• Author(s) :
  • Andres Rios-Gutierrez (Universidad Nacional de Colombia)
  • Andres Rincon-Prieto (Universidad Nacional de Colombia)
  • VISWANATHAN ARUNACHALAM (Universidad Nacional de Colombia)

[00395] What can be the potential risk of Mpox outbreak in the endemic country?: Non-Markovian stochastic modeling study

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A201
• Type : Contributed Talk
• Abstract : In 2022, the Mpox outbreak shocked the world, with a completely different pattern and scale compared to past incidences in non-endemic countries, more than 80,000 cases have been confirmed. In this talk, we present how we analyzed the risk of local spread using a non-Markovian stochastic model. Multiple factors, which are suspected to affect the early stage of the outbreak significantly, the contact tracing, self-report-related behavior of the primary case, and secondary infectees were examined.
• Classification : 92D30, 60H30, 62M09
• Format : Talk at Waseda University
• Author(s) :
  • Youngsuk Ko (Department of mathematics, Konkuk university)
  • Victoria May Mendoza (Institute of Mathematics, University of the Philippines Diliman)
  • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman)
  • Yubin Seo (Hallym University College of Medicine)
  • Jacob Lee (Hallym University College of Medicine)
  • Eunok Jung (Department of mathematics, Konkuk University)

[00212] Optimal control for a SIR epidemic model with limited quarantine

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A201
• Type : Contributed Talk
• Abstract : Social distance and total lock-downs are interventions that have been used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs. Using optimal control tools and numerical computations we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model.
• Classification : 92D30, 34H05, 49N90
• Format : Online Talk on Zoom
• Author(s) :
  • Rocio Celeste Balderrama (Departamento de Matematica-Universidad de Buenos Airesu)
  • Javier Peressutti (Universidad de Mar del Plata)
  • Juan Pablo Pinasco (Universidad de Buenos Aires-IMAS-CONICET)
  • Constanza Sanchez de la Vega (Universidad de Buenos Aires_IMAS_CONICET)
  • Federico Vazquez (Universidad de Buenos Aires-IC-CONICET)

[01106] An alternative approach to generating the Covid-19 dynamics

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A201
• Type : Contributed Talk
• Abstract : The dynamics of the mysterious Covid-19 spread are interesting for further exploration and investigation. We propose a generating dynamic operator of cumulative case functions to recover all the dynamics of the SEIR model. This approach can also provide estimates of unrecorded cases based on the dynamics of the Covid-19 test, IFR, CFR, and recorded cases. This approach directly measures daily transmission indicators, which can be used effectively for day-to-day epidemic control.
• Classification : 92D30, 92B05, 92D25
• Format : Online Talk on Zoom
• Author(s) :
  • Muhammad Fakhruddin (Bina Nusantara University)
  • Kamal Khairudin Sukandar (Institut Teknologi Bandung)
  • Andy Leonardo Louismono (Institut Teknologi Bandung)
  • Metra Volisa (Institut Teknologi Bandung)
  • Rudy Kusdiantara (Institut Teknologi Bandung)
  • Muhammad Fakhruddin (The Republic of Indonesia Defense University)
  • Nuning Nuraini (Institut Teknologi Bandung)
  • Edy Soewono (Institut Teknologi Bandung)

MS [00963] Nonconvex and nonsmooth optimization

room : A206

• [01977] A lifted L1 framework for sparse recovery
  • Format : Talk at Waseda University
  • Author(s) :
    • Yifei Lou (University of Texas at Dallas)
    • Yaghoub Rahimi (Georgia Institute of Technology)
    • Sung Ha Kang (Georgia Institute of Technology)
  • Abstract : Motivated by re-weighted $\ell_1$ approaches for sparse recovery, we propose a lifted $\ell_1$ (LL1) regularization that can be generalized to several popular regularizations in the literature. During the course of reformulating the existing methods into our framework, we discover two types of lifting functions that can guarantee that the proposed approach is equivalent to the $\ell_0$ minimization. Computationally, we design an efficient algorithm via the alternating direction method of multiplier (ADMM) and establish the convergence for an unconstrained formulation. Experimental results are presented to demonstrate how this generalization improves sparse recovery over the state-of-the-art.
• [02344] A generalized formulation for group selection via ADMM
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunyoung Shin (Pohang University of Science and Technology)
    • Chengyu Ke (Southern Methodist University)
    • Yifei Lou (University of Texas at Dallas)
    • Miju Ahn (Southern Methodist University)
  • Abstract : The talk considers a statistical learning model where the model coefficients have a pre-determined group sparsity structure. A loss function is combined with a regularizer to recover the sparsity. We analyze the stationary solution of the formulation, obtaining a sufficient condition for the stationary solution to achieve optimality. We develop an efficient ADMM algorithm, showing the iterates converge to a stationary solution under certain conditions. With the algorithm implemented for GLM, we perform numerical experiments.
• [02395] A novel tensor regularization of nuclear over Frobenius norms for low rank tensor recovery
  • Format : Talk at Waseda University
  • Author(s) :
    • Huiwen Zheng (Southern University of Science and Technology)
    • Yifei Lou (University of Texas at Dallas)
    • Guoliang Tian (Southern University of Science and Technology)
    • Chao Wang (Southern University of Science and Technology)
  • Abstract : In this talk, we consider low-rank tensor recovery (LRTR) problems, which include the low-rank tensor completion (LRTC) problem and the tensor robust principal component analysis (TRPCA) problem. Based on tensor singular value decomposition (t-SVD), we use the ratio of the tensor nuclear norm and tensor Frobenius norm as a new nonconvex surrogate of tensor rank in our models. We adopt the alternating direction method of multipliers (ADMM) to tackle the model and analyze the convergence of the models. Extensive experiments demonstrate the superiority of the proposed models.
• [02672] Tractable continuous approximations for a constraint selection problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • Miju Ahn (Southern Methodist University)
    • Harsha Gangammanavar (Southern Methodist University)
    • David Troxell (Stanford University)
  • Abstract : This presentation introduces a constraint selection problem where the decision-maker solves an optimization problem with a set of constraints that are preferred to be satisfied. We formulate the problem as a cardinality minimization problem (CMP) that penalizes the number of unsatisfied such soft constraints using an indicator function. Our approach reformulates the discrete CMP as continuous problems. We present an equivalent formulation of a mathematical program with complementarity constraints and an approximation as a difference-of-convex program. The stationary solutions of the alternative formulations are investigated, emphasizing the recovery of the local solutions of the CMP. Our numerical study results demonstrate our method's effectiveness in enforcing desired conditions on several applications.

contributed talk: CT191

room : A207

[00520] Controllability of Generalized Fractional Dynamical Systems

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
• Type : Contributed Talk
• Abstract : In this paper necessary and sufficient conditions are established for the controllability of linear fractional dynamical system of the form \begin{eqnarray} ^CD^{\alpha,\rho}_{0^+}x(t)&=& Ax(t)+Bu(t), \ \ t\in J=[0,T]\\ x(0)&=&x_0 \end{eqnarray} where $0<\alpha<1,\rho>0, \rho\neq 1$ and $x\in R^n$ is the state vector, $u\in R^m$ is the control vector, $x_0\in R^n$ and $A$ is an $n\times n$ matrix and $B$ is an $n\times m$ matrix. Here the generalized fractional derivative is taken as \begin{eqnarray*} ^CD^{\alpha,\rho}_{0^+}x(t)=\frac{\rho^{\alpha}}{\Gamma(1-\alpha)} \int_0^t \frac{1}{(t^{\rho}-s^{\rho})^{\alpha}}x^{\prime}(s)ds \end{eqnarray*} Further sufficient conditions are obtained for the following nonlinear fractional system \begin{eqnarray} ^CD^{\alpha,\rho}_{0^+}x(t)&=& Ax(t)+Bu(t)+f(t,x(t)), \\ x(0)&=&x_0 \end{eqnarray} where the function $f:J\times R^n\to R^n$ is continuous. The results for linear systems are obtained by using the Mittag-Leffler function and the Grammian matrix. Controllability of nonlinear fractional system is established by means of Schauder's fixed point theorem. Examples are provided to illustrate the results.
• Classification : 93B05, 34A08, Controllability, Fractional Dynamical Systems
• Format : Talk at Waseda University
• Author(s) :
  • Balachandran Krishnan (Department of Mathematics, Bharathiar University, Coimbatore-641046)

[00100] Pointwise Controllability of Degenerate/Singular PDEs

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
• Type : Contributed Talk
• Abstract : This work deals with some controllability results of a one-dimensional degenerate and singular parabolic equation. We provide approximate and null controllability conditions based on the moment method by Fattorini and Russel.
• Classification : 93B05, 35K65, 35K67
• Format : Talk at Waseda University
• Author(s) :
  • AMINE SBAI (Hassan 1st University and Granada University)

[00181] Control of the Stefan problem

• Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
• Type : Contributed Talk
• Abstract : The Stefan problem is the quintessential macroscopic model of phase transitions in liquid-solid systems. We consider the one-phase Stefan problem with surface tension, set in two-dimensional strip-like geometry. We discuss the local null controllability of the system in any positive time, by means of control supported within an arbitrary open and non-empty subset.
• Classification : 93B05, 35R35, 35Q35, 93C20, Stefan problem, free boundary problem, controllability
• Author(s) :
  • Debayan Maity (TIFR Centre for Applicable Mathematics)

MS [00033] Recent Advances on Quantitative Finance

room : A510

• [04926] Neural Stopping Boundaries
  • Format : Talk at Waseda University
  • Author(s) :
    • Halil Mete Soner (Princeton University)
    • Anders Max Reppen (Boston University Questrom School of Business)
    • Valentin Tissot-Daguette (Princeton University)
  • Abstract : A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several examples related to financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions. We also briefly show how this method applies tis the classical Stefan problem of solidification.
• [05322] Learning Equilibrium Mean-Variance Strategy
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Dai (The Hong Kong Polytechnic University)
    • Yuchao Dong (Tongji University)
    • Yanwei Jia (Columbia University)
  • Abstract : We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time–inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium policy. Under an incomplete market setting, we obtain a semi-analytical, exploratory, equilibrium mean-variance policy that turns out to follow a Gaussian distribution. We then focus on a Gaussian mean return model and propose a reinforcement learning algorithm to find the equilibrium policy. Thanks to a thoroughly designed policy iteration procedure in our algorithm, we prove the convergence of our algorithm under mild conditions, despite that dynamic programming principle and the usual policy improvement theorem failing to hold for an equilibrium policy. Numerical experiments are given to demonstrate our algorithm. The design and implementation of our reinforcement learning algorithm apply to a general market setup.
• [05301] On Consistency of Selecting Signatures Using Lasso: A Tale of Ito and Stratonovich
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Guo (UC Berkeley)
    • Ruixun Zhang (Peking University)
    • Chaoyi Zhao (Peking University)
  • Abstract : We investigate the statistical consistency of using Lasso to select signatures in machine learning predictions. Signatures are defined as iterated path integrals of stochastic processes, and their universal nonlinearity warrants Lasso as a common tool to select sparse linear approximations. We study the consistency of Lasso for selecting signatures for the Brownian motion, the Ornstein--Uhlenbeck process, and the fractional Brownian motion, both theoretically and numerically. Our findings show that, for signatures defined by Ito integrals, Lasso is more consistent for processes that are closer to Brownian motion and have weaker inter-dimensional correlations. For signatures defined by Stratonovich integrals, we observe better Lasso consistency for mean-reverting processes than for mean-averting processes. Our results emphasize the importance of choosing appropriate definitions of signatures in statistical inference and machine learning, particularly for non-Brownian processes.
• [02766] Portfolio choice with transaction costs and reinforcement learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Dai (Hong Kong Polytechnic University)
  • Abstract : We provide a reinforcement learning approach for portfolio choice with transaction costs. Numerical results are provided to demonstrate the efficiency of our approach.

MS [00305] Computational Modeling on Biomedical Diseases

room : A511

• [01194] The role of the autoregulation mechanism in hypertension and hypotension in humans
  • Format : Talk at Waseda University
  • Author(s) :
    • Radu C Cascaval (University of Colorado Colorado Springs)
  • Abstract : We present a nonlinear model for the propagation of the pressure and flow velocity waves in the human cardiovascular system, including deep learning tools with available physiological data. This model is used for understanding the system-level dynamics of the pressure and flow rates. This time-domain analysis is best to describe time-dependent controls, collectively known as the autoregulation mechanism. We discuss an application of our model to the study of the hypertension and hypotension.
• [01215] Collaborative research toward data driven mathematical modeling of cancer to arrive at effective treatments
  • Format : Talk at Waseda University
  • Author(s) :
    • Leili Shahriyari (University of Massachusetts Amherst)
  • Abstract : Cancer is a complex disease with many unknown features. The evolution of tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. To overcome some of the outstanding challenges of mathematical modeling of cancer, we have utilized and integrated several computational techniques. Importantly, in collaboration with scientists with diverse backgrounds, we have used patients’ data and rich spatio-temporal mouse data to develop data-driven mathematical models for tumors’ progression. We believe a collaborative model for conducting research and sharing resources, including codes, data, and results would improve our chances to arrive at more effective treatments and ultimately eliminate cancer as a major health problem for this and future generations. In this talk, I will provide an overview of some of our recent collaborative works and outline several outstanding challenges and possible next steps to address them.
• [01334] Phase-field model of mechanical stability of blood clot
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhiliang Xu (University of Notre Dame)
  • Abstract : Deformation and detachment of blood clot (thrombus) under different flow conditions are studied. The fibrin and activated platelets are assumed to concentrate in the core of a thrombus and less-activated platelets are assumed to concentrate in the shell region near the boundary of a thrombus. Interactions among different components are simulated by using Cahn-Hilliard type systems of equations. The macroscopic motion of fluid is described by incompressible Navier-Stokes equations with terms representing viscos, elastic and phase interaction forces as well as porous media drag force. Model simulations predict that the permeability and porosity o of the shell region are shown to effect the stalbility of the blood clot. The stablity of the red blood cell cavity at different position in the blood clot are also illustrated.

MS [00216] Recent Advances on interfaces dynamics modeling and simulation

room : A601

• [01225] Solving elliptic interface problems using neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Ming-Chih Lai (National Yang Ming Chiao Tung University)
  • Abstract : In this talk, we shall introduce a series of neural network methodology for solving elliptic interface problems that comprise of variable-coefficient Poisson equation and Stokes equations with interfaces. There are three novel features in the present network; namely, (i) jump discontinuities are accurately captured, (ii) it is completely shallow, comprising only one hidden layer, (iii) it is completely mesh-free so the problems in irregular domains with irregular interfaces can be handled easily. Numerical results show better accuracy than the traditional finite difference method such as the immersed interface method.
• [01276] Role of Cohesive Fiber-Fiber Interactions in Fibrin Networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhiliang Xu (University of Notre Dame)
  • Abstract : A novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using newly developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders.
• [01217] Variational Lagrangian schemes for interface problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yiwei Wang (University of California, Riverside)
    • Chun Liu (Illinois Institute of Technology)
  • Abstract : In this talk, we present a systematic framework for deriving variational numerical methods for generalized diffusions and gradient flows. The numerical framework is based on the energy-dissipation law, which describes all the physics and the assumptions in each system and can combine different types of spatial discretizations including Eulerian, Lagrangian, and particle-based approaches. The resulting semi-discrete equation inherits the variational structures from the continuous energy-dissipation law. We apply such an approach to construct variational Lagrangian schemes to several interface problems, including the Allen-Cahn type phase-field models and the porous medium equation. Numerical examples show the advantages of the variational Lagrangian schemes in capturing thin diffuse interfaces and free boundaries. This is joint work with Professor Chun Liu.
• [01256] Helical organization of DNA-like liquid crystal filaments in cylindrical viral capsids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Pei Liu (Florida Institute of Technology)
  • Abstract : We study equilibrium configurations of ds-DNA in a cylindrical viral capsid. The state of the encapsidated DNA consists of a disordered inner core enclosed by an ordered outer region, next to the capsid wall. The DNA configuration is described by a unit helical vector field, tangent to an associated center curve, passing through properly selected locations. We postulate an expression for the energy of the encapsulated DNA based on that of columnar chromonic liquid crystals. A thorough analysis of the Euler--Lagrange equations yields multiple solutions. We demonstrate that there is a trivial, non-helical solution, together with two solutions with nonzero helicity of opposite sign. Using bifurcation analysis, we derive the conditions for local stability and determine when the preferred coiling state is helical. The bifurcation parameters are the ratio of the twist versus the bend moduli of DNA and the ratio between the sizes of the ordered and the disordered regions.