MS and CT list / Aug. 24, 15:30-17:10.

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

room : G301

• [03274] The image reconstruction problem in magnetic particle imaging and an application of the deep image prior
  • Format : Talk at Waseda University
  • Author(s) :
    • Tobias Kluth (University of Bremen)
  • Abstract : Magnetic particle imaging (MPI) is a tracer-based imaging modality detecting the concentration of superparamagnetic iron oxide nanoparticles. The imaging problem is a linear inverse problem given by a Fredholm integral equation of the first kind describing the concentration-to-voltage mapping. The talk provides a general introduction to MPI and the imaging problem. We further investigate general deep image prior concepts for inverse problems and their application to image reconstruction in MPI.
• [05253] A hybrid model for image reconstruction in MPI using a FFL
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jürgen Frikel (OTH Regensburg)
  • Abstract : In Magnetic Particle Imaging (MPI), most model-based reconstruction methods rely on idealized assumptions, such as an ideal field-free line (FFL) topology. However, real MPI scanners generate magnetic fields with distortions that often lead to inaccurate reconstructions and artifacts. To improve the reconstruction quality in MPI, it is essential to develop more realistic models. In this talk, we present a hybrid MPI model that can integrate real measurements of the applied magnetic fields into a physical model. Based on this model, we introduce a novel calibration procedure that allows the acquisition of the required magnetic field measurements, independent of the resolution, and with significantly less time consumption than a measurement-based model. In addition, we present a discretization strategy for the model that can be used in algebraic reconstructions.
• [04125] MPI using an FFL-scanner: Radon-based image reconstruction for realistic setup assumptions
  • Format : Talk at Waseda University
  • Author(s) :
    • Stephanie Blanke (Universität Hamburg)
    • Christina Brandt (Universität Hamburg)
  • Abstract : Magnetic particle imaging is a tracer-based imaging modality exploiting the nonlinear magnetization response of magnetic particles to changing magnetic fields. We adapt forward model and reconstruction methods towards more realistic setup assumptions for the specific choice of using a field-free line scanner. In this case, the scanning geometry resembles those of computerized tomography and we are able to jointly reconstruct particle concentration and corresponding Radon data by means of total variation regularization.
• [04651] Parameter estimation for modeling of nanoparticle dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hannes Albers (Universität Bremen)
    • Tobias Kluth (University of Bremen)
  • Abstract : In order to overcome the limitations of needing full delta probe calibrations for MPI, accurate and fast model-based image reconstruction with as few as possible calibration measurements are highly desirable. We discuss methods for estimating particle parameters from calibration measurements and subsequently applying them to dynamic particle models, such as the Néel relaxation model, to obtain modeled system matrices of high quality for reconstruction.

MS [01029] Extremal Combinatorics and Probabilistic Combinatorics

room : G304

• [04610] Embeddings in “random like” hypergraphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Guanghui Wang (Shandong University)
  • Abstract : An archetype problem in extremal combinatorics is to study the structure of subgraphs appearing in different classes of (hyper)graphs. We will focus on such embedding problems in “random like” hypergraphs. In precise, we will mention Turan problems in quasi-random hypergraphs.
• [03333] Spectral extremal graphs for disjoint cliques
  • Format : Talk at Waseda University
  • Author(s) :
    • Liying Kang (Shanghai University)
  • Abstract : Let $kK_{r+1}$ be the graph consisting of $k$ vertex-disjoint copies of the complete graph $K_{r+1}$. Moon [Canad. J. Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] independently showed that if $n$ is sufficiently large, then the join of a complete graph $K_{k-1}$ and an $r$-partite Tur\'{a}n graph $T_{n-k+1,r}$ is the unique extremal graph for $kK_{r+1}$. In this talk we consider the graph which has the maximum spectral radius among all graphs without $k$ disjoint cliques. We show that if $G$ attains the maximum spectral radius over all $n$-vertex $kK_{r+1}$-free graphs for sufficiently large $n$, then $G$ is isomorphic to the join of a complete graph $K_{k-1}$ and an $r$-partite Tur\'{a}n graph $T_{n-k+1,r}$. This is a joint work with Zhenyu Ni, Jing wang.
• [03579] Co-degree threshold for rainbow perfect matchings in uniform hypergraphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongliang Lu (Xi'an Jiaotong University)
    • Yan Wang (Shanghai Jiao Tong University)
    • Xingxing Yu (Georgia Institute of Technology)
  • Abstract : Let $k$ and $n$ be two integers, with $k\geq 3$, $n\equiv 0\pmod k$, and $n$ sufficiently large. We determine the $(k-1)$-degree threshold for the existence of a rainbow perfect matchings in $n$-vertex $k$-uniform hypergraph. This implies the result of R\"odl, Ruci\'nski, and Szemer\'edi on the $(k-1)$-degree threshold for the existence of perfect matchings in $n$-vertex $k$-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of R\"odl, Ruci\'nski, and Szemer\'edi.
• [03715] Recent progress on non-separating subgraphs in highly connected graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Shinya Fujita (Yokohama City University)
  • Abstract : Let $k$ be a positive integer. A connected graph $G$ is said to be $k$-connected, if for any vertex subset $S$ of $V(G)$ such that $|S|

MS [00970] High Performance Linear Algebra Software toward Extreme Heterogeneity

room : G305

• [05190] Responsibly Reckless Matrix Algorithms for HPC Scientific Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Hatem Ltaief (KAUST)
  • Abstract : Referred to by Jack Dongarra, the 2021 ACM Turing Award Laureate, as “responsibly reckless” matrix algorithms, we highlight the implications of mixed-precision (MP) computations for HPC applications. Reducing precision comes at the price of trading away some accuracy for performance (reckless) but in noncritical segments of the workflow (responsible) so that the accuracy requirements of the application can still be satisfied. We illustrate the MP impact on seismic imaging, climate/environment geospatial predictions, and computational astronomy.
• [04598] A scalable multi-GPU approach for solving H2-approximated dense linear systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Qianxiang Ma (Tokyo Institute of Technolgy)
    • Rio Yokota (Global Scientific Information and Computing Center, Tokyo Institute of Technology)
  • Abstract : In this talk, we present a novel approach for directly solving a dense linear system emerged from 3-D geometry approximated using $\mathcal{H}^2$-matrices. From the pre-compressing the fill-ins, we are able to ULV-factorize and apply forward and backward substitution in an entirely parallel manner by batched BLAS/LAPACK operations on GPUs. Using 512 NVIDIA V100 GPUs, we are able to factorize a matrix of N=29,242,368 under 1 second, utilizing 0.808 PFLOPS/s of performance.
• [05233] Towards a Unified Micro-kernel Abstraction for GPU Linear Algebra
  • Format : Talk at Waseda University
  • Author(s) :
    • Vijay Thakkar (NVIDIA | Georgia Tech)
    • Richard Vuduc (Georgia Tech)
  • Abstract : We have created a micro-kernel abstraction for GPUs robust enough to represent the tensor core and data movement operations from NVIDIA GPU architectures spanning Maxwell all the way to Hopper. In this talk, we discuss how CuTe layouts and layout algebra allow us to uniformly represent GPU architecture specific operations in a consistent programming model regardless of the threads and data they operate upon to build CUTLASS 3.x’s core abstractions.

MS [00484] Matrix Analysis and Applications

room : G306

• [03621] Log-majorization and inequalities of power means
  • Format : Talk at Waseda University
  • Author(s) :
    • Sejong Kim (Chungbuk National University)
  • Abstract : As non-commutative versions of the quasi-arithmetic mean, we consider the Lim-Palfia’s power mean, Renyi right mean, and Renyi power mean of positive definite matrices. We see that the Lim-Palfia’s power mean of negative order converges increasingly to the log-Euclidean mean with respect to the weak log-majorization. Furthermore, we establish the weak log-majorization relationships between power means and provide the boundedness of Renyi power mean.
• [00868] Matrix Problems in International Economics
  • Format : Talk at Waseda University
  • Author(s) :
    • Konstantin Kucheryavyy (University of Tokyo)
  • Abstract : Analyzing properties of general equilibrium models in economics amounts to analyzing properties of nonlinear systems of equations. The standard questions asked in this context are about existence and uniqueness of solutions to a nonlinear system of equations, characterization of multiplicity of solutions, and behavior of solutions in response to changes in parameters. One approach to address these questions is to formulate them in terms of matrix algebra. This approach has been especially fruitful when applied to classes of models arising in international economics. Such models often give rise to matrices with striking properties, but formally proving the observed properties usually constitutes a challenge. In my presentation, I will consider several matrix problems that arise in the international economics context and sketch related proofs. I will also discuss open questions in this literature.
• [01404] Spectral inequalities for Kubo-Ando and Heinz means
  • Format : Talk at Waseda University
  • Author(s) :
    • Rute Correia Lemos (CIDMA, University of Aveiro)
    • Graça Soares (CMAT-UTAD, University of Trás-os Montes e Alto Douro)
  • Abstract : In this talk, spectral inequalities, involving Kubo-Ando operator connections and means of positive semidefinite matrices, are surveyed. Some Log-majorization type results are presented. Singular values inequalities for Heinz mean of matrices, which are not of Kubo-Ando type, and its 'harmonic' variant are also given.
• [00800] Limit of the induced Aluthge transformations
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeaki Yamazaki (Toyo University)
  • Abstract : Let $\mathcal{H}$ and $B(\mathcal{H})$ be a complex Hilbert space and the algebra of all bounded linear operators on $\mathcal{H}$, respectively. For $T\in B(\mathcal{H})$ with the polar decomposition $T=U|T|$, Aluthge transformation is known as $\Delta(T):=|T|^{1/2}U|T|^{1/2}$. In this talk, we shall introduce a generalization of Aluthge transformations and limit point of its iterations.

MS [00294] Machine Learning and Differential Equations

room : G401

• [04777] Dynamic Control in Machine Learning: Geometric Interpretation of deep neural networks for Multi-Classification and Universal Approximation.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Martin Sebastian Hernandez Salinas (Friedrich-Alexander-Universität Erlangen-Nürnberg)
    • Enrique Zuazua (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : In this talk, we will present recent results on the interplay between control and Machine Learning. We analyze the Residual Neural Networks architecture and the Multilayer Perceptron with minimal width. Adopting a dynamic control and geometric interpretation of the neural networks, we train them in a constructive manner to solve multi-classification problems and achieve simultaneous controllability. We also derive the so-called universal approximation theorems in $L^p$ spaces for both architectures.
• [04705] An Operator-Learning Approach for Computational Fluid Dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Viktor Hermann Grimm (University of Cologne)
    • Axel Klawonn (University of Cologne)
    • Alexander Heinlein (Delft University of Technology (TU Delft))
  • Abstract : We present an operator-learning approach for Computational Fluid Dynamics using Convolutional Neural Networks (CNNs). We aim to approximate the solution operator for the incompressible Navier-Stokes equations in varying geometries using CNNs trained only on the underlying physics. No reference simulations are required for training. We show that our method is able to predict the flow field in various geometries sufficiently accurate and compare its performance to traditional numerical methods.

MS [02470] Chaotic Supremacy Revolution

room : G402

• [03967] Quantification of Orbital Instability of Chaotic Laser Diodes by Modified Orbital Expansion Exponent
  • Format : Talk at Waseda University
  • Author(s) :
    • Satoshi Ebisawa (Niigata Institute of Technology)
  • Abstract : Controlling the strength of orbital instability of chaotic laser, is useful for applications. To realize this, it is important to quantify the characteristics. The chaotic laser has three dynamic variables, but only the amplitude can be easily measured experimentally. Then, we introduce a modified orbital expansion exponent that considers the chaotic laser dynamics. By comparing this with the Lyapunov exponent calculated from the rate equations representing its dynamics, we show the usefulness of proposed exponent.
• [03992] Development of MLD-TDS applying spintronic THz emitters excited by laser chaos light
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Moriyasu (University of Fukui)
    • Ryunosuke Noda (University of Fukui)
    • Kaede Miyaguchi (University of Fukui)
    • Shudai Katono (University of Fukui)
    • Masahiko Tani (University of Fukui)
    • Hideaki Kitahara (University of Fukui)
    • Fumiyoshi Kuwashima (Fukui University of Technology)
    • Mitsutaka Kumakura (University of Fukui)
  • Abstract : A terahertz time-domain spectrometer with a multimode laser diode as light source (MLD-TDS) is an inexpensive terahertz spectrometer, since an expensive pulse laser system is not used. However, MLD-TDS has not been widely adopted in practical applications due to the sub-optimal radiation efficiency and stability etc. We propose the applying of spintronic THz emitters and laser chaos light into the MLD-TDS system, with the aim of compensating for the deficiencies and enhancing the overall performance.
• [04083] Quantum walk analysis of spatial distribution of dressed-photon-phonon
  • Format : Online Talk on Zoom
  • Author(s) :
    • Motoichi Ohtsu (Research Origin for Dressed Photon)
    • Etsuo Segawa (Yokohama National University)
    • Kenta Yuki (Middenii)
    • Seiken Saito (Kogakuin University)
  • Abstract : This paper analyzes the spatial distribution of a dressed-photon–phonon (DPP) that is confined by a boron (B) atom-pair in a silicon light-emitting diode by using a two-dimensional quantum walk model. It is confirmed that the DPP is confined by the B atom-pair, which is oriented along a direction perpendicular to that of the incident light propagation. The dependence of the confined DPP probability on the length of the B atom-pair is analyzed.
• [04616] Quantum Fields as Category Algebras
  • Author(s) :
    • Hayato Saigo (Nagahama Institute of Bio-Science and Technology)
  • Abstract : In the present talk we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. Based on this framework, we propose a foundation for off-shell sciences such as dressed phoon studies.

MS [01111] Mathematical and numerical analysis on blow-up phenomena

room : G501

• [03241] Collapse Versus Blowup and Global Existence in Generalized Constantin–Lax–Majda Equation with dissipation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Pavel M Lushnikov (University of New Mexico)
    • David M Ambrose (Drexel University)
    • Michael Siegel (Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology,)
    • Denis A Silantyev (Department of Mathematics, University of Colorado, Colorado Springs,)
  • Abstract : We analyze dynamics of singularities and finite time blowup of generalized Constantin-Lax-Majda equation for non-potential effective motion of fluid with competing convection, vorticity stretching and dissipation. Multiple exact solutions are found with blowups. Global existence of solutions is proven for small data in periodic case. The analytical solutions on real line allow finite-time singularity formation for arbitrarily small data illustrating critical difference between real line and periodic cases. Analysis is complemented by accurate numerical simulations.

MS [01070] PDE Based Image Processing

room : G502

• [01942] A new PDE model for Image Inpainting
  • Format : Online Talk on Zoom
  • Author(s) :
    • Abdul Halim (King Abdullah University of Science and Technology)
    • B.V. Rathish Kumar (IIT Kanpur)
  • Abstract : In this talk, I will present a fourth-order PDE model with a multi-well potential function for grayscale image inpainting. Convexity splitting in time and Fourier spectral method in space has been used to derive an unconditional scheme on time. The stable scheme is both consistent and convergent. Also, I present the fractional variant of the time discretized scheme by replacing the Laplacian with its fractional counterpart. Numerical results for some standard test images will be presented and will be compared with the results of other existing models in the literature. To quantify the quality of the recovered image, we calculate the image quality metric such as PSNR, SNR, and SSIM.
• [01962] Fractional Calculus Based Approach for Retinal Blood Vessel Segmentation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)
    • Varun Makkar (Indian Institute of Technology (BHU) Varanasi)
    • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
  • Abstract : We will discuss a new fractional filter and an algorithm for retinal blood vessel segmentation. The proposed fractional filter is designed with the help of a weighted fractional derivative and an exponential weight factor. Firstly, the image is denoised using developed fractional. Then, multi-scale line detector is used to compute the line responses at multiple lengths using a punctured window of fixed dimensions. The final response is the computed as the arithematic mean of all responses at different scales and the underlying image intensity. This enhances the retinal blood vessels and suppresses rest of the background. Finally, hysteresis thresholding is applied to obtain the segmented vessels. Experiments are performed on two well-studied evaluation databases named STARE and DRIVE and the simulation results are discussed.
• [02860] Game theoretic Approach for Image segmentation and Image restoration by using Fractional PDE
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kedarnath Buda (Indian Institute of Technology Kanpur, India)
    • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
  • Abstract : In this study, a game theoretic algorithm through which a noisy image is both restored and segmented simultaneously is proposed. We define a two cost functions for two players of a Game. One player is Image restoration and another one is Image segmentation. Both of them are further constrained by fractional PDEs.The establish the Nash equilibrium for this game, which is an ideal strategy for deciding the amount of image restoration and image segmentation that can be done through the optimization of the bi-objective cost functions. We then numerically compute this with some real images.
• [02862] Higher Order PDE Model for Effective Image Denoising
  • Format : Talk at Waseda University
  • Author(s) :
    • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
    • Abdul Halim (KAUST)
  • Abstract : In this talk we will introduce a new higher order nonlinear PDE model for image denoising and demonstrate its ability to denoise without any staircase effect as routinely noticed with lower order PDE models. We use convexity splitting based Fourier Spectral scheme for the computation of the denoised version of a given noisy image. Fourier spectral method is both accurate and faster than many standard approaches. Performance of the model and the method will be discussed based on the benchmark test images and the related computational metrics.

MS [00306] Mathematical approaches to nonlinear phenomena with singularities

room : G601

• [03754] Variational models for segmentation in non-euclidian settings
  • Format : Talk at Waseda University
  • Author(s) :
    • Salvador Moll (Universitat de Valencia)
  • Abstract : I will present some new results on image segmentation in the general framework of perimeter measure spaces; including the anisotropic case and non-euclidian settings such as random walk spaces or metric graphs. I will show the linkage between the ROF model for denoising and the two phases piecewise constant segmentation and I will show different applications of the results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.
• [04356] Periodic solution to KWC-type system under dynamic boundary condition
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryota Nakayashiki (Salesian Polytechnic)
    • Ken Shirakawa (Chiba University)
  • Abstract : The aim of this study is to observe the periodic stability for KWC-type system of grain boundary motion under dynamic boundary condition. The KWC-type system is a collective term of PDE model of grain boundary motion (cf. Kobayashi et al, Physica D 140, 2000), which is governed by variable-dependent singular diffusion equation. As one of key-results of the study, we will prove the main theorem concerned with the existence of periodic solution.
• [03968] Cahn-Hilliard equations with forward-backward dynamic boundary condition and non-smooth potentials
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierluigi Colli (Università degli Studi di Pavia)
    • Takeshi Fukao (Ryukoku University)
    • Luca Scarpa (Politecnico di Milano)
  • Abstract : The asymptotic behavior as the coefficient of the surface diffusion acting on the boundary phase variable goes to 0 is investigated. By this analysis we obtain a forward-backward dynamic boundary condition at the limit. We can deal with a general class of potentials having a double-well structure, including the non-smooth double-obstacle potential. We illustrate that the limit problem is well-posed by also proving a continuous dependence estimate
• [04411] Optimal control for shape memory alloys of the simplipied Fr'emond model in the one-dimensional case
  • Format : Talk at Waseda University
  • Author(s) :
    • Noriaki Yamazaki (Kanagawa University)
    • Ken Shirakawa (Chiba University)
    • Pierluigi Colli (Universita a degli Studi di Pavia)
    • M. Hassan Farshbaf-Shaker (Weierstrass Institute for Applied Analysis and Stochastics)
  • Abstract : In this talk, we consider optimal control problems for the one-dimensional Fremond model for shape memory alloys. Then, we prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems.

contributed talk: CT037

room : G602

[01629] Constructive approaches for the controllability of semi-linear heat and wave equations

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : We addresses the controllability of the semi-linear heat equation $\partial_t y- \partial_{xx} y+f(y)=0$, $x\in (0,1)$. Assuming that the function $f$ is $C^1$ over $\mathbb{R}$ and $\limsup_{\vert r\vert\to \infty} \vert f^\prime(r)\vert/\ln^{3/2}\vert r\vert\leq \beta$ for some $\beta>0$ small enough, we show that a fixed point application related to a linearized equation is contracting yielding a constructive method to approximate boundary controls for the semi-linear equation. Similar ideas are used to address the controllability for semi-linear wave type equations.
• Classification : 35K58, 93B05
• Format : Talk at Waseda University
• Author(s) :
  • Arnaud Munch (Clermont Auvergne University)

[02235] Numerical simulation of dislocation multiple cross-slip

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : Our contribution deals with the phenomenon in material science called multiple cross-slip of dislocations in slip planes. The numerical model is based on a mean curvature flow equation with additional forcing terms included. The curve motion in 3D space is treated using our tilting method, i.e., mapping of a 3D situation onto a single plane where the curve motion is computed. The physical forces acting on a dislocation curve are evaluated in the 3D setting.
• Classification : 35K57, 35K65, 65N40, 65M08, 53C80
• Format : Talk at Waseda University
• Author(s) :
  • Petr Pauš (Czech Technical University in Prague)
  • Miroslav Kolář (Czech Technical University in Prague)
  • Michal Beneš (Czech Technical University in Prague)

[01073] About reaction-diffusion systems with exponential growth: Numerical study

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : The modeling and mathematical analysis of concrete phenomena are of great interest to better understand our environment and its evolution. Several analogies between chemistry and biological systems have led researchers to introduce mathematical models of "reaction-diffusion", whose objective is to follow the evolution of the quantities interacting during the process. In this talk, we are interested in reaction-diffusion systems with exponential growth, modeling an irreversible chemical reaction. Since the 86's, considerable efforts have been devoted to the study of this systems. We provide a general overview of the different theoretical results obtained, as well as our investigation from a numerical point of view on open cases.
• Classification : 35K57, 35K58, 80A25, 80A19
• Author(s) :
  • Rajae Malek (Moulay Ismail University, Meknes, Morocco)

[00750] Bayesian inverse problems for some hyperbolic conservation laws

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : We study some inverse problems for hyperbolic conservation laws. Given observations of the entropy solution, we consider the problem of identifying the initial field or the flux function. Due to shockwaves, direct observations of the entropy solution are not "regulated" enough to fit in the Bayesian framework in Stuart (2010). To get round this, we propose a new approach by studying the trajectories for hyperbolic conservation laws and exploring their existence, uniqueness and stability.
• Classification : 35L65, 35R30, 62F15, Partial Differential Equations, Inverse Problems
• Format : Talk at Waseda University
• Author(s) :
  • Duc-Lam Duong (LUT University)
  • Duc-Lam Duong (LUT University)
  • Masoumeh Dashti (University of Sussex)

[00434] Three pieces Riemann problem for $2$-D full Euler system in the Noble-Abel gas

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : We present Riemann problem governed by $2$-D full Euler system in the Noble-Abel gas. Riemann data, consisting three constants, are distributed in three distinct regions with an assumption that two adjoining regions can be connected by only one planar elementary wave. We present criteria for existence of different configurations of elementary waves for isentropic, as well as full, Euler system. We also discuss the effect of the Noble-Abel gas and the angle of regions on elementary waves and corresponding stream curves. Note: The present article has been published on 17 May 2022 in the journal ''Mathematical Methods in the Applied Sciences''/ Volume 45, Issue 16 with DOI:10.1002/mma.8377.
• Classification : 35L65, 35L67, 35Q30, 35Q31, 35Q35, Hyperbolic Conservation Laws, Shocks and Singularities for Hyperbolic equations, Navier-Stokes equations, Euler equations, PDEs in connection with fluid mechanics.
• Format : Talk at Waseda University
• Author(s) :
  • Harsita Srivastava (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab)
  • M. Zafar (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab)

MS [00413] Numerical Methods for Dispersive PDEs and Applications

room : G605

• [05510] Numerical studies of two regularized versions of the cubic NLS
  • Format : Online Talk on Zoom
  • Author(s) :
    • Christof Sparber (University of Illinois Chicago)
  • Abstract : We consider two types of regularization for the focusing, cubic nonlinear Schrödinger equation (NLS) posed in two and/or three spatial dimensions. One type of regularization is given by a defocusing quintic nonlinearity, while the other is given by a second order elliptic differential operator, describing off-axis variations of the NLS in the context of laser physics. While the non-regularized NLS is know to exhibit finite-time blow-up, these augmented equations are proved to be globally well-posed. In both cases we numerically investigate the long time behavior of solutions using a time-splitting method. In particular, we are interested in the orbital (in-)stability of least action ground states in the radially symmetric case. This is joint work with Christian Klein, Remi Carles, and Jack Arbunich.
• [05557] Dirac equations for the modeling of electron dynamics on strained graphene surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Emmanuel Lorin de la Grandmaison (Carleton University)
  • Abstract : This talk is devoted to the modelling of the dynamics of electrons on strained graphene surfaces. A hierarchy of mathematical models will be derived, and some numerical experiments illustrating the scattering of wave packets on locally deformed graphene will be proposed
• [02732] Low regularity exponential-type integrators for the "good" Boussinesq equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Chunmei Su (Tsinghua University)
    • Hang Li (Tsinghua University )
  • Abstract : We introduce a series of semi-discrete low regularity exponential-type time integrators for the “good” Boussinesq equation. Compared to the existing numerical methods, the temporal convergence of ours can be achieved under weaker regularity assumptions on the exact solutions. The methods are constructed based on twisted variables and some harmonic analysis techniques in approximating the exponential integral. The methods are explicit and easy to be implemented efficiently when combined with pseudospectral method for spatial discretization.
• [04017] Computational methods for stationary states of nonlinear Schrödinger/Gross-Pitaevskii equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei Liu (National University of Singapore)
  • Abstract : I will present some recent advances in the computation of stationary-state solutions to the nonlinear Schrödinger/Gross-Pitaevskii equations, primarily in the context of Bose-Einstein condensation. The (normalized) energy ground/excited states and action ground states will be mainly considered. Based on the analysis of variational characterizations and stabilities/instabilities for these stationary-state solutions, efficient and accurate numerical methods utilizing novel artificial dynamical flows and/or optimization techniques will be developed, with further extensions to challenging high-spin or fast-rotating models.

MS [00783] PDE Eigenvalue Problems: Computational Modeling and Numerical Analysis

room : G701

MS [00057] Many-agent systems and mean-field models for socio-economic and life sciences dynamics

room : G702

• [04768] Kinetic modelling of swarming dynamics with transient leadership
  • Format : Talk at Waseda University
  • Author(s) :
    • Giacomo Albi (University of Verona)
  • Abstract : In this talk, we will focus on swarming dynamics with topological interactions and where leaders' emergence initializes spontaneous changes of direction. In this context, we will provide a kinetic model for leader-follower dynamics with mass transfer among the two populations modeled as a transition process on a space of labels. This model allows the transition from followers to leaders and vice-versa, with scalar-valued transition rates depending on the state of the system. Furthermore, we will propose an efficient stochastic algorithm for the identification of the $k$-nearest neighbors at mesoscopic level, and the simulation of the swarming dynamics. Several numerical experiments are presented for different scenarios both to validate the algorithm and to study the collective dynamics.
• [02465] Kernel learning method for multiagent systems and its mean-field limit
  • Format : Talk at Waseda University
  • Author(s) :
    • Chiara Segala (RWTH Aachen University)
    • Michael Herty (RWTH Aachen University)
    • Christian Fiedler (RWTH Aachen University)
  • Abstract : Kernel methods are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of kernels and function spaces generated by kernels. Motivated by recent developments of learning approaches in the context of interacting particle systems, we investigate kernel methods acting on data with many measurement variables. We present efficient learning algorithms both on microscopic and mean-field level.
• [03937] Bounded-confidence models of opinion dynamics on networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Heather Zinn Brooks (Harvey Mudd College)
  • Abstract : In this talk, I will introduce you to a class of models of opinion dynamics on networks called bounded-confidence models. These relatively simple models can produce delightfully complicated dynamics and provide a rich source of study for the interplay between dynamics and structure. I will discuss some novel twists on bounded-confidence models that my collaborators and I have been developing, including information cascades, bifurcations in “smoothed” bounded-confidence models, and extensions to hypergraphs.
• [03493] Mean-field models for many agent systems with co-evolving network structure
  • Format : Online Talk on Zoom
  • Author(s) :
    • Martin Burger (DESY and University of Hamburg)
  • Abstract : In this talk we discuss the derivation of kinetic and sub mean-field equations for processes related to processes on networks, such as opinion formation on social networks. We consider in particular the case when networks are co-evolving during other processes and discuss suitable descriptions as well as issues to derive simple closure relations. Moreover, we discuss aspects of pattern formation such as consensus or the formation of echo chambers.

MS [00608] Limit behavior and asymptotic properties in fluid mechanics

room : G703

• [04660] Multiscale analysis - from compressible to incompressible system
  • Format : Talk at Waseda University
  • Author(s) :
    • Aneta Wróblewska-Kamińska (Institute of Mathematics, Polish Academy of Sciences)
  • Abstract : We will show asymptotic analysis for hydrodynamic systems as a tool in in the situation when certain parameters vanish or become infinite. We will concentrate on rigorous mathematical analysis of low Mach number limits with so called ill-prepared dat. I will present some results which concerns passage from compressible to incompressible models including Navier-Stokes-Fourier system on varying domains, a multi-scale problem for viscous heat-conducting fluids in fast rotation and FENE model for dilute polymeric fluids.
• [04114] Mixing and enhanced dissipation for fluid suspensions
  • Format : Talk at Waseda University
  • Author(s) :
    • David Gerard-Varet (Universite Paris Cite et IMJ-PRG)
  • Abstract : We consider a model introduced by D. Saintillan and M. Shelley to describe active suspensions of elongated particles. This model couples a Stokes equation for the fluid substrate and a transport equation for the density distribution of particles in space and orientation. We investigate mixing properties of this model (damping and enhanced dissipation). The main new feature of the analysis is that the usual velocity variable of the euclidean space is replaced by an orientation variable on the sphere, which is responsible for strong qualitative changes and new mathematical difficulties. This is joint work with M. Coti Zelati and H. Dietert.
• [05036] Resolvent estimate for the Stokes equations in the Besov spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Jou chun Kuo (Graduate School of Fundamental Science and Engineering, Waseda University)
  • Abstract : This talk is devoted to proving the resolvent estimates of the linearized system of the compressible Navier-Stokes equations with homogeneous boundary conditions in the half-space. We construct the solution in $B^s_{q,1}$ for $1
• [05215] Conditions for energy balance in 2D incompressible ideal fluid flow
  • Format : Online Talk on Zoom
  • Author(s) :
    • Milton da Costa Lopes Filho (Universidade Federal do Rio de Janeiro)
    • Samuel Lanthaler (California Institute of Technology)
    • Fabian Jin (ETH-Zurich)
    • Helena Judith Nussenzveig Lopes (Universidade Federal do Rio de Janeiro)
  • Abstract : In this talk I will discuss necessary and sufficient conditions on the regularity of the external force for energy balance to hold for weak solutions of the 2D incompressible Euler equations. This is motivated by turbulence modeling and the result is in contrast with the situation in 3D and the existence of wild solutions.

MS [00753] Numerical methods for high-dimensional problems

room : G704

• [04069] Multi-level Monte Carlo methods in stochastic density functional theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Huajie Chen (Beijing Normal University)
  • Abstract : The stochastic density functional theory (sDFT) has become an attractive approach in electronic structure calculations. The computational complexity of Hamiltonian diagonalization is replaced by introducing a set of random orbitals leading to sub-linear scaling of evaluating the ground-state observables. This work investigates the convergence and acceleration of the self-consistent field (SCF) iterations for sDFT in the presence of statistical error. We also study some variance reduction schemes by multi-level Monte Carlo methods that can accelerate the SCF convergence.
• [04185] Inchworm Monte Carlo Method for Spin Chain Models in Open Quantum Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhenning Cai (National University of Singapore)
  • Abstract : We consider open quantum systems where the quantum system is coupled to a harmonic bath. When the coupling is weak, we can mimic Feynman's methodology to represent the dynamics as the sum of infinite integrals represented by diagrams. In this talk, we will discuss an efficient diagrammatic approach, known as the inchworm Monte Carlo method, to compute the observables in open quantum systems. Applications to spin chain models will be considered in the numerical tests.
• [04220] A short-memory operator splitting scheme for constant-Q viscoelastic wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yunfeng Xiong (Beijing Normal University)
    • Xu Guo (Shandong University)
  • Abstract : We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit its extension problem by converting the flat singular kernels into strongly localized ones, so that the major contribution of weakly singular integrals over a semi-infinite interval can be captured by a few Laguerre functions with proper asymptotic behavior. An operator splitting scheme is introduced to solve the resulting set of equations, where the auxiliary dynamics can be solved exactly, so that it gets rid of the numerical stiffness and discretization errors. Numerical experiments on both 1-D diffusive wave equation and 2-D constant-Q P-and S-wave equations are presented to validate the accuracy and efficiency of the proposed scheme.
• [04363] Solving Boltzmann equation with neural sparse representation
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhengyi Li (Peking Univeristy)
    • Yanli Wang (Beijing Computational Science Research Center)
    • Hongsheng Liu (Huawei Technologies Co. Ltd)
    • Zidong Wang (Huawei Technologies Co. Ltd)
    • Bin Dong (Beijing International Center for Mathematical Research & Center for Machine Learning Research, Peking University)
  • Abstract : We consider the neural sparse representation to solve Boltzmann equation. The different low-rank representations are utilized in the microscopic velocity for the BGK and quadratic collision model, resulting in a significant reduction in the degree of freedom. We approximate the discrete velocity distribution in the BGK model using the canonical polyadic decomposition. For the quadratic collision model, a data-driven, SVD-based linear basis is built based on the BGK solution.

MS [00969] Eigenvalue Problems in Electronic Structure Calculations

room : G709

• [05006] An efficient LOBPCG solver for Kohn-Sham solution
  • Format : Talk at Waseda University
  • Author(s) :
    • Guanghui Hu (University of Macau)
  • Abstract : In this talk, an efficient implementation of the LOBPCG solver in the self-consistent field iteration for the Kohn-Sham solution is introduced. It is found that in an $h$-adaptive finite element framework, the precondition in the LOBPCG method plays an important role to guarantee the fast convergence of the solver. Several choices are introduced, and the comparison of the performance among those choices will be demonstrated in detail.
• [03997] Sampling-based approaches for multimarginal optimal transport problems with Coulomb cost
  • Format : Talk at Waseda University
  • Author(s) :
    • Yukuan Hu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Mengyu Li (Renmin University of China)
    • Xin Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Cheng Meng (Renmin University of China)
  • Abstract : The multimarginal optimal transport problem with Coulomb cost find applications in understanding strongly correlated systems. We develop for its Monge-like reformulation novel methods that favor highly scalable subiteration schemes and avoid the full matrix multiplications in the existing ones. Convergence properties are built on the random matrix theory. For large-scale global resolution, we embed the proposed methods into a grid refinements-based framework. The numerical results corroborate the effectiveness and better scalability of our approach.
• [03145] A mixed precision LOBPCG algorithm
  • Format : Online Talk on Zoom
  • Author(s) :
    • Daniel Kressner (EPF Lausanne)
    • Yuxin Ma (Fudan University)
    • Meiyue Shao (Fudan University)
  • Abstract : The LOBPCG algorithm is a popular approach for computing a few smallest eigenvalues of a large Hermitian positive definite matrix. We propose a mixed precision variant of LOBPCG that uses a (sparse) Cholesky factorization computed in lower precision as the preconditioner. We carry out a rounding error and convergence analysis of PINVIT, a simplified variant of LOBPCG. Our theoretical results predict and our numerical experiments confirm that the impact on convergence remains marginal.
• [04317] An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuzhi Zhou
    • Xiaoying Dai (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Aihui Zhou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk, we introduce extensions of our PW framework for the practical electronic calculations of twisted bilayer material systems in the following aspects: (1) a tensor-producted basis set with PWs in the incommensurate dimensions and localized functions in z direction, (2) the practical application of our newly developed cutoff techniques, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2), we have remarkably reduced the dimensions of hamiltonian matrix, which makes the electronic structure calculations of twisted bilayer 2D material systems affordable to most modern computers. And (3) helps us better organize the calculations as well as understand results. We further use the linear TGB system with magic twisted angles as numerical examples. We have reproduced the famous flat bands with key features in good quantitative with other theoretical and experimental results. In terms of efficiency, our framework has much less computational cost compared to the commensurate cell approximations. While it is also more extendable compared to the traditional model hamiltonians and tight binding calculations. Lastly, nonlinear terms like Hartree energy and exchange-correlation energy can be readily included in the framework thus more effective and accurate DFT calculations of incommensurate 2D material systems can be expected in the near future.

MS [01272] Interface motion and related topics

room : G710

• [02736] Numerical computation of the Plateau problem by the method of fundamental solutions
  • Format : Talk at Waseda University
  • Author(s) :
    • Koya Sakakibara (Okayama University of Science / RIKEN)
    • Yuuki Shimizu (The University of Tokyo)
  • Abstract : We propose a numerical scheme for the Plateau problem based on the method of fundamental solutions. After giving the existence of approximate surfaces and convergence analysis, some numerical experiments show the usefulness of the proposed scheme.
• [04050] Novel numerical methods for solving nonlinear evolutionary equations with application in mathematical finance optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Cyril Izuchukwu Udeani (Comenius University in Bratislava)
    • Daniel Sevcovic (Comenius University)
  • Abstract : This study employs physics-informed DeepONet (PI-DeepONet), which incorporates known physics into the neural network via two networks, to approximate the solution operator of a nonlinear Hamilton--Jacobi--Bellman (HJB) equation arising from the stochastic optimization problem, where an investor's goal is to maximize the conditional expected value of the terminal utility. We first transform the nonlinear HJB equation into a quasilinear parabolic equation using the Ricatti transform and then approximate the solution of the transformed equation using PI-DeepONet.
• [02939] Mathematical modeling of flame/smoldering front-evolution and its application
  • Format : Talk at Waseda University
  • Author(s) :
    • Shunsuke Kobayashi (University of Miyazaki)
    • Shigetoshi Yazaki (Meiji University)
    • Kazunori Kuwana (Tokyo University of Science)
  • Abstract : The Kuramoto--Sivashinsky equation is well-known as a mathematical model describing the interfacial dynamics of combustion phenomena. In this talk, we focus on flame spreading over thin solid fuels and report the results of applying the Kuramoto--Sivashinsky equation to the following two topics: 1. the behavior of flame/smoldering fronts expanding circle with time. 2. the spreading speed of flame front in a spatially non-uniform region with a bellows shape.
• [04059] Multidimensional partial integro-differential equation in Bessel potential spaces with applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Sevcovic (Comenius University)
    • Cyril Izuchukwu Udeani (Comenies University)
  • Abstract : In the talk we analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We prove existence and uniqueness of a solution to the PIDE. As an application to option pricing in the one-dimensional space, we consider a general shift function arising from nonlinear option pricing models.

MS [00304] Phase transition and control of PDE models in applied sciences

room : G801

• [01375] Crowd pressure and turbulence in crowd disasters
  • Format : Talk at Waseda University
  • Author(s) :
    • Liangze Yang (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
  • Abstract : In this study, a mixed-type continuum model for multidirectional pedestrian flow was developed that explicitly considers the different movement characteristics of pedestrians under different situations: laminar flow in a low-density system and turbulent flow in a high-density system. In addition to the phase transition, the proposed model can reveal the effects of both force chains and panic sentiment, which are commonly observed phenomena during crowd disasters, by estimating the aggregated pushing pressure.
• [01721] Traceability of Water Pollution governed by an Inverse Source Problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Shenwen Yu (Yau Mathematical Sciences Center, Tsinghua University)
    • Lingyun Qiu (Yau Mathematical Sciences Center, Tsinghua University)
    • Zhongjing Wang (Department of Hydraulic Engineering, Tsinghua University)
    • Hui Yu (Yau Mathematical Sciences Center, Tsinghua University)
  • Abstract : We aim to find the time-dependent source term in the diffusion equation from the boundary measurement. Based on the idea of dynamic complex geometrical optics (CGO) solutions, we analyze a variational formulation of the inverse source problem and prove the uniqueness and stability result. A two-step reconstruction algorithm is proposed, which first recovers the locations of the point sources, and then the emission concentration functions. Some numerical experiments on simulated data are conducted.
• [03877] A Cucker-Smale inspired deterministic Mean Field Game with velocity interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Woojoo Shim (Kyungpook National University)
    • Filippo Santambrogio (Université Claude Bernard - Lyon 1)
  • Abstract : In this talk, I would like to introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference between their own velocity and that of the other agents they meet. During the talk, we will study the existence of an equilibrium in a Lagrangian setting using its variational structure and then study its properties and regularity.
• [05554] Provable convergence of blow-up time of numerical approximations for a class of convection-diffusion equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yang Yang (Michigan Technological University)
  • Abstract : In this talk, we investigate the numerical algorithms to capture the blow-up time for a class of convection-diffusion equations with blow-up solutions, such as the chemotaxis model. The blow-up time is difficult to capture since we cannot distinguish whether the blow-up is physical or is due to the instability. We propose two ways to define the numerical blow-up time and prove the convergence to the exact one.

MS [00507] Stochastic Dynamical Systems and Applications

room : G802

MS [00506] Inverse Problems for Anomalous Diffusion

room : G808

• [04435] Long-Short time asymptotic estimates for time-fractional diffusion-wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Xinchi HUANG (Tokyo Institute of Technology)
    • Xinchi Huang (Tokyo Institute of Technology)
    • Yikan Liu (Hokkaido University)
  • Abstract : In this talk, we consider the time-fractional diffusion-wave equations and show the long-time asymptotic estimate of the solution, which can be used to prove the long-time strict positivity of the solution and the uniqueness for an inverse source problem of determining the time-varying factor. Besides, we discuss the short-time asymptotic behavior and provide an application to the determination of the spatial varying factor in the source.
• [04612] Numerical identification of conductivity in (sub)diffusion equations from terminal measurement
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bangti Jin (Chinese University of Hong Kong)
    • Xiliang Lu (Wuhan University)
    • Qimeng Quan (Wuhan University)
    • Zhi Zhou (The Hong Kong Polytechnic University)
  • Abstract : This talk focuses on the inverse diffusion problems in (sub)diffusion equation. Typically, we employ Tikhonov strategy and discretize the regularized model by finite element methods. One critical issue is to establish a priori error estimate on the concerned parameter. In this talk, the speaker will discuss their recent study of recovering a space-dependent diffusion coefficient from terminal observation by a novel conditional stability.

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

room : G809

• [04375] Solution of inverse problems in three-dimensional singularly perturbed PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Dmitrii Chaikovskii (Shenzhen MSU-BIT University)
    • Ye Zhang (Beijing Institute of Technology)
  • Abstract : We present an efficient asymptotic expansion method for solving forward and inverse problems in a nonlinear, time-dependent, singularly perturbed reaction-diffusion-advection equation. We prove the existence and uniqueness of a smooth solution in 3D PDEs using asymptotic expansion. A simplified equation for the inverse source problem is derived, maintaining accuracy even with noisy data. We propose an asymptotic expansion regularization algorithm for the 3D inverse source problem and demonstrate its feasibility through a model problem.
• [05101] The coupled complex boundary methods for inverse problems of partial differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Rongfang Gong (Nanjing University of Aeronautics and Astronautics)
  • Abstract : In this talk, a coupled complex boundary method (CCBM) is proposed for an inverse source problem. With the introduction of imaginary unit, the CCBM transfers the original real problem to a complex one. The CCBM has several merits and is further improved. Also, the applications of the CCBM to bioluminescence tomography, inverse Cauchy problem, chromatography etc. are delivered.
• [05498] Physics-informed invertible neural network for the Koopman operator learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Yue Qiu (Chongqing University)
  • Abstract : The Koopman operator is used to embed a nonlinear system into an infinite, yet linear system with a set of observable functions. However, manually selecting observable functions that span the invariant subspace of the Koopman operator based on prior knowledge is inefficient and challenging, particularly when little or no information is available about the underlying systems. Furthermore, current methodologies tend to disregard the importance of the invertibility of observable functions, which leads to inaccurate results. To address these challenges, we propose the so-called FlowDMD, a Flow-based Dynamic Mode Decomposition that utilizes the Coupling Flow Invertible Neural Network (CF-INN) framework. FlowDMD leverages the intrinsically invertible characteristics of the CF-INN to learn the invariant subspaces of the Koopman operator and accurately reconstruct state variables. Numerical experiments demonstrate the superior performance of our algorithm compared to state-of-the-art methodologies.

MS [00342] Localized waves in nonlinear discrete systems

room : F308

• [00658] Existence of multi-pulse discrete breathers in Fermi-Pasta-Ulam-Tsingou lattices
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuyuki Yoshimura (Tottori University)
  • Abstract : Discrete breathers are spatially localized periodic solutions in nonlinear lattices. We prove the existence of odd symmetric, even symmetric, and multi-pulse discrete breathers in strong localization regime in one-dimensional infinite Fermi-Pasta-Ulam-Tsingou (FPUT) lattices with even interaction potentials. The multi-pulse discrete breather consists of an arbitrary number of the odd-like and/or even-like primary discrete breathers located separately on the lattice. The proof applies to both cases of pure attractive and repulsive-attractive interaction potentials.
• [01557] Spectral properties of nonlinear excitations in semiclassical systems with charge transport
  • Format : Online Talk on Zoom
  • Author(s) :
    • Juan FR Archilla (Universidad de Sevilla)
    • Janis Bajars (University of Latvia)
    • Yusuke Doi (Osaka University)
    • Masayuki Kimura (Setsunan University)
  • Abstract : We study the spectral properties of polarobreathers, that is, breathers carrying charge in a semi-classical model. Lattice particles are described mathematically, while the charged particle is described as a quantum one within the tight-binding approximation. Three different spectra are considered: the spectra of the atom positions, the spectra of the charge carrier probability and the spectra of charge carrier probability amplitude. The observed spectrum properties are related with the physical properties of the semiclassical system.
• [01269] Nonlinear waves in multistable mechanical metamaterials
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiromi Yasuda (Japan Aerospace Exploration Agency)
    • Hang Shu (University of Pennsylvania)
    • Weijian Jiao (University of Pennsylvania)
    • Vincent Tournat (Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université)
    • Jordan R. Raney (University of Pennsylvania)
  • Abstract : We explore collision behaviors of nonlinear waves in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We show that the system can support two different types of nonlinear waves, specifically elastic vector solitons and topological solitons. Moreover, we experimentally and numerically demonstrate the nucleation of topological solitons via collisions of vector solitons. Our findings show a new potential way of generating and controlling nonlinear waves in a mechanical structure.
• [01230] Soliton billiards
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jesus Cuevas-Maraver (University of Seville)
  • Abstract : A point particle elastically reflected within an enclosed 2D domain is known as a billiard. Depending on the features of this domain, the trajectory of the particle can be closed or ergodic. In this talk, we show the similarities and differences when, instead of a classical particle, a soliton is scattered from closed 2D potentials. To this aim, we have considered a 2D NLS equation with saturable nonlinearity and square barriers (among other potentials).

MS [02083] Integrable Aspects of Nonlinear Wave Equations, Solutions and Asymptotics

room : F309

• [04907] On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Engui Fan (Fudan University)
  • Abstract : We study the long time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation in the solitonic regions. Our main technical tool is the representation of the Cauchy problem with an associated matrix Riemann-Hilbert (RH) problem and the consequent asymptotic analysis of this RH problem. Based on the spectral analysis of the Lax pair associated with the mCH equation and scattering matrix, the solution of the Cauchy problem is characterized via the solution of a RH problem in the new scale (y,t). Further using the ∂ generalization of the Deift-Zhou steepest descent method, we derive different long time asymptotic expansions of the solution u(y,t) in different space-time solitonic regions of ξ = y/t. We divide the half-plane {(y,t) : −∞ 0} into four asymptotic regions: The phase function θ(z) has no stationary phase point on the jump contour in the space-time solitonic regions ξ ∈ (−∞, −1/4) ∪ (2, +∞), corresponding asymptotic approximations can be characterized with an N(Λ)-solitons with diverse residual error order O(t−1+2ρ); The phase function θ(z) has four phase points and eight phase points on the jump contour in the space-time solitonic regions ξ ∈ (0, 2) and ξ ∈ (−1/4, 0), respectively. The corresponding asymptotic approximations can be characterized with an N(Λ)-soliton as well as an interaction term between soliton solutions and the dispersion term with diverse residual error order O(t−3/4). Our results also confirm the soliton resolution conjecture and asymptotically stability of the N-soliton solutions for the mCH equation.
• [05585] Local and global analyticity for a generalized Camassa-Holm system
  • Format : Talk at Waseda University
  • Author(s) :
    • Hideshi Yamane (Kwansei Gakuin University)
  • Abstract : We solve the analytic Cauchy problem for the generalized two-component Camassa-Holm system introduced by R. M. Chen and Y. Liu. We show the existence of a unique local/global-in-time analytic solution under certain conditions. This is the first result about global analyticity for a Camassa-Holm-like system. The proof is based the technique by Barostichi, Himonas and Petronilho.
• [04390] Long-time asymptotics for the defocusing NLS equation with step-like boundary conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Deng-Shan Wang (Beijing Normal University)
  • Abstract : The long-time asymptotics for the defocusing NLS equation with step-like boundary conditions is investigated by the Riemann-Hilbert formulation. Whitham modulation theory shows that there are six cases for this initial discontinuity problem according to the orders of the Riemann invariants. We formulate the leading-order terms and the corresponding error estimates for each region of the six cases by Deift-Zhou nonlinear steepest-descent method. It is demonstrated that the asymptotic solutions match very well with the results from Whitham modulation theory and the direct numerical simulations.
• [05490] New revival phenomena for bidirectional dispersive hyperbolic equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jing Kang (Northwest University)
  • Abstract : In this talk, the dispersive revival and fractalisation phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles are investigated. Firstly, we study the periodic initial-boundary problem of the linear beam equation with step function initial data, and analyze the manifestation of the revival phenomenon for the corresponding solutions at rational times. Next, we extend the investigation to the periodic initial-boundary problems of more general bidirectional dispersive equations. We prove that, if the initial functions are of bounded variation, the dynamical evolution of such periodic initial-boundary problem depend essentially upon the large wave number asymptotics of the associated dispersion relations. Integral polynomial or asymptotically integral polynomial dispersion relations produce dispersive revival/fractalisation rational/irrational dichotomy effects, whereas those with non-polynomial growth results in fractal profiles at all times. Finally, numerical experiments are used to demonstrate how such effects persist into the nonlinear regime, in the concrete case of the nonlinear beam equation. This is a joint work with Peter J. Olver, Xiaochuan Liu and Changzheng Qu.

MS [00185] AAA rational approximation: extensions and applications

room : F310

• [02698] Linearization of dynamical systems using the AAA algorithm
  • Format : Talk at Waseda University
  • Author(s) :
    • Karl Meerbergen (KU Leuven)
  • Abstract : We provide an overview of the use of AAA for the linearization of all kinds of nonlinear equations arising from dynamical systems. This includes nonlinear eigenvalue problems, nonlinear frequency dependent dynamical systems and nonlinear time dependent systems. The concept linearization is key for these problems, since linear problems are usually easier to handle in numerics.
• [02371] Time-domain model reduction in the Loewner framework
  • Format : Talk at Waseda University
  • Author(s) :
    • Athanasios Antoulas (Rice University)
  • Abstract : In this talk we will present the main features of the Loewner Framework for rational approximation and model reduction. In particular, time domain methods will be of central importance.
• [05435] AAA and numerical conformal mapping
  • Format : Online Talk on Zoom
  • Author(s) :
    • Olivier Sète (University of Greifswald)
  • Abstract : In this talk, we explore applications of AAA rational approximation in numerical conformal mapping.
• [05536] AAA rational approximation on a continuum
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuji Nakatsukasa (University of Oxford)
  • Abstract : AAA has normally been applied on a discrete set, typically hundreds or thousands of points in a (real or complex) domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as it goes, which often also reduces the number of samples required. The key idea is that the support points tend to indicate where more samples are required. Execution is fast since SVDs are computed only for matrices that are nearly square.

MS [00088] Machine learning in infinite dimensions

room : F311

• [05609] Vector-valued Barron spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Yury Korolev (University of Bath)
  • Abstract : Approximation properties of infinitely wide neural networks have been studied by several authors in the last few years. New function spaces have been introduced that consist of functions that can be efficiently (i.e., with dimension-independent rates) approximated by neural networks of finite width, e.g. Barron spaces fornetworks with a single hidden layer. Typically, these functions act between Euclidean spaces, typically with a high-dimensional input space and a lower-dimensional output space. As neural networks gain popularity in inherently infinite-dimensional settings such as inverse problems and imaging, it becomes necessary to analyse the properties of neural networks as nonlinear operators acting between infinite-dimensional spaces. In this talk, I will discuss a generalisation of Barron spaces to functions that map between Banach spaces and present Monte-Carlo (1/sqrt(n)) approximation rates.
• [04824] Analysis of Neural Networks : Blessings of Width, Curses of Depth
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lénaïc Chizat (EPFL)
  • Abstract : I will present several results around the large-width limit of gradient-based algorithms for artificial neural networks (NNs). After a review of two-layer NNs, I will discuss the case of deep NNs where the non-linear dynamics that arises turns out much less tractable, because of how the random matrices of the initialization interact. I will finally elaborate on the case of deep linear NNs where we have obtained a complete description of the dynamics.
• [02466] Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Korba (ENSAE/CREST)
    • Pierre-Cyril Aubin-Frankowski (INRIA/Ecole Normale Supérieure)
    • Flavien Léger (INRIA)
  • Abstract : Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman divergences through directional derivatives, we derive the convergence of the scheme for relatively smooth and convex pairs of functionals. Such assumptions allow to handle non-smooth functionals such as the Kullback–Leibler (KL) divergence. Applying our result to joint distributions and KL, we show that Sinkhorn’s primal iterations for entropic optimal transport in the continuous setting correspond to a mirror descent, and we obtain a new proof of its (sub)linear convergence. We also show that Expectation Maximization (EM) can always formally be written as a mirror descent. When optimizing only on the latent distribution while fixing the mixtures parameters – which corresponds to the Richardson–Lucy deconvolution scheme in signal processing – we derive sublinear rates of convergence.
• [05291] Covariance-Modulated Optimal Transport Geometry
  • Format : Talk at Waseda University
  • Author(s) :
    • Franca Hoffmann (California Institute of Technology)
    • André Schlichting (University of Münster)
    • Martin Burger (DESY and University of Hamburg)
    • Daniel Matthes (Technische Universitaet Muenchen)
    • Matthias Erbar (Universitaet Bielefeld)
  • Abstract : We present a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the current distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble Kalman methods for solving inverse problems. We show that the transport problem splits into two coupled minimization problems up to degrees of freedom given by rotations: one for the evolution of mean and covariance of the interpolating curve, and one for its shape. Similarly, on the level of the gradient flows a similar splitting into the evolution of moments and shapes of the distribution can be observed. Those show better convergence properties in comparison to the classical Wasserstein metric in terms of exponential convergence rates independent of the Gaussian target.

MS [00426] Variational methods for thin structures and free-boundary problems

room : F312

• [04117] Stable Möbius bands obtained by isometrically deforming circular helicoids
  • Format : Talk at Waseda University
  • Author(s) :
    • Eliot Fried (Okinawa Institute of Science and Technology)
    • Vikash Chaurasia (Okinawa Institute of Science and Technology)
  • Abstract : We consider a variational problem for finding an isometric deformation from a (circular helicoid to a stable Möbius band. Helicoids with certain specific numbers of turns yield stable bands with \(n=2k+1\), \(k\ge1\), half twists and \(n\)-fold rotational symmetry. Each such band has the least energy of any stable competitor with the same number of half twists. Helicoids with other numbers of turns yield two stable bands with equal energy but different numbers of half twists.
• [02967] Rectifiability for flat singularities of higher codimension area minimizers
  • Format : Talk at Waseda University
  • Author(s) :
    • Camillo De Lellis (Institute for Advanced Study)
    • Paul Minter (Princeton University)
    • Anna Skorobogatova (Princeton University)
  • Abstract : Integral currents provide a natural setting in which to study the Plateau problem, but permit the formation of singularities in area-minimizers. The problem of determining the size and structure of the interior singular set of an area-minimizer in this setting has been studied in great detail since the 1960s, with many ground-breaking contributions. When the codimension is higher than 1, due to the presence of singular points with high multiplicity flat tangent cones, little progress has been made since Almgren's celebrated (m-2)-Hausdorff dimension bound on the singular set, the proof of which has since been simplified by De Lellis and Spadaro. In this talk I will discuss joint work with Camillo De Lellis and Paul Minter, in which we achieve (m-2)-rectifiability for the singular set.
• [03455] Interior regularity for stationary two-dimensional multivalued maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Jonas Hirsch (University of Leipzig)
    • Luca Spolaor (UCSD)
  • Abstract : $Q$-valued maps minimizing a suitably defined Dirichlet energy were introduce by Almgren in his proof of the optimal regularity of area minimizing currents in any dimension and codimension. In this talk I will discuss the extension of Almgren's result to stationary $Q$-valued maps in dimension $2$. This is joint work with Jonas Hirsch (Leipzig).
• [03306] Transport of currents and geometric Rademacher-type theorems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Paolo Bonicatto (University of Warwick)
  • Abstract : Given a vector field $b$ on $\mathbb R^d$, one usually studies the transport/continuity equation drifted by $b$ looking for solutions in the class of functions or at most in the class of measures. I will talk about recent efforts, motivated by the modeling of defects in crystalline materials, aimed at extending the previous theory to the case when the unknown is instead a family of k-currents in $\mathbb R^d$.

MS [01181] Variational methods for multi-scale dynamics

room : F401

• [04828] Variational numerical schemes for gradient flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yiwei Wang (University of California, Riverside)
    • Chun Liu (Illinois Institute of Technology)
  • Abstract : We'll present a numerical framework for developing structure-preserving variational schemes for various types of gradient flows. The numerical approach starts with the energy-dissipation law of the underlying system and can combine different spatial discretizations, including Eulerian, Lagrangian, particle, and neural-network-based approaches. The numerical procedure guarantees the developed schemes are energy stable and can preserve the intrinsic physical constraints. Several applications and theoretical justifications will be discussed.
• [04971] Quantitative coarse-graining of Markov chains
  • Format : Online Talk on Zoom
  • Author(s) :
    • Upanshu Sharma (UNSW Sydney)
    • Bastian Hilder (Lund University)
  • Abstract : Coarse-graining is the procedure of approximating large and complex systems by simpler and lower-dimensional ones. It is typically characterised by a mapping which projects the full state of the system onto a smaller set; this mapping captures the relevant (often slow) features of the system. Starting from a (non-reversible) continuous-time Markov chain and such a mapping, I will discuss an effective dynamics which approximates the true projected Markov chain and present error estimates on the approximation error.
• [04391] Variational convergence from mean-field stochastic particle systems to the exchange-driven growth model
  • Format : Online Talk on Zoom
  • Author(s) :
    • Chun Yin Lam (Universität Münster)
    • André Schlichting (Universität Münster)
  • Abstract : We consider the hydrodynamic limit of mean-field stochastic particle systems on a complete graph using variational methods. The evolution is driven by particle exchanges with its rate depending on the population of the initial and final vertices. This model is a generalisation of the zero-range process and has applications in cloud formation, polymerization, and wealth exchange. Under detailed balance conditions, the evolution equation has a gradient structure motivated by the Large Deviations Principle. The variational formulation is based on the LDP rate function.
• [05130] On time-splitting methods for gradient flows with two dissipation mechanisms
  • Format : Talk at Waseda University
  • Author(s) :
    • Artur Stephan (Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany)
  • Abstract : A gradient system consists of a state space $X$, an energy functional $E:X\to\mathbb{R}\cup\{\infty\}$ and a dissipation potential $R:X\to[0,\infty[$ and defines a gradient-flow equation. Considering the case where the dual dissipation potential $R^*$ is given by the sum $R^*=R_1^*+R_2^*$, we show how convergence of a time-splitting method where the solution of the combined gradient system is approximated by concatenating the separate gradient-flows. This is joint work with Alexander Mielke (Berlin) and Riccarda Rossi (Brescia).

MS [00941] Numerical methods for Hamilton-Jacobi equations and their applications

room : F402

MS [00151] Recent trends in SHM: damage modeling and optimal experimental design from a mechanical and mathematical point of view

room : F403

• [00230] A low power autonomous SHM node for aerospace applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Carol Featherston (School of Engineering, Cardiff University)
    • Rhys Pullin (School of Engineering, Cardiff University)
    • Stepehn Griggs (School of Engineering, Cardiff University)
    • Matthew Pearson (School of Engineering, Cardiff University)
  • Abstract : Acoustic emission(AE) monitors the release of energy resulting from the growth of damage to determine structural integrity. It is difficult to apply in low‐power systems as sensors must either be wired together or time synchronised, which is power intensive. A method based on three piezoelectric sensors in a small triangular array is proposed. Hardware is developed and the feasibility of powering the unit through energy harvesting explored. Results are obtained for a complex composite structure.
• [00270] Damage parameter estimation in composite materials using data assimilation with reduced order models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nanda Kishore Bellam Muralidhar (TU Braunschweig)
    • Carmen Gräßle (TU Braunschweig)
    • Natalie Rauter (HSU Hamburg)
    • Rolf Lammering (HSU Hamburg)
    • Andrey Mikhaylenko (HSU Hamburg)
    • Dirk Lorenz (TU Braunschweig)
  • Abstract : In this work, we are concerned with estimating parameters that describe damage in composite materials. In particular, we consider fiber metal laminates which consist of metals and fiber reinforced plastics. Such materials are of great interest in e.g. aviation and automotive industries. We study structural health monitoring using guided ultrasonic waves utilizing an integrated sensor. In order to determine the damage parameters, we use techniques from Bayesian inference and data assimilation together with model order reduction which enables to alleviate the computational efforts. Numerical simulations illustrate the approaches.
• [00256] Coefficient Control for Variational Inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolai Simon (Universität Hamburg)
    • Winnifried Wollner (Universität Hamburg)
  • Abstract : We consider the effects of introducing a control variable into the coefficients of a variational inequality in an optimal control problem with complementarity constraints. The novelty of this talk is the utilization of H-convergence methods to formulate limit arguments as the basis for a bootstrapping approach, used to prove strong $L^p$ convergence of the coefficient control variable. Using the example of an obstacle problem, we compute a set of limiting optimality conditions using these arguments.
• [00269] Optimal sparse sensor location for structural health monitoring
  • Format : Online Talk on Zoom
  • Author(s) :
    • Olga Weiß (Helmut Schmidt University/ University of the Federal Armed Forces Hamburg)
    • Kathrin Welker (TU Bergakademie Freiberg)
    • Volker Schulz (Trier University)
  • Abstract : Bridge structures are indispensable components of the infrastructure of modern industrial societies, and maintaining their functionality and reliability is essential. Hence, monitoring processes of the structure and health of bridges are indispensable. For this purpose, the efficient and optimal placement of appropriate sensors for the non-destructive permanent monitoring of the structures is an important component. Determining the number and placement of sensors to provide valuable information about damage and impact to the structure is essential for cost-efficient monitoring and for minimizing the volume of data, however, to this date represents a challenge. We consider this issue from a mathematical point of view and derive a suitable optimization problem in infinite-dimensional function spaces. This modeled optimization problem is to be solved numerically by adapted optimization methods. As a special feature, the desired resulting sparsity of the solution for the positioning of the sensors is to be incorporated and considered in the solving method.

MS [00888] Geometric Shape Generation I: Structures

room : F411

• [02770] Shape modeling of umbrella surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Maekawa (Waseda University)
    • Kenji Takizawa (Waseda University)
    • Takuya Terahara (Waseda University)
  • Abstract : We introduce a geometric modeling method of the umbrella by defining the rib curves as the intersection of two bilinear patches. Furthermore, we investigate various differential geometric properties of the umbrella surface and introduce a method to unfold it onto a plane that can be used to fabricate a wooden template for cutting canopy fabrics.
• [04221] Geometrical and structural design of pseudo-geodesic gridshells
  • Format : Talk at Waseda University
  • Author(s) :
    • Romain Mesnil (Ecole des Ponts ParisTech)
    • Olivier Baverel (Ecole des Ponts ParisTech)
  • Abstract : Gridshells are efficient structures built using a network of straight members that are deformed into doubly curved shapes. In this presentation, we propose to construct gridshells with pseudo-geodesic curves, which are characterized by the equality between torsion and geodesic torsion. We show that existence of parametrization by pseudo-geodesic network is impossible when integral of Gaussian curvature is superior to an upper bound. Structural performance and fabrication are discussed with the case-study of an architectural pavilion.
• [02774] Preliminary research on shape searching method for curved crease origami using bending deformation
  • Format : Talk at Waseda University
  • Author(s) :
    • Tianhao Zhang (The University of Tokyo)
    • Ken'ichi Kawaguchi (The University of Tokyo)
  • Abstract : Curved crease origami is focused on by the researchers and designers in the field of building structure owing to the foldability and mechanical properties. In this paper, a shape searching method is proposed based on an optimization approach. This approach can form a shape close to the target surface defined by the designers. This research aims to search the shape concerning bending deformation to explores the application of curved origami to architectural structures.
• [02924] Shape design of free-form shells with specified projected membrane forces
  • Format : Talk at Waseda University
  • Author(s) :
    • Makoto Ohsaki (Kyoto University)
    • Yusuke Sakai (Sony Computer Science Laboratories)
    • Taku Nakajima (Kyoto University)
    • Riree Takeoka (Takenaka Corporation)
  • Abstract : A shape design method is proposed for membrane free-form shells modeled as a graph surface. The distribution of membrane forces projected to the plane is specified to satisfy horizontal equilibrium as a function of shear stress. The shape is determined as a solution to the vertical equilibrium equations discretized by the finite difference method. The shape is iteratively corrected to achieve the specified projected stress distribution considering the material property.

MS [00539] Extreme value theory and statistical analysis

room : F412

• [03480] Asymptotic theory for extreme value generalized additive model
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuma Yoshida (Kagoshima University)
  • Abstract : The classical approach to analyzing extreme value data is the generalized Pareto distribution (GPD). When the GPD is used to explain a target variable with the large dimension of covariates, the shape and scale function of covariates included in GPD are sometimes modeled using the generalized additive models (GAM). In contrast to many results of application, there are no theoretical results on the hybrid technique of GAM and GPD, which motivates us to develop its asymptotic theory. We provide the rate of convergence of the estimator of shape and scale functions, as well as its local asymptotic normality.
• [03597] Comparative study on accuracy of sample maximum distribution estimators in IID settings
  • Format : Online Talk on Zoom
  • Author(s) :
    • Taku Moriyama (Yokohama City University)
  • Abstract : Comparative study on the accuracy of sample maximum distribution estimators in IID settings will be reported. The distribution of sample maximum is approximated by the generalized extreme value distribution. However, the approximation accuracy heavily depends on the tail index. This study investigates a nonparametric estimator as the alternative approach and compares the accuracies both theoretically and numerically. Future prospects of the study will also be discussed.
• [02777] Subsampling inference for nonparametric extremal conditional quantiles
  • Format : Talk at Waseda University
  • Author(s) :
    • Daisuke Kurisu (The University of Tokyo)
    • Taisuke Otsu (London School of Economics)
  • Abstract : In this talk, we study asymptotic properties of the local linear (LL) quantile estimator under the extremal-order quantile asymptotics and develop a practical inference method for conditional quantiles in extreme tail areas. The asymptotic distribution of the LL quantile estimator is derived as a minimizer of certain functional of a Poisson point process. We also propose a subsampling inference method for conditional extreme quantiles based on a self-normalized version of the LL estimator.
• [03093] Measuring non-exchangeable tail dependence using tail copulas
  • Format : Talk at Waseda University
  • Author(s) :
    • Takaaki Koike (Hitotsubashi University)
    • Shogo Kato (Institute of Statistical Mathematics)
    • Marius Hofert (The University of Hong Kong)
  • Abstract : We propose a novel framework of quantifying and comparing the degree of tail dependence using tail copula. Our proposed measures have clear probabilistic interpretations, and capture various features of non-exchangeable tail dependence depending on the purpose of the analysis. Analytical forms of the proposed measures are derived for various parametric copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.

MS [02435] Scaling Limits of Interacting Particle Systems

room : E501

• [04551] Wave propagation for reaction-diffusion equations on infinite trees
  • Format : Online Talk on Zoom
  • Author(s) :
    • Grigory Terlov (UNC Chapel Hill )
    • Wai-Tong (Lous) Fan (Indiana University)
    • Wenqing Hu (Missouri University of S&T)
  • Abstract : The asymptotic speed of the wavefront of the solution to FKPP equation on $\mathbb{R}$ is well understood. I will present a probabilistic approach to the same problem on infinite metric trees. When the reaction rate is large enough we show that a travelling wavefront emerges. Its speed is slower than that of the same equation on the real line, and we can estimate this slow-down in terms of the structure of the tree.
• [03975] From the KPZ equation to the directed landscape
  • Format : Online Talk on Zoom
  • Author(s) :
    • XUAN WU (University of Illinois Urbana-Champaign)
  • Abstract : This talk presents the convergence of the KPZ equation to the directed landscape, which is the central object in the KPZ universality class. This convergence result is the first to the directed landscape among the positive temperature models.
• [05115] Longtime behaviour of the stochastic FKPP equation conditioned on non-fixation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Oliver Kelsey Tough (University of Bath)
    • Wai-Tong (Louis) Fan (Indiana University)
  • Abstract : In population genetics, fixation is the phenomenon in which all members of a population have the same copy of a given gene. Whilst most genes are fixed (most genes are shared by all individuals), not all genes are fixed (individuals aren't identical). The prototypical continuum model for the spread of a genetic type in a spatially distributed population under the effects of genetic drift, selection and migration is the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation. We consider the stochastic FKPP equation on the circle. We establish existence and uniqueness of the quasi-stationary distribution (QSD) for solutions of the stochastic FKPP, considered to be absorbed upon fixation. We show that the distribution of the solution conditioned on non-fixation converges to this unique QSD as time $t\rightarrow \infty$, for any initial distribution. Moreover we characterise the leading-order asymptotics for the tail distribution of the fixation time. This is based on joint work with Wai-Tong Fan.
• [03336] The interacting multiplicative coalescent and Levy-like random fields
  • Format : Online Talk on Zoom
  • Author(s) :
    • David J Clancy, Jr. (University of Wiscons)
  • Abstract : The multiplicative coalescent describes the evolution of blocks where blocks of masses $x$ and $y$ form a single block of mass $x+y$ at rate $xy$. This process naturally appears when studying many random graph models at criticality. Their marginal laws are described using (mixtures of) Levy-type processes. Using stochastic blockmodels, we show that one can describe the marginal law of two interacting multiplicative coalescences using a Levy-type random field. Based on work with V. Konarovskyi and V. Limic.

MS [00322] Methodological advancement in rough paths and data science

room : E502

• [01331] Optimal stopping with signatures
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Bayer (Weierstrass Institute)
    • John Schoenmakers (Weierstrass Institute)
    • Paul Hager (Humboldt-Universität zu Berlin)
    • Sebastian Riedel (University of Hagen)
  • Abstract : We propose a new method for solving optimal stopping problems under minimal assumptions on the underlying stochastic process $X$. We consider stopping times represented by functionals of the rough path signature $\mathbb{X}^{<\infty}$, and prove that maximizing over these classes of signature stopping times solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a deterministic optimization problem on the expected signature.
• [01439] Analysis on unparameterised path space: towards a coherent mathematical theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Cass (Imperial College London)
    • William Turner (Imperial College London)
  • Abstract : The signature is a non-commutative exponential that appeared in the foundational work of K-T Chen in the 1950s. It is also a fundamental object in the theory of rough paths (Lyons, 1998). More recently, it has been proposed, and used, as part of a practical methodology to give a way of summarising multimodal, possibly irregularly sampled, time-ordered data in a way that is insensitive to its parameterisation. A key property underpinning this approach is the ability of linear functionals of the signature to approximate arbitrarily any compactly supported and continuous function on (unparameterised) path space. We present some new results on the properties of a selection of topologies on the space of unparameterised paths. We discuss various applications in this context. Based on joint work with Will Turner.
• [01370] On some stability results in mathematical finance via rough path theory
  • Format : Talk at Waseda University
  • Author(s) :
    • CHONG LIU (ShanghaiTech University)
  • Abstract : In this talk I will present some recent progress on establishing some stability results in mathematical finance, e.g., in portfolio theory and utility maximization problems, via an approach of rough path theory.
• [01438] Kernels Methods for Stochastic Processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Harald Oberhauser (University of Oxford)
  • Abstract : Kernels provide a powerful approach to learning from structured data. An important case of structured data arises when there is a natural sequential order in a data point; classic examples are time series or text. I will talk about the signature kernel that allows the computation of inner products of the signature of paths after they've been lifted to paths evolving in an infinite-dimensional Hilbert space.

MS [00570] Title: Machine Learning and Statistical Approaches for PDE Based Inverse Problems in Imaging

room : E503

• [04986] Data-Driven Design of Thin-Film Optical Systems using Deep Active Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Youngjoon Hong (Sungkyunkwan University)
  • Abstract : A deep learning aided optimization algorithm for the design of flat thin-film multilayer optical systems is developed. We introduce a deep generative neural network, based on a variational autoencoder, to perform the optimization of photonic devices. This algorithm allows one to find a near-optimal solution to the inverse design problem of creating an anti-reflective grating, a fundamental problem in material science. As a proof of concept, we demonstrate the method’s capabilities for designing an anti-reflective flat thin-film stack consisting of multiple material types. We designed and constructed a dielectric stack on silicon that exhibits an average reflection, which is lower than other recently published experiments in the engineering and physics literature. In addition to its superior performance, the computational cost of our algorithm based on the deep generative model is much lower than traditional nonlinear optimization algorithms. These results demonstrate that advanced concepts in deep learning can drive the capabilities of inverse design algorithms for photonics. In addition, we develop an accurate regression model using deep active learning to predict the total reflectivity for a given optical system. The surrogate model of the governing partial differential equations can then be broadly used in the design of optical systems and to rapidly evaluate their behavior.
• [04138] Implicit Solutions of Electrical Impedance Tomography Using Deep Neural Network
  • Format : Talk at Waseda University
  • Author(s) :
    • Taufiquar Khan (UNC Charlotte)
    • Thilo Strauss (Bosch)
  • Abstract : In this talk, we will discuss deep learning approach for the electrical impedance tomography (EIT). In the last several decades, researchers have made significant improvement for image reconstruction for the EIT inverse problem. However, there is still need for much improvement. In this talk, we will discuss a shape reconstruction approach using machine learning. We propose a neural network architecture where the neural network model estimates the probability for a point of whether the conductivity belongs to the background region or to the non-homogeneous region. We present our numerical results to show the performance of the architecture and compare the proposed method with other known algorithms.

contributed talk: CT088

room : E504

[00836] Reynolds-blended weights for BDDC in applications to Navier-Stokes equations

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : We solve incompressible Navier-Stokes equations by the finite element method with one step of the Balancing Domain Decomposition by Constraints (BDDC) method. This method requires a scaling operator at the interface between subdomains. We introduce a new interface scaling tailored to Navier-Stokes equations. The weights in this averaging consider a local Reynolds number. This Reynolds-blended scaling is compared with several existing approaches on 3D lid-driven cavity and backward-facing step problems.
• Classification : 65Y05
• Format : Talk at Waseda University
• Author(s) :
  • Martin Hanek (Czech Technical University in Prague, Institute of Mathematics of the Czech Academy of Sciences)

[02267] A Massively Parallel Performance Portable Free Space Spectral Poisson Solver for Beam and Plasma Physics Problems

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : Recently, a new fast algorithm for computing volume potentials has been proposed by Vico, Greengard, and Ferrando, which provides a spectral accuracy free-space Poisson equation solver, useful for plasma and beam physics. We write a parallel performance portable implementation in the IPPL library, using the Exascale Computing Project's heFFTe and Kokkos libraries, and MPI for parallelization. A comparison with the traditional Hockney-Eastwood algorithm manifests the memory benefits of using the new algorithm, especially on GPUs.
• Classification : 65Y05, 78A30, 35Q61, 65K05, 65N80
• Format : Talk at Waseda University
• Author(s) :
  • Sonali Mayani (Paul Scherrer Institute)
  • Antoine Cerfon (NYU)
  • Matthias Frey (University of St. Andrews)
  • Veronica Montanaro (Paul Scherrer Institute)
  • Sriramkrishnan Muralikrishnan (Jülich Supercomputing Centre)
  • Andreas Adelmann (Paul Scherrer Institute)

[01997] Robust continuation method for computing solution curves with critical points

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : To better compute the solution curve of challenging problems, numerical continuation methods have proved to be a very efficient tool. However, these methods can still lead to undesired results, particularly near critical points. This paper will therefore present a robust continuation method that will include two key aspects to solve difficult problems: detection of problematic regions during the solution process and additional steps to deal with them. Numerical examples will be presented.
• Classification : 65Y20, 65Z05, 74S05
• Format : Online Talk on Zoom
• Author(s) :
  • Sophie Leger (Université de Moncton)

[00947] Statistical analysis of neonatal mortality predictors in Ghana

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : In this study, we identify and investigate the main factors influencing newborn mortality in the Ghanaian locality and predict the occurrence of future infant mortality based on the 2017 Demographic and Health Survey data using logistic regression. Our work shows that the child’s weight and sex have a strong correlation with its survival. The study reveals that mortality is more than 50% greater in underweight children and also, 62.7% infant deaths happen in infant males.
• Classification : 62Pxx, 92-11, 92-08, Bio Statistics
• Format : Online Talk on Zoom
• Author(s) :
  • Elizabeth Dufie Amankwah (Kwame Nkrumah University of Science and Technology)
  • Juliet Amegble Richardson (Kwame Nkrumah University of Science and Technology)
  • Solomon Kyei Mensah (Kwame Nkrumah University of Science and Technology)

[00116] Multi-Scale Modelling of three phase lag (TPL) of lung cancer during cryosurgery

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : On the basis of the study of cryosurgery with mathematical modelling we discuss about the study related to non-Fourier bio-heat transfer available numerically with various boundary conditions for frozen and non frozen region. By the CAD/ANSYS study a specific region is developed for the tumor detected area. We’ll elaborate three phase lag (TPL) bio-heat transfer model to analysis of the temperature distribution in living tissue. By this work of mathematical modelling of cryosurgery in lung cancer to elaborate the knowledge of TPL bio-heat model by using numerical methods.
• Classification : 92-XX, 92Bxx, 92B05
• Format : Online Talk on Zoom
• Author(s) :
  • Sarita Singh (Doon University Dehradun Uttarakhand IndiaDoon University Dehradun Uttarakhand )

MS [02163] Recent Developments in Stochastic Numerics and Computational Finance

room : E505

• [03674] New deep NN architecture using higher-order weak approximation
  • Format : Talk at Waseda University
  • Author(s) :
    • Syoiti Ninomiya (Tokyo Institute of Technology)
    • Yuming MA (Tokyo Institute of Technology)
  • Abstract : New deep learning neural networks based on high-order weak approximation algorithms for stochastic differential equations are proposed. The behavior of these new algorithms when applied to the problem of pricing financial derivatives is also reported. The architectural key to the deep learning neural network proposed here is a high-order discretization method of Runge-Kutta type, in which the weak approximation of stochastic differential equations is realized by iterative substitutions and their linear summation.
• [03488] A higher order discretization scheme for backward stochastic differential equations combined with a non-linear discrete Clark-Ocone formula
  • Format : Talk at Waseda University
  • Author(s) :
    • Kaori Okuma (Ritsumeikan University)
  • Abstract : In this talk, the author first introduces a discretization scheme of arbitrary order for backward stochastic differential equations. Then, by establishing a mathematical algorithm based on a non-linear discrete Clark-Ocone formula, which was previously established by the author and her collaborators, the author claims that the scheme is potentially implementable in a “deep solver” type numerical algorithm —- a scheme using approximation by deep neural networks and stochastic gradient descent — for a semi-linear partial differential equation.
• [03622] New deep learning-based algorithms for high-dimensional Bermudan option pricing
  • Format : Talk at Waseda University
  • Author(s) :
    • Riu Naito (Hitotsubashi University)
    • Toshihiro Yamada (Hitotsubashi University)
  • Abstract : In this talk, we introduce efficient algorithms for pricing high-dimensional Bermudan options. The proposed methods provide an accurate approximation for Bermudan options by discretizing the interval of early-exercise dates with weak approximation schemes for stochastic differential equations. The deep learning-based approximation for conditional expectations at each exercise date works well for high-dimensional problems compared to the least squares Monte Carlo method. Numerical experiments confirm the validity of the methods.
• [05412] On-Policy and Off-Policy q-Learning in Continuous Time
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanwei Jia (Chinese University of Hong Kong )
    • Xunyu Zhou (Columbia University)
  • Abstract : We study the continuous-time counterpart of Q-learning for reinforcement learning (RL) under the entropy-regularized, exploratory formulation introduced by Wang et al (2020). As the conventional (big) Q-function collapses in continuous time, we consider its first-order approximation and coin the term ``(little) q-function". This function is related to the instantaneous advantage rate function as well as the Hamiltonian. We develop a ``q-learning" theory around the q-function that is independent of time discretization. Given a stochastic policy, we jointly characterize the associated q-function and value function by martingale conditions of certain stochastic processes, in both on-policy and off-policy settings. We then apply the theory to devise different actor-critic algorithms for solving underlying RL problems, depending on whether or not the density function of the Gibbs measure generated from the q-function can be computed explicitly.

MS [00421] When random comes to the rescue of numerical computation

room : E506

• [02748] The computer arithmetic new deal: AI is pushing the frontier
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Petit (Intel)
  • Abstract : Recent years have seen a tremendous number of new research contributions to computer arithmetic, challenging lower precision arithmetic and rounding mode, leaving the IEEE754 standard far behind. This all comes from the rise of AI workloads as one of the main driver in the data center software and architecture design. Keeping on par with the incredibly fast changing usage of computer arithmetic has push our algorithms, tools, and capacity to their limit. This is an opportunity to rethink and redesign our approach about floating point hardware and software, promoting new tools and methodologies, and allowing ground breaking solution to be promoted to main stream software and hardware implementation. In this talk I will provide some more context about this change and discuss some of the exciting work I am sharing with collaborators inside and outside intel.
• [01590] New stochastic rounding modes for numerical verification
  • Format : Talk at Waseda University
  • Author(s) :
    • Bruno LATHUILIERE (EDF R&D)
    • Nestor Demeure (Data and analytics services group, National Energy Research Scientific Computing Center, Berkeley)
  • Abstract : In the context of industrial code verification, the use of stochastic rounding modes allows to estimate the numerical quality of the results through multiple independent executions of the software. But in some rare cases, the introduction of stochastic rounding can lead to a runtime error because the software implicitly relies on the determinism of IEEE floating-point operations. To overcome this problem, we propose new deterministic stochastic rounding modes: these maintain the stochastic properties between different executions of the software while guaranteeing the determinism of the floating operations having the same parameters within one execution. Results based on an implementation of the method in the Verrou tool will be presented.
• [04711] Stochastic rounding as a model of round-to-nearest
  • Format : Talk at Waseda University
  • Author(s) :
    • Devan Sohier (LI-PaRAD, UVSQ)
  • Abstract : Round-to-nearest (RN), the default rounding mode in the omnipresent IEEE754 standard, is difficult to analyze. Deterministic bounds, as well as their refinements like interval arithmetic, generally prove overly pessimistic, compared to the day-to-day observations of numerical scientists. Stochastic rounding (SR) may be used as a model of RN, the results of which are easier to analyze, and closer to these observations. In this talk, I will present a methodology to analyze results of a SR simulation of RN. The widely used formula for the number of significant bits $-\log\frac\sigma\mu$ can be refined and given a precise statistical ground in the case when the error has a normal distribution; when no normality assumption is substantiated, other tools based on Bernoulli estimations need to be used. Using SR as a model for RN also has some limits: SR does not present stagnation phenomena typical of RN, and SR also does not give the same results when the program recomputes twice the same operation. Finally, I will discuss flaws of various severeness of some software implementations of SR, and present some remarks regarding possible future implementations of SR, both in software and hardware.
• [03452] VPREC to analyze the precision appetites and numerical abnormalities of several proxy applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Roman Iakymchuk (Umeå University)
    • Pablo de Oliveira Castro (Université Paris-Saclay)
  • Abstract : The energy consumption constraint for large-scale computing encourages scientists to revise the architecture design of hardware but also applications, algorithms, as well as the underlying working/ storage precision. We introduce an approach to address the issue of sustainable computations from the perspective of computer arithmetic tools. We employ the variable precision backend (VPREC) to identify parts of code that can benefit from smaller floating-point formats. Finally, we show preliminary results on several proxy applications.

MS [01054] Scalable Solvers for Multiphysics Problems

room : E507

• [01909] On the Use of Algebraic Multigrid in Various Applications on High Performance Computers
  • Format : Talk at Waseda University
  • Author(s) :
    • Ulrike Meier Yang (Lawrence Livermore National Laboratory)
  • Abstract : The hypre software library provides a variety of parallel linear solvers implemented for high performance computers. Its focus is on algebraic multigrid methods (AMG), which provide excellent scalability. With the increasing inclusion of accelerators into current and future high-performance computers, various new programming models have been added to take advantage of the increased performance potential of GPUs. This talk will discuss porting challenges and present results of use of hypre’s GPU-enabled multigrid solvers within several application codes.
• [03924] Implications of multiphysics problems in multigrid methods from a linear algebra view point
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthias Bolten (University of Wuppertal)
  • Abstract : Multiphysics problems require special attention in multigrid methods, as standards methods often do not converge. To overcome this, different approaches have been considered, e.g, special smoothers and special grid transfer and coarse grid selection. We are studying methods for block matrices, as they arise when systems of PDEs are considered. Different approaches for block matrices are presented, including block smoothers as well as analysis of multigrid methods resulting in requirements on grid transfer operators.
• [03818] Parallel scalable solvers for Helmholtz problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Cornelis Vuik (Delft University of Technology)
    • Jinqiang Chen (Delft University of Technology)
    • Vandana Dwarka (Delft University of Technology)
  • Abstract : A matrix-free, parallel multi-level deflation preconditioning method is proposed for Helmholtz problems. The method integrates the geometric multi-grid-based Complex Shifted Laplace Preconditioner (CSLP) and higher-order deflation, employing re-discretization schemes derived from Galerkin coarsening approach for a matrix-free parallel implementation. The method shows close to wavenumber-independent convergence and satisfactory strong, and weak parallel scalability. Numerical experiments demonstrate the effectiveness of our approach for complex mo problems, solving large-scale heterogeneous Helmholtz problems with minimized pollution error.
• [02018] Reynolds-robust preconditioners for the stationary incompressible viscoresistive MHD equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Emmet Farrell (University of Oxford)
    • Fabian Laakmann (University of Oxford)
  • Abstract : We present an augmented Lagrangian preconditioner for the incompressible viscoresistive equations of magnetohydrodynamics. For stationary problems, our solver achieves robust performance with respect to the Reynolds and coupling numbers. We extend our method to fully implicit methods for time-dependent problems. Our approach relies on specialized parameter-robust multigrid methods for the hydrodynamic and electromagnetic blocks. The scheme ensures exactly divergence-free approximations of both the velocity and the magnetic field up to solver tolerances.

contributed talk: CT095

room : E508

[00823] Weighted Trace-Penalty Minimization for Full Configuration Interaction

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the Full Configuration Interaction (FCI) method. The coordinate descent method is adapted to WTPM and results in WTPM-CD method. With the sparse features of both FCI matrices and the global minimizers in mind, the reduction of computational and storage costs shows the efficiency of the algorithm.
• Classification : 65F15, Electron Structure Calculation
• Format : Talk at Waseda University
• Author(s) :
  • Weiguo Gao (Fudan University)
  • Yingzhou Li (Fudan University)
  • Hanxiang Shen (Fudan University)

[02325] A Hybrid Method for Solving Linear KKT Systems

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : We propose an iterative method for solving linear systems arising from optimization problems with a separable objective function and dense constraints and suitable preconditioner for quick convergence. The method is implemented in Julia using Krylov.jl for the iterative solution, CUDA.jl to enable GPU capabilities, and a custom kernel for construction of the preconditioner. The method attains faster solution times than direct methods common in solvers such as Mosek and Gurobi in theory and in practice.
• Classification : 65F10, 15A29, 90C05, 65K05, 90C25
• Format : Talk at Waseda University
• Author(s) :
  • Shaked Regev (Gridmatic)
  • Shaked Regev (Gridmatic)

[00337] Extending Matrix-less Methods for Eigenvalues and Eigenvectors

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : Toeplitz and Toeplitz-like matrices arise in many fields; of special interest are the discretisations of differential equations. Matrix-less methods exploit the fact that we can view these Toeplitz(-like) matrices as part of a sequence of matrices and that the eigenvalues in the sequence behave as samplings of a function, called the symbol. We will discuss recent developments to handle the case of variable coefficient matrices, the approximation of eigenvectors, and Toeplitz(-like) matrices with non-monotone symbols.
• Classification : 65F15, 15B05, 15A18
• Format : Talk at Waseda University
• Author(s) :
  • David Meadon (Uppsala University)

[02227] A discrete-time competition model of Ricker type with reproductive delay

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : We study a discrete-time competition model of Ricker type with reproductive delay. The model is examined under the assumption that species 1 and 2 have the same vital rates except that a fraction of species 1 individuals delays the initiation of reproduction. This assumption ensures that species 2 can always increase whenever species 1 can increase. This study shows that, even under this situation, species 1 can eliminate species 2 if the population is fluctuating.
• Classification : 92B05, 37N25, 39A60, 92D40, 92D25
• Format : Online Talk on Zoom
• Author(s) :
  • Ryusuke Kon (University of Miyazaki)

[01816] Optimal-control problem for a fractional order chickenpox mathematical model

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : In our modern world, we are still fighting against the 19th-century varicella virus. Researchers made many studies to prevent individuals from chickenpox, but still, it is spreading because of its high transmission rate. To study and overcome this, we introduce a model of SIQVR type having a quarantine compartment. The well-posedness and the stable nature are explored. Further, the optimal-control technique is applied to control the spread of the virus. Finally, numerical simulations are performed.
• Classification : 92B05, 49J15, 34D20, 34A08
• Format : Online Talk on Zoom
• Author(s) :
  • Hariharan Soundararajan (National Institute of Technology Goa)
  • Shangerganesh Lingeshwaran (National Institute of Technology Goa)

MS [00107] Randomized numerical linear algebra

room : E603

• [04958] RandNLA for Faster Convex Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Zachary Frangella (Stanford University)
  • Abstract : In this talk, we show how to accelerate linear system solves and convex optimization, by exploiting low rank structure. Employing randomized low rank approximation, we design a new randomized preconditioner for the conjugate gradient method, and a method called NysADMM, for composite convex optimization. These methods come with strong theoretical and numerical support. Indeed, a simple implementation of NysADMM solves important problems like lasso, logistic regression, and support vector machines 2--42x faster than standard solvers.
• [03373] Sketched Gaussian Model Linear Discriminant Analysis via the Randomized Kaczmarz Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Jocelyn T. Chi (Rice University)
    • Deanna Needell (University of California at Los Angeles)
  • Abstract : We present an iterative randomized approach to Gaussian model linear discriminant analysis (LDA) for large data. Harnessing a least squares formulation, we mobilize the stochastic gradient descent framework and obtain a sketched classifier that is very comparable to full data LDA. Our convergence guarantees for the sketched predictions on new data account for both modeling and algorithmic randomness. Our experiments demonstrate that sketched LDA can offer a very viable alternative for very large data.
• [03665] Moment Estimation of Nonparametric Mixtures Through Implicit Tensor Decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Joe Kileel (UT Austin)
    • Yifan Zhang (UT Austin)
  • Abstract : I will present methods to estimate conditionally-independent multivariate mixture models, without assuming parameterizations of the distributions. Following the method of moments, I will tackle an incomplete tensor decomposition problem to compute the mixing weights and componentwise means. Then I will explain how to compute the cumulative distribution functions and other statistics through linear solves. Crucially for computations in high dimensions, methods in this talk evade steep costs associated with high-order tensors, via efficient tensor-free operations.
• [04802] Are sketch-and-precondition least squares solvers numerically stable?
  • Format : Talk at Waseda University
  • Author(s) :
    • Maike Meier (University of Oxford)
    • Yuji Nakatsukasa (University of Oxford)
    • Alex Townsend ( Cornell University)
    • Marcus Webb (University of Manchester)
  • Abstract : Sketch-and-precondition solvers, such as Blendenpik and LSRN, are popular for solving large least squares (LS) problems of the form $Ax=b$ with $A\in\mathbb{R}^{m\times n}$ and $m\gg n$. In this talk, we show that the sketch-and-precondition technique is not numerically stable for highly ill-conditioned LS problems. We propose an alternative method, which we call $\textit{sketch-and-apply}$, based on directly applying the randomized preconditioner and show it is numerically stable under moderate conditions.

MS [02411] Recent Advances in Numerical Methods for Nonlinear Equations and Applications

room : E604

• [03928] Iterative Newton type methods with fractional derivatives
  • Format : Online Talk on Zoom
  • Author(s) :
    • Juan R. Torregrosa (Universitat Politècnica de València)
    • Alicia Cordero (Universitat Politècnica de València)
    • Paula Triguero Navarro (Universitat Politècnica de València)
  • Abstract : Recently, several iterative methods using fractional derivatives have been designed. In this work, we propose some iterative schemes with fractal and conformable derivatives for solving nonlinear equations $f(x)=0$. We analyze the local convergence of these algorithms and study their stability and computational performance. This stability is compared with those of iterative procedures using standard derivatives.
• [03702] A Hybrid Genetic Algorithm for Solving Nonlinear Systems and Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Fiza Zafar (CASPAM, Bahauddin Zakariya University, Pakistan)
    • Nabeera Ahmad Gillani (CASPAM, Bahauddin Zakariya University, Pakistan)
  • Abstract : In this talk, a hybrid genetic algorithm has been proposed to solve nonlinear systems of equations by combining genetic algorithm and a fourth order convergent Jarratt type method to guarantee convergence and to accelerate the process of obtaining the solution. The proposed method is then applied to optimize biochemical systems to maximize the production and minimize the reaction’s concentration. The performance and computational time of genetic algorithm and hybrid genetic algorithm have also been analyzed.
• [03357] Iterative Method for Efficiently Computing Generalized Inverses of Matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • MANPREET KAUR (Lovely Professional University)
  • Abstract : The study of generalized inverses of matrices has been extensively explored in recent years. An iterative approach for finding the Moore-Penrose inverse of a matrix is discussed. The method’s convergence is analyzed, achieving fourth-order convergence under certain conditions, with a suggested parameter choice for improved convergence order. Testing on real-life matrices from the Matrix-Market Library shows the proposed scheme’s superiority over existing methods. The study also investigates the most efficient parameter choice.
• [03376] Globally convergent iterative method for evaluating matrix sign function
  • Format : Talk at Waseda University
  • Author(s) :
    • Munish Kansal (Thapar Institute of Engineering and Technology, Patiala, Punjab 147004)
  • Abstract : The matrix sign function plays a vital role in the various fields of scientific computing. This work proposes an iterative method to compute the matrix sign function of a matrix having no eigenvalues on the imaginary axis and is analyzed for convergence and asymptotic stability. Global convergence behavior is provided by drawing basins of attraction. Numerical experiments of different dimensions support the theoretical results and illustrate the efficiency of the proposed method.

MS [00573] Emerging Methods for Shape- and Topology Optimization

room : E605

• [02707] Geometry Segmentation with Total Variation Regularization
  • Author(s) :
    • Lukas Baumgärtner (Humboldt Universität zu Berlin)
    • Ronny Bergmann (NTNU Trondheim)
    • Roland Herzog (Uni Heidelberg)
    • Manuel Weiß (Uni Heidelberg (IWR))
    • Stephan Schmidt (Humboldt-Universität zu Berlin)
  • Abstract : The total variation has proven as a useful regularizer for various applications in Inverse imaging and Shape optimization problems. For the task of shape segmentation, we consider two models that combine normal vector data of a discrete surface with a total variation penalty that is evaluated in the assignment space and the label space. We show how to solve the model problems using the Chambolle-Pock algorithm and ADMM.
• [03021] Topology optimisation with general dilatations via the topological state derivative
  • Author(s) :
    • Phillip Baumann (TU Wien)
    • Idriss Mazari-Fouquer (CEREMADE, Paris Dauphine Université, PSL)
    • Kevin Sturm (TU Wien)
  • Abstract : In this work we introduce the topological state derivative, a noval approach to treat PDE-constrained topology optimisation problems. This notion allows to deal with point perturbations as well as more general perturbations like smooth hypersurfaces in a similar way. Furthermore, we draw a connection from the topological state derivative to the asymptotic expansion of the state equation, which is usually derived using boundary layer correctors. Finally, we present numerical results based on these ideas.
• [03573] Combining parameterized aerodynamic shape optimization with Sobolev smoothing
  • Author(s) :
    • Nicolas R. Gauger (University of Kaiserslautern-Landau)
    • Stephan Schmidt (Humboldt University Berlin)
    • Thomas Dick (University of Kaiserslautern-Landau)
  • Abstract : On the one hand, Sobolev gradient smoothing can considerably improve the performance of aerodynamic shape optimization and prevent issues with regularity. On the other hand, Sobolev smoothing can also be interpreted as an approximation for the shape Hessian. This paper demonstrates, how Sobolev smoothing, interpreted as a shape Hessian approximation, offers considerable benefits, although the parameterization is smooth in itself already. Such an approach is especially beneficial in the context of simultaneous analysis and design, where we deal with inexact flow and adjoint solutions, also called One Shot optimization. Furthermore, the incorporation of the parameterization allows for direct application to engineering test cases, where shapes are always described by a CAD model. The new methodology presented in this paper is used for reference test cases from aerodynamic shape optimization and performance improvements in comparison to a classical Quasi-Newton scheme are shown.
• [03630] A combined phase field - Lipschitz method for PDE constrained shape optimization
  • Author(s) :
    • Michael Hinze (Universität Koblenz)
    • Philip Herbert (Heriot-Watt University)
    • Christian Kahle (Universität Koblenz)
  • Abstract : Abstract: We present a general shape optimisation framework for PDE constrained shape optimization, which combines phase field methods and the method of mappings in the Lipschitz topology. In a first step the phase field approach determines the topology of the sought shape, and with the zero level set of the phase field simultaneously provides an approximation of the optimal shape. The latter serves as starting point for a sharp interface shape optimization method in the Lipschitz topology. To illustrate our approach we present a selection of PDE constrained shape optimisation problems and compare our findings to results from so far classical Hilbert space methods and recent p-Laplace -approximations.

MS [00763] Long-time dynamics of numerical methods for nonlinear evolution equations

room : E606

• [04423] Quantum computation of partial differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Shi Jin (Shanghai Jiao Tong University)
  • Abstract : Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to technology revolution in the 21st century. Since quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. The most efficient quantum PDE solver is quantum simulation based on solving the Schrodinger equation. It became challenging for general PDEs, more so for nonlinear ones. Our talk will cover two topics: 1) We introduce the “warped phase transform” to map general linear PDEs and ODEs to Schrodinger equation or with unitary evolution operators in higher dimension so they are suitable for quantum simulation; 2) For (nonlinear) Hamilton-Jacobi equation and scalar nonlinear hyperbolic equations we use the level set method to map them—exactly—to phase space linear PDEs so they can be implemented with quantum algorithms and we gain quantum advantages for various physical and numerical parameters.
• [05333] Asymptotic expansions for the linear PDEs with oscillatory input terms: Analytical form and error analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Karolina Joanna Kropielnicka (Institute of Mathematics of Polish Academy of Sciences)
  • Abstract : Partial differential equations with highly oscillatory input term are hardly ever solvable analytically and they are difficult to treat numerically. Modulated Fourier expansion used as an ansatz is a well known and extensively investigated tool in asymptotic numerical approach for this kind of problems. In this talk I will consider input term with single frequency and will show that the ansatz need not be assumed – it can be derived naturally while developing formulas for expansion coefficients. Moreover I will present the formula describing the error term and its estimates. Theoretical investigations will be illustrated by results of the computational simulations.
• [03756] A new picture on the Strang Splitting
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Del Valle (University of Gdansk)
    • Karolina Kropielnicka (Polish Academy of Sciences)
  • Abstract : Strang splitting is a well-established and widely used technique for finding approximate solutions of linear differential equations of the type u’=(A+B)u, where A and B are time-independent components. However, it can also be used for the case of time-dependent component B(t) after the application of the mid-point quadrature rule at the level of the Magnus expansion. However, the error estimate is absent in the case of singular cases of unbounded operators B(t). In this talk, I will show how Strang splitting scheme for time-dependent components can be derived using the Duhamel formula. Based on this approach, I will (i) present a new proof of convergence of this scheme and (ii) elaborate on the possibilities brought by this approach for higher order methods. A concrete analysis of the error estimated and numerical simulations will be presented for the physically relevant example of a hydrogen atom featuring the singular Coulomb potential.
• [05308] The role of breathers in the formation of extreme ocean waves
  • Format : Talk at Waseda University
  • Author(s) :
    • Amin Chabchoub (Kyoto University )
  • Abstract : The modulation instability is a fundamental mechanism, which explains localized wave focusing processes in dispersive wave systems. When considering the nonlinear Schrödinger equation as underlying wave model, exact breather solutions are particularly useful to initiate and control unstable wave dynamics in a numerical or laboratory experiment. This talk will summarize the main experimental achievements on breathers and connect these findings to the dynamics of ocean rogue waves.

MS [00727] Recent Advances in Fast Iterative Methods for PDE Problems

room : E701

• [04605] A single-sided all-at-once preconditioning for linear system from a non-local evolutionary equation with weakly singular kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Xuelei Lin (Harbin Institute of Technology Shenzhen)
    • Jiamei Dong (Hong Kong Baptist University)
    • Sean Hon (Hong Kong Baptist University)
  • Abstract : We propose a preconditioning technique for the multilevel Toeplitz all-at-once linearsystem arising from a time-space fractional diffusion equation. The preconditioning tech-nique is based on replacing the spatial discretization matrix with aτ-matrix, due to whichthe preconditioner can be fast inverted. Theoretically, we show that the condition numberof the intermediate two-sided preconditioned matrix is bounded by 3. And the norm of ourpreconditioner residual is bounded by the residual of intermediate preconditioner .
• [04933] Fast algorithms for space fractional Cahn-Hilliard equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xin Huang (Huazhong University of Science and Technology)
  • Abstract : In this talk, the space fractional Cahn-Hilliard (CH) equation is considered. Combining the scale auxiliary variable (SAV) technique with the leapfrog scheme, an unconditional energy-stable, non-couple and linearly implicit numerical scheme is derived. The fully-discrete scheme gives rise to an ill-conditioned system. The Krylov subspace method combing with the preconditioning technique is adopted to solve the resulting system. Numerical results are given to show the efficiency of the proposed method.
• [05262] A parallel preconditioner for the all-at-once linear system from evolutionary PDEs with Crank-Nicolson discretization in time
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xian-Ming Gu (Southwestern University of Finance and Economics)
    • Yong-Liang Zhao (Sichuan Normal University)
  • Abstract : The Crank-Nicolson (CN) method is a fashionable time integrator for evolutionary partial differential equations (PDEs) arisen in many areas of applied mathematics, however since the solution at any time depends on the solution at previous time steps, thus the CN method will be inherently difficult to parallelize. In this talk, we consider a parallel approach for the solution of evolutionary PDEs with the CN scheme. Using an all�at-once approach, we can solve for all time steps simultaneously using a parallelizable over time preconditioner within a standard iterative method. Due to the diagonalization of the proposed preconditioner, we can minutely prove that most eigenvalues of preconditioned matrices are equal to 1 and the others $z\in\mathbb{C}$ have the model with 1/(1 + α) < |z| < 1/(1 - α), where 0 < α < 1 is a free parameter. Meanwhile, the efficient and parallel implementation of this proposed preconditioner is described in details. Finally, we will verify our theoretical findings via numerical experiments.
• [05468] A preconditioned MINRES method for optimal control of wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Sean Hon (Hong Kong Baptist University)
  • Abstract : In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear coefficient matrices from the optimal control problem. Namely, we first show that the all-at-once system stemming from the wave control problem is associated to a structured coefficient matrix-sequence possessing an eigenvalue distribution. Then, based on such a spectral distribution of which the symbol is explicitly identified, we develop an ideal preconditioner and two parallel-in-time preconditioners for the saddle point system composed of two block Toeplitz matrices. For the ideal preconditioner, we show that the eigenvalues of the preconditioned matrix-sequence all belong to the set $\left(-\frac{3}{2},-\frac{1}{2}\right)\bigcup \left(\frac{1}{2},\frac{3}{2}\right)$ well separated from zero, leading to mesh-independent convergence when the minimal residual method is employed. The proposed parallel-in-time preconditioners can be implemented efficiently using fast Fourier transforms or discrete sine transforms, and their effectiveness is theoretically shown in the sense that the eigenvalues of the preconditioned matrix-sequences are clustered around $\pm 1$, which leads to rapid convergence. When these parallel-in-time preconditioners are not fastly diagonalizable, we further propose modified versions which can be efficiently inverted. Several numerical examples are reported to verify our derived localization and spectral distribution result and to support the effectiveness of our proposed preconditioners.

MS [00843] Innovative numerical methods for complex PDEs

room : E702

• [01855] Accelerating nonlinear solvers with continuous data assimilation
  • Format : Talk at Waseda University
  • Author(s) :
    • Leo Rebholz (Clemson University)
  • Abstract : We show how continuous data assimilation can be used to accelerate convergence in nonlinear solvers for steady PDE. We prove that for incompressible flow problems, with sufficient measurement data the linear convergence rate of Picard iterations can be improved. Numerical tests illustrate the theory.
• [01739] Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaoming He (Missouri University of Science and Technology)
    • Yali Gao (Northwestern Polytechnical University)
    • Daozhi Han (University at Buffalo)
    • Ulrich Rüde (Friedrich-Alexander-University of Erlangen-Nuremberg)
  • Abstract : In this presentation, we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by several domain interface conditions. It is showed that the coupled model satisfies an energy law. Then we first propose a coupled unconditionally stable finite element method for solving this model and analyze the energy stability for this method. Furthermore, based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of this decoupled scheme with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Numerical experiments are also performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.
• [01884] Modified exponential Rosenbrock methods to increase their accuracy
  • Format : Online Talk on Zoom
  • Author(s) :
    • Begoña Cano (Universidad de Valladolid)
    • María Jesús Moreta (Universidad Complutense de Madrid)
  • Abstract : In this talk a technique will be described to avoid order reduction when integrating nonlinear initial boundary value problems with exponential Rosenbrock methods. The technique does not require to impose any stiff order conditions but to add some terms related to the information on the boundary. Theoretical results on local and global error will be given as well as some numerical comparisons.
• [01971] Low Regularity Integrators for Semilinear Parabolic Equations with Maximum Bound Principles
  • Format : Talk at Waseda University
  • Author(s) :
    • Cao-Kha Doan (Auburn University)
    • Lili Ju (University of South Carolina)
    • Thi-Thao-Phuong Hoang (Auburn University)
    • Katharina Schratz (Sorbonne Université)
  • Abstract : This work is concerned with structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen-Cahn type. Important properties of such equations include maximum bound principle (MBP) and energy dissipation law; for the former, that means the absolute value of the solution is pointwisely bounded for all the time by some constant imposed by appropriate initial and boundary conditions. The model equation is first discretized in space by the central finite difference, then by iteratively using Duhamel’s formula, first and second-order low regularity integrators (LRIs) are constructed for time discretization of the semi-discrete system. The proposed LRI schemes are proved to preserve the MBP and the energy stability in the discrete sense. Furthermore, some semi-discrete and fully-discrete error estimates are also successfully derived under the low regularity requirement that the corresponding exact solution is only assumed to be continuous in time. Numerical results show that the proposed LRI schemes can be more accurate and achieve better convergence than classic exponential time differencing (ETD) schemes, especially when the interfacial parameter approaches zero.

MS [02438] Recent advances in numerical multiscale methods

room : E703

• [03763] Super-Localized Generalized Finite Element Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Moritz Hauck (University of Augsburg)
    • Philip Freese (Technical University Hamburg)
    • Tim Keil (University of Münster)
    • Daniel Peterseim (University of Augsburg)
  • Abstract : We present a multi-scale method for elliptic PDEs with arbitrarily rough coefficients. The method constructs operator-adapted solution spaces with uniform algebraic approximation rates by combining techniques from numerical homogenization and partition of unity methods. Localized basis functions with the same super-exponential localization properties as the Super-Localized Orthogonal Decomposition (SLOD) allow for an efficient implementation of the method. We derive higher-order versions of the method and demonstrate its application to high-contrast channeled coefficients and Helmholtz problems.
• [03861] An efficient multiscale approach for simulating Bose-Einstein condensates
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Döding (Ruhr-University Bochum)
    • Patrick Henning (Ruhr-University Bochum)
    • Johan Wärnegård (Columbia University)
  • Abstract : In this talk we consider the numerical treatment of nonlinear Schrödinger equations as they appear in the modeling of Bose-Einstein condensates. We give numerical examples that demonstrate the influence of the discrete energy on the accuracy of numerical approximations and that a spurious energy can create artificial phenomena such as drifting particles. In order to conserve the exact energy of the equation as accurately as possible, we propose a combination of a class of conservative time integrators with a suitable multiscale finite element discretization in space. This space discretization is based on the technique of Localized Orthogonal Decompositions (LOD) and allows to capture general time invariants with a 6th order accuracy with respect to the chosen mesh size H. This accuracy is preserved due to the conservation properties of the time stepping method. The computational efficiency of the method is demonstrated for a numerical benchmark problem with known exact solution, which is however barely solvable with traditional methods on long time scales.
• [04037] Multigrid/multiscale solver for the radiative transfer equation in heterogeneous media
  • Format : Talk at Waseda University
  • Author(s) :
    • QINCHEN SONG (Shanghai Jiao Tong University)
  • Abstract : The radiative transfer equation describes the interaction between particles and media such as gases, semitransparent liquids , solids, and porous materials, which is widely used in nuclear engineering, thermal radiation transport, etc. In the first part of our work, we construct a multigrid scheme for 1D neutron transport equation based on a second-order discretization scheme that is uniform with respect to $\epsilon$ in the diffusion regime and valid up to the boundary layer and interface layer. We prove its multigrid convergence theoretically and justify it numerically. This multigrid scheme is special in a way that the smoothing procedure in the typical multigrid method can be skipped, which saves a large amount of computation. The 1D scheme can be adapted to the 2D case, and the resulting 2D scheme performs well in the diffusion regime. In the second part, we focus on the 2D radiative transport equation in the transport regime. After discretization of the equation, we get a sparse linear system of extremely high dimensions. Typically, we have 3 ways to solve the linear system: direct methods, iterative methods, and rank-structured methods, which requires computation cost of $I^{6}$, $I^{3}$ and $I^{3}$ respectively (provided that the physical domain is discretized as a $I\times I$ grid). In our work, we use a hybrid scheme of iterative methods and rank-structured methods and reduce the computation cost down to $I^{5/2}$. This is joint work with Min Tang (SJTU) and Lei Zhang (SJTU).
• [03533] EXPONENTIALLY CONVERGENT MULTISCALE METHODS FOR HIGH FREQUENCY HETEROGENEOUS HELMHOLTZ EQUATIONS
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Y Hou (California Institute of Technology)
    • Yifan Chen (California Institute of Technology)
    • Yixuan Wang (California Institute of Technology)
  • Abstract : We present a multiscale framework for solving the high frequency Helmholtz equation in heterogeneous media without scale separation. Our methods achieve a nearly exponential rate of convergence without suffering from the well-known pollution effect. The key idea is a coarse-fine scale decomposition of the solution space that adapts to the media property and wavenumber. The coarse part is of low complexity while the fine part is local such that it can be computed efficiently.

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

room : E704

• [01756] Arbitrarily high order finite element methods for arbitrarily shaped domains with automatic mesh generation
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhiming Chen (Chinese Academy of Sciences)
  • Abstract : We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. Numerical examples are presented to illustrate the competitive performance of the method. This talk is based on a joint work with Yong Liu.
• [01921] An iterative method for inverse lithography problem with TV regularization
  • Format : Talk at Waseda University
  • Author(s) :
    • Junqing Chen (Tsinghua University)
  • Abstract : I will introduce an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. The convergence analysis is given. Some numerical examples are shown to illustrate the effectiveness of the method.
• [03833] A SOURCE TRANFER DOMAIN DECOMPOSITION METHOD FOR MAXWELL’S EQUATIONS
  • Format : Talk at Waseda University
  • Author(s) :
    • TAO CUI (NCMIS, LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • ZIMING WANG (School of Mathematical Sciences, University of Chinese Academy of Sciences)
    • XUESHUANG XIANG (Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology)
  • Abstract : In this paper, we develop an efficient solver for the Maxwell’s equations in unbounded domain by extending the source transfer domain decomposition method (STDDM) proposed by Chen et al. Through the analysis of the fundamental solution of the Maxwell’s equations, the convergence of STDDM is proved for the case of constant wave number. Numerical experiments are included, demonstrating that the proposed method can be used as an efficient preconditioner in the preconditioned GMRES method for solving the PML equation of the Maxwell’s equations with constant and heterogeneous wave numbers, including an example for lithography.
• [01824] Numerical simulation for quantum transports in nano-semiconductor device
  • Format : Talk at Waseda University
  • Author(s) :
    • Haiyan Jiang (Beijing Institute of Technology)
    • tiao Lu (Peking University)
    • Weitong Zhang (Peking University)
  • Abstract : We develop a new hybrid scheme for the coupled systems of quantum transport in nano-semiconductor device. Sinc-Galerkin method is used to solve the time-dependent Wigner equation numerically with the spectral convergence of the cardinal sine basis function solution of Wigner function in velocity space. A second-order semi-implicit time integration scheme is designed for the Wigner-Poisson equations (TWPEs). The numerical method is applied to study a double-barrier resonant tunneling diode (RTD), Error estimation, stability, and convergence are also investigated concretely. Numerical experiments validate the theoretical results and present the reliability and efficiency of the proposed algorithm to simulate quantum effects.

MS [00555] Advanced Numerical Methods for PDEs with Applications

room : E705

• [02811] TVD property of second order method for two-dimensional scalar conservation laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Lilia Krivodonova (University of Waterloo)
    • Alexey Smirnov (University of Waterloo)
  • Abstract : The total variation diminishing (TVD) property plays a crucial role in ensuring the stability and convergence of numerical solutions for one-dimensional scalar conservation laws. It was established in 1985 that in the two-dimensional space, a TVD method can be at most first order accurate. We consider a new definition of TV and propose a condition on scheme coefficients for a second-order method to be TVD for nonlinear scalar conservation laws.
• [02206] Using Adaptive Time-Steppers to Explore Stability Domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Mary Pugh (University of Toronto)
  • Abstract : Stability domains for ODE time-steppers are well-understood when the linearized system is diagonalizable. I'll discuss an implicit-explicit time-stepper for which the linearized system isn't diagonalizable. An adaptive time-stepper can be used to explore the stability domain. I'll present a system whose stability domain has a discontinuous boundary; a small change in a parameter can cause a jump in the time-step-size stability threshold. This is joint work with my former PhD student, Dave Yan.
• [02320] Extended Statistical Modelling and Advanced Computational Approaches for Disperse Multiphase Flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Lucian Ivan (Canadian Nuclear Laboratories)
    • Benoit Allard (University of Ottawa)
    • Francois Forgues (Canadian Nuclear Laboratories)
    • James McDonald (University of Ottawa)
  • Abstract : This talk presents an Eulerian-based polydisperse Gaussian-moment model (PGM) family for the description of particle-laden multiphase flows. The modelling approach leads to a set of first-order, robustly-hyperbolic balance laws that provide a direct treatment for local higher-order statistics, such as covariances between particle distinguishable properties (e.g., diameter, temperature, etc.) and particle velocity. A massively parallel discontinuous-Galerkin-Hancock framework is employed to efficiently obtain computational PGM-solutions for a range of flows, including bio-aerosol dispersion and fuel sprays.
• [02260] tost.II: A temporal operator splitting template library for deal.II
  • Format : Talk at Waseda University
  • Author(s) :
    • Raymond Spiteri (University of Saskatchewan)
    • Kevin Green (University of Saskatchewan)
  • Abstract : Operator splitting is a popular and often necessary means for solving PDEs. Software that implements operator splitting, however, generally only allows specific splitting methods, with only specific sub-integrators, and only for specific problems. In this talk, I describe the tost.II temporal operator splitting library built on the deal.II finite-element library. tost.II enables easy experimentation with splittings for an arbitrary number of operators and with arbitrary order of convergence, including methods with negative or complex coefficients.

MS [01088] Differential Equations meet Data: Scientific Machine Learning for Cardiovascular Applications

room : E708

• [04920] Fast and accurate reduced order modelling techniques for the simulation of blood flow dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Gianluigi Rozza (SISSA Trieste)
  • Abstract : Heart disease is one of the main cause of death worldwide, therefore in the last years the medical profession has shown a growing attention for simulating blood flow dynamics through numerical methods. The main purpose is to build a support for surgical procedure and to predict the progression of a disorder. Full order mathematical models can be adopted for patient-specific cases, varying physical and geometrical parameters, however the complexity of the computational domain requires a fine discretization and as a result a considerable amount of time. Our works focus on the study of Reduced Order Models (ROMs), which are specifically formulated to reduce the computational cost of complex dynamics such as biomedical ones. A complete decoupling between an offline and an online stage is adopted to speed up high fidelity simulations, by splitting what can be done only once and what need to be evaluated for every new parameter to obtain e good ROM solution. Both intrusive and data-driven approaches are tested for patient-specific applications to investigate both the efficiency and the accuracy of the ROM framework.
• [04420] Parameter estimation in cardiac biomechanical models based on physics-informed neural networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Federica Caforio (Institute of Mathematics and Scientific Computing, NAWI Graz, University of Graz)
    • Francesco Regazzoni (MOX, Dipartimento di Matematica, Politecnico di Milan)
    • Stefano Pagani (MOX, Department of Mathematics, Politecnico di Milano)
    • Alfio Maria Quarteroni (MOX, Department of Mathematics, Politecnico di Milano)
    • Gernot Plank (Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz)
    • Gundolf Haase (Institute of Mathematics and Scientific Computing, NAWI Graz, University of Graz)
  • Abstract : In this talk a novel methodology is proposed, based on the integration of physics-informed neural networks methodologies with biophysically detailed three-dimensional cardiac biomechanical models, to generate robust and effective surrogate reduced-order models that are able to reconstruct displacement fields and locally estimate heterogeneous passive mechanical properties. The accuracy and robustness of the proposed method are demonstrated in several benchmarks. This methodology potentially paves the way for the robust and effective identification of patient-specific physical properties.
• [03697] Super-resolution and denoising of 4D flow MRI via implicit neural representations
  • Format : Talk at Waseda University
  • Author(s) :
    • Simone Saitta (Politecnico di Milano)
    • Marcello Carioni (University of Twente)
    • Subhadip Mukherjee (University of Bath)
    • Carola-Bibiane Schönlieb (University of Cambridge)
    • Alberto Redaelli (Politecnico di Milano)
  • Abstract : We trained sinusoidal representation networks (SIRENs) for denoising and super-resolution of time-varying 3-directional velocity fields measured in the aorta by 4D flow MRI. The performance of different SIREN architectures was evaluated on synthetic measurements and then we applied the best architecture to real 4D flow data of an aortic aneurysm. Our method provides a continuous representation of 4D velocity fields (super-resolution) and achieves denoising thanks to SIREN’s spectral bias, outperforming state-of-the-art techniques.

MS [00837] Particle Methods for Bayesian Inference

room : E709

• [04703] Metropolis-adjusted interacting particle sampling
  • Format : Talk at Waseda University
  • Author(s) :
    • Bjoern Sprungk (TU Bergakademie Freiberg)
    • Simon Weissmann (University of Mannheim)
    • Jakob Zech (Universität Heidelberg)
  • Abstract : In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and implemented as ensembles of particles that move in the product state space according to coupled stochastic differential equations. The ensemble approximation and numerical time stepping used to simulate these systems can introduce bias and affect the invariance of the particle system with respect to the target distribution. To correct for this, we investigate the use of a Metropolization step, similar to the Metropolis-adjusted Langevin algorithm. We examine both ensemble- and particle-wise Metropolization and prove basic convergence of the resulting ensemble Markov chain to the target distribution. Our results demonstrate the benefits of this correction in numerical examples for popular interacting particle samplers such as ALDI, CBS, and stochastic SVGD.
• [05149] Computing log-densities of time-reversed diffusion processes through Hamilton-Jacobi-Bellman equations
  • Format : Talk at Waseda University
  • Author(s) :
    • David Sommer
    • Robert Gruhlke (FU Berlin)
    • Martin Eigel (WIAS Berlin)
  • Abstract : Sampling from densities is a common challenge in uncertainty quantification. Langevin dynamics are a popular tool for this task but rely on certain properties of the log-density. To assimilate a larger class of distributions, a time-inhomogeneous drift term can be defined using intermediate log-densities. We propose learning these log-densities by propagation of the target distribution through an Ornstein-Uhlenbeck process, solving the associated Hamilton-Jabobi-Bellman equation using an implicit scheme and compressed polynomials for spatial discretization.
• [04723] Simulation of Wasserstein gradient flows with low-rank tensor methods for sampling
  • Format : Talk at Waseda University
  • Author(s) :
    • Vitalii Aksenov (Weierstrass Institute for Applied Analysis and Stochastics)
    • Martin Eigel (Weierstrass Institute for Applied Analysis and Stochastics)
  • Abstract : We try to adapt the Eulerian methods for Wasserstein gradient flows for high-dimensional problems such as Bayesian inversion, importance sampling and generative modelling by utilizing low-rank tensor methods. The normalized density is approximated in tractable format, which allows additional application to density estimation and rare event detection. An ODE governing the evolution of samples can be defined with help of intermediate density and flux variables, linking the approach to particle methods.
• [05014] Overparameterization of Deep ResNet: Zero Loss and Mean-Field Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhiyan Ding (University of California, Berkeley)
    • Qin Li (University of Wisconsin, Madison)
    • Shi Chen (University of Wisconsin, Madison)
    • Stephen Wright (University of Wisconsin, Madison)
  • Abstract : In this talk, I will mainly focus on using mean-field analysis to analyze the overparameterization of neural networks. Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with the perfect fit (zero-loss) in many practical situations. In this talk, I will investigate this phenomenon in the case of Residual Neural Networks (ResNet) with smooth activation functions in a limiting regime in which both the number of layers (depth) and the number of weights in each layer (width) go to infinity. First, I will rigorously show that the gradient descent for parameter training becomes a gradient flow for a probability distribution that is characterized by a partial differential equation (PDE) in the large-NN limit. Next, I will introduce the conditions that make sure the solution to the PDE converges in the training time to a zero-loss solution. Together, these results suggest that the training of the ResNet gives a near-zero loss if the ResNet is large enough.

MS [00919] Recent Advances in Hybridizable Discontinuous Galerkin Methods and Applications

room : E710

• [05082] Discontinuous Galerkin Methods for High Speed Flows
  • Author(s) :
    • Ngoc Cuong Nguyen (Massachusetts Institute of Technology)
    • Jaime Peraire (Massachusetts Institute of Technology)
    • Jordi Perez (Massachusetts Institute of Technology)
    • Loek Van Heyningen (Massachusetts Institute of Technology)
  • Abstract : We present discontinuous Galerkin (DG) methods for high-speed flows with particular focus on transition, turbulence, and shock capturing. We describe LDG, HDG, EDG methods and parallel iterative solvers with matrix-free preconditioners. We develop an adaptive viscosity regularization method for capturing shocks by minimizing the artifial viscosity field while enforcing smoothness contraints on the numerical solution. We present numerical results to demonstrate the DG methods and our shock capturing scheme on transonic, supersonic, and hypersonic flows.

contributed talk: CT114

room : E711

[02603] AN $H^1$ GALERKIN MIXED FINITE ELEMENT METHOD FOR ROSENAU EQUATION

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : In this paper, by applying a splitting technique, the non-linear fourth order Rosenau equation is split into a system of coupled equations. Then, an $H^1$ Galerkin mixed finite element method is proposed for the resultant equations after employing a suitable weak formulation. Semi-discrete and fully discrete schemes are discussed and respective optimal order error estimates are obtained without any constraints on the mesh. Finally, numerical results are computed to validate the efficacy of the method. The proposed method has advantages in respect of higher order error estimate, less requirement of regularity on exact solution and also with reduced size i.e. less than half of the size of resulting linear system over that of mentioned in Manickam et al., Numerical Methods for Partial Differential Equations, (14), (1998), pp. 695-716.
• Classification : 65N30, 65N06, 65M60, 65M06
• Format : Talk at Waseda University
• Author(s) :
  • Jones Tarcius Doss (Department of Mathematics, Anna University, Chennai)

[02112] Adaptive Virtual Element Methods: convergence and optimality

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : We consider a Virtual Element discretization of elliptic boundary-value problems, using triangular or quadrilateral meshes with hanging nodes of arbitrary, but fixed, maximal index. We design a two-stage adaptive algorithm, based on a stabilization-free a posteriori error estimator, which alternates data approximation and solution approximation with increasing accuracy. We prove the convergence of the inner and outer loops, we establish the optimality of the adaptive procedure in suitable approximation classes, and we provide numerical results.
• Classification : 65N30, 65N50
• Format : Talk at Waseda University
• Author(s) :
  • Claudio Canuto (Politecnico di Torino)
  • Lourenco Beirao da Veiga (University of Milan Bicocca)
  • Ricardo H Nochetto (University of Maryland)
  • Giuseppe Vacca (University of Bari)
  • Marco Verani (Politecnico di Milano)

[02640] High-Order Finite Element Schemes for Multicomponent Flow Problems

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : The Stokes–Onsager–Stefan–Maxwell (SOSM) equations model the flow of concentrated mixtures of distinct chemical species in a common thermodynamic phase. We derive a novel variational formulation of these nonlinear equations in which the species mass fluxes are treated as unknowns. This new formulation leads to a large class of high-order finite element schemes with desirable linear-algebraic properties. The schemes are provably convergent when applied to a linearization of the SOSM problem.
• Classification : 65N30, 76T30, 35Q35
• Format : Talk at Waseda University
• Author(s) :
  • Aaron Matthew Baier-Reinio (University of Oxford)
  • Patrick Farrell (University of Oxford)

[02174] A mathematical model to predict how obesity raises the risk of diabetes

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : Nowadays, obesity is a serious global issue. Obesity increases the risk of developing significant health issues like diabetes, cancer, and heart attacks. This work tries to depict the link between pancreatic damage, blood insulin levels, and blood glucose in a mathematical model. The model also illustrates how the increased obesity index raises diabetes risk. Additionally, we incorporated a delay term in the model to depict insulin production lag brought on by dysfunctional beta-cells due to obesity. We analytically analyzed both delay and non-delay models. Moreover, numerical simulations are demonstrated to support the theoretically-based analysis.
• Classification : 92B05, 34H05, 34D05
• Author(s) :
  • Parimita Roy (Thapar Institute of Engineering and Technology)
  • Ani Jain (Thapar Institute of Engineering and Technology)

[01815] Time-fractional SVIR chicken-pox mathematical model with quarantine compartment

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : This work considers a time-fractional SVIR chicken-pox reaction-diffusion model with nonlinear diffusion operators. The model also contains the quarantine compartment and therefore, it consists of five unknown variables. Further suitable initial and boundary conditions are also given along with the model. The existence of weak solutions proved for the proposed time-fractional model in the bounded domain with appropriate assumptions and a-priori energy estimates. The main results of the work demonstrated using the Faedo-Galerkin method and approximation problem. Finally, numerical simulations are provided to understand the evolution of the chicken-pox virus among the population.
• Classification : 92B05, 35K57, 35A01
• Author(s) :
  • Shangerganesh Lingeshwaran (National Institute of Technology Goa)
  • Hariharan Soundararajan (National Institute of Technology Goa)
  • Manimaran Jeyaraj (Vellore Insitute of Technology)

MS [02109] Recent Advances on Numerical Analysis of Integral and Integro-differential Equations

room : E802

• [03563] Numerical solution of fractional integro-differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Arvet Pedas (University of Tartu)
    • Mikk Vikerpuur (University of Tartu)
  • Abstract : We consider a wide class of linear multi-term fractional integro-differential equations with Caputo derivatives and weakly singular kernels. First, we discuss the existence, uniqueness and smoothness of the exact solution. Then, using a suitable smoothing transformation and spline collocation techniques, we construct a high-order method for the numerical solution of the underlying problem. Finally, a numerical illustration of the proposed method is presented.
• [04175] A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yin Yang (Xiangtan University)
    • Biao Zhang (Xiangtan University)
  • Abstract : In this talk, we present a new linearized two-level second-order scheme for the space fractional Allen-Cahn equation, which is based on the Crank-Nicolson method in time, second-order weighted and shifted Gr\"{u}nwald difference formula in space and Newton linearized technology to deal with nonlinear term. And we only need to solve a linear system at each time level. Then, the unique solvability of the scheme is given. Under the reasonable time step constraint, the discrete maximum principle, energy stability and error analysis are also studied. At last, some numerical experiments show that the proposed method is reasonable and effective.
• [03914] High accuracy analysis of FEMs for several time-fractional PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanmin Zhao (Xuchang University)
  • Abstract : In this talk, convergence and superconvergence analysis for several kinds of time-fractional partial differential equations will be discussed by use of finite element methods and proper finite difference schemes. At the same time, unconditional stability properties of fully-discrete schemes are presented. Moreover, numerical experiments are provided to confirm the theoretical results. And, some relevant topics are included.
• [02240] Discontinuous piecewise polynomial collocation methods for integral-algebraic equations of Hessenberg type
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Liang (Harbin Institute of Technology, Shenzhen)
    • Hecong Gao (Harbin Institute of Technology, Shenzhen)
  • Abstract : We mainly consider the integral-algebraic equations of Hessenberg type. The tractability index is investigated. The existence, uniqueness, and regularity are analyzed, and the resolvent representation is given. First, the convergence theory of perturbed collocation methods in discontinuous piecewise polynomial space is established for first-kind Volterra integral equations, then it is used to derive the optimal convergence properties of discontinuous piecewise polynomial collocation methods for Hessenberg-type integral-algebraic equations. Numerical examples illustrate the theoretical results.

MS [01072] Data-Driven Methods in Scientific Machine Learning

room : E803

• [05116] Acceleration of multiscale solvers via adjoint operator learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Emanuel Eld Ström (KTH Royal Institute of Technology)
    • Ozan Öktem (KTH Royal Institute of Technology)
    • Anna-Karin Tornberg (KTH Royal Institute of Technology)
  • Abstract : We leverage recent advances in operator learning to accelerate multiscale solvers for laminar fluid flow over a rough boundary. We focus on the HMM method, which involves formulating the problem through a coupled system of microscopic and macroscopic subproblems. Solving microscopic problems can be viewed as a nonlinear operator mapping from the space of micro domains to the solution space. Our main contribution is to use an FNO-type architecture to perform this mapping.
• [05635] A Stochastic MaxiIn this work, we introduce a stochastic maximum principle (SMP) approach for solving the reinforcement learning problem with the assumption that the unknmum Principle Approach for Reinforcement Learning with Parameterized Environment
  • Format : Talk at Waseda University
  • Author(s) :
    • Feng Bao (Florida State University)
    • Richard Archibald (Oak Ridge National Lab)
    • Jiongmin Yong (University of Central Florida)
  • Abstract : In this work, we introduce a stochastic maximum principle (SMP) approach for solving the reinforcement learning problem with the assumption that the unknowns in the environment can be parameterized based on physics knowledge. For the development of numerical algorithms, we apply an effective online parameter estimation method as our exploration technique to estimate the environment parameter during the training procedure, and the exploitation for the optimal policy is achieved by an efficient backward action learning method for policy improvement under the SMP framework. Numerical experiments are presented to demonstrate that the SMP approach for reinforcement learning can produce reliable control policy, and the gradient descent type optimization in the SMP solver requires less training episodes compared with the standard dynamic programming principle based methods.
• [05649] A pseudo-reversible normalizing flow for stochastic dynamical systems with various initial distributions
  • Format : Talk at Waseda University
  • Author(s) :
    • Guannan Zhang (Oak Ridge National Laboratory)
  • Abstract : We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDE, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE's final state without simulating trajectories. Existing normalizing flow model for SDEs depend on the initial distribution, meaning the model needs to be re-trained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudo-reversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudo-reversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

MS [00047] Combining Machine Learning and Stochastic Methods for Modeling and Forecasting Complex Systems

room : E804

• [05228] Embedding classical dynamics in a quantum computer
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dimitrios Giannakis (Dartmouth College)
  • Abstract : We present a framework for simulating classical dynamical systems by quantum systems running on a quantum computer. The framework employs a quantum feature map for representing classical states by density operators on a reproducing kernel Hilbert space, $\mathcal{H}$. Simultaneously, a mapping is employed from classical observables into self-adjoint operators on $\mathcal{H}$ such that quantum expectation values are consistent with pointwise function evaluation. We illustrate our approach with quantum circuit simulations and experiments on quantum computers.
• [05225] Machine learning correction operators for capturing extremes in coarse scale climate models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Themistoklis Sapsis (MIT)
  • Abstract : This work presents a systematic framework for improving the predictions of statistical quantities for turbulent systems, with a focus on correcting coarse climate simulations. We also provide quantification measures for the value of data towards this goal. Machine learning correction operators for chaotic systems is challenging as learning errors due to chaotic divergence is not meaningful. The presented approach combines dynamical systems and probabilistic data-driven ideas. We apply the framework to E3SM climate simulations.
• [04015] A Framework for Machine Learning of Model Error in Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthew Levine (Caltech)
    • Andrew Stuart (Caltech)
  • Abstract : The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. Here, we present a unifying framework for blending mechanistic and machine-learning approaches for identifying dynamical systems from data. This framework is agnostic to the chosen machine learning model parameterization, and casts the problem in both continuous- and discrete-time. We will also show recent developments that allow these methods to learn from noisy, partial observations. We first study model error from the learning theory perspective, defining the excess risk and generalization error. For a linear model of the error used to learn about ergodic dynamical systems, both excess risk and generalization error are bounded by terms that diminish with the square-root of T (the length of the training trajectory data). In our numerical examples, we first study an idealized, fully-observed Lorenz system with model error, and demonstrate that hybrid methods substantially outperform solely data-driven and solely mechanistic-approaches. Then, we present recent results for modeling partially observed Lorenz dynamics that leverages both data assimilation and neural differential equations. Joint work with Andrew Stuart.
• [05032] Combining physical and machine learning forecasts for Earth system prediction
  • Format : Talk at Waseda University
  • Author(s) :
    • Eviatar Bach (California Institute of Technoloy)
  • Abstract : Machine learning (ML) holds the potential to improve Earth system prediction by learning directly from data, bypassing deficiencies in existing dynamical models. Hybrid methods, which combine ML with dynamical models, leverage the strengths of both approaches. I will present two hybrid methods that use tools from data assimilation: Ensemble Oscillation Correction, a forecasting method for combining ML forecasts of specific modes with a full-field dynamical model, and the Multi-Model Ensemble Kalman Filter, a more general method for integrating multiple forecast models with observations.

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

room : E811

• [05418] Machine learned regularization for inverse problems - the dos and don‘ts
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : Inverse problems are about the reconstruction of an unknown physical quantity from indirect measurements. They appear in a variety of places, from medical imaging, for instance MRI or CT, to remote sensing, for instance Radar, to material sciences and molecular biology, for instance electron microscopy. Here, inverse problems is a tool for looking inside specimen, resolving structures beyond the scale visible to the naked eye, and to quantify them. It is a mean for diagnosis, prediction and discovery. Most inverse problems of interest are ill-posed and require appropriate mathematical treatment for recovering meaningful solutions. Classically, such approaches are derived almost conclusively in a knowledge driven manner, constituting handcrafted mathematical models. Examples include variational regularization methods with Tikhonov regularization, the total variation and several sparsity-promoting regularizers such as the L1 norm of Wavelet coefficients of the solution. While such handcrafted approaches deliver mathematically rigorous and computationally robust solutions to inverse problems, they are also limited by our ability to model solution properties accurately and to realise these approaches in a computationally efficient manner. Recently, a new paradigm has been introduced to the regularization of inverse problems, which derives solutions to inverse problems in a data driven way. Here, the inversion approach is not mathematically modelled in the classical sense, but modelled by highly over-parametrised models, typically deep neural networks, that are adapted to the inverse problems at hand by appropriately selected training data. Current approaches that follow this new paradigm distinguish themselves through solution accuracies paired with computational efficieny that were previously unconceivable. In this talk I will give an introduction to this new data-driven paradigm for inverse problems. Presented methods include data-driven variational models and plug-and-play approaches, learned iterative schemes aka learned unrolling, and learned post-processing. Throughout presenting these methodologies, we will discuss their theoretical properties and provide numerical examples for image denoising, deconvolution and computed tomography reconstruction. The talk will finish with a discussion of open problems and future perspectives.
• [04644] Data-driven Regularization based on Diagonal Frame Decompostion
  • Format : Talk at Waseda University
  • Author(s) :
    • Yunseok Lee (Ludwig Maximilian University Munich)
    • Samira Kabri (Deutsches Elektronen-Synchrotron (DESY) Hamburg)
    • Martin Burger (Deutsches Elektronen-Synchrotron (DESY) Hamburg and University of Hamburg)
    • Gitta Kutyniok (Ludwig Maximilian University Munich)
  • Abstract : In this talk, we propose a data-driven framework to design optimal filters for inverse problems using frame decompositions, which generalize classical spectral filters. Frames are sets of vectors that allow for stable and redundant representations of signals in a Hilbert space. Our framework works by learning a linear transformation that modifies the frame coefficients of a measured signal to enhance or suppress certain features. This is achieved by formulating this as an optimization problem with a data-driven regularizer that incorporates prior knowledge from noise and ground truth data. Our approach comes with theoretical guarantees in terms of convergence as well as in terms of generalization to unseen data. We also illustrate its effectiveness on several numerical experiments using the Wavelet-Vaguelette decomposition as an example.
• [03944] Fourier Neural Operators for data-driven regularization
  • Format : Talk at Waseda University
  • Author(s) :
    • Samira Kabri (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : In this talk we investigate the use of Fourier Neural Operators (FNOs) for image processing in comparison to standard Convolutional Neural Networks (CNNs). FNOs - which are so-called neural operators with a specific parametrization - have been applied successfully in the context of parametric PDEs. We derive the FNO architecture as an example for continuous and Fréchet-differentiable neural operators on Lebesgue spaces and show how CNNs can be converted into FNOs and vice versa. Based on these insights, we explore possibilities of incorporating the ideas of FNOs into the data-driven regularization of inverse problems in imaging.
• [05027] Data-driven regularization theory of invertible ResNets for solving inverse problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Clemens Arndt (ZeTeM University of Bremen)
    • Alexander Denker (ZeTeM University of Bremen)
    • Sören Dittmer (ZeTeM University of Bremen)
    • Nick Heilenkötter (ZeTeM University of Bremen)
    • Meira Iske (ZeTeM University of Bremen)
    • Tobias Kluth (University of Bremen)
    • Judith Nickel (ZeTeM University of Bremen)
  • Abstract : Data-driven solution techniques for inverse problems, typically based on specific learning strategies, exhibit remarkable performance in image reconstruction tasks. These learning-based reconstruction strategies often follow a two-step scheme. First, one uses a given dataset to train the reconstruction scheme, which one often parametrizes via a neural network. Second, the reconstruction scheme is applied to a new measurement to obtain a reconstruction. We follow these steps but specifically parametrize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility opens the door to new investigations into the influence of the training and the architecture on the resulting reconstruction scheme. To be more precise, we analyze the effect of different iResNet architectures, loss functions, and prior distributions on the trained network. The investigations reveal a formal link to the regularization theory of linear inverse problems for shallow network architectures. Moreover, we analytically optimize the parameters of specific classes of architectures in the context of Bayesian inversion, revealing the influence of the prior and noise distribution on the solution.

MS [00638] Minisymposium on Interaction between Harmonic Analysis and Data Science

room : E812

• [04309] Direct method for function approximation on data defined manifolds, II
  • Format : Talk at Waseda University
  • Author(s) :
    • Hrushikesh Mhaskar (Claremont Graduate University)
    • Ryan Michael O'Dowd (Claremont Graduate University)
  • Abstract : In theoretical analysis of function approximation in the context of machine learning, a standard approach is to assume that given data lies on an unknown manifold. We view the unknown manifold as a sub-manifold of an ambient hypersphere and construct a one-shot approximation using spherical polynomials. Our approach does not require pre-processing of the data to obtain information about the manifold other than its dimension. We give optimal rates of approximation for relatively ``rough'' functions.
• [04364] Distribution learning for count data
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Guo (The University of Queensland)
    • Qiang Fu (The University of British Columbia)
    • Tian-Yi Zhou (Georgia InstitGeorgia Institute of Technologyute of Technology)
    • Hien Nguyen (The University of Queensland)
  • Abstract : Parameter and density estimation for count models are classical problems in statistics, and are widely used in many branches of physical and social sciences. Grouped and right-­censored (GRC) counts are widely used in criminology, demography, epidemiology, marketing, sociology, psychology and other related disciplines to study behavioural and event frequencies, especially when sensitive research topics or individuals with possibly lower cognitive capacities are at stake. Yet, the co-­existence of grouping and right-­censoring poses major difficulties in regression analysis. To implement generalised linear regression of GRC counts, we derive modified Poisson estimators and their asymptotic properties, develop a hybrid line search algorithm for parameter inference, demonstrate the finite-sample performance of these estimators via simulation, and evaluate its empirical applicability based on survey data of drug use in America. This method has a clear methodological advantage over the ordered logistic model for analysing GRC counts. We will also present our recent works on mixing density estimation through kernel methods and deep neural networks.
• [05188] Hierarchical systems of exponential bases for partitions of intervals
  • Format : Online Talk on Zoom
  • Author(s) :
    • Goetz Pfander (Catholic University Eichstätt Ingolstadt, Mathematical Institute for Machine Learning and Data Science)
    • David Walnut (George Mason University)
  • Abstract : Fourier series form a cornerstone of analysis; it allows the expansion of a complex valued 1-periodic function in the basis of integer frequency exponentials. A simple rescaling argument shows that by splitting the integers into evens and odds, we obtain orthogonal bases for functions defined on the first, respectively the second half of the unit interval. We develop generalizations of this curiosity and show that, for example, for any finite partition of the unit interval into subintervals exists a partition of integers into subsets, each of which forms a basis for functions supported on the respective subinterval.

MS [02349] Deep Implicit and Explicit Models for Inverse Problems: Hybrid Data-Driven Models, Neural ODEs, PDEs and Beyond

room : E817

• [05328] Physics Informed Graph Transformer for PDEs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andrey Bryutkin (University of Cambridge)
    • Angelica Aviles-Rivero (University of Cambridge)
    • Jiahao Huang (Imperial College London)
  • Abstract : In recent years, robust PDE solvers have become increasingly important, necessitating more input variety. The physics-informed graph transformer (PhysGTN) uses graphs to solve underlying problems described on an irregular grid and combines multiple parameter inputs of the PDE. It applies a transformer network to learn specific resemblances of data and additional inputs, which the PDE provides. The architecture is designed to be discretization invariant and flexible enough to handle irregular meshes. The PhysGTN offers several advantages over traditional numerical methods, including increased computational efficiency, reduced time needed for obtaining solutions, and increased robustness to additional noise. This can lead to various challenges and applications for the setup.
• [03627] Continuous U-Net: Faster, Greater and Noiseless
  • Format : Talk at Waseda University
  • Author(s) :
    • Chun-Wun Cheng (City University of Hong Kong)
    • Christina Runkel (University of Cambridge)
    • Lihao Liu (University of Cambridge)
    • Raymond Honfu Chan (City University of Hong Kong)
    • Carola-Bibiane Schönlieb (University of Cambridge)
    • Angelica Aviles-Rivero (University of Cambridge)
  • Abstract : Image segmentation is a fundamental task in image analysis and clinical practice. The current state-of-the-art techniques are based on U-shape type encoder-decoder networks with skip connections called U-Net. Despite the powerful performance reported by existing U-Net type networks, they suffer from several major limitations. These issues include the hard coding of the receptive field size, compromising the performance and computational cost, as well as the fact that they do not account for inherent noise in the data. They have problems associated with discrete layers, and do not offer any theoretical underpinning. In this work we introduce continuous U-Net, a novel family of networks for image segmentation. Firstly, continuous U-Net is a continuous deep neural network that introduces new dynamic blocks modelled by second order ordinary differential equations. Secondly, we provide theoretical guarantees for our network demonstrating faster convergence, higher robustness and less sensitivity to noise. Thirdly, we derive qualitative measures to tailor-made segmentation tasks. We demonstrate, through extensive numerical and visual results, that our model outperforms existing U-Net blocks for several medical image segmentation benchmarking datasets.
• [05633] Why Deep Surgical Models Fail?: Revisiting Surgical Action Triplet Recognition through the Lens of Robustness
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanqi Cheng (University of Cambridge )
  • Abstract : Surgical action triplet recognition is of high relevance as it provides the surgeon with context-aware support and safety. The go-to strategy develops new network mechanisms. However, the performance of state-of-the-art techniques is substantially lower than other surgical tasks. Why is this happening? This is the question that we address in this work. We present the first study to understand the failure of existing deep learning models through the lens of robustness and explainability.
• [05634] On Implicit Neural Representation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhenda Shen (City University of Hong Kong)
  • Abstract : In this talk, we explore a novel approach to implicit neural representations, introducing a novel function that capitalizes on the advantages of Strong Spatial and Frequency attributes. Unlike conventional methods, our proposed technique exhibits remarkable performance improvements across a diverse range of downstream tasks. Through rigorous experimentation and validation, we demonstrate the superior capabilities of our new function in critical applications such as denoising, CT reconstruction, and 3D reconstruction. Implicit neural representations have garnered significant interest in recent years due to their ability to model complex and high-dimensional data without requiring explicit parameterization. Our novel function leverages both spatial and frequency domains, enhancing its ability to capture intricate patterns and relationships within the data. During the presentation, we delve into the technical details of our approach, providing insights into how we use spatial and frequency information effectively. We highlight the advantages of our technique over existing methods, emphasizing the superior performance and efficiency it offers. Through extensive experimental evaluations, we showcase how our new function excels in denoising tasks, enabling high-fidelity reconstructions even in noisy environments. Additionally, we demonstrate its exceptional capabilities in CT reconstruction, where our approach delivers accurate and robust results with reduced artifacts. Furthermore, in the realm of 3D reconstruction, our method outperforms existing techniques, offering more precise and detailed representations.

MS [01868] An introduction of “Journal of Machine Learning” for applied mathematicians

room : E818

• [02598] Embedding Principle: A Hierarchical Structure of Loss Landscape of Deep Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Yaoyu Zhang (Shanghai Jiao Tong University)
  • Abstract : This talk is about the Embedding Principle of loss landscape of deep neural networks ((NNs)), i.e., loss landscape of an NN "contains" all critical points of all the narrower NNs. We will introduce a general class of embedding operators which map any critical point of a narrower NN to a critical point of the target NN preserving the output. Our results uncover a hierarchical structure of loss landscape special to the deep learning models.
• [02247] Perturbational Complexity and Reinforcement Learning in Reproducing Kernel Hilbert Space
  • Format : Talk at Waseda University
  • Author(s) :
    • Jihao Long (Princeton University)
  • Abstract : This talk will offer some fresh insight into the challenge for analyzing reinforcement learning (RL) in a general reproducing kernel Hilbert space (RKHS). We define a quantity called “perturbational complexity by distribution mismatch” and show that the perturbational complexity gives both the lower bound and upper bound of the error for the RL problem in RKHS. We will provide some concrete examples and discuss whether the complexity decays fast or not in these examples.
• [02258] The Random Feature Method for Solving Partial Differential Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jingrun Chen (University of Science and Technology of China)
  • Abstract : In this presentation, we will give a description of the random feature method for solving partial differential equations, including its basic formulation for both static and time-dependent problems and the application for three dimensional problems with complex geometries.
• [02957] DeePN$^2$: A deep learning-based non-Newtonian hydrodynamic model
  • Format : Talk at Waseda University
  • Author(s) :
    • Huan Lei
    • Lidong Fang (Michigan State University)
    • Pei Ge (Michigan State University)
    • Lei Zhang (Shanghai Jiao Tong University)
    • Weinan E (Peking University)
  • Abstract : A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. We developed a deep learning-based non-Newtonian hydrodynamic model, DeePN$^2$, that enables us to systematically pass the micro-scale structural mechanics information to the macro-scale hydrodynamics for polymer suspensions. The model retains a multi-scaled nature with clear physical interpretation, and strictly preserves the frame-indifference constraints.

MS [01136] Advances in Variational Models and PDEs for Images

room : E819

• [04373] A deep quasiconformal approach for topological preserving image segmentation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ronald Lok Ming LUI (The Chinese University of Hong Kong)
  • Abstract : In this talk, we address the problem of topology-preserving image segmentation based on quasiconformal (QC) theories. We introduce a variational model to obtain an optimal QC map that deforms a template mask to the segmentation mask while preserving the topology of the template mask. The bijectivity of the mapping is controlled by the Beltrami coefficient, which measures the QC distortion. We demonstrate that the proposed QC segmentation model can be effectively incorporated into a deep neural network architecture. The resulting deep QC segmentation network takes an image and a template mask with a prescribed topological prior as inputs and outputs the optimal QC map. The QC map is further used to deform the template mask to obtain the segmentation result. Experimental results show that the proposed approach outperforms existing state-of-the-art methods, making it a promising approach for topological preserving image segmentation. This work is supported by HKRGC GRF (Project IDs: 14306721,14307622).
• [02523] Geodesic Models with Curvature Penalization for Image Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Da CHEN (Shandong Artificial Intelligence Institute)
  • Abstract : Geodesic models establish the connection between the minimization of a weighted curve length and the viscosity solutions to the HJB PDEs. In contrast to globally minimizing a simplified first-order energy, as done by the classical geodesic models, we have recently extended the geodesic models to cover different curvature regularization terms, in conjunction with convexity shape prior and curvature prior constraint. We also show their applications in tubular structure tracking and image segmentation.
• [02808] Texture edge detection via Patch consensus
  • Format : Talk at Waseda University
  • Author(s) :
    • Guangyu Cui (Georgia Institute of Technology)
    • Sung Ha Kang (Georgia Institute of Techonology)
  • Abstract : While well-known segmentation method are often based on homogeneity of regions, we focus on finding boundaries between different textured regions. We propose a training-free method to detect the boundary of texture by considering consensus of patch responses away from the boundary. We derive the necessary condition for textures to be distinguished, and analyze the size of the patch with respect to the scale of textures. Various experiments are presented to validate our model.
• [04153] Density-equalizing map with applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Gary Choi (The Chinese University of Hong Kong)
  • Abstract : We present surface and volumetric mapping methods based on a natural principle of density diffusion. Specifically, we start with a prescribed density distribution in a surface or volumetric domain, and then create shape deformations with different regions enlarged or shrunk based on the density gradient. By changing the density distribution, we can achieve different mappings including area-preserving parameterizations. Applications of the methods to medical shape analysis, data visualization, remeshing and shape morphing will be presented.

MS [02130] Fluid-structure interactions in geophysical flows

room : E820

• [04348] How Fluid-Mechanical Erosion Creates Anisotropic Porous Media
  • Format : Talk at Waseda University
  • Author(s) :
    • Bryan Quaife (Florida State University)
    • Nick Moore (Colgate University)
    • Jake Cherry (Florida State University)
    • Shang-Huan Chiu (Lehigh University)
  • Abstract : When a porous medium erodes, microscopic changes of the grain morphology give rise to larger-scale features such as channelization. Using a boundary integral formulation, we characterize these changes by simulating erosion of porous media. A Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe that substantial anisotropy develops over the course of erosion; that is, the configurations that result from erosion permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. These results suggest that the erosion of solid material from groundwater flows may contribute to previously observed anisotropy of natural porous media.
• [04569] Moving boundaries in thermal convection
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Zhang (New York University)
  • Abstract : With simple experiments, we study how mobile boundaries interact with thermally convective flows. When turbulence intensity in thermal convection is sufficiently large, flow patterns are random. However, if a mobile boundary is added to the system, and allowed to freely interact with the surrounding flows, the structure-fluid system may show orderly behaviors, and the flow patterns also become more regular. Geophysical motivations and potential applications will also be discussed in this talk.
• [04835] Using asymptotic analysis to improve numerical methods for multiphase flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric William Hester (UCLA)
    • Andrea Bertozzi (UCLA)
  • Abstract : Diffuse-interface methods approximate discontinuous boundary conditions with smooth source terms - avoiding the need to explicitly discretise multiphase interfaces. But this approximation only converges in the limit. Using the signed-distance function I will outline a general framework for the asymptotic analysis of diffuse-interface methods. I will thereby optimise diffuse-interface simulations of fluid-structure interaction, melting and dissolving ocean icebergs, and dynamic contact lines in three-phase fluids.
• [04665] Laser shot on water and ice
  • Format : Online Talk on Zoom
  • Author(s) :
    • Daosheng Deng (Fudan University)
  • Abstract : The strong interaction between laser and ice or water, arising from the strong photothermal effect, can lead the diverse intriguing phenomena. This talk will present the dancing bubble generated in water by laser, and report the melting of ice under the laser illumination.

MS [00435] Multiscale Numerical Methods for Complex Fluids

room : D101

• [03437] Simulation of micro-scale particulate motion in gases
  • Format : Talk at Waseda University
  • Author(s) :
    • Duncan Lockerby (University of Warwick)
    • Josiah Jordan (University of Warwick)
  • Abstract : Low-speed gas flow around micro-scale particles (e.g. soot and other pollutants), and through suspensions of particles, are rich in physics and challenging to simulate. The hydrodynamic reach of a single particle is broad, making application of conventional approaches (e.g. finite-volume CFD) computationally expensive. Furthermore, their scale renders the conventional Navier-Stokes equations, and associated boundary conditions, inaccurate. In this talk we discuss recent developments in simulating micro-scale particulate flows using the Method of Fundamental Solutions.
• [03686] Synchronized Molecular-Dynamics simulation of the thermal lubrication of an entangled polymer melt
  • Format : Talk at Waseda University
  • Author(s) :
    • Shugo Yasuda (University of Hyogo)
  • Abstract : The thermo-rheological property of an entangled polymer melt in wall-driven shear flows is investigated by using a multiscale hybrid method, coupling molecular dynamics and hydrodynamic. The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value, and the rheological properties drastically change at around the critical drive force. A remarkable observation is the re-entrant transition in the stress–optical relation at this threshold point.
• [03368] Simulation of multiphase flows based on Lagrangian methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Bian (Zhejiang University)
  • Abstract : We study dynamics of a solid particle, a droplet, a vesicle, and a red blood cell (RBC) suspended in a Newtonian fluid, respectively. These four systems share common features, while distinct behaviors are also very apparent. We employ the smoothed particle hydrodynamics (SPH) method to solve the matrix fluid universally, but deal with the suspended object differently. We investigate their rich behaviors in Couette/Poiseuille flows.
• [03717] Lagrangian Heterogeneous Multiscale Methods: A generalized multiphysics model for complex fluids with memory
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicolas Moreno (Basque Center for Applied Mathematics)
    • Marco Ellero (Basque Center for Applied Mathematics)
  • Abstract : We present a Lagrangian multiscale/multiphysics framework for modeling complex fluids in various flow configurations. Our method employs Smoothed Dissipative Particle Dynamics (SDPD) to model fluids at both micro and macro scales, allowing us to incorporate complex physical models such as polymer solutions and multiphase flows. The method accurately captures stresses and enables the simulation of mixed flows. We validate the framework with benchmark configurations for Newtonian and non-Newtonian fluids, demonstrating its effectiveness in modeling complex fluids at both scales. Our methodology provides a natural link between macro and microscales and accounts for memory effects, resulting in a richer fluid response at the continuum.

MS [01024] Multiscale modeling and simulation methods of inhomogeneity in defected systems

room : D102

• [03366] Phase field model for self-climb of prismatic dislocation loops by vacancy pipe diffusion
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaohua NIU (Xiamen University of Technology)
  • Abstract : In this talk, we present a phase field model for the self-climb motion of prismatic dislocation loops via vacancy pipe diffusion driven by elastic interactions. This conserved dynamics model is developed under the framework of the Cahn-Hilliard equation with incorporation of the climb force on dislocations, and is based on the dislocation self-climb velocity formulation established in Ref. (Niu et al., 2017). Asymptotic analysis shows that the proposed phase field model gives the dislocation self-climb velocity accurately in the sharp interface limit. Numerical simulations of evolution, translation, coalescence and repelling of prismatic loops by self-climb show excellent agreement with discrete dislocation dynamics simulation results and the experimental observation. Also a phase field model for the motion of prismatic dislocation loops by both conservative climb and non-conservative climb is also developed. The simulations will be shown to illustrate the influence of the self-climb in the dislocation climb process.
• [05129] Global weak solutions to an initial-boundary value problem of a phase-field model for motion of grain boundaries
  • Author(s) :
    • Luchan Zhang (Shenzhen University)
    • Peicheng Zhu (Shanghai University)
  • Abstract : We shall prove global existence of weak solutions to an initial-boundary value problem for a novel phase-field model which is proposed as an attempt to describe the motion of grain boundaries, a type of interface motion by interface diffusion driven by bulk free energy in elastically deformable solids. Its applications include important processes arising in Materials science, e.g., Sintering. In this model the evolution equation for an order parameter is a non-uniformly, degenerate parabolic equation of fourth order, which differs from the Cahn-Hilliard equation by a non-smooth term of the gradient of the unknown.

contributed talk: CT142

room : D401

[00261] Translational motion of a slightly deformed viscous spherical droplet in Stokes flow

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D401
• Type : Contributed Talk
• Abstract : The problem of steady translational motion of a slightly deformed spherical droplet immersed in an immiscible viscous fluid is studied analytically under the consideration of vanishing Reynolds number. The flow fields in both the regions i.e. in the interior of droplet and exterior of droplet are governed by steady Stokes equations that are solved asymptotically using a method of perturbed expansions undersuitable boundary conditions. The deformation from spherical shape is characterized by a small parameter called deformation parameter, therefore, we have solved the problem up to the second order of the deformation parameter by neglecting the higher orders. The effect of deformation parameter is observed by means of force expression. The explicit expressions for the hydrodynamic drag force exerted on the droplet surface are obtained for the special cases of prolate and oblate spheroids. Our results are in good agreement with the exisitng results in literature for deformed solid sphere up to first and second order.
• Classification : 76D07, 76T06, Transport Phenomena, Motion of bubbles and drops
• Format : Talk at Waseda University
• Author(s) :
  • Jai Prakash (Mahindra University, Hyderabad)
  • Huan J. Keh (National Taiwan University, Taipei)

[01119] Miscible Flows Based On Darcy-Stokes-Brinkman Model: Existence and Uniqueness

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D401
• Type : Contributed Talk
• Abstract : Flows in a porous or vuggy medium are encountered in several physical phenomena, including oil recovery. A vast literature use the unsteady Brinkman and continuity equations for numerical modeling of such flow systems. We couple these equations with a convection-diffusion equation for the solute concentration to take the miscibility of fluids into account. For the first time, we show the well-posedness of this problem by employing regularized Galerkin method and hemivaritional inequalities.
• Classification : 76Dxx, 76Sxx, 35Qxx, 35Dxx
• Format : Talk at Waseda University
• Author(s) :
  • Sahil Kundu (Indian Institute of Technology Ropar,Ropar, India)
  • Manoranjan Mishra (Indian Institute of Technology Ropar, India)
  • Surya Narayan Maharana (Indian Institute of Technology Ropar)

[00518] Unsteady Stokes flow past a sphere with mixed slip-stick boundary conditions

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D401
• Type : Contributed Talk
• Abstract : A general solution to unsteady Stokes equations for an incompressible, viscous flow past a sphere with mixed slip-stick boundary conditions is given. Faxén’s laws for drag and torque exerted on the sphere are derived, and the results have been compared in special cases of no-slip and shear-free boundary conditions with the existing literature. We extend this work to bodies of arbitrary shape under the same boundary conditions.
• Classification : 76D07, 76D05
• Format : Talk at Waseda University
• Author(s) :
  • Dimple Satya Sree Dadi (University of Hyderabad)
  • Dimple Satya Sree Dadi (University of Hyderabad)
  • Sri Padmavati B (University of Hyderabad)

[02353] Finite volume coupled with finite element scheme for the chemotaxis-fluid model

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D401
• Type : Contributed Talk
• Abstract : We propose a linear decoupled positivity-preserving scheme for the chemotaxis-fluid system modeling the mutual interaction of the swimming aerobic bacteria with the surrounding fluid flow. The scheme consists of the finite element method (FEM) for the fluid equations on a regular triangulation and an upwind finite volume method (FVM) for the chemotaxis system on two types of dual mesh. The discrete cellular density and chemical concentration can be regarded as the piecewise constant functions on the dual mesh $($or equivalently, the piecewise linear functions on the triangulation in the mass-lumping sense$)$, which are obtained by the upwind finite volume approximation satisfying the positivity-preserving and mass conservation laws. The numerical velocity is computed by the finite element method in the triangulation and is utilized to define the upwind-type numerical flux in the dual mesh. We examine the $M$-property of the matrices from the discrete system and prove the well-posedness and the positivity-preserving property. By using the $L^p$-estimate of the discrete Laplace operators, semigroup analysis, and induction method, we establish the optimal error estimates for chemical concentration, cellular density and velocity field in $(l^\infty(W^{1,p}), l^\infty(L^p),l^\infty(W^{1,p}))$-norms. Several numerical examples are presented to confirm the theoretical results.
• Classification : 76Dxx, 65Mxx, 76Mxx
• Format : Talk at Waseda University
• Author(s) :
  • Ping Zeng (University of Electronic Science and Technology of China)
  • Guanyu Zhou (University of Electronic Science and Technology of China)

[00691] GROWTH TUMOR, PROLIFERATION AND DIFFUSION IN CELL LINES OF OSTEOSARCOMA

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D401
• Type : Contributed Talk
• Abstract : Osteosarcoma is a bone cancer. According to medical studies, it has a high genetic complexity, with different mechanisms of appearance and evolution. Our goal is to describe how is the diffusive behavior of cell lines at early times, that is, times close to the instant of inoculation and when the volumes are still small compared to the largest experimental volume reached by the cell lines studied.
• Classification : 92-XX, 92Bxx, 92B05, Biomathematics
• Format : Online Talk on Zoom
• Author(s) :
  • Maria Isabel Romero Rodriguez (Universidad Militar Nueva Granada)
  • María Isabel Romero Rodríguez (Universidad Militar Nueva Granada)
  • Eduard Leonardo Sierra Ballén (Universidad Militar Nueva Granada )
  • Juan Camilo Vargas Pino (Universidad Militar Nueva Granada)

MS [00253] Modelling and Simulation of Lithium-Ion Batteries

room : D403

• [04505] Simulation and analysis of space charge layers in a solid electrolyte
  • Format : Talk at Waseda University
  • Author(s) :
    • Laura Marie Keane (York University)
    • Iain Moyles (York University)
  • Abstract : We consider the zero-charge flux equilibrium problem in a solid electrolyte. We introduce an auxiliary variable to remove singularities from the domain, facilitating robust numerical simulations. We use asymptotic reduction to uncover the true width of the boundary layer of the electrolyte. Exploiting the asymptotic regimes, we generate a nonuniform discretization grid enabling more computationally efficient simulations without sacrificing accuracy as we focus computational power in regions where the solution changes more rapidly.
• [03112] Machine Learning of Electrochemistry Battery Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Brian Wetton (University of British Columbia)
    • Maricela Best-Mckay (University of British Columbia)
  • Abstract : We present a surrogate modeling approach that uses synthetic data generated by an electrochemical model to approximate Li-ion battery dynamics using a Deep Neural Network. Our approach uses the Pseudo-Two Dimensional model and a well defined use-cycle, fit to a Network of convolution type for the particle concentrations. The Network is able to accurately predict future behaviour. Extensions to initial State of Charge correction and the identification of a State of Health parameter are given.
• [05150] Parameterisation of reduced-order battery models from non-invasive characterisation
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicola Courtier (University of Oxford)
    • Ross Drummond (University of Sheffield)
    • David Howey (University of Oxford)
  • Abstract : Robust parameterisation methods exist for equivalent circuit models of batteries but, to understand the underlying processes and battery design, electrochemical models are needed. Progress is limited by a lack of robust parameterisation methods for nonlinear systems of differential equations, containing parameters which are unidentifiable from non-invasive measurements. Reduced-order modelling offers a pathway to systematically estimate lumped parameters from data using prediction-error minimisation. Furthermore, we apply the measure-moment approach to optimisation to estimate optimal charging profiles.
• [05185] Early prediction of battery remaining useful life using AI and physics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Edwin Khoo (Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR))
  • Abstract : Accurate prediction of the remaining useful life (RUL) of a lithium-ion battery (LIB) using early cycle data aids in scheduling predictive maintenance, avoiding catastrophic failure during operation and optimizing battery manufacturing. In this talk, we discuss our recent work in building a hybrid deep learning model that combines physics-informed features with statistical features to achieve better generalization performance in early RUL prediction when benchmarked against several AI models. If time permits, we will also discuss our recent parametric study of LIB capacity fade using a cell OCV model.

MS [00497] Advances in numerical methods for nonlinear optics

room : D404

• [03183] High-Order Accurate Approaches for Maxwell's Equations with Nonlinear Active Media on Overlapping Grids
  • Format : Talk at Waseda University
  • Author(s) :
    • Jeffrey Banks (Rensselaer Polytechnic Institute)
    • Gregor Kovacic (Rensselaer Polytechnic Institute)
    • William Henshaw (Rensselaer Polytechnic Institute)
    • Donald Schwendeman (Rensselaer Polytechnic Institute)
    • Qing Xia (KTH Royal Institute of Technology)
    • Alexander Kildeshev (Purdue University)
    • Ludmila Prokopeva (Purdue University)
  • Abstract : Here I discuss efficient numerical methods for Maxwell's equations in nonlinear active media. Complex geometry is treated with overlapping grids, and interfaces between different materials are accurately and efficiently treated using compatibility coupling conditions. A novel hierarchical modified equation (ME) approach leads to an explicit scheme that does not require nonlinear iteration, and also gives local update equations without any tangential coupling along interfaces that would otherwise occur using a traditional high-order ME time stepper.
• [02203] Energy stability and active Q-factor control in numerical models of nonlinear electromagnetic resonance effects
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lutz Angermann (Clausthal University of Technology)
  • Abstract : The talk deals with the modeling and some properties of mathematical models to describe the excitation of a nonlinear material by electromagnetic waves, including typical questions such as the existence and uniqueness of a solution, the derivation of energy laws or estimates, the evaluation of the resonance quality and the transfer of these properties to numerical models.
• [02291] Energy stable finite element method for nonlinear Maxwell's equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Maohui Lyu (Beijing University of Posts and Telecommunications)
    • Vrushali Bokil (Oregon State University)
    • Yingda Cheng (Michigan State University)
    • Fengyan Li (Rensselaer Polytechnic Institute)
    • Weiying Zheng (LSEC, Chinese academy of sciences)
  • Abstract : In this talk, we consider the time-domain nonlinear Maxwell’s equations in multi-dimensions. With special discretizations for the nonlinear terms, we introduce a class of provably energy stable finite element method. Numerical experiments are provided to validate the performance of the proposed methods.
• [03742] High Order Energy Stable FDTD Methods for Maxwell Duffing models in Nonlinear Photonics
  • Format : Talk at Waseda University
  • Author(s) :
    • Vrushali A Bokil (Oregon State University)
    • Daniel Appelo (Michigan State University)
    • Yingda Cheng (Michigan State University)
    • Fengyan Li (Rensselaer Polytechnic Institute)
  • Abstract : We present electromagnetic models that describe nonlinear optical phenomenon in which the nonlinear polarization is driven by the electric field and modeled as an anharmonic oscillator(s). The models for the nonlinear polarization are given by Duffing equations and incorporate both nonlinearity and dispersion. Using the auxiliary differential equation approach, we present discretizations of the coupled Maxwell-Duffing models which are high order and energy stable methods based on finite difference time domain (FDTD) techniques.

MS [00605] Recent advances in theory and application of quantum computing technology

room : D405

• [04414] Performance Evaluation of Ising Machines using Constraint Combinatorial Optimization Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuhiko Komatsu (Tohoku University)
    • Makoto Onoda (Tohoku University)
    • Masahito Kumagai (Tohoku University)
    • Hiroaki Kobayashi (Tohoku University)
  • Abstract : Ising machines have been developed rapidly by various implementations. However, the characteristics of Ising machines have not been clarified yet because a unified evaluation method and commonly used benchmark program for Ising machines have not been established. This research evaluates various Ising machines using constraint combinatorial optimization problems. Through the evaluation, the characteristics of Ising machines are clarified.
• [04218] Nonnegative binary matrix factorization by continuous relaxation and reverse annealing
  • Format : Talk at Waseda University
  • Author(s) :
    • Renichiro Haba (Tohoku University)
    • Masayuki Ohzeki (Tohoku University)
    • Kazuyuki Tanaka (Tohoku University)
  • Abstract : In this talk, we introduce a reverse annealing framework with relaxation strategies for nonnegative/binary matrix factorization, a feature extraction technique. Reverse annealing is one of the quantum annealing techniques and its specific usage has not been well explored. Experimental results reveal performance comparable to exact optimization methods, indicating the potential for expanding the applicability of reverse annealing.
• [03976] Kernel learning by quantum annealer
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasushi Hasegawa (Tohoku University)
    • Hiroki Oshiyama (Tohoku University)
    • Masayuki Ohzeki (Tohoku University)
  • Abstract : Kernel methods are powerful in machine learning. It is known that shift-invariant kernels can be represented by Fourier transformation of a probability distribution of frequencies. Recently the method called Implicit Kernel Learning is proposed, which learns the probability distribution according to the given data by generative model. We developed a new method that uses quantum annealing as a sampler to train Boltzmann machines for the probability distribution. We demonstrate our method by using D-Wave quantum annealer.

MS [00449] Atomistic simulations in the exascale era

room : D407

• [03771] Adaptive parareal method for the simulation of atomistic defects
  • Format : Online Talk on Zoom
  • Author(s) :
    • Olga Gorynina
    • Tony Lelievre (Ecole des Ponts)
    • Frederic Legoll (Ecole des Ponts)
    • Danny Perez (Los Alamos National Laboratory)
  • Abstract : Molecular dynamics simulations demand extensive computational resources to accurately calculate ensemble averages and dynamical quantities over long trajectories. In this study, we employ an adaptive parareal algorithm to enhance the speed of MD simulations by breaking down time calculations into smaller segments. We focus on the diffusion of a self-interstitial atom in a body-centered cubic tungsten lattice, utilizing LAMMPS molecular dynamics software and employing machine-learned spectral neighbor analysis potentials (SNAP) and embedded-atom method potentials (EAM). The adaptive parareal algorithm, which iteratively refines approximate solutions using parallel fine solvers, demonstrates significant computational gains. The goal of the talk is to highlight the potential of the adaptive parareal algorithm for accelerating MD simulations.
• [04027] Fast, Accurate and Large-scale Ab-initio Calculations for Materials Modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Vikram Gavini (University of Michigan)
    • Sambit Das (University of Michigan)
    • Phani Motamarri (Indian Institute of Science)
  • Abstract : This talk will present our recent advances towards the development of computational methods and numerical algorithms for conducting fast and accurate large-scale DFT calculations using adaptive finite-element discretization, which form the basis for the recently released DFT-FE open-source code (https://github.com/dftfeDevelopers/dftfe). The computational efficiency, scalability and performance of DFT-FE will be presented. Some application problems that highlight the utility of DFT-FE in tackling complex aperiodic systems will be demonstrated.
• [04848] The Chunks and Tasks Matrix Library
  • Format : Talk at Waseda University
  • Author(s) :
    • Emanuel Rubensson (Uppsala University)
  • Abstract : We present the Chunks and Tasks Matrix Library, which is a parallel sparse matrix library able to dynamically take advantage of data locality in matrices to avoid movement of data. The library uses a sparse quadtree representation of sparse matrices and is implemented using the Chunks and Tasks programming model. We demonstrate the scaling capabilities for operations used in large-scale electronic structure calculations, including sparse matrix-matrix multiplication and algorithms for inverse factorization.
• [05282] From Langevin dynamics to kinetic Monte Carlo: mathematical foundations of accelerated dynamics algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tony LELIEVRE (Ecole des Ponts ParisTech)
  • Abstract : We will discuss models used in classical molecular dynamics, and some mathematical questions raised by their simulations. In particular, we will present recent results on the connection between a metastable Markov process with values in a continuous state space (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process with values in a discrete state space. This is useful to analyze and justify numerical methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques à la A.F. Voter). It also provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models. References: - G. Di Gesù, T. Lelièvre, D. Le Peutrec and B. Nectoux, Jump Markov models and transition state theory: the Quasi-Stationary Distribution approach, Faraday Discussion, 195, 2016. - G. Di Gesù, T. Lelièvre, D. Le Peutrec et B. Nectoux, Sharp asymptotics of the first exit point density, Annals of PDE, 5(1), 2019. - T. Lelièvre, Mathematical foundations of Accelerated Molecular Dynamics methods, In: W. Andreoni and S. Yip (Eds), Handbook of Materials Modeling, Springer, 2018. - T. Lelièvre, D. Le Peutrec and B. Nectoux, Eyring-Kramers exit rates for the overdamped Langevin dynamics: the case with saddle points on the boundary, https://arxiv.org/abs/2207.09284.

contributed talk: CT167

room : D408

[00213] Advances in Derivative-free Methods and the DFO VU-algorithm

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D408
• Type : Contributed Talk
• Abstract : The VU-algorithm is a method of minimizing convex, nonsmooth functions by splitting the space into two subspaces: the V-space, on which the objective function's nonsmooth behavior is captured, and the orthogonal U-space, on which the function behaves smoothly. The algorithm's convergence is accelerated, as it takes a (slow) proximal point step in the V-space, then a (fast) quasi-Newton step in the U-space, since gradients and Hessians exist there. New convergence rates and subroutines are presented.
• Classification : 90C25, 49J52
• Format : Talk at Waseda University
• Author(s) :
  • Chayne Planiden (University of Wollongong)

[02238] A Generalized Multi-Parameterized Proximal Point Algorithm

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D408
• Type : Contributed Talk
• Abstract : Proximal point algorithm (PPA) is an important class of methods for solving convex problems. In this article, a generalized multi-parameterized proximal point algorithm (GM-PPA) is developed to solve linearly constrained convex optimization problems. Compared with existing PPAs, the proposed method is much more general as well as flexible. Many existing PPAs reduce to our algorithm when some newly introduced parameters are fixed. Furthermore, by appropriately setting the algorithm parameters, our GM-PPA is potentially able to reduce the computation time and iteration number whereas the convergence result can still be guaranteed. Numerical experiments on synthetic problem are conducted to demonstrate the efficiency of our algorithm.
• Classification : 90C25, 90C30
• Format : Talk at Waseda University
• Author(s) :
  • Yuan Shen ( Nanjing University of Finance & Economics)

[01123] Parameterized Douglas-Rachford dynamical systems for generalized DC programming

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D408
• Type : Contributed Talk
• Abstract : In this work, we consider the difference of convex functions (DC) programming problems which are the backbone of nonconvex programming and global optimization. The classical problem contains the difference between two proper convex and lower semicontinuous functions. This paper deals with the generalized DC programming problem, which deals with the minimization of three convex functions. We propose a novel parametrized Douglas Rachford dynamical system to solve the problem and study its convergence behavior in the Hilbert space. Moreover, we also conduct numerical experiments to support our theoretical findings.
• Classification : 90C26, 90C30
• Format : Online Talk on Zoom
• Author(s) :
  • Avinash Dixit (Kirori Mal College, University of Delhi, Delhi)
  • Pankaj Gautam (NTNU )
  • Tanmoy Som (IIT (BHU), Varanasi)

[01592] Optimal blood distribution using a matheuristic approach

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D408
• Type : Contributed Talk
• Abstract : The problem of distribution of blood has been extensively studied, but models relating to different blood types have not been specifically considered in the literature to the best of our knowledge. This paper describes a new mathematical model for optimising blood distribution in residential areas. A Lagrangian relaxation-based matheuristic is developed to solve the problem. Hypothetical data sets were generated to mimic real blood distribution system in an urban setting. Results obtained using CPLEX solver on the AMPL platform reveal that the model described in this study is able to achieve quality results within very short times. Specifically, the number of located blood facilities is minimized for each problem instances as well as covering much of the demand points on the distribution network. We observe that the proposed system, when compared to the existing system, provides a better approach to blood distribution and is adaptable to related areas of supply chain.
• Classification : 90C26, 90C27
• Author(s) :
  • Olawale Joshua Adeleke (Redeemer's University )
  • Olawale Joshua Adeleke (Redeemer's University)
  • Idowu Ademola Osinuga (Federal University of Agriculture, Abeokuta, Nigeria)

[02702] A mathematical model of cell expansion for cultivated meat production

• Session Time & Room : 4D (Aug.24, 15:30-17:10) @D408
• Type : Contributed Talk
• Abstract : Cultivated meat represents a cruelty-free alternative to conventional production methods of animal protein. However, it currently faces pressing technological challenges that curtail its commercial viability. To facilitate its industrial scale-up, we propose a mathematical model of metabolism of a stem cell expansion system, a key step in the production of lab-grown meat. We evaluate our model with numerical simulations and perform a global parameter sensitivity analysis to gain further insights about our system
• Classification : 92-10, 92C75, 92B05
• Author(s) :
  • Julia Krol (Mathematical Institute, University of Oxford)
  • Sarah Waters (Mathematical Institute, University of Oxford)
  • Hua (Cathy) Ye (Department of Engineering, Univeristy of Oxford)
  • Akin Odeleye (Ivy Farm Technologies)

MS [00625] Mathematical Modeling and Combinatorial Optimization

room : D501

• [02859] A core selection method for the robust traveling salesman problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuki Hasegawa (Shizuoka University)
    • Wei Wu (Shizuoka University)
    • Mutsunori Yagiura (Nagoya University)
  • Abstract : We consider the robust traveling salesman problem with interval costs under a min–max regret criterion. We first show that the iterated dual substitution method is applicable for solving this problem, and we examine 18 implementations based on different cut generation rules and mathematical models of the classical traveling salesman problem. Then, we propose a new heuristic approach: core selection method. The core selection method achieved state-of-the-art results on all benchmark instances.
• [02909] Algorithms for two-machine job-shop scheduling problem with one joint job
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroki Numaguchi (Tokyo University of Science)
    • Wei Wu (Shizuoka University)
    • Yannan Hu (Tokyo University of Science)
  • Abstract : We introduce a two-machine job-shop scheduling problem with one joint job where a joint job is defined as a job whose operations are to be processed by different machines. We prove that this problem is strongly NP-hard and propose a polynomial-time algorithm based on dynamic programming when the number of jobs is given as a fixed number. We further improve time complexity using various techniques, including the two-pointers method.
• [04538] A New Multivariate Decision Tree Based on Mixed Integer Linear Programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryo Kurosu (University of Kyoto)
    • Kazuya Haraguchi (University of Kyoto)
  • Abstract : We study a novel framework of inferring molecule structures that are expected to have desired properties (e.g., high boiling point, low solubility), exploiting machine learning and operations research, where accurate prediction tools are indispensable. In this paper, we propose a new classification decision tree algorithm that builds a multivariate decision tree (i.e., node split is done by hyperplane) based on mixed integer linear programming. Our algorithm is a generalization of conventional ones in the sense that their decision trees are univariate. We describe experimental results on how accurate decision trees are built by our algorithm and by conventional ones, using data sets from cheminformatics.
• [04561] A Linear Delay Algorithm for Enumeration of $2$-Edge/Vertex-connected Induced Subgraphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Takumi Tada (Graduate School of Informatics, Kyoto University, Japan)
    • Kazuya Haraguchi (Graduate School of Informatics, Kyoto University, Japan)
  • Abstract : In this paper, we present the first linear delay algorithms to enumerate all 2-edge-connected induced subgraphs and to enumerate all 2-vertex-connected induced subgraphs for a given simple undirected graph. We treat these subgraph enumeration problems in a more general framework based on set systems. For an element set $V$, $(V,{\mathcal C}\subseteq 2^V)$ is called a {\em set system}, where we call $C\in{\mathcal C}$ a {\em component}. A nonempty subset $Y\subseteq C$ is a {\em removable set of $C$} if $C\setminus Y$ is a component and $Y$ is a {\em minimal removable set} ({\em MRS}) {\em of $C$} if it is a removable set and no proper nonempty subset $Z\subsetneq Y$ is a removable set of $C$. We say that a set system has {\em subset-disjoint} ({\em SD}) property if, for every two components $C,C'\in{\mathcal C}$ with $C'\subsetneq C$, every MRS $Y$ of $C$ satisfies either $Y\subseteq C'$ or $Y\cap C'=\emptyset$. We assume that a set system with SD property is implicitly given by an oracle that returns an MRS of a component which is given as a query. We provide an algorithm that, given a component $C$, enumerates all components that are subsets of $C$ in linear time/space with respect to $|V|$ and oracle running time/space. We then show that, given a simple undirected graph $G$, the pair of the vertex set $V=V(G)$ and the family of vertex subsets that induce 2-edge-connected (or 2-vertex-connected) subgraphs of $G$ has SD property, where an MRS in a 2-edge-connected (or 2-vertex-connected) induced subgraph corresponds to either an ear or a single vertex with degree greater than two.

MS [00467] Volatility modeling in finance

room : D502

• [04506] Understanding how market impact shapes rough volatility
  • Author(s) :
    • Mathieu Rosenbaum (École Polytechnique )
    • Gregoire Szymanski (Ecole Polytechnique)
  • Abstract : We explain the subtle connection between the shape of market impact curves and the rough behavior of the volatility. We particularly focus on the celebrated square-root law and on the role of the participation rate in the price and volatility formation process.
• [04065] Pricing in affine forward variance models
  • Format : Talk at Waseda University
  • Author(s) :
    • Jim Gatheral ( Baruch College, CUNY)
  • Abstract : In affine forward variance (AFV) models, the moment generating function may be expressed as the convolution of the forward variance curve and the solution of an associated convolution integral equation. In the case of the rough Heston model, this convolution integral equation may be solved numerically using the Adams scheme and approximately using a rational approximation. We show that in the general case, AFV models may be simulated efficiently using a hybrid version of Andersen's QE scheme. We illustrate convergence of the scheme numerically in the special case of the rough Heston model.
• [02829] The rough Hawkes Heston model
  • Format : Talk at Waseda University
  • Author(s) :
    • Sergio Andres Pulido Nino (ENSIIE-LaMME, Evry)
    • Alessandro Bondi (Scuola Normale Superiore di Pisa)
    • Simone Scotti (Universita di Pisa)
  • Abstract : We introduce an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. Prices of options on the underlying and its volatility index can then be obtained using Fourier-inversion techniques. We show that a parsimonious setup, characterized by a power kernel and an exponential law for the jumps, is able to simultaneously capture the behavior of the implied volatility smile for both S&P 500 and VIX options. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to jointly calibrate S&P 500 and VIX smiles.
• [05086] Recent advances on rough volatility
  • Format : Talk at Waseda University
  • Author(s) :
    • Antoine Jacquier (Imperial College London)
  • Abstract : Empirical evidence has recently highlighted that volatility of financial markets was not Markovian, giving rise to a new paradigm called "rough volatility". In this talk, we consider several recent advances in the topic, from a modelling point of view (suggesting interesting extensions of fractional Brownian motion) and from numerical aspects.

MS [00468] Stochastic Modelling in Finance


room : D505

• [01313] Portfolio optimization in the family of 4/2 stochastic volatility models.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marcos Escobar-Anel (Western University, Department of Statistical and Actuarial Sciences.)
  • Abstract : The state-of-the-art 4/2 stochastic volatility model was recently proposed by Grasselli in 2017 and has gained great attention ever since. This model is a superposition of a Heston (1/2) component and a 3/2 component, bringing the best of the two nested models. This talk gives an overview of recent progress in the application of the model, as well as a multivariate generalization, to portfolio optimization, in particular within expected utility theory. The work includes the study of CRRA and HARA utilities, the presence of consumption, as well as considerations about complete/incomplete markets and ambiguity-aversion. All is complemented with the analysis of wealth-equivalent losses to gain insight into popular suboptimal strategies.
• [01486] Parrondo's paradox and financial applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bruno N Remillard (HEC Montreal)
  • Abstract : In this talk, I will start by giving an introduction to Parrondo's paradox, then I will present recent results on this topic, and finally I will talk about financial applications.
• [01304] Optimal portfolio analysis on finite and small-time horizons
  • Format : Online Talk on Zoom
  • Author(s) :
    • Indranil SenGupta (North Dakota State University)
  • Abstract : In this presentation, we consider the portfolio optimization problem in a financial market under a general utility function. We consider an incomplete stochastic volatility market model that is driven by both Brownian motion and jump process. We obtain a closed-form formula for an approximation to the optimal portfolio in a small-time horizon. This is obtained by finding the associated Hamilton-Jacobi-Bellman integro-differential equation and then approximating the value function by constructing appropriate supersolution and subsolution.
• [01292] Stochastic Modelling of Big Data in Finance
  • Format : Talk at Waseda University
  • Author(s) :
    • Anatoliy Swishchuk (University of Calgary)
  • Abstract : This talk will review some recent results in stochastic modelling of big data in finance, including semi-Markov modelling, modelling with Hawkes processes, multivariate modelling, to name a few. Numerical results are used to explain, visualize and justify the proposed models, and are based on real data such as LOBster, CISCO, Xetra and Francfurt markets stocks and other data.

MS [02612] Mathematical modeling of biofilm systems and applications

room : D514

• [05492] Long time behaviour of a thin-film model for early biofilm development
  • Author(s) :
    • John Ward (Loughborough University)
  • Abstract : We will present a model describing the interaction of a thin, surface growing biofilm and planktonic cells. Assuming the biofilm can be described as homogeneous, thin, highly viscous fluid, a coupled system of nonlinear reaction-diffusion equations is derived, one of which having a fourth-order ``diffusion'' term. Key results using numerical computation and asymptotic analysis will be presented that indicate the dominant processes in early biofilm expansion and the subtle complxities of the travelling wave solutions.

MS [00471] Recent Advancements in Electrical Impedance Tomography

room : D515

• [04744] Monitoring of hemorrhagic stroke using Electrical Impedance Tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Ville Kolehmainen (Department of Technical Physics, University of Eastern Finland)
  • Abstract : In this talk, we present recent progress in development of electrical impedance tomography (EIT) based bedside monitoring of hemorrhagic stroke. We present the practical setup and pipeline for this novel application of EIT and the image reconstruction method we have developed for it. Feasibility of the approach is studied with simulated data from anatomically highly accurate simulation models and experimental phantom data from a laboratory setup
• [04874] Exploration of deep generative modelling approaches to electrical impedance tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Valentina Candiani (University of Genoa)
  • Abstract : Reconstruction of conductivity images in electrical impedance tomography (EIT) requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and solution algorithms need either simplifying assumptions or regularization based on a priori knowledge. In this work we study the applicability, the challenges and the limitations of some relatively new deep generative models such as score-based generative diffusion models and normalising flows, for both image reconstruction and medical anomaly detection. This talk will present some preliminary results obtained with such approaches in the application of EIT to the detection of stroke.
• [04904] Fast CGO-based absolute reconstructions for 3D EIT
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Muller (Villanova University)
    • Sarah Hamilton (Marquette University)
  • Abstract : Complex geometrical optics (CGO)-based methods for 3-D electrical impedance tomography are presented. Calderón’s method and the $\mathbf{t}^{\mathrm{exp}}$ method are adapted for reconstructions from 3-D electrode data. These are the first absolute images to be produced from these methods for 3-D electrode data, both simulated and experimental. Some benefits of these CGO-based methods are that they provide real-time imaging and are shown to be robust to modelling errors such as electrode location and domain size.
• [05054] Use of reference measurements in electrical tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Aku Seppänen (University of Eastern Finland )
    • Laura E. Dalton (Duke University)
    • Mikko Räsänen (University of Eastern Finland)
    • Moe Pourghaz (North Carolina State University)
  • Abstract : Reconstruction methods in electrical resistance/capacitance tomography are often divided into classes of absolute and difference methods. While absolute reconstructions are based on data from a single time instant, difference reconstructions use reference data, to image the change of conductivity/permittivity from the reference state qualitatively. In this talk, we demonstrate that absolute reconstructions can also benefit from the use of reference data, when available, especially because it improves their tolerance to modeling errors.

MS [02491] Mathematics of Epidemics: modelling, data analysis, and control

room : A201

• [03453] Optimal vaccination at high reproductive numbers: sharp transitions and counter-intuitive allocations
  • Format : Talk at Waseda University
  • Author(s) :
    • Nir Gavish (Technion - Israeli Institute of Technology)
    • Guy Katriel (Braude College of Engineering)
  • Abstract : Optimizing vaccine allocation is crucial for effective vaccination campaigns against epidemics. Contrary to intuition and classic vaccination theory, we show that for leaky vaccines and high basic reproduction numbers, the optimal allocation strategy for minimizing infections prioritizes those least likely to be infected. These findings have important implications for managing vaccination campaigns against highly transmissible infections.
• [04794] An epidemic model for reinfection dynamics with heterogeneous susceptibility
  • Format : Talk at Waseda University
  • Author(s) :
    • Yukihiko Nakata (Aoyama Gakuin University)
  • Abstract : Individuals in a population vary in susceptibility. To explore the impact of the distributed susceptibility, we consider an epidemic model, where individuals acquire a degree of susceptibility with a probability after infection. It is shown that heterogeneous susceptibility adds complexity to the reinfection dynamics, and changes in the distribution of susceptibility may cause unexpected epidemics. We revisit the epidemic model studied by Katriel in 2010. The study is partly a joint work with Ryosuke Omori.
• [03972] Effective screening with rapid antigen tests for COVID-19 patients: simulation with viral dynamics model
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Dam Jeong (Nagoya University)
    • Keisuke Ejima (Nanyang Technological University)
    • Ajelli Marco (Indiana University School of Public Health-Bloomington)
    • Shingo Iwami (Nagoya University)
  • Abstract : In this study, we assessed the effectiveness of various screening strategies with rapid antigen tests in schools and workplaces. For this, we developed two models with different scales: a transmission model in the community where those facilities under screening tests belong, and a viral dynamics model of each infected case in those facilities. Those screening strategies were compared through quantitative simulations. Our computational framework will be useful to evaluate screening strategies for infectious disease transmission.
• [03510] Evaluation of Effectiveness of Global COVID-19 Vaccination Campaign in 2021
  • Format : Talk at Waseda University
  • Author(s) :
    • Daihai He (Hong Kong Polytechnic University)
  • Abstract : To model estimated deaths averted by COVID-19 vaccines, we used state-of-the-art mathematical modeling, likelihood-based inference, and reported COVID-19 death and vaccination data. We estimated that >1.5 million deaths were averted in 12 countries. Our model can help assess effectiveness of the vaccination program, which is crucial for curbing the COVID-19 pandemic.

MS [00521] Recent advances on non-convex optimization in inverse problems, imaging and machine learning

room : A206

• [04271] Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Antonio José Silveti-Falls (Université Paris-Saclay, CentraleSupélec, INRIA OPIS, France)
    • Edouard Pauwels (Université Toulouse 3 Paul Sabatier)
    • Jérôme Bolte (Université Toulouse Capitole, Toulouse School of Economics)
  • Abstract : Understanding the differentiability and regularity of the solution to a monotone inclusion problem is an important question with consequences for convex optimization, machine learning, signal processing, and beyond. Past attempts have been made either under very restrictive assumptions that ensure the solution is continuously differentiable or using mathematical tools that are incompatible with automatic differentiation. In this talk, we discuss how to leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable and provide formulas for computing its generalized gradient. Our approach is fully compatible with automatic differentiation and comes with assumptions which are easy to check, roughly speaking: semialgebraicity and strong monotonicity. We illustrate the scope of our results by considering three fundamental composite problem settings: strongly convex problems, dual solutions to convex minimization problems and primal-dual solutions to min-max problems.
• [01315] Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yifei Zack Wang (Stanford University)
    • Peng Chen (Georgia Institute of Technology)
    • Mert Pilanci (Stanford University)
    • Wuchen Li (University of South Carolina)
  • Abstract : The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. For finite samples, we approximate the score function in the family of two-layer networks with squared-ReLU activations. We derive a semi-definite programming (SDP) relaxation of the variational problem, which can be efficiently solved by standard interior point method. Numerical experiments including PDE-constrained Bayesian inference and parameter estimation in COVID-19 modeling demonstrate the effectiveness of the proposed method.
• [01537] Data-informed deep optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Lulu Zhang (Shanghai Jiao Tong University)
  • Abstract : Motivated by the impressive success of deep learning, we explore the application of deep learning into a specific class of optimization problems lacking explicit formulas for both objective function and constraints. In this work, we propose a data-informed deep optimization (DiDo) approach emphasizing on the adaptive fitting of the the feasible region. To demonstrate the effectiveness of our DiDo approach, we consider a practical design case in industry and a 100-dimension toy example.

MS [01545] Interplay between controllability and qualitative aspects of stochastic dynamical systems

room : A207

• [05477] Mixing via controllability
  • Format : Talk at Waseda University
  • Author(s) :
    • Vahagn Nersesyan (NYU Shanghai)
  • Abstract : In this talk, we will review some recent results where controllability is used to derive mixing for PDEs perturbed by bounded noise.
• [05602] Multi-bubble blow-ups and multi-solitons to focusing (stochastic) nonlinear Schrödinger equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Deng Zhang (Shanghai Jiao Tong University)
  • Abstract : In this talk we mainly review the recent results on multi-bubble blow-ups and multi-solitons to the focusing (stochastic) nonlinear Schrödinger equations. In the mass-critical case, the construction and conditional uniqueness of multi-bubble Bourgain-Wang type blow-up solutions will be presented, which provide new examples for the mass quantization conjecture. In the deterministic case without noise, this also provides new examples of non-pure multi-solitons (including dispersive part) for the soliton resolution conjecture. Furthermore, the refined uniqueness of pure multi-bubble blow-ups and multi-solitons in the very low asymptotic regime is obtained. At last, in both the mass critical and subcritical cases, the direct construction of stochastic multi-solitons will also be presented, particularly, in the absence of the classical pseudo-conformal symmetry.
• [04445] Controllability results for a class of bilinear degenerate wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Piermarco Cannarsa (University of Rome Tor Vergata)
    • Patrick Martinez (Université de Toulouse)
    • Cristina Urbani (University of Rome Tor Vergata & Accademia Nazionale dei Lincei)
  • Abstract : I will present a result of exact controllability along the ground state for a degenerate wave equation by means of a bilinear control. We prove that there exists a threshold time $T_0$ such that: for $T>T_0$ (and $T=T_0$ and strong degeneracy) a classical controllability result can be achieved; for $T
• [02831] Small-time approximate controllability for nonlinear Schrödinger equations via bilinear controls
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessandro Duca (Centre Inria Nancy - Grand Est)
  • Abstract : Consider the nonlinear Schrödinger equation (NLS) on a torus of arbitrary dimension in presence of an external potential field whose time-dependent amplitude plays the role of control. We ensure the approximate controllability between eigenstates in arbitrarily small time with respect to the $L^2-$norm. We use specific saturation properties to develop a multiplicative version of the geometric approach introduced for additive controls by Agrachev and Sarychev.

MS [02285] New Trends in Tensor Networks and Tensor Optimization

room : A208

• [03267] Efficient Machine Learning with Tensor Networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qibin Zhao (RIKEN AIP)
  • Abstract : Tensor Networks (TNs) are factorizations of high dimensional tensors into networks of many low-dimensional tensors, which have been studied in quantum physics, high-performance computing, and applied mathematics. In recent years, TNs have been increasingly investigated and applied to machine learning and signal processing, due to its significant advances in handling large-scale and high-dimensional problems, model compression in deep neural networks, and efficient computations for learning algorithms. This talk aims to present some recent progress of TNs technology applied to machine learning from perspectives of basic principle and algorithms, novel approaches in unsupervised learning, tensor completion, multi-model learning and various applications in DNN, CNN, RNN and etc.
• [05506] Accelerated Doubly Stochastic Gradient Descent for Tensor CP Decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Chunfeng Cui (Beihang University)
  • Abstract : In this talk, we focus on the doubly stochastic gradient descent (SGD) method for computing the canonical polyadic decomposition (CPD) of tensors. This method not only exploits the block structure of CPD but also enables us to handle large-scale tensors. Based on the momentum acceleration and the variance reduction technique, we propose several acceleration methods, including the heavy-ball acceleration, inertial acceleration, and variance reduction. We also present the global convergence and convergence rates of the proposed methods.
• [03184] Tensor network strcuture search
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Li (RIKEN)
  • Abstract : In this talk, we present a novel problem related to model selection for tensor networks, which we call tensor network structure search (TN-SS). TN-SS aims to find the optimal tensor network structure for a given dataset and task by exploring a large space of possible network structures. We propose several promising solutions to the TN-SS problem, including evolutionary algorithms, stochastic search, and alternating enumeration. Our methods are designed to efficiently explore the space of tensor network structures and identify the most promising candidates based on their performance on the given task.
• [04779] Towards Multi-modes Outlier Robust Tensor Ring Decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuning Qiu (Guangdong University of Technolog)
  • Abstract : The outliers assumption in conventional robust tensor decomposition is often not true in tensors since high-order tensors are prone to be corrupted by outliers in more than one direction. To mitigate this weakness, we propose a novel outlier robust tensor decomposition (ORTD) model by capturing low-rank tensors corrupted from multi-mode outliers. To theoretically guarantee statistical performance, we rigorously analyze a non-asymptotic upper bound of the estimation error for the proposed ORTD model.

MS [00391] Recent Advances in Multiscale Transforms for Image Analysis

room : A502

• [01735] Multiscale monogenic image representations using Poisson kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Brian Knight (University of California, Davis)
    • Naoki Saito (University of California, Davis)
  • Abstract : By viewing a 1D signal as the boundary value of a harmonic function in the unit disc in $\mathbb{C}$, one can obtain a multiscale analytic signal representation by supplementing its conjugate counterpart. This is done by the Poisson/Cauchy integral formula. We generalize this for a 2D image by sandwiching it by quaternionic Poisson/Cauchy kernels. This leads to a natural multiscale monogenic image representation. We also plan to discuss its application in oriented texture image analysis.
• [02090] Image Interpolation Technique by the PCA of the Gradient Distribution
  • Format : Talk at Waseda University
  • Author(s) :
    • Masaki Morita (Meijo University)
    • Yuto Kimura (Meijo University)
    • Katsu Yamatani (Meijo University)
    • Masayoshi Nakagawa (Meijo University)
  • Abstract : We propose a method to reconstruct local image patches with gradient data and boundary information. In this talk, we present an image interpolation technique based on the principal component analysis of the gradient distribution of image intensities. Our numerical experiments show superiority of our proposed method over previous method based on the interpolation using harmonic functions.
• [02079] Improvement of coding procedures for Haar transform-based lossy image compression
  • Format : Talk at Waseda University
  • Author(s) :
    • Keita Ashizawa (Shizuoka Institute of Science and Technology)
    • Katsu Yamatani (Meijo University)
  • Abstract : We discuss an improved version of our Multi−neighbor Predictors and Residual Orthogonal Transformations, MPROT, which was a Haar transform-based lossy image compression method without generating mosquito noise. Due to the slow decay of the Haar coefficients, however, the PSNR values of certain test images compressed by the MPROT were not entirely satisfactory. Our new coding scheme takes advantage of redundancy of the MPROT coefficients and improves high-resolution image compression quality.
• [02086] Edge enhancement with directional wavelet transform
  • Format : Talk at Waseda University
  • Author(s) :
    • Kensuke Fujinoki (Kanagawa University)
    • Keita Ashizawa (National Institute of Technology, Maizuru College)
  • Abstract : We introduce a two-dimensional directional discrete wavelet transform that can decompose an image into twelve multiscale nearly isotropic directional edge components. The transform is designed in fully discrete setting and therefore is easy to implement in the spatial domain. Experimental results for image edge detection and enhancement show that both global and local edge structures of images are successfully represented.

MS [00114] Computational Biology

room : A508

• [04349] Mathematical model of mTORC1 pathway sensing intracellular amino-acids and glucose
  • Format : Talk at Waseda University
  • Author(s) :
    • Takanori Nakamura (Ehime University)
    • Shigeyuki Nada (Osaka University)
    • Takashi Suzuki (Osaka University)
    • Masato Okada (Osaka University)
  • Abstract : mTORC1, a master regulator of metabolism, is activated upon Insulin and Amino-acids (AA) addition, but its regulatory mechanism is not fully understood. We therefore constructed an integrated mathematical model of mTORC1 regulation through the two distinct AA- and Insulin-sensing axes. Using the mathematical simulation with experimental data, we found the selective dephosphorylation during AA deprivation, which ensures full mTORC1 activation only upon the concurrently sensing of nutrient Insulin and AA.
• [05379] Mathematical modeling of cancer immune escape
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Haeno (Tokyo University of Science)
    • Koichi Saeki (Tokyo University of Science)
  • Abstract : A tumor evolves under the pressure of immune responses. Immune checkpoint inhibitors (ICIs) are expected to reactivate antitumor immunity and inhibit tumor progression. Here, we developed a mathematical model of the tumor evolution under immune responses. As a result, we confirmed that patients who had high mutational load were likely to have a durable benefit. Moreover, we found that the growth rate of tumor cells would be informative to identify responders to ICIs.
• [02179] Computational modelling of cancer invasion using organotypic invasion assay data
  • Format : Talk at Waseda University
  • Author(s) :
    • Mark Chaplain (University of St Andrews)
    • Nikoloas Sfakianakis (University of St Andrews)
    • Linnea Franssen (Roche, Basel)
  • Abstract : We present computational simulation results from a three-dimensional hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between these cell phenotypes. The full model consists of a hybrid system of partial and stochastic differential equations describing the evolution of cancer cells, extracellular matrix and matrix-degrading enzymes.
• [05467] The prognostic value of immune infiltration patterns on the outcome of chemotherapy in breast cancer
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nikolaos Ioannis Kavallaris (Karlstad University)
  • Abstract : In this work, based on a breast cancer biopsy dataset, taken from the ADAPT clinical trial, we shed light on the changes of tumor microenvironment after cytostatic chemotherapy. We combine machine learning workflow to identify cell density patterns identifying responders and non-responders. We also develop a dynamic model that allows us to elucidate the reasons of therapy failure. Finally, using our model we can reason on therapy combinations that could improve the therapeutic outcomes.

MS [00739] Inequalities and entropy with applications

room : A510

• [01998] The reduced quantum relative entropy
  • Format : Talk at Waseda University
  • Author(s) :
    • Frank Hansen (University of Copenhagen)
  • Abstract : We introduce the notion of reduced relative quantum entropy and prove that it is convex. The result is used to give a simplified proof of a theorem of Lieb and Seiringer. We then proceed to describe an interpolation inequality between Golden-Thompson’s trace inequality and Jensen’s trace inequality.
• [02970] On the quantum Tsallis relative entropy of real order
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Seo (Osaka Kyoiku University)
  • Abstract : In 2005, Furuichi-Yanagi-Kuriyama showed 1-parameter extension of matrix trace inequalities due to Hiai-Petz, and it revealed relationships between two quantum Tsallis relative entropies. In this talk, we show matrix trace inequalities related to quantum Tsallis relative entropy of real order, and improve on Furuichi-Yanagi-Kuriyama's result by using Furuta inequality.
• [02482] On log-sum inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • Supriyo Dutta (National Institute of Technology Agartala)
    • Shigeru Furuichi (Nihon University)
  • Abstract : I shall present our recently published article entitled "On log-sum inequalities" in Linear and Multilinear Algebra. The log-sum inequality is a fundamental tool which indicates the nonnegativity for the relative entropy. We establish a set of inequalities which are similar to the log-sum inequality. We extend these inequalities for the commutative matrices. In addition, utilizing the L ̈owner partial order relation and the Hansen-Pedersen theory for non-commutative positive semi-definite matrices we demonstrate several matrix-inequalities.
• [02313] On certain properties of Shannon's Entropy
  • Format : Talk at Waseda University
  • Author(s) :
    • Eleutherius Symeonidis (Faculty of Mathematics and Geography, Catholic University of Eichstaett-Ingolstadt)
  • Abstract : Let $P:=(p_1,\ldots,p_n)$ be a discrete probability distribution, $$ H(P):=-\sum_{j=1}^n p_j \log p_j $$ its Shannon entropy. Motivated by studies on the permutation entropy of time series of temperatures in combustion experiments we fix an integer $k$, $1\le k\le n$, and consider the largest set $\Delta\subset {\mathbb R}^k$ such that $$ H(p_1,\ldots,p_{n-k},p_{n-k+1},\ldots,p_n)\ge H\left(0,\ldots,0,\frac{1}{k},\ldots,\frac{1}{k}\right)\;(=\log k) $$ for all $P$ such that $(p_{n-k+1},\ldots,p_n)\in\Delta$. In particular, we are interested in the smallest value of $p$ such that $(p,\ldots,p)\in\Delta$.

contributed talk: CT179

room : A511

[00463] A kinetic model of crowd evacuation dynamics coupled with infectious disease contagion

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A511
• Type : Contributed Talk
• Abstract : We propose a kinetic theory model coupling crowd evacuation and disease spreading. Movement of individuals is modeled by a description of interactions among individuals. Interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and awareness to contagion is also considered. The model is qualitatively studied and different scenarios related to gathering formation within indoor venues under the spread of an infectious disease are explored.
• Classification : 92-10, 92C60, 92D30
• Format : Talk at Waseda University
• Author(s) :
  • Juan Pablo Agnelli (CIEM CONICET & FaMAF Universidad Nacional de Córdoba)
  • Bruno Buffa (FaMAF Universidad Nacional de Córdoba)
  • Damian Alejandro Knopoff (CONICET, Argentina & Intelligent Biodata SL, Spain)
  • German Torres (IMIT CONICET & FaCENA UNNE)

[00620] Development of an ion channel model-framework

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A511
• Type : Contributed Talk
• Abstract : Ion channels in cell membranes are of ultimate importance in physiology. They control a large fraction of biological processes and are mainly investigated by current-voltage experiments. To support the interpretation of measured results, we develop a model-framework based on non-equilibrium thermodynamics that accounts for various important aspects, e.g., finite-volume effects and the surface charges of the channel. Julia-based numerical simulations are performed to compute current-voltage relations, with varying ion concentrations, applied voltages, and channel properties.
• Classification : 92-10, 92C40, 92-08
• Format : Talk at Waseda University
• Author(s) :
  • Christine Keller (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))
  • Juergen Fuhrmann (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))
  • Manuel Landstorfer (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))
  • Barbara Wagner (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))

[00677] Mathematical Epidemiology as a decision tool

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A511
• Type : Industrial Contributed Talk
• Abstract : Mathematics is a powerful tool for tackling real world problems; concretely, we are interested in monitoring epidemics. Some members of the MOMAT Research Group -Complutense University of Madrid- have worked in collaboration with veterinary groups, healthcare companies and public entities of the Spanish healthcare system. In this talk, we present some mathematical models developed by this research group for both animal -e.g., Classical Swine Fever, Bluetongue- and human -e.g., COVID-19, Ebola- infectious diseases.
• Classification : 92-10, 92Dxx, Mathematical Epidemiology
• Format : Talk at Waseda University
• Author(s) :
  • Alicja B. Kubik (Universidad Complutense de Madrid)
  • Benjamin Ivorra (Universidad Complutense de Madrid)
  • Angel M. Ramos (Universidad Complutense de Madrid)
  • María Vela-Pérez (Universidad Complutense de Madrid)
  • Miriam R. Ferrández (Instituto de Matemática Interdisciplinar)

[00438] Network stability in co-evolved spatially-explicit model ecological communities

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A511
• Type : Contributed Talk
• Abstract : The self-assembly of ecological communities on complex spatial networks from an initial species can be mathematically modelled by a combination of ecological and evolutionary processes. We investigate how the topology of the spatial network influences the structure of the co-evolved populations, and hence the stability of the resulting meta-community of species against perturbations including invasion, extinction, patch removal, and alterations to the spatial environment. In response, different nature reserve configurations can simulate biodiversity conservation strategies.
• Classification : 92-10, 37N25
• Format : Online Talk on Zoom
• Author(s) :
  • Gavin Michael Abernethy (University of Stirling)

[00745] Fluid flow and nutrient transport in hollow fibre membrane bioreactors

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A511
• Type : Contributed Talk
• Abstract : We present an axisymmetric model of fluid flow through a hollow fibre membrane bioreactor for applications in tissue engineering. We derive a reduced model by exploiting the small aspect ratio of bioreactor radius to length. Coupled to a system of reduced-order advection-reaction-diffusion equations for nutrient transport, we reveal how nutrient delivery to cells depends on membrane permeability. We then determine how spatial variations in scaffold permeability can be established to tune nutrient delivery to cells.
• Classification : 92-10, 92C35, 76Z05, 92C50, 76D08, Tissue Engineering
• Format : Online Talk on Zoom
• Author(s) :
  • George Booth (University of Oxford)
  • Mohit Dalwadi (University College London)
  • Cathy Ye (University of Oxford)
  • Pierre-Alexis Mouthuy (University of Oxford)
  • Sarah Waters (University of Oxford)

MS [00955] Incorporating Immune System and Heterogeneous Dynamics into Infectious Disease Modeling

room : A512

• [04157] Basic concepts for the Kermack and McKendrick model with individual heterogeneity
  • Format : Talk at Waseda University
  • Author(s) :
    • Hisashi Inaba (Tokyo Gakugei University)
  • Abstract : The main purpose of my talk is to provide a mathematical basis for the recent arguments and calculations triggered by COVID-19 based on the heterogeneous Kermack-McKendrick model. The basic epidemiological concepts such as basic reproduction number, effective reproduction number, herd immunity threshold and final size are rigorously formulated based on the Kermack-McKendrick model with individual heterogeneity. Furthermore, we discuss a systematic recipe to reduce the infinite-dimensional system to the finite-dimensional ODE system.
• [04524] Statistical analysis of global COVID-19 wave dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Jessica Stockdale (Simon Fraser University)
  • Abstract : Different countries around the world experienced vastly different COVID-19 pandemics, and in many cases the complex interplay of driving forces behind this remain unclear. Patterns of hybrid and partial immunity affect the ability of new variants to invade, and therefore must be understood to build insightful predictive models. I will present our work in statistically modelling the relative influence of immunity, demographic, social, and other factors on the size and timing of variant-driven COVID-19 waves.
• [03113] Will cross-immunity protect the community from COVID-19 variants?
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marina Mancuso (Arizona State University)
    • Steffen Eikenberry (Arizona State University)
    • Abba Gumel (University of Maryland, College Park)
  • Abstract : The emergence of SARS-COV-2 variants threaten the efficacy of COVID-19 vaccines. Not only can variants be potentially more infectious than the wild-type strain, but they may also partially evade existing vaccines. A two-strain, two-group mechanistic mathematical model is designed to assess the impact of vaccine-induced, cross-protective efficacy of COVID-19 transmission in the United States. We present conditions for achieving vaccine-derived herd immunity and results from global sensitivity analysis under different transmissibility and cross-protection scenarios.
• [04936] SARS-CoV-2 variant transition dynamics are associated with vaccination rates, number of co-circulating variants, and convalescent immunity
  • Format : Talk at Waseda University
  • Author(s) :
    • Sara Del Valle (Los Alamos National Laboratory)
  • Abstract : I will discuss a retrospective analysis that characterized differences in the speed, timing, and magnitude of 16 SARS-CoV-2 variant waves/transitions for 230 regions, between October 2020 and January 2023. Our results show associations between the behavior of an emerging variant and the number of co-circulating variants as well as demographics and vaccination rates. These results suggest the behavior of a variant may be sensitive to the immunologic and demographic context of its location.

contributed talk: CT180

room : A601

[00300] Coupling macro-micro simulations in complex fluids

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : Some of the most remarkable properties and functions served by some complex fluids originate from the interplay between external fields and microstructural dynamics. From a computational point of view this generates a set of challenges related to the need of coupling dynamics at different length and times scales, sometimes spanning several orders of magnitude. Micro-macro simulations have gained a lot of recognition within the field because these methods allow capturing full dynamics at the macroscale without losing resolution at the microscale. In this talk, we will review our efforts to couple existing macroscopic solvers for the Navier-Stokes equations with microstructural dynamics described by Langevin-type equations. In particular, we will discuss dumbbells models -under viscometric and capillary thinning flows fields- and parallel computing using GPUs.
• Classification : 92B05, 76A05, 76A10, 76D05, 97M60
• Format : Talk at Waseda University
• Author(s) :
  • Paula A Vasquez (University of South Carolina)
  • Michael Cromer (RIT)

[00035] Effects of toxicity and zooplankton selectivity under seasonal pattern of viruses on plankton dynamics

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : A mathematical model for the interacting dynamics of phytoplankton-zooplankton is proposed. The phytoplankton have ability to take refuge and release toxins to avoid over predation by zooplankton. The zooplankton are provided some additional food to persist in the system. The phytoplankton are assumed to be affected directly by an external toxic substance whereas zooplankton are affected indirectly by feeding on the affected phytoplankton. We incorporate seasonal variations in the model, assuming the level of nutrients, refuge and the rate of toxins released by phytoplankton as functions of time. Our results show that when high toxicity and refuge cause extinction of zooplankton, providing additional food supports the survival of zooplankton population and controls the phytoplankton population. Prey refuge and additional food have stabilizing effects on the system; higher values of the former results in extinction of zooplankton whereas phytoplankton disappear for larger values of the latter. Seasonality in nutrients level and toxins released by phytoplankton generates higher periodic solutions while time-dependent refuge of phytoplankton causes the occurrence of a period-three solution. The possibility of finding additional food for zooplankton may push back the ecosystem to a simple stable state from a complex dynamics.
• Classification : 92B05, 92D25, 92D30, 37A50, 34D05
• Format : Online Talk on Zoom
• Author(s) :
  • Samares Pal (University of Kalyani)

[00375] Modelling Typhoid Fever Transmission: Optimal control and Cost-Effectiveness Analysis

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Industrial Contributed Talk
• Abstract : Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of limited clinical efficacy of antibiotics administer to patients suffering from the disease with optimal control and cost-effectiveness analysis. Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of clinical efficacy of antibiotics administer to patients suffering from the disease. The basic reproduction number is analytically computed, and existence and local stability condition of disease-free equilibrium is investigated. Subsequently, the global sensitivity analysis of the model parameters is computed. The optimal control and cost-effectiveness analysis were also computed. Our results suggest that hygiene practice and awareness campaign, and disinfection or sterilization or bacteria decay control is the most cost-effective in eliminating the disease from the population and from preventing the susceptible individuals from contracting the bacteria disease.
• Classification : 92BXX, 92-XX, 92-10, 91-XX, 91-10, Mathematical modeling of infectious disease(Biomathematics)
• Author(s) :
  • kazeem Austin TIJANI (Federal University of Agriculture(J. S Tarka university), Makurdi)
  • Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria )
  • Iortyer Reuben GWERYINA (Federal university of Agriculture(J.S. Tarka University), Makurdi))

[00892] Predicting response to pediatric leukemia with flow cytometry data

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : 15% of children with B-cell acute lymphoblastic leukemia fail to achieve response or long-term remission. With new treatments being developed to provide an alternative for this subset of patients, an improved risk classification at diagnosis can help to plan and prepare for this eventuality. Flow cytometry is currently used to characterize the leukemic clone but it has no prognosis value. In this work we use flow cytometry data at diagnosis from 250 pediatric patients from hospitals in Spain to find features associated with response by means of an array of computational methods.
• Classification : 92Bxx
• Author(s) :
  • Alvaro Martínez-Rubio (University of Cadiz)
  • Salvador Chulián (University of Cádiz)
  • Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
  • Víctor Manuel Pérez-García (University of Castilla-La Mancha)
  • María Rosa (University of Cadiz)

MS [00498] Approximation and modeling with manifold-valued data

room : A615

• [05093] Multivariate Hermite Intepolation On Riemannian Manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Ralf Zimmermann (University of Southern Denmark)
    • Ronny Bergmann (NTNU, Trondheim)
  • Abstract : We consider two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing weighted Riemannian barycenters. This approach is intrinsic in the sense that it does not depend on local coordinates. As an alternative, we consider straightforward Hermite interpolation in a tangent space. Here, the actual interpolation is conducted via classical vector space operations. Both approaches are illustrated by means of numerical examples.
• [01628] Approximations and learning in the Wasserstein space
  • Format : Talk at Waseda University
  • Author(s) :
    • Caroline Moosmueller (University of North Carolina at Chapel Hill)
    • Alexander Cloninger (University of California, San Diego)
    • Varun Khurana (University of California, San Diego)
    • Harish Kannan (University of California, San Diego)
    • Keaton Hamm (University of Texas at Arlington)
  • Abstract : Detecting differences and building classifiers between distributions, given only finite samples, are important tasks in a number of scientific fields. Optimal transport and the Wasserstein distance have evolved as the most natural concept in dealing with such tasks, but they also have some computational drawbacks. In this talk, we describe an approximation framework through local linearizations that significantly reduces both the computational effort and the required training data in supervised learning settings.
• [05075] On multiscale quasi-interpolation of scattered scalar- and manifold-valued functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Nir Sharon (Tel Aviv University)
    • Holger Wendland (University of Bayreuth)
  • Abstract : In this talk, we introduce and analyze a combination of kernel-based quasi-interpolation and multiscale approximations for both scalar- and manifold-valued functions. We are particularly interested in the improvements coming from such a combination over simply using quasi-interpolation processes alone. We provide ample numerical evidence that multiscale quasi-interpolation has superior convergence to quasi-interpolation. In addition, we will provide examples showing that the multiscale quasi-interpolation approach offers a powerful tool for data analysis tasks.
• [03824] The de Casteljau algorithm on symmetric spaces
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fátima Silva Leite (Institute of Systems and Robotics, University of Coimbra)
    • Knut Huper (Institute of Mathematics, Julius-Maximilians-Universitat Wurzburg)
  • Abstract : An important task for interpolation problems in many areas of science and technology is the computation of smooth curves connecting two data points in a Riemannian symmetric space. For instance, the de Casteljau algorithm on manifolds, which is a geometric procedure to generate smooth polynomial splines, is based on recursive geodesic interpolation. Also in statistics, the efficient computation of (geometric) means of data in a symmetric space, as well as the computation of midpoints of smooth curves connecting two data points, is particularly important. While closed form solutions for the so called endpoint geodesic problem on general symmetric spaces are well known, often explicit exponentiation of matrices and/or SVD computations are still required. In most cases, these computations are rather expensive. We present much simpler closed form expressions for the particular case of Grassmannians, where only constant, linear and quadratic functions in the data points and scalar trigonometric functions are involved. This represents an important step in the implementation of the de Casteljau algorithm. We also comment on the general idea putting other important symmetric spaces, compact and noncompact ones, into perspective.

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

room : A618

• [00119] Weak and entropy solutions of time-fractional porous medium type equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Petra Wittbold (University of Duisburg-Essen)
  • Abstract : We present results on existence and uniqueness of bounded weak and also unbounded entropy solutions to a degenerate quasilinear subdiffusion problem of porous medium type with bounded measurable diffusion coefficients that may explicitly depend on time. The integro-differential operator in the equation includes, in particular, the time-fractional derivative case. A key ingredient in the proof of existence is a new compactness criterion of Aubin-Lions type which involves the non-local in time operator.
• [00167] On different formulations for time-fractional Stefan problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sabrina Roscani (CONICET - Universidad Austral)
  • Abstract : We present a one-dimensional fractional Stefan problem for a memory flux derived from thermodynamic balance statements and provide a memory enthalpy formulation related to the previous model. The Stefan condition for each problem at the free interface is analyzed and numerical simulations obtained from the enthalpy model are given.
• [00163] Numerical methods for nonlocal and nonlinear parabolic equations with applications in hydrology and climatology
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lukasz Plociniczak (Wroclaw University of Science and Technology)
  • Abstract : We present some of our results concerning numerical discretizations of nonlinear and fractional in time parabolic equations. Along with a collection of various methods and statements about their convergence and stability, we stress their motivation and real-world applications.
• [00160] Regularity of weak solutions to parabolic-type problems with distributed order time-fractional derivative
  • Format : Online Talk on Zoom
  • Author(s) :
    • Katarzyna Ryszewska (Warsaw University of Technology)
  • Abstract : In this talk we will discuss Holder continuity of weak solutions to evolution equations with distributed order time-fractional derivative. It is a generalization of the result for a single order fractional derivative obtained by Prof. Zacher in 2010. The main difficulty to overcome in this case, is the lack of a natural scaling property of the equation. This is a joint work with Adam Kubica and Prof. Rico Zacher.