[02626] Use of Origami Maths for minimizing packing & wrapping cost
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G301
Type : Contributed Talk
Abstract : By using the knowledge of mathametical Origami &Kirigami ( Japanese art using principles of topology, operational research & statistics) An analytical study was done to make 3D boxes,in triangular,cubical,spherical,Polihedron etc.shape with maximum volumes and minimum raw material. Boxes of different shape may be made by twisting & folding. Pop up boxes, cartons& Mobius strips can also be made by the same method to minimize the cost of packing & wraping of manufactured products.
[00756] Using photogrammetry for the objective morphological study of early violins
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G301
Type : Contributed Talk
Abstract : Some early violins were reduced during their history to fit imposed morphological standards. We propose an objective photogrammetric approach to differentiate between a reduced and an unreduced instrument by examining 3D meshes, previously validated with a sub-millimetre accuracy through a comparison with CT scans. We show how quantitative and qualitative features can be automatically extracted from the meshes with geometrical, statistical and machine learning tools, allowing to successfully highlight differences between reduced and unreduced instruments.
[02412] Randomized algorithms of AND-OR tree calculation regarding query complexity
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G301
Type : Contributed Talk
Abstract : We discuss the randomized algorithm of AND-OR tree calculation. It is known that for any nontrivial balanced AND-OR tree, there is a unique randomized input (eigen-distribution) which achieves the distributional complexity. In contrast, the dual problem has the opposite result; the optimal randomized algorithm is not unique. We extend the study on randomized algorithms to unbalanced cases and see that uniqueness still fails in most of the cases.
[01582] Parameter Estimation in Mathematical Models Using Uncertainty and Sensitivity Analyses
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G301
Type : Contributed Talk
Abstract : The accurate estimation of uncertain parameters in a mathematical model is still considered a laborious task. We propose a systematic methodology based on uncertainty and sensitivity analyses framework applied on a dynamic population balance model representing a crystallization process for the precise estimation of model parameters. For models involving many uncertain parameters, the proposed strategy can be adopted to rank parameters by their decreasing importance and then achieve precise estimation of the more significant parameters.
PRIYANKA SEHRAWAT (Indian Institute of Technology Kharagpur)
Priyanka Sehrawat (Indian Institute of Technology Kharagpur)
Debasis Sarkar (Indian Institute of Technology Kharagpur)
Jitendra Kumar (Indian Institute of Technology Ropar)
MS [02060] Topics in extremal graph theory
room : G302
[02678] Spanning trees in sparse pseudorandom graphs
Format : Online Talk on Zoom
Author(s) :
Jie Han (Beijing Institute of Technology)
Donglei Yang (Shandong University)
Abstract : Let $\mathcal{T}(n, \Delta)$ be the class of trees with $n$ vertices and maximum degree at most $\Delta$. Confirming a conjecture of Kahn, Montgomery established for every fixed tree $T\in\mathcal{T}(n, \Delta)$, the smallest value of $p$ for which $G(n, p)$ a.a.s. contains a copy of $T$. There have been a wealth of results and open problems on embedding spanning trees in (pseudo)random graphs in the past few decades. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap forcing an $(n, d, \lambda)$-graph to be $\mathcal{T}(n, \Delta)$-universal. In this talk, we introduce some recent works and open questions. Similar questions for expander graphs are also considered.
[03075] Extremal results on 4-cycles
Format : Talk at Waseda University
Author(s) :
Tianchi Yang (National University of Singapore)
Abstract : The study of 4-cycles has important implications for the progression of Turan type problems, particularly in their degenerate forms. In this presentation, novel upper bounds are derived for the maximum number of edges in n-vertex graphs without cycles of length four. These findings not only augment our comprehension of combinatorial structures but also disprove certain conjectures of Erdos.
[03224] Many Hamiltonian subsets in large graphs with given density
Format : Talk at Waseda University
Author(s) :
Stijn Cambie (Institute for Basic Science)
Jun Gao (Institute for Basic Science)
Hong Liu (Institute for Basic Science)
Abstract : A set of vertices in a graph is a Hamiltonian subset if it induces a subgraph containing a Hamiltonian cycle. Kim, Liu, Sharifzadeh and Staden proved that among all graphs with minimum degree $d$, $K_{d+1}$ minimises the number of Hamiltonian subsets. We prove a near optimal lower bound that takes also the order and the structure of a graph into account. For many natural graph classes, it provides a much better bound than the extremal one ($\approx 2^{d+1}$). Among others, our bound implies that an $n$-vertex $C_4$-free graphs with minimum degree $d$ contains at least $n2^{d^{2-o(1)}}$ Hamiltonian subsets.
This is a joint work with Stijn Cambie and Hong Liu.
[03146] Balanced Subdivisions in Graphs
Format : Talk at Waseda University
Author(s) :
Donglei Yang (Shandong University)
Abstract : A balanced subdivision of a graph H is obtained from $H$ by equally subdividing every edge. In 1984, Thomassen conjectured that for each integer $k\ge 1$, high average degree forces a balanced subdivision of $K_k$, and this was recently resolved by Liu and Montgomery. We give an optimal estimate on the average degree condition forcing every balanced $H$-subdivision, resolving a question of Fern\'{a}ndez et al. Similar problems on clique immersions are also considered.
MS [01029] Extremal Combinatorics and Probabilistic Combinatorics
room : G304
[03243] Turan problem for graphs from geometric shapes
Format : Talk at Waseda University
Author(s) :
Hong Liu (Institute for Basic Science)
Abstract : While Tur\'{a}n type problem is the most studied topic in extremal combinatorics, some of the most basic bipartite degenerate Tur\'{a}n problems remain elusive. In this talk, I will discuss some recent advancements on this topic and new results on bipartite graphs arising from geometric shapes and periodic tilings commonly found in nature, including even prisms, planar hexagonal tiling and quadrangulations of plane, cylinder and torus. This is joint work with Jun Gao, Oliver Janzer, Zixiang Xu.
[03233] Robust linear algebra methods and some applications
Format : Talk at Waseda University
Author(s) :
Jun Gao (Institute for Basic Science)
Hong Liu (Institute for Basic Science)
Zixiang Xu (Institute for Basic Science)
Abstract : Given a set $L\subseteq [n]$, what can we say about the size or structure of a set system $\mathcal{F}\subseteq 2^{[n]}$ if $A\star B\in L$ for $A,B\in\mathcal{F}$, where $\star\in\{\cap,\cup,\setminus,\triangle\}$. Many important results have been produced around the above questions, and several far-reaching methods have been developed. In this talk, I will explain how to apply the linear algebra methods in the above problems, and introduce an algebraic proof of the stability result for Kleitman's theorem.
[03332] Optimal bisections of directed graphs
Format : Talk at Waseda University
Author(s) :
Guanwu Liu (University of Science and Technology of China)
Jie Ma (University of Science and Technology of China)
Chunlei Zu (Shanghai Jiaotong Univerisity)
Abstract : In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with $m$ arcs and minimum semidegree at least $d$ admits a bisection in which at least $\left(\frac{d}{2(2d+1)}+o(1)\right)m$ arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu in a stronger form.
[03231] Hypergraphs with infinitely many extremal constructions
Format : Online Talk on Zoom
Author(s) :
JIANFENG HOU (Fuzhou University)
Abstract : We give the first exact and stability
results for a hypergraph Tur\'{a}n problem with infinitely many extremal constructions
that are far from each other in edit-distance.
This includes an example of triple systems with Tur\'{a}n density $2/9$,
thus answering some questions posed by the third and fourth authors and Reiher about the feasible region of hypergraphs. Our results also provide extremal constructions whose shadow density is a transcendental number.
Our novel approach is to construct certain multilinear polynomials that attain
their maximum (in the standard simplex) on a line segment and then to use these polynomials to define an operation on hypergraphs that gives extremal constructions.
MS [00970] High Performance Linear Algebra Software toward Extreme Heterogeneity
room : G305
[03921] Using the StarPU task-based runtime system for heterogeneous platforms as the core engine for a linear algebra software stack.
Format : Talk at Waseda University
Author(s) :
Olivier Aumage (Inria)
Abstract : StarPU is a runtime system developed by Team STORM at Inria in Bordeaux,
France, to support computing platforms based on heterogeneous
architectures composed of combination of CPUs, GPUs and FPGAs. This talk
will present how the Sequential Task Flow programming model offered by
StarPU is being used to build a scalable, comprehensive linear algebra
software stack for heterogeneous supercomputers.
[04285] A Look at the Future of High-Performance Linear Algebra with DPLASMA and PaRSEC
Format : Online Talk on Zoom
Author(s) :
george bosilca (The University of Tennessee)
Abstract : This talk will focus on the dataflow programming to address some of the linear algebra challenges. I will focus in particular on two open-source projects, the PaRSEC runtime and the DPLASMA dense linear algebra library, and discuss the programming approach, the handling of heterogeneity and the opportunities to cover a large spectrum of linear algebra needs.
[04413] Multiple- and Mixed-Precision BLAS with C++ Template
Format : Talk at Waseda University
Author(s) :
Toshiyuki Imamura (RIKEN Center for Computational Science)
Daichi Mukunoki (RIKEN Center for Computational Science)
Atsushi Suzuki (RIKEN Center for Computational Science)
Abstract : We propose a new design for BLAS that can handle multiple- and mixed-precision computations. Our templated mixed-precision BLAS (tmBLAS) addresses weaknesses in existing BLAS by decoupling the data types of each operand and operator using C++ generic programming, with explicit descriptions of operators and type-castings. We demonstrate a prototype implementation that instantiates routines with FP{16, 32, 64, 128}, and DD data types with those operations in one level with higher precision than the data precision.
[05194] MatRIS: A Scalable and Performance Portable Math Library for Heterogeneous and Multi-Device Systems based on the IRIS Runtime
Format : Talk at Waseda University
Author(s) :
Keita Teranishi (Oak Ridge National Laboratory)
Pedro Valero-Lara (Oak Ridge National Laboratory)
Abstract : Vendor libraries are tuned for one architecture and are not portable to others. Moreover, these lack support for heterogeneity and multi-device computation orchestration. We introduce MatRIS, a scalable and performance portable library for sparse/dense BLAS/LaPACK operations to address these challenges. MatRIS separates linear algebra algorithms and vendor libraries by using IRIS runtime. Such abstraction makes the implementation completely agnostic to the vendor libraries/architectures, providing high programming productivity. We demonstrate that MatRIS can fully utilize different multi-device heterogeneous systems, achieving high performance and scalability on three heterogeneous systems, Summit (#5 TOP500), Frontier (#1 TOP500), and CADES with four NVIDIA A100 GPUs and four AMD MI100 GPUs. A detailed performance study is presented for sparse and dense LU factorization where MatRIS provides a speedup of up to 8× from the previous version of the library (LaRIS). Along with better scalability, MatRIS provides competitive and even better performance than vendor libraries.
MS [00484] Matrix Analysis and Applications
room : G306
[01267] Combinatorial Perron Parameters and Classes of Trees
Format : Talk at Waseda University
Author(s) :
Enide Cascais Andrade (CIDMA, University of Aveiro, Portugal)
Lorenzo Ciardo (University of Oxford)
Geir Dahl (University of Oslo)
Abstract :
The main goal of this talk is to present recent results related with the combinatorial Perron
parameters
introduced in previous papers for certain classes of trees, and related bounds for these parameters.
These parameters are related to algebraic connectivity of trees and corresponding centers.
[01379] Poset matrices and associated algebras
Format : Talk at Waseda University
Author(s) :
Gi-Sang Cheon (Sungkyunkwan University)
Abstract : We introduce the constructions of poset matrices by defining several partial compositions on the species of poset matrices. Some of these partial composition operations are shown to define a set operad structure. We also obtain various matrix algebras obtained from incidence algebras of Riordan posets.
[01266] Majorization orders for $(0,\pm 1)$-matrices
Format : Talk at Waseda University
Author(s) :
Geir Dahl (University of Oslo)
Alexander Guterman (Bar-Ilan University)
Pavel Shteyner (Bar-Ilan University)
Abstract : Matrix majorization is a generalization of classical majorization for vectors; an important notion in many areas of mathematics. The talk gives some majorization background, and then presents a study of matrix majorization for $(0, \pm 1)$-matrices, i.e., matrices whose entries are restricted to $0$, $1$ and $-1$. In particular, we characterize when the zero vector is weakly majorized by a matrix, and discuss related results. Different connections are discussed, and characterizations of majorization are given.
[00830] The ranks and decompositions of quaternion tensors
Format : Talk at Waseda University
Author(s) :
Yang Zhang (University of Manitoba)
Yungang Liang (University of Manitoba)
Abstract : Quaternion tensors have attracted more and more attentions in recent years. Many applications have been found in various areas. In this talk, we discuss the maximal ranks of quaternion tensors, in particular, the third-order case. We also investigate the canonical forms, CP and Tucker decompositions of some quaternion tensors.
MS [00294] Machine Learning and Differential Equations
room : G401
[05167] Fourier Neural Poisson Reconstruction
Format : Talk at Waseda University
Author(s) :
Aras Bacho (Ludwig-Maximilians-Universität München)
Abstract : 3D Shape Poisson reconstruction is a method for recovering a 3D mesh from an oriented point cloud by solving the Poisson equation. It is widely used in industrial and academic 3D reconstruction applications, but typically requires a large number of points for a reasonable reconstruction. In this talk, I will present a new approach that utilizes Fourier Neural Operators to improve Poisson reconstruction in the low and middle-sampling regime. This method outperforms existing methods in terms of reconstructing fine details and is also resolution-agnostic. This allows for training the network at lower resolutions with less memory usage and evaluating it at higher resolutions with similar performance with much less data points. Furthermore, we demonstrate that the Poisson reconstruction problem is well-posed on a theoretical level by providing a universal approximation theorem for the Poisson problem with distributional data utilizing the Fourier Neuronal Operator which underpins our practical findings.
[01809] Certified machine learning: Rigorous a posteriori error bounds for physics-informed neural networks
Format : Talk at Waseda University
Author(s) :
Birgit Hillebrecht (SimTech, University of Stuttgart)
Benjamin Unger (SimTech, University of Stuttgart)
Abstract : Prediction error quantification has been left out of most methodological investigations of neural networks for both purely data-driven and physics-informed approaches. Beyond statistical investigations and generic a-priori results on the approximation capabilities of neural networks, we present a rigorous upper bound on the prediction error of physics-informed neural networks applied to linear PDEs. Our bound can be calculated without knowing the true solution and using only the characteristic properties of the underlying dynamical system.
[04004] Control of kinetic collective dynamics by deep neural feedback laws
Format : Talk at Waseda University
Author(s) :
Sara Bicego (Imperial College London)
Giacomo Albi (Università degli Studi di Verona)
Dante Kalise (Imperial College London)
Abstract : We address how to successfully condition high dimensional multi agent systems towards designed cooperative goals via dynamic optimization. The problem reads as the minimization of a cost functional subject to individual-based dynamics; thus, its solution becomes unfeasible as the number of agents grows. We propose a NN-accelerated Boltzmann scheme for approaching the solution from suboptimality. Under the quasi-invariant limit of binary interactions we approximate the mean field PDE governing the dynamics of the agents’ distribution.
[05373] Adaptive Time Stepping in Deep Neural Networks
Format : Talk at Waseda University
Author(s) :
Harbir Antil (George Mason University)
Hugo Diaz (University of Delaware)
Evelyn Herberg (University Heidelberg)
Abstract : We highlight the common features of optimal control problems with partial differential equations and deep learning problems. Furthermore, we introduce a new variable in the neural network architecture, which can be interpreted as a time step-size. The proposed framework can be applied to any of the existing networks such as ResNet or Fractional-DNN. This framework is shown to help overcome the vanishing and exploding gradient issues. The proposed approach is applied to an ill-posed 3D-Maxwell's equation.
MS [02470] Chaotic Supremacy Revolution
room : G402
[05241] Exactly Solvable Chaos and Its Use to Realize Chaotic Supremacy
Author(s) :
Ken Umeno (Kyoto University)
Abstract : Theory of exactly solvable chaos, whose ergodic invariant measure is explicitly obtained, is firstly
reviewed as a key concept to analyze chaotic supremacy analytically. Superefficient
chaotic Monte Carlo computation is one of the key examples to realize chaotic supremacy.
Then we discuss a possible relation between chaotic supremacy and quantum supremacy from the
view point of the connection of chaotic superefficiency realized by primitive root codes (discretization of exactly solvable chaos) with quantum Grover's algorithm.
[04036] Stable THz waves using laser chaos
Format : Talk at Waseda University
Author(s) :
Fumiyoshi Kuwashima (Fukui Univ. of Tech.)
Mona Jarrahi (Electrical and Computer Engineering Department, University of California Los Angeles)
Semih Cakmakyapan (Electrical and Computer Engineering Department, University of California Los Angeles)
Osamu Morikawa (Chair of Liberal Arts, Japan Coast Guard Academy)
Takuya Shirao (Fukui Univ. of Tech.)
Kazuyuki Iwao (Fukui Univ. of Tech.)
Kazuyoshi Kurihara (School of Education., University. of Fukui)
Hideaki Kitahara (Research Center for Development of Far-Infrared Region, University of Fukui)
Takashi Furuya (Research Center for Development of Far-Infrared Region, University of Fukui)
Yuki Kawakami ( National Institute of Technology (KOSEN), Fukui College)
Takeshi Moriyasu (UniversFaculty of Engineering, University of Fukuiity of Fukui)
Kenji Wada (Osaka Metropolitan University)
Makoto Nakajima (Institute of Laser engineering, Osaka Univ.)
Masahiko Tani ( Research Center for Development of Far-Infrared Region)
Abstract : Efficiency of optical beats in a chaotically oscillating laser is confirmed comparing that of free running CW laser using a highly efficient plasmonic photomixer. The great potential of chaotically oscillating lasers is verified for THz systems. This is one of the proof of Chaotic Supremacy in real system.
[04023] Application of entropic chaos degree to Lorenz system
Format : Talk at Waseda University
Author(s) :
Kei Inoue (Sanyo-Onoda City University)
Abstract : The entropic chaos degree was introduced to measure the chaos of a dynamical system in Information Dynamics. It is computable for any time series, even if the dynamical system is unknown. Recently the extended entropic chaos degree was proposed, equal to the total sum of the Lyapunov exponents under typical chaotic conditions. In this study, I try to measure the chaos of the Lorenz system by the extended entropic chaos degree.
[03810] Chaos-like behavior of two-dimensional optical bistable device with external feedback
Format : Talk at Waseda University
Author(s) :
Takashi Isoshima (RIKEN-CPR)
Abstract : Bistable system with a spatial expanse can provide a wavefront, an interface between two stable states, that can propagate. We investigate a two-dimensional optical bistable device (2DOBD) based on thermo-optical positive feedback for natural computing including maze exploration. Addition of external feedback to the device can realize complex spatio-temporal behavior. Refractory feedback, inspired by the refractory period of a nerve cell, provides propagating pulse generation, and under some condition, chaotic behavior of the pulses.
MS [01768] Computer-assisted proofs in differential equations
room : G405
[05292] Global Dynamics and Blowup in Some Quadratic PDEs
Format : Talk at Waseda University
Author(s) :
Jonathan Jaquette
Jean-Philippe Lessard (McGill University)
Akitoshi Takayasu (University of Tsukuba)
Abstract : Conservation laws and Lyapunov functions are powerful tools for proving the global existence of stability of solutions, but for many complex systems these tools are insufficient to completely understand non-perturbative dynamics. In this talk I will discuss a complex-scalar PDE which may be seen as a toy model for vortex stretching in fluid flow, and cannot be neatly categorized as conservative nor dissipative.
In a recent series of papers we have shown that this equation exhibits rich dynamical behavior that exist globally in time: non-trivial equilibria, homoclinic orbits, heteroclinic orbits, and integrable subsystems foliated by periodic orbits. On the other side of the coin, we show several mechanisms by which solutions can blowup. I will discuss these results, and current work toward understanding unstable blowup.
[05275] Worrisome Properties of Symbolic Representations of Deep Neural Network Controllers
Format : Talk at Waseda University
Author(s) :
Jacek Cyranka (Warsaw University)
Kevin Church ( Université de Montréal )
Jean-Philippe Lessard (McGill University)
Abstract : We studied dynamics of simple controlled problems like Pendulum and CartPole, where the controllers were trained using reinforcement learning algorithms. We raise concerns about symbolic controllers' robustness.
A typical symbolic controller reaching high mean return values still generates an abundance of unstabilized solutions, which is highly undesirable property, easily exploitable by an adversary. We provide an algorithm for a systematic robustness study and prove the unstabilized solutions and periodic orbits, using a computer-assisted proof methodology.
[05090] A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
Format : Talk at Waseda University
Author(s) :
Gabriel William Duchesne (McGill)
Abstract :
In this talk, we introduce a general constructive method to compute solutions of initial and boundary value problems of semilinear parabolic partial differential equations via semigroup theory and computer-assisted proofs. We will present techniques to prove the global existence of solutions in the 2D/3D Swift-Hohenberg equation and to prove the existence of a solution of a projected boundary value problem in the 2D Ohta-Kawasaki equation.
MS [01111] Mathematical and numerical analysis on blow-up phenomena
room : G501
[01625] On the convergence order of the numerical blow-up time
Author(s) :
Chien-Hong Cho (National Sun Yat-sen University)
Abstract : It is quite often that the solutions of initial-value problems become unbounded in a finite time. Such a phenomenon is called blow-up and the finite time is called the blow-up time. In this talk, we put our attention on the computation of an approximate blow-up time and its convergence order.
[01957] The blow-up curve for systems of semilinear wave equations
Author(s) :
Takiko Sasaki (Department of Mathematical Engineering, Faculty of Engineering, Musashino University and Mathematical Institute, Tohoku University)
Abstract : In this talk, we consider a blow-up curve for systems of semilinear wave equations with different propagation speeds in one space dimension. The blow-up curve has been studied from the view point of its differentiability and singularity. We show that the blow-up curve has a singular point under suitable initial conditions. We also show some numerical examples of blow-up curves.
[01774] Lifespan estimates of semilinear wave equations of derivative type with characteristic weights in one space dimension
Author(s) :
Shunsuke Kitamura (Tohoku University, Graduate School of Science)
Abstract : In this talk, I discuss the initial value problems for semilinear wave equations of derivative type with characteristic weights in one space dimension. Such equations provide basic principles on extending the general theory for nonlinear wave equations to the non-autonomous case. The results are quite different from the results of a series of joint work with Takamura, Wakasa and Morisawa about the nonlinear terms of unknown function itself.
[01740] On degenerate blow-up profiles for the semilinear heat equation
Author(s) :
Hatem Zaag (CNRS and Université Sorbonne Paris Nord)
Abstract : We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the origin, with a completely new blow-up profile, which is cross-shaped. Our method is general and extends to the construction of other solutions blowing up only at the origin, with a large variety of blow-up profiles, degenerate or not.
contributed talk: CT031
room : G502
[00502] The Helmholtz-Hodge decomposition of polynomial vector fields
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
Type : Contributed Talk
Abstract : The Helmholtz-Hodge decomposition is a fundamental tool in the study of vector fields and has many applications. In this talk, we will focus on the case of polynomial vector fields. First, we will introduce results on the general properties and methods for finding a decomposition. As an application, we will explain the relationship between the Helmholtz-Hodge decomposition and the construction of Lyapunov functions.
[00921] Inverse Coefficient Problem - Coupling Fourth and Second Order Equations
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
Type : Contributed Talk
Abstract : In this paper, the recovery of the diffusion coefficient from the final time-measured data is carried out using the quasi-solution approach. The inverse coefficient problem is formulated as a minimization problem using an objective functional. The existence of the minimizer is proved, then the necessary optimality condition is derived, and by using that condition, the stability results are proved. To illustrate the efficiency of this method, numerical results are investigated using the conjugate gradient method.
NAVANEETHA KRISHNAN M (CENTRAL UNIVERSITY OF TAMIL NADU, THIRUVARUR - 610005)
[00532] Pullback Operator Methods in Dynamical Systems: Theory and Computation
Session Time & Room : 4C (Aug.24, 13:20-15:00) @G502
Type : Contributed Talk
Abstract : Koopman operator methods along with the associated numerical algorithms have provided a powerful methodology for the data-driven study of nonlinear dynamical systems. In this talk, we will give a brief outline of how the Koopman group of operators can be generalized beyond function spaces to the space of sections of various vector bundles over the state space. We describe their relationship with the standard Koopman operator on functions as well as describe the new spectral invariants produced by these generalized operators. We then demonstrate how the recently developed spectral exterior calculus framework can be utilized to compute the spectral properties of the generator of the induced operator on sections of the cotangent bundle. We conclude with some applications of the algorithm to some well-known dynamical systems.
MS [00306] Mathematical approaches to nonlinear phenomena with singularities
room : G601
[04427] Crystalline inverse mean curvature flow
Format : Talk at Waseda University
Author(s) :
Marcos Solera Diana (Universidad Autónoma de Madrid/Universitat de València)
Abstract : We obtain existence of minimizers for the $p$-capacity functional defined with a symmetric anisotropy for $1 < p<\infty$ and the associated Euler-Lagrange equation. After a change of variables and letting $p\downarrow 1$ we are led to the existence of solutions to the elliptic PDE associated with the level set formulation of the crystalline inverse mean curvature flow.
[04365] Pseudo-parabolic model of grain boundary motion coupled with solidification effect
Format : Talk at Waseda University
Author(s) :
Daiki Mizuno (Chiba University)
Ken Shirakawa (Chiba University)
Abstract : In this talk, we consider a coupled nonlinear system, which consists of an Allen-Cahn type equation and a pseudo-parabolic KWC type system. The system is based on the $\phi$-$\eta$-$\theta$ model of grain boundary motion with solidification (cf. RIMS Kokyuroku, 1210, 2001). Under suitable assumptions, the mathematical results concerned with the well-posedness, including open question of uniqueness, and fine-regularity of the solution will be discussed in the Main Theorems of this talk.
[04655] Elliptic problems involving a Hardy potential
Format : Talk at Waseda University
Author(s) :
Alexis Molino (University of Almeria)
Abstract : In this talk we consider different elliptic differential equations with a potential Hardy type singularity in a domain and Dirichlet conditions on the boundary. Specifically, the regularizing effect of lower order terms is revealed, as well as the existence of solutions beyond the well-known Hardy constant.
[04200] Solvability of a phase-field model of 3D-grain boundary motion
Format : Talk at Waseda University
Author(s) :
Salvador Moll (Universitat de Valencia)
Ken Shirakawa (Chiba University)
Hiroshi Watanabe (Oita University)
Abstract : We consider a phase-field model of 3D-grain boundary motion. The model is based on the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. To formulate our 3D-model, we use a quaternion formulation for the orientation variable.
In this talk, we obtain existence of solutions to the $L^2$-gradient descent flow of the constrained energy functional via several approximating problems. Moreover, we also obtain an invariance principle for the orientation variable.
MS [02219] Pattern formation and propagation in reaction-diffusion systems on metric graphs
room : G602
[04149] The effect of advection on spike solutions for the Schnakenberg model on Y-shaped metric graph
Format : Talk at Waseda University
Author(s) :
Yuta Ishii (National Institute of Technology, Ibaraki College)
Abstract : In this talk, we consider one-peak solutions for the Schnakenberg model with advection term on Y-shaped metric graph. The location and amplitude of the spike are decided by the interaction of the advection with the geometry of Y-shaped graph. In particular, the effect of the advection on the location of the spike depends on the choice of boundary conditions strongly.
[03837] Turing instability and bifurcation in reaction-diffusion systems on metric graphs
Format : Talk at Waseda University
Author(s) :
Junping Shi (College of William & Mary)
Abstract : We show that under a general framework, a constant equilibrium in a time-evolution system could lose its stability with
the addition of distinct dispersal rates for different species. Spontaneous symmetry breaking bifurcations occur so non-constant stationary patterns emerge. This is the classical Turing instability and bifurcations. We will show the application of this general scenario to the case of (i) an ODE system on a weighted directed graph, and (ii) a reaction-diffusion system on a metric graph.
[04417] Front propagation for Lotka-Volterra competition-diffusion system on unbounded star graphs
Format : Talk at Waseda University
Author(s) :
Ken-Ichi Nakamura (Meiji University)
Abstract : We consider the 2-component Lotka-Volterra competition-diffusion system in an infinite star graph with a single junction. Under strong competition conditions, we give sufficient conditions for the success/failure of the invasion of superior species beyond the junction. The method is based on a standard argument by constructing super-subsolutions with the help of a new result on the speed of traveling waves for the Lotka-Volterra competition-diffusion system on the whole line.
MS [01043] Applications of applied mathematics towards ocean engineering and related technologies
room : G605
[03120] The Li-based quaternary Heusler compound LiYPdSn: A promising thermoelectric material
Format : Online Talk on Zoom
Author(s) :
Jaspal Singh Dhillon (Mata Sundri University Girls College)
Abstract : A newly discovered Li-based quaternary Heusler compound LiYPdSn is investigated which is the 18 Valence Electron Count (VEC) rule follower, non-magnetic, stabilized in FCC cubic structure of F-43m space group, possessing a melting point of 1700K. The Boltzmann transport equations and the Density Functional Theory is employed to investigate its dynamic stability, electronic band structure, thermodynamic response, motivating mechanical and elastic properties, thermodynamic response, which finally results in favorable thermoelectric performances and safe environmental opportunities.
[03204] Structural, electronic, dynamical and thermoelectric performance of LaCoTiSn Heusler alloy
Format : Online Talk on Zoom
Author(s) :
Yuhit Gupta (GSSS Badbar, Department of School Education, Punjab, India )
Abstract : In the present report, the physical properties of LaCoTiSn have been investigated by employing density functional theory. The calculated electronic band structure revealed the half-metallic character and 100% spin-polarization ratio suggest the ferromagnetic nature of the alloy. The evaluated value of Poisson’s ratio ‘0.34’ revealed the metallic bonding. To examine lattice dynamical stability, the phonon frequencies have been computed for first time. To measure the efficiency, the figure of merit is achieved to be 0.35.
MS [00733] Compressible fluid dynamics and related PDE topics
room : G606
MS [00783] PDE Eigenvalue Problems: Computational Modeling and Numerical Analysis
room : G701
[02157] Continuity and differentiability of eigenvalues of Laplacian with respect to general domain perturbations
Format : Talk at Waseda University
Author(s) :
Takuya Tsuchiya (Ehime University)
Abstract : We consider the eigenvalue problems of Laplacian on bounded domains with Lipschitz boundaries. Suppose that a domain is smoothly perturbed, and the perturbation is parametrized in $t$.
In this talk, we discuss about continuity and differentiability of perturbed eigenvalues with respect to the parameter $t$.
[01803] GPU-accelerated high order mimetic finite difference methods for Maxwell equations and eigenproblems
Format : Talk at Waseda University
Author(s) :
Yan Xu (University of Science and Technology of China)
Abstract : In this paper, we consider the eigenvalue problem of the three-dimensional time-harmonic Maxwell equations. The problem is discretized by the general mimetic finite difference method (MFDM), which is based on $L^2$ de Rham complex and has a deep relation with finite element exterior calculus theory. The discretization for the shifted differential operator is also covered. The main challenge arises from the large null space of the approximate curl operator. We introduce an auxiliary scheme to reach nontrivial eigenpairs without going through null space. We design a multigrid-type preconditioner for the algorithm to reduce the iteration count of the iterative eigensolver. Most of the algorithm are basic matrix and vector operators, which are fine-grained parallelism and can be easily accelerated by GPU. Numerical examples of the band structures of three-dimensional photonic crystals are presented to demonstrate the capability and efficiency of the algorithm.
[01881] Compatible Approximation of Holomorphic Eigenvalue Problems
Format : Online Talk on Zoom
Author(s) :
Martin Halla (eorg-August Universität Göttingen, Institut für Numerische und Angewandte Mathematik)
Abstract : I consider Galerkin approximations of EVP for holomorphic operator functions, which arise e.g. from finite element discretizations of PDE eigenvalue problems. The convergence is ensured for "regular" approximations (Karma (1996)). This property is unconditionally satisfied for weakly coercive problems. However, for non weakly coercive problems there exist hardly any results. I present a technique to prove the regularity for such cases, which builds upon the weak T-coercivity of the continuous problem.
[01914] The new computational method on elastic transmission eigenvalue problem
Format : Online Talk on Zoom
Author(s) :
Yingxia Xi (Nanjing University of Science and Technology)
Xia Ji (Beijing Institute of Technology)
Shuo Zhang (Academy of Mathematics and Systems Science)
Abstract : We will present a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.
MS [00057] Many-agent systems and mean-field models for socio-economic and life sciences dynamics
room : G702
[04044] Data-driven kinetic model for opinion dynamics and contacts
Format : Talk at Waseda University
Author(s) :
Giacomo Dimarco (University of Ferrara, Department of Mathematics and Computer Science)
Abstract : Opinion dynamics is an important area of research that studies how individuals
form and change their opinions in a social context. Understanding the mechanisms
that drive opinion formation and change is essential for predicting social phenomena,
such as political polarization and the spread of misinformation. In this talk, we
present a new model for opinion dynamics in presence of social media contacts,
using real-life data from Twitter in order to retrieve the parameters appearing in our
model so to make it as close as possible to what happens in reality.
[02360] Asymptotic-preserving neural networks for kinetic equations in socio-epidemics
Format : Talk at Waseda University
Author(s) :
Giulia Bertaglia (University of Ferrara)
Abstract : Data-driven approaches have proven to be powerful tools with a direct impact on society. However, the use of standard neural networks to investigate multiscale dynamics can lead to erroneous inferences and predictions, because the presence of small scales leads to reduced-order models that must be considered in the learning phase. In this talk, I will address these issues by presenting asymptotic-preserving neural networks, focusing on their use to study the spatial spread of epidemics.
[04507] Many-agent systems and mean-field models for semi-supervised learning
Format : Talk at Waseda University
Author(s) :
Lisa Maria Kreusser (University of Bath)
Marie-Therese Wolfram (University of Warwick)
Abstract : In many problems in data classification, it is desirable to assign labels to points in a point cloud where a certain number of them is already correctly labeled. In this talk, we propose a microscopic ODE approach, in which information about correct labels propagates to neighbouring points. Its dynamics are based on alignment mechanisms, often used in collective and consensus models. We derive the respective continuum description, which corresponds to an anisotropic diffusion equation with a reaction term. Solutions of the continuum model inherit interesting properties of the underlying point cloud. We discuss the qualitative behaviour of solutions and exemplify the results with micro- and macroscopic simulations.
[03820] Trends to equilibrium for nonlocal Fokker-Planck equations with discontinuous drift
Format : Talk at Waseda University
Author(s) :
Mattia Zanella (University of Pavia)
Abstract : We study equilibration rates for nonlocal Fokker-Planck equations with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarms of agents, feeling each other in terms of their distance, towards the steady profile characterized by a uniform spreading over a finite domain. The result follows by combining entropy methods for quantifying the decay of the solution towards its quasi-stationary distribution, with the properties of the quasi-stationary profile.
MS [00608] Limit behavior and asymptotic properties in fluid mechanics
room : G703
[04842] Invariant manifolds for the thin film equation
Format : Talk at Waseda University
Author(s) :
Christian Seis (University of Munster)
Dominik Winkler (University of Munster)
Abstract : The large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on R^N is examined: We investigate the higher order asymptotics of solutions converging towards self-similar Smyth--Hill solutions under certain symmetry assumptions on the initial data. The analysis is based on a construction of finite-dimensional invariant manifolds that solutions approximate to an arbitrarily prescribed order.
[03881] The Navier-Stokes flow in the exterior Lipschitz domain
Format : Talk at Waseda University
Author(s) :
Keiichi Watanabe (Suwa University of Science)
Abstract : Consider the three-dimensional Navier-Stokes equations in an exterior Lipschitz domain $\Omega$. In this talk, we show the unique existence of a global strong solution $u$ to the Navier-Stokes equations and investigate the large time behavior of the solution $u$. Although the boundary is not smooth, we show that the large time behavior of the Navier-Stokes flow is completely recovered in the exterior Lipschitz domain $\Omega$ along exactly the same argument as usual.
[04533] Anisotropically spatial-temporal behavior of the Navier-Stokes flow past an obstacle
Format : Talk at Waseda University
Author(s) :
Tomoki Takahashi (Tokyo Institute of Technology)
Abstract : We consider the spatial-temporal behavior of the Navier-Stokes flow past a three dimensional rigid body and deduce
the temporal decay rate with the spatial weight caused by translation. The key tool is the $L^q$-$L^r$ estimate of the Oseen semigroup in exterior domains and we develop the weighted $L^q$ theory of the Oseen semigroup. New results on the Stokes semigroup in isotropic $L^q$ spaces are also discussed.
[01603] Stokes and Oseen fundamental solutions: asymptotic properties of fluid flows and applications in computational fluid dynamics
Format : Talk at Waseda University
Author(s) :
Ana Leonor Silvestre (Instituto Superior Técnico, Universidade de Lisboa)
Abstract : Starting from the Stokes and Oseen steady and unsteady fundamental solutions, we discuss asymptotic properties of fluid flow around a translating and rotating rigid body. This part of the talk includes joint work with Toshiaki Hishida, from Nagoya University, Japan, and Takéo Takahashi, from INRIA Nancy - Grand Est, France. In the second part of the talk, based on joint work with Carlos Alves, Rodrigo Serrão, from Instituto Superior Técnico, Portugal, and Svilen Valtchev, from Instituto Politécnico de Leiria, Portugal, we present a numerical study of the Method of Fundamental Solutions for Stokes and Oseen boundary value problems. The accuracy of the method is illustrated through a series of numerical tests, which include a comparison between analytic and numerical solutions and the application of the method to classical benchmark problems.
MS [00753] Numerical methods for high-dimensional problems
room : G704
[04360] An efficient stochastic particle method for high-dimensional nonlinear PDEs
Format : Talk at Waseda University
Author(s) :
Sihong Shao (Peking University)
Abstract : We introduce a stochastic particle method (SPM) to solve high-dimensional nonlinear PDEs in the weak sense. The weak formulation is a time-dependent high-dimensional integral, and different test functions can bring us various information about the solution. To determine the dynamics of the particle system, we linearize the nonlinear terms using the previous time step solutions and establish a relationship of weak formulation between adjacent time steps via the Lawson-Euler scheme. The resulting stochastic particles follow the behavior of the solution in an adaptive manner, therefore mitigating curse of dimensionality to a certain extent. Numerical experiments on the 6-D Allen-Cahn equation and 7-D Hamiltonian-Jacobi-Bellman equation demonstrate the accuracy and efficiency of SPM. This work is joint with Zhengyang Lei and Yunfeng Xiong.
[04066] Overcoming the dynamical sign problem via adaptive particle annihilation
Format : Talk at Waseda University
Author(s) :
Yunfeng Xiong (Beijing Normal University)
Abstract : The dynamical sign problem poses a fundamental obstacle to particle-based simulations in high dimensional space. To resolve it, we propose an adaptive particle annihilation algorithm, termed Sequential-clustering Particle Annihilation via Discrepancy Estimation (SPADE). SPADE follows a divide-and-conquer strategy: Adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each cluster. Combining SPADE with the stationary phase approximation, we attempt to simulate the Wigner dynamics in 6-D and 12-D phase space.
[02525] A splitting Hamiltonian Monte Carlo method for efficient sampling
Format : Talk at Waseda University
Author(s) :
Lei Li (Shanghai Jiao Tong University)
Lin Liu (Shanghai Jiao Tong University)
Yuzhou Peng (Shanghai Jiao Tong University)
Abstract : In this talk, I will introduce a splitting Hamiltonian Monte Carlo algorithm, which can be computationally efficient when combined with the random mini-batch strategy. By splitting the potential energy into numerically nonstiff and stiff parts, one makes a proposal using the nonstiff part, followed by a Metropolis rejection step using the stiff part that is often easy to compute. The splitting allows efficient sampling from systems with singular potentials and/or multiple potential barriers. We also use random batch strategies to reduce the computational cost in generating the proposals for problems arising from many-body systems and Bayesian inference, and estimate both the strong and the weak errors in the Hamiltonian induced by the random batch approximation.
[02255] Ergodicity and sharp error estimate of Stochastic Gradient Langevin Dynamics
Format : Talk at Waseda University
Author(s) :
Yuliang Wang (Shanghai Jiao Tong University)
Abstract : We establish a sharp error estimate for the Stochastic Gradient Langevin Dynamics (SGLD). Under mild assumptions, we obtain a uniform-in-time $O(\eta^2)$ bound for the KL-divergence between SGLD and the Langevin diffusion, where $\eta$ is the step size. Based on this, we are able to obtain an $O(\eta)$ bound for its sampling error in terms of Wasserstein or total variation distances. Moreover, we prove the geometric ergodicity of SGLD algorithm under $W_1$ distance without global convexity.
MS [00969] Eigenvalue Problems in Electronic Structure Calculations
room : G709
[04472] Recent Advances in Self-Consistent-Field Iterations for Solving Eigenvector-Dependent Nonlinear Eigenvalue Problems
Format : Talk at Waseda University
Author(s) :
Zhaojun Bai (University of California, Davis)
Abstract : Much like the power method for solving linear eigenvalue problems,
self-Consistent-Field (SCF) iteration is a gateway algorithm to
solve eigenvector-dependent nonlinear eigenvalue problems such as
ones arising from electronic structure calculations. The SCF was
introduced in computational physics back in the 1950s. In this talk,
from numerical linear algebra perspective, we present recent advances
in the SCF, such as sharp estimation of convergence rate and
geometry interpretation of the SCF for a class of NEPv.
[04337] Kohn-Sham GGA Models and Their Approximations
Format : Talk at Waseda University
Author(s) :
Aihui Zhou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract : In this presentation, I will talk about the finite dimensional approximations of Kohn-Sham GGA models, which are often used in electronic structure calculations. I will show the convergence of the finite dimensional approximations and present the a priori error estimates for ground state energy and solution approximations.
[04173] Model and data driven electromagnetic inverse problems with optimal transport
Format : Online Talk on Zoom
Author(s) :
Yanfei Wang (Institute of Geology and Geophysics, Chinese Academy of Sciences)
Abstract : Electromagnetic inverse problems have important applications in non-destructive testing and evaluation of materials. By using electromagnetic measurements to probe the properties of materials like metals and composites, researchers can gain insight into the structural integrity, conductivity, and other important properties of these materials. In this study, we consider application of electromagnetic inverse problems is in geophysics, i.e., using electromagnetic measurements to study the composition and structure of the Earth's subsurface. We propose a new attempt to use the probability metric (Wasserstein metric) for electromagnetic inversion. This lays the foundation for the future application of probability metric type of methods to large-scale electromagnetic inversion. In addition, data driven electromagnetic inverse problems will be also addressed.
[05566] Porting Quantum ESPRESSO Eigensolvers on GPUS
Format : Talk at Waseda University
Author(s) :
Stefano de Gironcoli (SISSA - Trieste)
Abstract : I will report on the effort by the Quantum ESPRESSO developing team regarding the porting of the main iterative eigensolvers employed in the solution the Kohn-Sham self-consistent equations in electronic structure applications to new hybrid hardware architectures including both CPUS and GPUS chips. Directions for future developments will be briefly outlined.
MS [00247] Interfaces and Free Boundaries in Fluid Mechanics and Materials Science
room : G710
[03054] Variational methods for time-dependent problems on dynamically changing domains
Format : Talk at Waseda University
Author(s) :
Malte Kampschulte (Charles University Prague)
Abstract : In this talk I will present a general, energetically consistent method that can be used to show the existence of weak solutions for nonlinear problems in fluid structure-interaction and related fields. Not only can this be done without the need to make simplifying assumptions on domain or equations, in fact it crucially relies on all physical terms being present. This talk is based on several recent results primarily with B.Benesova, S.Schwarzacher but also D.Breit, A.Cesik, G.Gravina and G.Sperone.
[04468] Sharp-interface limit of models with mechanics and contact lines
Format : Talk at Waseda University
Author(s) :
Dirk Peschka (WIAS Berlin & Freie Universität Berlin)
Leonie Schmeller (Weierstrass Institute)
Abstract : First, we construct gradient structures for free boundary problems including nonlinear elasticity, phase fields and moving contact lines, where the convergence of phase-field models to certain sharp-interface limits is analyzed numerically. Then, in the second part of the talk, it will be shown how shapes of droplets on soft elastic substrates can be predicted by corresponding (sharp-interface) models, and some emergent phenomena - cloaking and phase separation near the contact line - are pointed out.
[03766] Uniform Rectifiability for Minimizers of the Griffith Fracture Energy
Format : Talk at Waseda University
Author(s) :
Kerrek Stinson (University of Bonn)
Manuel Friedrich (University of Erlangen-Nuremberg)
Camille Labourie (University of Erlangen-Nuremberg)
Abstract : Recent studies for minimizers of the Griffith energy, which penalizes elastic energy and fracture, have relied on topological constraints for the (codimension-1) crack. Regularity results effectively say that if the crack locally separates the domain into different connected components, then the crack is in fact a smooth surface. Our analysis looks at minimizers without topological constraints. As a first step, we prove uniform rectifiability, which shows that on sufficiently small scales, the crack is nearly topologically separating. The purpose of this talk is to illuminate the new techniques applied in this setting and discuss how a similar approach can be used to prove a regularity result for the crack.
MS [00237] Recent progress in multiscale modeling and computational methods in material sciences
room : G801
[01430] A Continuum Model for Dislocation Climb Velocity and Numerical Simulations
Format : Talk at Waseda University
Author(s) :
Chutian Huang (Hong Kong University of Science and Technology)
Yang Xiang (Hong Kong University of Science and Technology)
Abstract : Dislocations are primary carriers for the crystal plastic deformation. The study of dislocation climb plays an important role in understanding plastic deformation of crystalline deformation at high temperature. In this work, we propose a new continuum formulation for dislocation climb velocity. Numerical simulations are implemented to compare our model with mobility law and discrete model.
MS [00507] Stochastic Dynamical Systems and Applications
room : G802
[04756] Mean Asymptotic Behavior for Stochastic Kuramoto-Sivashinshy Equation in Bochner Spaces
Format : Online Talk on Zoom
Author(s) :
Xiaopeng Chen (Shantou University)
Abstract : In this talk we mainly present some asymptotic behavior of the Kuramoto-Sivashinshy equation with stochastic perturbation. We define the mean random dynamical systems for the stochastic Kuramoto-Sivashinshy equation in Bochner spaces. Then we consider the so-called weak pullback mean random attractor and invariant manifold for the stochastic Kuramoto-Sivashinshy equation with odd initial conditions.
[04325] The Poisson Equation and Application to Multi-Scale SDEs with State-Dependent Switching
Format : Online Talk on Zoom
Author(s) :
Xiaobin Sun (Jiangsu Normal University)
Abstract : In this talk, we discuss the Poisson equation associated with a Markov chain. By investigating the differentiability of the corresponding transition probability matrix with respect to parameters, we establish the regularity of the Poisson equation solution. As an application, we further study the averaging principle for a class of multi-scale stochastic differential equations with state-dependent switching, ultimately achieving an optimal strong convergence order of 1/2. This talk is based on a joint work with Yingchao Xie.
[04954] A stochastic fractional Schrodinger equation with multiplicative noise
Format : Talk at Waseda University
Author(s) :
Yan jie Zhang (Zhengzhou University)
Yanjie Zhang (Zhengzhou University )
Abstract : We establish the stochastic Strichartz estimate for the fractional Schr\"odinger equation with multiplicative noise. With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to the stochastic fractional nonlinear Schr\"odinger equation
in $L_2(\mathbb{R}^n)$ and $H^{1}(\mathbb{R}^n)$, respectively. In addition, we also prove a general blow up result by deriving a localized virial estimate and the generalized Strauss inequality with $E[u_0]<0$.
[05083] The most probable dynamics of receptor-ligand binding on cell membrane
Format : Online Talk on Zoom
Author(s) :
Xi Chen (Xi'an University of Finance and Economics)
Abstract : We devise a method for predicting receptor-ligand binding behaviors, based on stochastic dynamical modelling. We consider the receptor and ligand perform different motions and are thus modeled by stochastic differential equations with Gaussian noise or non-Gaussian noise. We use neural networks based on Onsager-Machlup function to compute the probability of the receptor diffusing to the cell membrane. In this way, we conclude with some indication about where the ligand will most probably encounter the receptor.
MS [00506] Inverse Problems for Anomalous Diffusion
room : G808
[04736] Classical Unique Continuation Property for Time Fractional Evolution Equations
Format : Talk at Waseda University
Author(s) :
Gen Nakamura (Hokkaido University)
Ching-Lung LIn (National Cheng Kung University)
Abstract : Let $q_j=q_j(x),\,\,2\le j\le m$ with $q_1=1$ and let $2>\alpha=\alpha_1>\alpha_2>\cdots>\alpha_m>0$.
Then, the classical unique continuation property of solutions in $H^{\alpha,2}((0,T)\times\Omega)$ holds for the time
fractional evolution equation (tfEE) whose leading part given as
$\sum_{j=1}^mq_j\partial_t^{\alpha_j} u(t,y)-{\it L}\, u(t,y)$ over a domain $\Omega\subset{\mathbb R}^n$
with a time dependent strongly eilliptic operator $L$ of oder $2$, where $\partial_t^{\alpha_j}$ is the Caputo derivative whenever $\alpha_j\not\in{\mathbb Z}$.
See C-L. Lin and G. Nakamura, Math. Ann. 385 (2023), pp. 551–574 for the details.
[02704] The Calderón problem for nonlocal parabolic operators
Format : Talk at Waseda University
Author(s) :
Yi-Hsuan Lin (Department of Applied Mathematics, National Yang Ming Chiao Tung University)
Abstract : We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that
we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder´on problems, respectively.
[02699] Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
Format : Online Talk on Zoom
Author(s) :
Bangti Jin (The Chinese University of Hong Kong)
Yavar Kian (Aix Marseille University)
Zhi Zhou (The Hong Kong Polytechnic University)
Abstract : Time-fractional subdiffusion equations represent an important class of mathematical models with a broad range of applications. The related inverse problems of recovering space-dependent parameters, e.g., initial condition, space dependent source or potential coefficient, from the terminal observation have been extensively studied in recent years. However, all existing studies have assumed that the terminal time at which one takes the observation is exactly known. In this talk, we present uniqueness and stability results for three canonical inverse problems, e.g., backward problem, inverse source and inverse potential problems, from the terminal observation at an unknown time. The subdiffusive nature of the problem indicates that one can simultaneously determine the terminal time and space-dependent parameter.
[04403] Numerical Recovery of Multiple Parameters from One Lateral Boundary Measurement
Format : Talk at Waseda University
Author(s) :
Siyu Cen (The Hong Kong Polytechnic University)
Bangti Jin (Chinese University of Hong Kong)
Yikan Liu (Hokkaido University)
Zhi Zhou (The Hong Kong Polytechnic University)
Abstract : This talk is concerned with numerically recovering multiple parameters in a partly unknown subdiffusion model from one lateral measurement on the boundary. We prove that the boundary measurement uniquely determines the fractional order and the polygonal support of the diffusion coefficient, without knowing either the initial condition or the source. We present an algorithm for recovering the fractional order and diffusion coefficient which combines small-time asymptotic expansion, analytic continuation and the level set method.
MS [02277] New regularizing algorithms for solving inverse and ill-posed problems
room : G809
[02839] Stochastic asymptotical regularization for nonlinear ill-posed problems
Format : Talk at Waseda University
Author(s) :
Haie Long (Shenzhen SMU-BIT University)
Abstract : In this paper, we establish an initial theory regarding the stochastic asymptotical regularization (SAR) for the uncertainty quantification of the stable approximate solution of ill-posed nonlinear-operator equations, which are deterministic models for numerous inverse problems in science and engineering. By combining techniques from classical regularization theory and stochastic analysis, we prove the regularizing properties of SAR with regard to mean-square convergence. The convergence rate results under the canonical sourcewise condition are also studied. Several numerical examples are used to show the accuracy and advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can provide the uncertainty quantification of a solution and escape local minimums for nonlinear problems.
[03062] A new framework to quantify the uncertainty in inverse problems
Format : Talk at Waseda University
Author(s) :
Wenlong Zhang (Southern University of Science and Technology)
Abstract : In this work, we investigate the regularized solutions and their finite element solutions to the inverse problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element convergence rates of these solutions, under point wise measurement data with random noise. The regularization error estimates and the finite element error estimates are derived with explicit dependence on the noise level, regularization parameter, mesh size, and time step size, which can guide practical choices among these key parameters in real applications. The error estimates also suggest an iterative algorithm for determining an optimal regularization parameter.
[03104] Numerical algorithms for solving the nonlinear Schrödinger equation
Format : Talk at Waseda University
Author(s) :
Shuang Liu (Novosibirsk State University)
Abstract : In this paper, the Physical Information Neural Networks algorithm is used to solve the nonlinear Schrödinger equation in a dispersed medium. Adaptive activation functions are used to accelerate PINN convergence, and this approach uses very little data to obtain an exact solution. Due to the approximation capability of the neural network, the results are used in semiconductor optical amplifier fiber lasers where nonlinear effects allow spectral tuning of the generated pulses.
[03354] Multidimensional Ill-Posed Problems in Applications
Format : Talk at Waseda University
Author(s) :
Anatoly Yagola (Lomonosov Moscow State University)
Abstract : The report will consider applied multidimensional inverse problems of geophysics (magnetometry and gravimetry) and electron microscopy (electron backscattering), regularizing algorithms for their solution and the results of experimental data processing.
MS [02499] Machine Learning for dynamics and its applications
room : F308
[05427] Reservoir Computing Generalized
Format : Talk at Waseda University
Author(s) :
Tomoyuki Kubota (The University of Tokyo)
Abstract : Reservoir computing (RC) is a machine learning framework that leverages a dynamical system as an information processor. This framework imposes a constraint on a system where the system must exhibit an identical response against an identical input sequence to work as a reproducible input processor; however, systems that violate the constraint can also process input. In this talk, we introduce a more general theoretical framework called generalized reservoir computing, covering the rest of irreproducible systems.
[05429] Reservoir computing with the Kuramoto model
Format : Talk at Waseda University
Author(s) :
Koichi Taniguchi (Tohoku University)
Abstract : The physical reservoir aims to achieve high-performance and low-cost machine learning by using real physical systems as reservoirs, but in general, there is no theoretical guideline for high-performance or optimality. In this talk, we discuss the reservoir computing with the Kuramoto model and the "edge of bifurcation" conjecture which means that its best performance is achieved by taking the model parameters just below the bifurcation point of the dynamical system.
[05431] Embedding bifurcation structures into a soft robotic actuator
Format : Talk at Waseda University
Author(s) :
Nozomi Akashi (Kyoto University)
Yasuo Kuniyoshi (The University of Tokyo)
Taketomo Jo (Bridgestone Corporation)
Mitsuhiro Nishida (Bridgestone Corporation)
Ryo Sakurai (Bridgestone Corporation)
Yasumichi Wakao (Bridgestone Corporation)
Kohei Nakajima (The University of Tokyo)
Abstract : We demonstrate that bifurcation structures can be embedded into a McKibben pneumatic artificial muscle, which is a common soft robotic actuator, through closed-loop control of physical reservoir computing. Our experiments reveal that both periodic and chaotic dynamics can be embedded into the artificial muscle by training only one side of these dynamics. Our results provide insight into reducing the amount and types of training data required for robot control through the utilization of bifurcation structures.
[05402] Physical reservoir computing using dynamics of biological neuronal network with modular structure
Format : Talk at Waseda University
Author(s) :
Takuma Sumi (Tohoku University)
Hideaki Yamamoto (Tohoku University)
Yuichi Katori (Future University of Hakodate)
Koki Ito (Tohoku University)
Shigeo Sato (Tohoku University)
Ayumi Hirano-Iwata (Tohoku University)
Abstract : Physical reservoir computing with biological neuronal network (BNN) has recently advanced the understanding of its computational principles. However, the BNN in conventional culture was randomly connected, generating non-physiological dynamics. Here, we employed micropatterning technology to fabricate BNNs with modular topology conserved evolutionarily in animal brains. We showed that the BNN reservoir exhibited higher classification when its network was functionally modular. Our findings provide insights into the link among non-random network connectivity, neuronal dynamics, and computing.
MS [02083] Integrable Aspects of Nonlinear Wave Equations, Solutions and Asymptotics
room : F309
[05581] Recent results on the Fractional Nonlinear Schroedinger Equation
Format : Talk at Waseda University
Author(s) :
Alejandro Aceves (Southern Methodist University)
Abstract : The Fractional Nonlinear Schroedinger Equation (fNLSE) has been a topic of recent interest as it may have applications to nononlinear photonics. In this work we will present motivation for the models considered and recent results on discrete and continuous fNLSE.
In particular we will discuss the existence of discrete localized modes and their properties. Rigorous and numerical results on existence for the continuous fNLSE will also be presented.
[05588] Duality of positive and negative integrable hierarchiesvia relativistically invariant fields
Format : Online Talk on Zoom
Author(s) :
Senyue Lou (Ningbo University)
Xing-Biao Hu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Qingping Liu (China University of Mining and Tenchnology (Beijing))
Abstract : This talk concerns the relativistic invariance in integrable systems. Using the invariant sine-Gordon, Tzitzeica, Toda fields and second heavenly equations as dual relations, some well-known continuous and discrete integrable positive hierarchies are converted to the negative hierarchies. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the mastersymmetry method and the relativistic invariance of the duality relations. Two elegant commuting recursion operators of the heavenly equation appear naturally from the formal series symmetry approach.
[04900] Integrable Deep Learning--PINN based on Miura transformations and discovery of new localized wave solutions
Format : Talk at Waseda University
Author(s) :
Yong Chen (East China Normal University)
Abstract : We put forth two physics-informed neural network (PINN) schemes based on Miura transformations. The novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs, which is an implementation method of unsupervised learning. The most noteworthy advantage of our method is that we can simply exploit the initial-boundary data of a solution of a certain nonlinear equation to obtain the data-driven solution of another evolution equation with the aid of Miura transformations and PINNs. In the process, the Miura transformation plays an indispensable role of a bridge between solutions of two separate equations. It is tailored to the inverse process of the Miura transformation and can overcome the difficulties in solving solutions based on the implicit expression. Moreover, two schemes are applied to perform abundant computational experiments to effectively reproduce dynamic behaviors of solutions for the well-known KdV equation and mKdV equation. Significantly, new data-driven solutions are successfully simulated and one of the most important results is the discovery of a new localized wave solution: kink-bell type solution of the defocusing mKdV equation and it has not been previously observed and reported to our knowledge. It provides a possibility for new types of numerical solutions by fully leveraging the many-to-one relationship between solutions before and after Miura transformations. Performance comparisons in different cases as well as advantages and disadvantages analysis of two schemes are also discussed. Based on the performance of two schemes and no free lunch theorem, they both have their own merits and thus more appropriate one should be chosen according to specific cases.
[04206] Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras
Format : Talk at Waseda University
Author(s) :
Chaozhong Wu (Sun Yat-Sen University)
Abstract : For a diagram automorphism of an affine Kac-Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld-Sokolov hierarchy also admits an induced automorphism. We also show how to obtain the Drinfeld-Sokolov hierarchy associated to the affine Kac-Moody algebra that corresponds to the folded Dynkin diagram from the invariant sub-hierarchy of the original Drinfeld-Sokolov hierarchy. This is based on a joint work with Si-Qi Liu, Youjin Zhang and Xu Zhou.
MS [00185] AAA rational approximation: extensions and applications
room : F310
[02196] Review of AAA approximation
Format : Talk at Waseda University
Author(s) :
Lloyd Nicholas Trefethen (University of Oxford)
Abstract : The AAA ("triple A") algorithm is a fast and reliable black box algorithm for computing rational approximations to real or complex functions. It has been used by many people since its publication in 2018. This talk will be an introduction to to AAA and its applications.
[05528] pAAA for multivariate functions and AAA-LQO for systems with quadratic outputs
Format : Online Talk on Zoom
Author(s) :
Serkan Gugercin (Virginia Tech)
Abstract : We first introduce the parametric-AAA (pAAA) algorithm for approximating multivariate functions, such as the transfer functions of parametric dynamical systems, where the approximant is constructed in the multivariate barycentric form. We then develop the barycentric form for linear dynamical systems with quadratic outputs (LQO). This new formulation leads to the AAA-LQO algorithm.
[02708] Rational approximation for noisy data
Format : Talk at Waseda University
Author(s) :
Anil Damle (Cornell University)
Abstract : Approximation of data by rational functions has many clear upsides over other representational forms. However, even if a rational function provides an effective underlying model for a given task the data it must be built from is often corrupted by noise. In this talk we will explore how existing rational approximation algorithms are impacted by noise, and discuss algorithms that are specifically tailored to effectively and efficiently build rational approximations of noisy data.
[03138] SO-AAA: learning systems with second-order dynamics
Format : Talk at Waseda University
Author(s) :
Ion Victor Gosea (Max Planck Institute for Dynamics of Complex Technical Systems)
Serkan Gugercin (Virginia Tech University)
Steffen W. R. Werner (New York University)
Abstract : The AAA (Adaptive Antoulas Anderson) algorithm is a rational approximation tool used to fit rational functions to data measurements. We present here an extension of AAA to fi tting systems with second-order dynamics (structured case). Toward this goal, the development of structured barycentric forms associated with the transfer function of second-order systems is needed. These allow the iterative construction of reduced-order models from given frequency domain data, by combining interpolation and least-squares fi t.
MS [00088] Machine learning in infinite dimensions
room : F311
[02760] Approximation by structured deep neural networks
Format : Talk at Waseda University
Author(s) :
Dingxuan Zhou (University of Sydney)
Abstract : Deep learning based on deep neural networks possessing network architectures has been powerful in practical applications but is less understood theoretically. Structured neural networks are particularly difficult to analyze. An important family of structured neural networks is deep convolutional neural networks possessing convolutional structures. The convolutional architecture is key for the computational efficiency but raises scientific challenges. We describe a mathematical theory of approximating and learning functions or operators by structured deep neural networks.
[03794] Learning High-Dimensional Banach-Valued Functions from Limited Data with Deep Neural Networks
Format : Talk at Waseda University
Author(s) :
Nick Dexter (Florida State University)
Ben Adcock (Simon Fraser University)
Sebastian Moraga (Simon Fraser University)
Simone Brugiapaglia (Concordia University)
Abstract : Reconstructing high-dimensional functions from few samples is important for uncertainty quantification in computational science. Deep learning has achieved impressive results in parameterized PDE problems with solutions in Hilbert or Banach spaces. This work proposes a novel algorithmic approach using DL, compressed sensing, orthogonal polynomials, and finite elements to approximate smooth functions in infinite-dimensional Banach spaces. Theoretical analysis provides explicit guarantees on error and sample complexity, and numerical experiments demonstrate accurate approximations on challenging benchmark problems.
[04519] Kernel methods for learning operators between infinite dimensional Banach spaces
Format : Talk at Waseda University
Author(s) :
Pau Batlle (California Institute of Technology)
Matthieu Darcy (California Institute of Technology )
Houman Owhadi (California Institute of Technology)
Bamdad Hosseini (University of Washington)
Abstract : We introduce a kernel-based framework for learning operators between Banach spaces. We show that even with simple kernels, our approach is competitive in terms of cost-accuracy trade-off and either matches or beats the performance of NN methods on a majority of PDE-based benchmarks. Additionally, our framework offers several advantages inherited from kernel methods: simplicity, interpretability, convergence guarantees, a priori error estimates, and Bayesian UQ. It is therefore a natural benchmark for operator learning problems.
[03223] A duality framework for generalization analysis of random feature models and two-layer neural networks
Format : Talk at Waseda University
Author(s) :
Hongrui Chen (Peking University)
Jihao Long (Princeton University)
Lei Wu (Peking University)
Abstract : We consider the problem of learning functions in the $\mathcal{F}_{p,\pi}$ and Barron spaces, which are natural function spaces that arise in the high-dimensional analysis of random feature models (RFMs) and two-layer neural networks. Through a duality analysis, we reveal that the approximation and estimation of these spaces can be considered equivalent in a certain sense. This enables us to focus on the easier problem of approximation and estimation when studying the generalization of both models. The dual equivalence is established by defining an information-based complexity that can effectively control estimation errors. Additionally, we demonstrate the flexibility of our duality framework through comprehensive analyses of two concrete applications.
The first application is to study learning functions in $\mathcal{F}_{p,\pi}$ with RFMs. We prove that the learning does not suffer from the curse of dimensionality as long as $p>1$, implying RFMs can work beyond the kernel regime. Our analysis extends existing results (Celentano et al., 2021) to the noisy case and removes the requirement of overparameterization.
The second application is to investigate the learnability of reproducing kernel Hilbert space (RKHS) under the {\em uniform metric}. We derive both lower and upper bounds of the minimax estimation error by using the spectrum of the associated kernel. We then apply these bounds to dot-product kernels and analyze how they scale with the input dimension. Our results suggest that learning with ReLU (random) features is generally intractable in terms of reaching high uniform accuracy.
MS [00426] Variational methods for thin structures and free-boundary problems
room : F312
[03469] On the Kircchoff-Plateau problem: critical points and regularity
Format : Talk at Waseda University
Author(s) :
Giulia Bevilacqua (Università di Pisa)
Abstract : In this talk I will discuss some generalization of the Plateau problem, which in its classical form asks if it exists a surface of minimal area spanning a given boundary. First-order necessary conditions and regularity properties are studied when a thick rod (with non vanishing thickness) and/or an elastic curve are assigned as the boundary spanned by the surface.
[02176] On Stationary Points of Polyconvex Functionals
Format : Talk at Waseda University
Author(s) :
Riccardo Tione (MPI MiS Leipzig)
Camillo De Lellis (Institute for Advanced Study)
Guido De Philippis (Courant Institute of Mathematics)
Antonio De Rosa (University of Maryland)
Jonas Hirsch (Universität Leipzig)
Bernd Kirchheim (Universität Leipzig)
Abstract : Quasi- and polyconvex energies arise naturally in modeling physical phenomena related to elasticity. From the mathematical viewpoint, a challenging question concerns the regularity of critical/stationary points and minimizers of these energies. My talk focuses on recent results in this direction concerning stationary points, i.e. critical points subject to outer and inner variations. I also address the application of this question to geometric measure theory.
[04199] Minimization of the Canham-Helfrich within generalised Gauss graphs
Format : Talk at Waseda University
Author(s) :
Anna Kubin (Politecnico di Torino)
Luca Lussardi (Politecnico di Torino)
Marco Morandotti (Politecnico di Torino)
Abstract : The Canham-Helfrich functional is the most widely used functional to study the equilibrium of biological membranes as a result of the competition between mean curvature and Gaussian curvature.
In this talk, we review some approaches to the minimisation problem for this functional and present novel results in the setting of generalised Gauss graphs.
This is joint work with Anna Kubin and Luca Lussardi.
[03181] A capillarity theory approach to the analysis of soap films
Format : Online Talk on Zoom
Author(s) :
Salvatore Stuvard (University of Milan)
Darren King (New York University)
Francesco Maggi (University of Texas at Austin)
Antonello Scardicchio (Abdus Salam ICTP)
Abstract : I will present a variational model, based on Gauss' theory of capillarity, which describes soap films as sets of finite perimeter enclosing a prescribed volume of fluid and satisfying a spanning condition of homotopic type, rather as minimal surfaces. I will discuss the corresponding existence theory, the sharp regularity properties of the minimizers, their asymptotic behavior in the vanishing volume limit, and I will attempt a qualitative description of their local and global geometry.
MS [01181] Variational methods for multi-scale dynamics
Abstract : In this talk, we study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we demonstrate that conservation laws with diffusion are "flux--gradient flows." We next construct variational problems for these flows, for which we derive dual PDE systems for regularized conservation laws. Several examples, including traffic flow and Burgers' equation, are presented. We successfully compute the control of conservation laws by incorporating both primal-dual algorithms and monotone schemes. This is based on joint work with Siting Liu and Stanley Osher.
[03821] Transport problems with non linear mobilities: a particle approximation result.
Format : Talk at Waseda University
Author(s) :
Lorenzo Portinale (Hausdorff Center for Mathematics, Bonn)
Simone Di Marino ( Università di Genova )
Emanuela Radici ( Università degli Studi dell’Aquila)
Abstract : We study discretisation of generalised Wasserstein distances with non linear mobilities on the real line via a Riemannian metrics on the space of N ordered particles. In particular, we provide a Γ-convergence result for the associated discrete metrics as N → ∞ to the continuous one and discuss applications to the approximation of one-dimensional conservation laws (of gradient flow type) via the so-called generalised minimising movements (or JKO scheme).
[04444] Variational convergence for irreversible population dynamics
Format : Talk at Waseda University
Author(s) :
Jasper Hoeksema (Eindhoven University of Technology)
Abstract : We consider the forward Kolmogorov equations corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics. In contrast to previous work, where we assumed detailed balance, we will now treat the irreversible case. We exchange gradient structures for more general dissipation structures, and show convergence of these structures in the large population limit. In particular we obtain convergence to the mean-field limit and establish entropic propagation of chaos.
[03883] Mathematical modeling of structured magnesium alloys
Format : Talk at Waseda University
Author(s) :
Karel Svadlenka (Kyoto University)
Abstract : Structured materials, such as metallic alloys with atomic-scale layers, show peculiar deformation patterns, which may have significant implications on material properties. In this talk, I will discuss one possible approach to modeling of this kind of pattern formation through the so-called rate-independent evolution in the variational setting of finite-strain elasto-plasticity. Besides mentioning connections to homogenization via Gamma-convergence, I will present the underlying mathematical theory and show numerical simulations in comparison to experimental measurements.
MS [00941] Numerical methods for Hamilton-Jacobi equations and their applications
room : F402
[03669] Sparse-grid WENO fast sweeping methods for Eikonal equations
Format : Online Talk on Zoom
Author(s) :
Zachary Miksis (University of Notre Dame)
Yong-Tao Zhang (University of Notre Dame)
Abstract : Fixed-point WENO fast sweeping methods are a class of explicit iterative methods for efficiently solving steady-state hyperbolic PDEs. For multidimensional nonlinear problems such as Eikonal equations, high-order fixed-point WENO fast sweeping methods still require quite a large amount of computational costs. In this talk, I shall present our recent work on applying sparse-grid techniques, an effective approximation tool for multidimensional problems, to fixed-point WENO fast sweeping methods for reducing their computational costs.
[03495] Efficient high frequency wave propagation with small sampling density
Format : Online Talk on Zoom
Author(s) :
Songting Luo (Iowa State University)
Qing Huo Liu (Duke University)
Abstract : In this talk, we will present a few approaches for simulating high frequency wave propagation with low sampling density. One approach is based on WKBJ approximation, which leads to Hamilton-Jacobi type equations for the phase and amplitude. Such equations will be solved efficiently by well-established schemes and their solutions will be used for building the wave. In order to resolve the difficulty of capturing the caustics in the WKBJ approximation, we will further transform the problem into a fixed-point iteration problem that can be solved by operator-splitting based pseudospectral methods, which leads to another approach. Both approaches have low sampling densities that ensure the efficiency, verified by numerical experiments.
[03786] Data-Driven Learning Method for Optimal Feedback Control
Format : Online Talk on Zoom
Author(s) :
Qi Gong (University of California, Santa Cruz)
Abstract : Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which, in high dimensions, is a well-known challenging problem due to the curse of dimensionality. In this talk, we present a model-based data-driven method to approximate solutions to HJB equations for high dimensional nonlinear systems. To accomplish this, we model solutions to HJB equations with neural networks trained on data generated without any state space discretization. Training is made more effective and efficient by leveraging the known physics of the problem and generating training data in an adaptive fashion. We further develop different neural networks approximation structures to improve robustness during learning and enhance closed-loop stability of the learned controller.
[03577] Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Format : Online Talk on Zoom
Author(s) :
Jerome Darbon (Brown University)
Paula Chen (Brown University)
Tingwei Meng (UCLA)
Zongren Zou (Brown University)
George Em Karniadakis (Brown University)
Abstract : We establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem.
MS [00151] Recent trends in SHM: damage modeling and optimal experimental design from a mechanical and mathematical point of view
room : F403
[00271] Optimization aspects of experimental design approaches for sensor placement
Format : Talk at Waseda University
Author(s) :
Volker Schulz (Trier University)
Abstract : The information from sensors has to be treated in order to obtain properties of technical systems. The accuracy expressed in statistical concepts like covariance matrix and confidence regions depends on constituents of the measurement process. This talk discusses the effect of sensor placement and actuator design on these statistical properties and presents mathematical optimization approaches to optimize them.
[00272] Fracture propagation by using shape optimization techniques on Riemannian spaces
Format : Talk at Waseda University
Author(s) :
Tim Suchan (Helmut Schmidt University/University of the Federal Armed Forces Hamburg)
Kathrin Welker (TU Bergakademie Freiberg)
Winnifried Wollner (University of Hamburg)
Abstract : The concept of smooth phase fields has been used successfully to predict fracture propagation. However, it usually requires minimum two regularization parameters to be tuned. We present a novel approach for numerical fracture simulation which avoids the usage of phase fields. Instead, an objective functional that drives the evolution of the fracture is minimized with shape optimization techniques. We present the mathematical approach and numerical results for various commonly-used benchmarks.
[00246] Numerical modeling of crack propagation in concrete by means of cohesive zone modeling and a novel phase-field fracture approach
Format : Talk at Waseda University
Author(s) :
Rasoul Najafi Koopas (Helmut-Schmidt University)
Abstract : Two methodologies are developed for analyzing failure initiation and crack propagation in the highly inhomogeneous concrete mesostructure. By implementing efficient algorithms in Python, geometric features are generated and packed into a continuous phase. In the case of concrete, the continuous phase represents the mortar matrix, while the geometric features are the aggregates and voids of different sizes distributed randomly within the mortar matrix to represent the complex two-dimensional mesostructures of the concrete. The failure initiation and crack propagation of mesoscale concrete specimens are investigated using two different approaches, namely the Cohesive Zone Model and a novel Phase-Field fracture model. In the first approach, crack propagation is realized by generating zero-thickness Cohesive Interface Elements at the interfaces of solid elements. For this purpose, two-dimensional cohesive interface elements are generated $(i)$ within the constituent elements of the mortar matrix, $(ii)$ within the elements constituting the aggregates, and $(iii)$ at the Interfacial Transition Zone. Hence, all potential crack paths are simulated by assigning different Traction Separation laws to the cohesive interface elements generated in different regions of the mesoscale concrete specimen. In the second approach, a novel cohesive phase-field is developed by incorporating the idea proposed by Wu and Nguyen $(2018)$ and Geelen et al. $(2019)$ in which by a group of optimal characteristic functions, a phase-field regularized cohesive zone model with linear softening law is realized and applied to brittle fracture. Moreover, the implemented cohesive phase-field fracture is insensitive to the length scale parameter, which allows the use of a relatively coarser mesh, thereby significantly reducing the computational cost $[3]$. A series of mesoscale concrete specimens with identical properties $(volume density, size distribution, and aggregate shape)$ are simulated using the above approaches and the predicted crack paths are compared with each other.
References:
1- Wu, Jian-Ying, and Vinh Phu Nguyen. "A length scale insensitive phase-field damage model for brittle fracture." Journal of the Mechanics and Physics of Solids 119 (2018): 20-42.
2- Geelen, Rudy JM, et al. "A phase-field formulation for dynamic cohesive fracture." Computer Methods in Applied Mechanics and Engineering 348 (2019): 680-711.
3- Rezaei, Shahed, et al. "An anisotropic cohesive fracture model: Advantages and limitations of length-scale insensitive phase-field damage models." Engineering Fracture Mechanics 261 (2022): 108177.
[00231] Sequential subspace optimization for recovering stored-energy functions in hyperelastic materials
Format : Talk at Waseda University
Author(s) :
Lukas Vierus (Saarland University)
Rebecca Rothermel (Saarland University)
Thomas Schuster (Saarland University)
Anne Wald (University of Göttingen)
Abstract : Structural Health Monitoring demands for an efficient computation of parameters which characterize the mechanical behavior of elastic materials. Hyperelasticity describes a nonlinear elastic behavior where the second Piola-Kirchhoff stress tensor is given as a derivative of a scalar function representing the stored strain energy that encodes all mechanical properties of the underlying material. The mathematical model is represented by a high-dimensional parameter identification problem for a nonlinear, hyperbolic system with given initial and boundary values. We present an iterative method based on sequential subspace optimization leading to a significant acceleration compared to the Landweber method.
MS [00702] Sequential Decision Making for Optimization, Learning and Search
room : F412
[05274] Constraint active search as an alternative to optimization
Format : Talk at Waseda University
Author(s) :
Michael McCourt (Unaffiliated)
Abstract : Bayesian optimization is a sample efficient method for identifying high performing configurations of a black box function. This strategy is extremely powerful, but it is often a misguided tool for many practical circumstances -- problems with heavy noise, input/output imprecision, many objectives, discrepancy in cost of objective evalution, or a human-in-the-loop defined objective/preference all are situations where optimization may be the wrong strategy. Here, we discuss the shortcomings of optimization and propose an alternate strategy: the search for a satisfactory set of outcomes, as guided by user-defined performance thresholds. We refer to this as Constraint Active Search, and we present our motivating application as well as some theoretical analysis.
[05604] Optuna: A Software to Solve Black-box Optimization
Format : Talk at Waseda University
Author(s) :
Hideaki Imamura (Preferred Networks, Inc)
Abstract : Optuna is a software tool for solving black-box optimization problems. It provides a Pythonic interface to describe the search space and objective functions. It supports various algorithms, extensive visualization capabilities, and easy distributed optimization. In this presentation, we will introduce some of the latest features of Optuna and discuss the problem awareness that arises in black-box optimization and its application field, specifically hyperparameter optimization in machine learning.
[04910] Combinatorial 3D Shape Assembly with Sequential Decision-Making Processes
Format : Talk at Waseda University
Author(s) :
Jungtaek Kim (University of Pittsburgh)
Abstract : We require unit primitives, e.g., voxels and points, to create a 3D shape. In particular, if we consider a way to construct a 3D shape with the connectivity of primitives, a problem of 3D shape creation is characterized by sequential and combinatorial properties. By dealing with the sequential and combinatorial properties, we present a method for 3D shape assembly using sequential decision-making processes, i.e., Bayesian optimization and reinforcement learning.
[05288] Evolution Strategies: Principles and Practical Issues
Format : Talk at Waseda University
Author(s) :
Masahiro Nomura (CyberAgent)
Abstract : Evolution strategies (ES) is one of the most powerful frameworks for black-box continuous optimization. This talk will describe the design principles behind the empirical success of ES and the representative methods that have often been employed in science and industry. In addition, key issues that may be encountered when using ES in practice will be discussed.
MS [02435] Scaling Limits of Interacting Particle Systems
room : E501
[05450] Ergodic properties of rank-based diffusions
Format : Online Talk on Zoom
Author(s) :
Sayan Banerjee (University of North Carolina, Chapel Hill)
Amarjit Budhiraja (University of North Carolina, Chapel Hill)
Abstract : We investigate the long-time behavior of rank-based diffusions with infinitely many particles where the drift and diffusivity of each particle depends on its relative rank in the system. Unlike their finite dimensional analogues, such systems have infinitely many stationary measures and domains of attraction and extremality properties of such measures have been long-standing open questions. In this talk, we will explore some of these questions and provide answers to them in certain cases.
Based on joint works with Amarjit Budhiraja.
[04342] Systems with Riesz Interactions in the Mean-Field Regime
Format : Online Talk on Zoom
Author(s) :
Matthew Rosenzweig (MIT)
Sylvia Serfaty (Courant Institute, NYU)
Antonin Chodron de Courcel (Ecole Polytechnique)
Abstract : We present recent results on the large particle number and large time effective behavior of conservative or gradient dynamics for particle systems with mean-field interactions governed by a Coulomb or more general Riesz potential and subject to possible noise modeling thermal fluctuations. The talk will discuss modulated energy/free energy techniques for studying the rate of mean-field convergence, how the rate deteriorates with time, and how fluctuations around the mean-field limit behave.
[03026] Large Deviations for Multiscale Weakly Interacting Diffusions
Format : Online Talk on Zoom
Author(s) :
Zachary Bezemek (Boston University)
Konstantinos Spiliopoulos (Boston University)
Abstract : In this talk, we consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero simultaneously. We derive several equivalent formulations of the rate function, making connections between a mean-field control formulation and the formulation of Dawson-Gärtner.
[05239] Hydrodynamic Limits of non-Markovian Interacting Particle Systems on Sparse Graphs
Format : Online Talk on Zoom
Author(s) :
Ankan Ganguly (University of Pennsylvania)
Kavita Ramanan (Brown University)
Abstract : We consider hydrodynamic limits of non-Markovian interacting particle systems on large sparse graphs. Under mild conditions on the jump intensities and underlying graphs, it is shown that if the sequence of interaction graphs $G_n$ converges locally in probability to a limit graph $G$, then the corresponding sequence of empirical measures of the particle trajectories converges weakly to the law of the marginal dynamics at the root vertex of $G$.
MS [00322] Methodological advancement in rough paths and data science
room : E502
[01385] A real analytic view on signatures
Format : Talk at Waseda University
Author(s) :
Josef Teichmann (ETH Zurich)
Valentin Tissot-Daguette (Princeton U)
Abstract : We introduce classical (convenient) concepts of real analytic functions on path spaces and apply them to the
approximation of path space functionals. We also provide an invariance theory perspective on the Hambly-Lyons
theorem that signatures characterize paths up to tree like equivalences.
[01366] PCF-GAN: generating sequential data via the characteristic function of measures on the path space
Format : Talk at Waseda University
Author(s) :
Hao Ni (UCL)
Hang Lou (UCL)
Siran Li (Shanghai Jiao Tong University )
Abstract : Implicit Generative Models(IGMs) are powerful tools for generating high-fidelity synthetic data. However, they struggle to capture the temporal dependence of time-series data. To tackle this issue, we directly compare the path distributions via the characteristic function of measures on the path space(PCF) from rough path theory, which uniquely characterises the law of stochastic processes. We then develop a novel PCF-GAN model by incorporating PCF with IGM for time series generation, leading to significant performance boost.
[01336] Nyström approximation and convex kernel quadrature
Format : Talk at Waseda University
Author(s) :
Satoshi Hayakawa (University of Oxford)
Abstract : We will discuss a refined analysis of Nyström approximation for an integral operator based on statistical learning theory, and demonstrate how we can use these results to obtain an improved estimate of the performance of convex kernel quadrature rules that are given by the low-rank kernel of Nyström approximation.
[01374] Taylor remainder estimate for rough differential equations
Format : Online Talk on Zoom
Author(s) :
Danyu Yang (Chongqing University)
Abstract : We consider a remainder estimate for truncated Taylor expansion for differential equations driven by inhomogeneous geometric rough paths. The estimate can be applied to differential equations driven by general stochastic processes with a regular drift term. It can also be useful when dealing with differential equations driven by branched rough paths and quasi-geometric rough paths which are isomorphic to inhomogeneous geometric rough paths.
MS [00570] Title: Machine Learning and Statistical Approaches for PDE Based Inverse Problems in Imaging
room : E503
[04498] Train Like a (Var)Pro: Efficient Training of DNNs
Format : Talk at Waseda University
Author(s) :
Elizabeth Newman (Emory University)
Lars Ruthotto (Emory University)
Bart van Bloemen Waanders (Sandia National Laboratories)
Joseph Hart (Sandia National Laboratories)
Abstract : Deep neural networks (DNNs) have excelled as high-dimensional function approximators and are trained by solving a challenging stochastic optimization problem. In this talk, we will make DNN training easier by exploiting separability of common architectures; i.e., linear in the final weights. We will leverage this linearity by eliminating the weights through variable projection. We will demonstrate the efficacy of this approach through numerical examples and will conclude with a discussion of extensions and new applications.
[05369] Machine Learning for Inverse Problems in Electrical Impedance Tomography
Format : Talk at Waseda University
Author(s) :
Hyeuknam Kwon (Yonsei University, Mirae campus)
Abstract : This paper discusses the application of machine learning techniques to solve inverse problems in electric impedance tomography (EIT). EIT is a non-invasive medical imaging technique used to reconstruct the distribution of conductivity within the human body using electrical measurements of surfaces. However, the inverse problem in EIT image reconstruction and its application suffers from various difficulties.The author provides these problems and machine learning techniques to solve them.
MS [00851] Mathematics for Big Data and Artificial Intelligence: models and challenges
room : E504
[01685] Equivariant non-expansive operators as a bridge between TDA and geometric deep learning
Format : Talk at Waseda University
Author(s) :
Patrizio Frosini (University of Bologna)
Abstract : Group equivariant non-expansive operators $(\mathrm{GENEOs})$ have been recently introduced as mathematical tools for approximating data observers when data are represented by real-valued or vector-valued functions $(\mathtt{{https://rdcu.be/bP6HV}})$. The use of these operators is based on the assumption that data interpretation depends on the observers' geometric properties. In this talk we will illustrate some recent results, showing how GENEOs can make available an interesting link between topological data analysis and geometric deep learning.
[01623] a new machine learning paradigm for protein pocket detection based on Group Equivariant Non Expansive Operators
Format : Talk at Waseda University
Author(s) :
Alessandra Micheletti (Università degli Studi di Milano)
Giovanni Bocchi (Università degli Studi di Milano)
Patrizio Frosini (Università degli Studi di Bologna)
Carmine Talarico (Dompè Farmaceutici)
Filippo Lunghini (Dompè Farmaceutici)
Andrea Beccari (Dompè Farmaceutici)
Carmen Gratteri (University Magna Grecia Catanzaro)
Alessandro Pedretti (Università degli Studi di Milano)
Abstract : Protein pockets detection is a key problem in the context of drug development, since the ability to identify a small number of potential binding sites, allows to speed up drug discovery procedures. In this talk we will show how Group Equivariant Non Expansive Operators (GENEOs) can be used to build a geometrical machine learning method, able to detect protein pockets better than ML techniques already in use, but being based only on 17 unknown parameters.
[01528] SLiSeS: Subsampled Line Search Spectral Gradient Method for Finite Sums
Format : Online Talk on Zoom
Author(s) :
Stefania Bellavia (University of Florence)
Natasa Krejic (University of Novi Sad)
Natasa Krklec Jerinkic (University of Novi Sad)
Marcos Alejandro Raydan (NOVA University Lisbon)
Abstract : In this paper, we aim to exploit advantages of spectral method in stochastic optimization framework, especially in mini-batch subsampling case which is often used in Big Data setup. In order to let the spectral coefficient explore the spectrum of the approximate Hessian, we keep the same sample for several iterations before we subsample again. We analyze conditions for almost sure convergence and present initial numerical results that show the advantages of the proposed method.
[01698] Interpretable models for large-scale tabular datasets
Format : Online Talk on Zoom
Author(s) :
Claudia Soares (NOVA School of Science and Technology)
Abstract :
The purpose of this work is two-fold: on the one hand, to demonstrate that machine learning models can be considered a powerful alternative to predicting real-world variables in high-stakes scenarios, and, on the other hand, to propose a new method that is empirically the state-of-the-art rule-based method for large datasets. We accompany our method with tailored algorithms for fast learning in large datasets.
MS [02163] Recent Developments in Stochastic Numerics and Computational Finance
room : E505
[03032] Policy improvement algorithm for an optimal consumption and investment problem under general stochastic factor models
Format : Talk at Waseda University
Author(s) :
Kazuhiro Yasuda (Hosei university)
Hiroaki Hata (Hitotsubashi university)
Abstract : In this talk, we propose a policy improvement algorithm for a consumption and investment problem on a finite time horizon to optimize a discounted expected power utility of consumption and terminal wealth. We employ a general stochastic factor model which means that the returns and volatilities of assets are random and affected by some economic factors, modeled as diffusion processes. We establish an iteration procedure converging to the value function and the optimal strategies obtained in Hata, Nagai and Sheu (2018). Some numerical results are shown to understand convergence behaviors of the algorithm.
[03381] Growth in Fund Models
Format : Talk at Waseda University
Author(s) :
Hyeng Keun Koo (Ajou University)
Constantinos Kardaras (London School of Economics)
Johannes Ruf (London School of Economics)
Abstract : We study estimation of growth in fund models, i.e., statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. The loss of growth due to estimation error in fund models under local frequentist estimation is determined entirely by the number of funds. A shrinkage method that targets maximal growth with the least amount of deviation is proposed.
[03015] Carbon Emissions Pricing by Forward and Double Barrier Backward SDE approach
Format : Talk at Waseda University
Author(s) :
Tadashi Hayashi (Mitsubishi UFJ Trust and Banking Corporation)
Abstract : Under the circumstances of global warming caused by increasing in greenhouse gases, there are many theoretical and empirical studies in carbon emissions to control and reduce the gases. Our study is focused on the carbon emissions pricing via Forward and Double Barrier BSDE as another pricing approach. This modelling would be a new approach of carbon emissions pricing and therefore lead to a new chance of empirical simulation.
[03307] Irreversible consumption habit under ambiguity: singular control and optimal G-stopping time
Format : Talk at Waseda University
Author(s) :
Kyunghyun Park (Nanyang Technological University)
HOI YING WONG (The Chinese University of Hong Kong )
Kexin Chen (The Hong Kong Polytechnic University)
Abstract : Consider robust utility maximization with an irreversible consumption habit, where an agent concerned about model ambiguity is unwilling to decrease consumption and must simultaneously contend with a disutility (i.e., an adjustment cost) due to a consumption increase. While the optimization is a robust analog of singular control problems over a class of consumption-investment strategies and a set of probability measures, it is a new formulation that involves non-dominated probability measures of the diffusion process for the underlying assets in addition to singular controls with an adjustment cost. This paper provides a novel connection between the singular controls in the optimization and the optimal $G$-stopping times in a $G$-expectation space, using a duality theory. This connection enables to derive the robust consumption strategy as a running maximum of the stochastic boundary, which is characterized by a free boundary arising from the optimal $G$-stopping times. The duality, which relies on arguments based on reflected $G$-BSDEs, is achieved by verifying the first-order optimality conditions for the singular control, the budget constraint equation for the robust strategies, and the worst-case realization under the non-dominated measures.
MS [01158] Oblique derivative boundary volume problems - numerical methods and applications
room : E506
[02007] The finite element method for solving the oblique derivative boundary value problems in geodesy
Author(s) :
Marek Macák (Slovak University of Technology )
Zuzana Minarechová (Slovak University of Technology )
Karol Mikula (Slovak University of Technology )
Robert Cunderlik (Slovak University of Technology )
Abstract : We present approach to approximate the solution of the Laplace equation with an oblique derivative boundary condition by the finite element method. For this approach we perform testing experiments to study its behaviour and convergence. Finally, the usefulness of this approach is demonstrated by using it to gravity field modelling, namely, to approximate the solution of a geodetic boundary value problem in Himalayas.
[02121] Curvature and Torsion of Gravitational Plumb Lines
Author(s) :
Zhi Yin (Jiangsu Ocean University)
Nico Sneeuw (University of Stuttgart)
Keifei Zhang (China University of Mining and Technology)
Abstract : In our previous research, we reformulate the gravitational field in terms of a potential flow; the gravitational vector field is mapped onto a potential-flow velocity field, in which the plumb line and the stream line are equivalent to each other. Here, we further investigate the curvature and the torsion of a gravitational plumb line by utilizing the fundamental equations of the potential flow. We expect them to have a good practical application in exploration geophysics.
[02131] The finite volume method for solving the oblique derivative BVP in geodesy
Author(s) :
Zuzana Minarechová (Slovak University of Technology)
Marek Macák (Slovak University of Technology )
Karol Mikula (Slovak University of Technology)
Róbert Čunderlík (Slovak University of Technology)
Abstract : We formulate the oblique derivative boundary value problem applied in gravity field and present two approaches to its solution by the finite volume method. In the first approach, the oblique derivative in the boundary condition is decomposed into normal and two tangential components and approximated by the central scheme. In the second approach, the oblique derivative in the boundary condition is treated by the first order upwind scheme. Both approaches are tested by various experiments.
[02887] Finite Volume Approximate Solutions of Some Oblique Derivative Boundary Value Problems and Applications
Author(s) :
Abdallah BRADJI (University of Annaba-Algeria)
Abstract : In this work, we review previous works on FVMs (Finite Volume methods) for Elliptic and Parabolic equations with oblique derivatives boundary conditions. We start by the first two works with Gallouet (Aix-Marseille University, France) which dealt with FV on the so-called Admissible meshes for Elliptic equations.
We subsequently describe our work with Fuhrmann (WIAS, Berlin-Germany) which dealt with FV using the nonconforming meshes and the SUSHI for Elliptic and Parabolic equations with oblique derivatives boundary conditions.
Finally, we focus on FVMs for Elliptic equations with mixed oblique boundary equations and application to Inverse Problems. This work is done jointly with Lesnic (Leeds University, UK).
We sketch at the end some works, related to the subject, which are in progress.
contributed talk: CT093
room : E507
[01725] Correlated random displacements computed by the Spectral Lanczos Decomposition Method and Barycentric Lagrange Treecode
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : Brownian Dynamics simulations require correlated random displacements ${\bf g} = \sqrt{D}{\bf z}$ to account for hydrodynamic interactions among solvated biomolecules and polymers, where $D$ is the diffusion matrix based on the Rotne-Prager-Yamakawa tensor and ${\bf z}$ is a normal random vector. The Spectral Lanczos Decomposition Method (SLDM) computes a sequence of approximations to ${\bf g}$, but each iteration requires a matrix-vector product $D{\bf q}_k$, where ${\bf q}_k$ is the $k$th Lanczos vector. The present work applies the barycentric Lagrange treecode (BLTC) to accelerate the matrix-vector product, and numerical results show the performance of the SLDM-BLTC in serial and parallel calculations.
[02108] Particle dynamics model for the coarsening process of phase separation
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : The Cahn-Hilliard equation describes phase separation phenomena well.
It has been proven that this solution converges to one of the Hele-Shaw problems in the limit of one coefficient parameter to zero, which is mathematically satisfactory as an order-reduction result.
However, the computation of the Hele-Shaw problem is also problematic.
Therefore, we observed the coarsening process of phase separation phenomena and subsequently considered a particle dynamics model that roughly reproduces the process.
[00241] Adaptive sparse interpolation in high dimensions and applications to surrogate modeling in chemical engineering.
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : We present theoretical and practical aspects on the development of accurate surrogate models from first-principles, multiscale, PDE models for industrial chemico-physical processes. We will present many applications in Phosphate industry done in collaboration with OCP-Group in Morocco.
The surrogate models are based on sparse multivariate polynomial interpolation. The goal is to reduce the computational time while preserving its physical properties such as monotonicity and positivity.
Saad Benjelloun (Makhbar Mathematical Sciences Research institute)
saad benjelloun (Makhbar institute)
Abdellah Chkifa (UM6P)
[02701] Pricing Multi-Asset American Options in Dynamic Programming with Sparse Grids
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : We introduce a sparse grid interpolation and quadrature scheme for pricing multi-asset American option based on dynamic programming. At each time step, we take advantage of the smoothness of the continuation value function, allowing for fast convergence of interpolation. In the multi-dimensional spatial domain, conditional expectations are estimated by sparse grid quadrature or QMC, depending on the asset models. Our algorithm is proven to have accurate error estimates, and numerical experiments demonstrate its efficiency.
[00229] Mathematical modeling of spatial distribution of COVID-19 epidemic
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : This study provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. We showed the spatial distribution of the model compartments when the basic reproduction rate R0 < 1 and R0 > 1. We demonstrate the model's effectiveness by performing numerical simulations and then investigated the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19 epidemic.
MS [02327] Stability of Numerical Linear Algebra Algorithms
room : E508
[04236] Numerical stability of block classical Gram-Schmidt process
Format : Talk at Waseda University
Author(s) :
Miroslav Rozloznik (Czech Academy of Sciences)
Erin Claire Carson (Charles University)
Kathryn Lund (Charles University)
Abstract : The block version of the classical Gram--Schmidt (BCGS) method is often employed to efficiently compute orthogonal bases for Krylov subspace methods and eigenvalue solvers, but a rigorous proof of its stability behavior has not yet been established. It is shown that the usual implementation of BCGS can lose orthogonality at a rate worse than $O(\varepsilon) \kappa^{2}(X)$, where $X$ is the input matrix and $\varepsilon$ is the unit roundoff. A useful intermediate quantity denoted as the Cholesky residual is given special attention and, along with a block generalization of the Pythagorean theorem, this quantity is used to develop more stable variants of BCGS. These variants are proven to have at most $O(\varepsilon) \kappa^2(X)$ loss of orthogonality with relatively relaxed conditions on the intrablock orthogonalization routine satisfied by the most commonly used algorithms. A variety of numerical examples illustrate the theoretical bounds.
[02742] Cross-interactive residual smoothing for block Lanczos-type methods for solving linear systems with multiple right-hand sides
Format : Talk at Waseda University
Author(s) :
Kensuke Aihara (Tokyo City University)
Akira Imakura (University of Tsukuba)
Keiichi Morikuni (University of Tsukuba)
Abstract : Block Lanczos-type methods often exhibit large oscillations in the residual norms, leading to a large residual gap and a loss of attainable accuracy of the approximations. Cross-interactive residual smoothing $(\text{CIRS})$ was recently developed for the standard/global Lanczos-type methods to obtain smooth convergence behavior and reduce the residual gap. We therefore extend CIRS to the block version. Rounding error analysis and numerical experiments demonstrate the effectiveness of the presented approach.
Abstract : We introduce a low-synch GMRES algorithm based on Gauss-Seidel (MGS) and Jacobi
(CGS) iterations. The correction matrix $T = (I + L)^{-1}$ for the projector $P = I - QTQ^T$
is a rank-1 perturbation, and results in low backward error. These ideas are applied to AMG.
The smoother performs a triangular solve and subsequent iterations apply Jacobi or
$(I - uv^T)r_k$, $u = L_{k,1:k-1}$ and $v = e_k$. GMRES convergence
remains the same with this iterative refinement.
[05049] Improving convergence and stability of Krylov subspace methods for solving linear systems
Format : Talk at Waseda University
Author(s) :
hassane sadok (université du Littoral Cote d OPale)
Abstract : Krylov subspace methods are widely used for the iterative solution of a large variety of linear systems of equations with one or several right hand sides or for solving nonsymmetric eigenvalue problems.
The purpose of this talk is to compare several variants of the implementation of Krylov subspace methods, including GMRES, QMR, and CMRH methods. These schemes are based on the two-sided Gram-Schmidt process methods and differ in their use of the inner product \(=
\) where \(P=I- C C^+\) is a projector. We provide a unified description of the methods discussed and derive new expressions and bounds for the residual errors.
MS [00107] Randomized numerical linear algebra
room : E603
[03344] Randomized low-rank approximation: Where we've been and where we're going
Format : Talk at Waseda University
Author(s) :
Robert Webber (California Institute of Technology)
Abstract : I will survey randomized algorithms for low-rank matrix approximation. These algorithms are helpful for speeding up computations involving high-dimensional matrices. When the singular values of the target matrix decay quickly, the most efficient low-rank approximation algorithms are "randomized SVD" and, if the matrix is positive semidefinite, "randomized Nyström". When the singular values of the target matrix decay slowly, low-rank approximation becomes more difficult and the best-performing algorithms are instead randomized block Krylov methods.
[04049] Efficient Bounds for Canonical Angles in Randomized Subspace Approximations
Format : Online Talk on Zoom
Author(s) :
Yijun Dong (UT Austin)
Per-Gunnar Martinsson (UT Austin)
Yuji Nakatsukasa (University of Oxford)
Abstract : Randomized subspace approximation is an effective approach for approximating partial SVDs of large matrices, whose accuracy has been extensively analyzed in terms of residual errors. However, our understanding of the computed singular subspaces remains limited. We present bounds and estimates for canonical angles of randomized subspace approximation that can be computed efficiently either a priori or a posteriori. Numerical experiments demonstrate the empirical effectiveness of these canonical angle approximations under various algorithmic choices.
[03767] Randomized Nyström approximation for symmetric indefinite matrices
Format : Talk at Waseda University
Author(s) :
Taejun Park (University of Oxford)
Yuji Nakatsukasa (University of Oxford)
Abstract : In this talk, we present a variant of the Nyström method for symmetric indefinite matrices. The Nyström method is a popular choice for symmetric positive semi-definite matrices. However, the method can fail when the matrix is indefinite, for which the error can be large. We first identify the main challenges in finding a robust Nyström approximation to symmetric indefinite matrices and describe an algorithm, whose robustness for symmetric indefinite matrices is illustrated with experiments.
[04567] The Cluster and the Gap in Randomized Subspace Iteration
Format : Talk at Waseda University
Author(s) :
Eric Hallman (Google)
Abstract : This talk concerns the convergence rates of the singular values and vectors when running randomized subspace iteration. Its aim is to present a single clean approach (based on the techniques of (Yuan/Gu/Li, 2018)) that can be used to derive a variety of existing bounds in the literature, both gap-dependent and gap-independent. Limitations of the proof strategy are discussed, as well as its extensions to randomized block Lanczos.
MS [02411] Recent Advances in Numerical Methods for Nonlinear Equations and Applications
room : E604
[03387] Efficient iterative scheme for system of nonlinear equations
Format : Online Talk on Zoom
Author(s) :
Himani Arora (Guru Nanak Dev University, Amritsar)
Abstract : Solving systems of nonlinear equations is an important and interesting task in science and engineering. But finding a solution of these systems using analytical methods is almost impossible, so one has to rely on iterative techniques for solution of such problems. The main motive of this talk is to discuss an efficient iterative technique for solving systems of nonlinear equations. The most time consuming and hard task while designing an iterative scheme is the evaluation of the inverse of the derivative. The main feature of the scheme presented is that it only utilizes one inverse evaluation per iteration, which makes the scheme computationally efficient. The efficiency of the scheme is verified through a number of real-world problems like integral equations and boundary value problems etc.
[03084] Non-Linear GAC Model for GIS Image Segmentation of Deforestation in Nusajaya Malaysia
Format : Online Talk on Zoom
Author(s) :
norma binti alias (universiti teknologi malaysia)
fiza zafar (Bahauddin Zakariya University)
Abstract : Based on the statistical data from website Global Forest Watch, from year 2001 to 2021, Nusajaya , Johor Malaysia experience a loss of 745kha of tree cover which is equivalent to a 47% decrease and a 292Mt of increase in CO2 emissions . GIS images able to visualize the deforestation problem. Digital transformation of images can be analysed by non-linear GAC Model for image segmentation. Numerical performance evaluation obtained the validation and verification of the analysis.
[03352] Analysis of Love-type wave in a nonlocal piezoelectric composite
Format : Talk at Waseda University
Author(s) :
Vanita Sharma (SVKM's NMIMS Chandigarh)
Abstract : The aim of this research article is to provide a more detailed investigation of the size influences in piezoelectric material subjected to Love-type wave propagation. With the goal to consider the size influences of the structure, the Eringen's nonlocal theory is utilized. The dispersion relations for piezoelectric composite are obtained. Thereafter, detailed investigations of various affecting parameters viz. nonlocal parameter, material parameters etc. on the wave dispersion characteristics of size-dependent nanoscaled structure are addressed.
[03396] Mathematical modelling of Wave Equation in Elastodynamics Problems
Format : Online Talk on Zoom
Author(s) :
Maryam Abdullah Alharbi (UTM)
Norma binti Alias (UTM)
Abstract : The study of the wave equation in elastodynamics is crucial for understanding various physical phenomena. We present a mathematical model that describes the behavior of waves in elastodynamics. The model is stable to solve using FDM, which means this model is convergent to the approximate solution. Additionally, we highlight the relationship between blood flow and elastodynamics. We discuss the behavior of blood vessels and their interaction with blood as a fluid.
MS [01064] Recent Advances on Manifold Optimization
room : E605
[04571] A Riemannian ADMM
Format : Online Talk on Zoom
Author(s) :
Shiqian Ma (Rice University)
Abstract : We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning and statistics such as the K-means clustering, sparse spectral clustering, and orthogonal dictionary learning. We propose a Riemannian alternating direction method of multipliers to solve this class of problems. Our algorithm adopts easily solvable subproblems in each iteration. The iteration complexity of the proposed algorithm for obtaining an $\epsilon$-stationary point is analyzed under mild assumptions. Numerical experiments are conducted to demonstrate the advantage of the proposed method.
[04455] Local stochastic algorithms for Riemannian optimization
Format : Online Talk on Zoom
Author(s) :
Sam Davanloo Tajbakhsh (The Ohio State University)
Abstract : We consider optimizing a function available through its first-order stochastic oracle over a Riemannian manifold in a distributed setting with the coordination of a central server. We develop local stochastic approximation methods that perform multiple local stochastic updates in parallel on different clients and merge them in some intervals. Theoretical convergence results in different optimization and communication settings will be presented.
[03649] Riemannian Interior Point Methods for Constrained Optimization on Manifolds
Format : Talk at Waseda University
Author(s) :
Zhijian Lai (University of Tsukuba)
Akiko Yoshise (University of Tsukuba)
Abstract : We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method (RIPM), is for solving Riemannian constrained optimization problems. We establish its locally superlinear and quadratic convergence under the standard assumptions. Moreover, we show its global convergence when it is combined with a classical line search. Numerical experiments show the stability and efficiency of our method.
[03887] Riemannian Adaptive Optimization Algorithms and Their Applications
Format : Talk at Waseda University
Author(s) :
Hiroyuki Sakai (Meiji University)
Hideaki Iiduka (Meiji University)
Abstract : We will talk about Riemannian adaptive optimization algorithms to solve the Riemannian stochastic optimization problems. In Euclidean space, adaptive optimization algorithms, such as AdaGrad, Adam, Adadelta, and AMSGrad, are widely used. However, adaptive optimization algorithms cannot be naturally extended to general Riemannian manifolds, due to the absence of a canonical coordinate system.
We introduce the ways to generalize adaptive optimization algorithms to Riemannian manifolds and consider their applications.
MS [00763] Long-time dynamics of numerical methods for nonlinear evolution equations
room : E606
[03792] Bourgain techniques for error estimates at low regularity
Format : Talk at Waseda University
Author(s) :
Alexander Ostermann (Universität Innsbruck)
Lun Ji (Universität Innsbruck)
Frédéric Rousset (Université Paris-Saclay)
Katharina Schratz (Sorbonne Université)
Abstract : Standard numerical integrators suffer from order reduction when applied to nonlinear dispersive equations with non-smooth initial data. For such problems, we present filtered integrators that exhibit superior convergence rates at low regularity. Furthermore, due to the nonexistence of suitable embedding results, the error analysis at very low regularity cannot be carried out in standard Sobolev spaces. Instead, new techniques are required. They are based on Bourgain’s seminal work and will be sketched in the talk.
[01832] Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schr\"odinger equation
Format : Talk at Waseda University
Author(s) :
Yue Feng (Laboratoire Jacques-Louis Lions)
Abstract : In this talk, I will present the improved uniform error bounds of the time-splitting Fourier pseudospectral methods for the long-time dynamics of the Schr\"odinger equation with small potential and the nonlinear Schr\"odinger equation with weak nonlinearity. The main technique introduced is the regularity compensation oscillation (RCO), which control the high frequency modes by the regularity of the exact solution and the low frequency modes by phase cancellation and energy method.
[04274] A symmetric low-regularity approximation to the nonlinear Schrödinger equation
Format : Talk at Waseda University
Author(s) :
Yvonne Alama Bronsard (Sorbonne Université, LJLL)
Abstract : In this talk we will discuss the approximation to nonlinear dispersive equations which ask for low-regularity assumptions on the initial data, both for deterministic and random initial data.
We will put forth a novel time discretization to the nonlinear Schrödinger equation which allows for low-regularity approximation while maintaining good long-time preservation of the density and energy on the discrete level
[04742] Symmetric low regularity integrators via a forest formula
Format : Talk at Waseda University
Author(s) :
Yvain Bruned (Université de Lorraine)
Abstract : In this work, we will present general low regularity schemes that should encompass some of the symmetries of a given dispersive PDEs. We extend the low resonance decorated trees approach to a richer framework where we explore different ways of iterating Duhamel'formula and interpolating the lower part of the resonance for a Taylor approximation. This gives more degrees of freedom, encapsulated via a new forest formula that provides the general form for these new schemes. From this formula, we are able to derive conditions on the coefficients for finding new symmetric schemes. We believe that such an approach could tackle other symmetries.
MS [00727] Recent Advances in Fast Iterative Methods for PDE Problems
room : E701
[02883] Multigrid Methods for Saddle-Point Matrices with Structured Blocks
Format : Talk at Waseda University
Author(s) :
Isabella Furci (University of Genoa)
Matthias Bolten (University of Wuppertal)
Marco Donatelli (University of Insubria)
Paola Ferrari (University of Wuppertal)
Abstract : We consider efficient multigrid methods for large linear systems with particular saddle-point structures. Often, powerful smoothers are used to take into account the special coupling. Alternatively, Notay recently proposed an algebraic approach that analyzes properly preconditioned saddle-point problems.
We provide theoretical tools to analyze the latter procedure when applied to saddle-point systems whith (multilevel) block-Toeplitz blocks. As a test problem, we consider the linear system stemming from the Finite Element approximation of the Stokes equation.
[05299] New Linear Solvers Features and Improvements in Trilinos
Format : Online Talk on Zoom
Author(s) :
Jennifer Ann Loe (Sandia National Laboratories)
Ichitaro Yamazaki (SNL)
Sivasankaran Rajamanickam (Sandia National Laboratories)
Heidi Thornquist (Sandia National Laboratories)
Christian Glusa (Sandia National Laboratories)
Abstract : Trilinos is a large open-source mathematical software library which includes algorithms for discretization, optimization, preconditioners, non-linear solvers, and linear solvers. Its Tpetra linear algebra backend allows it to run effectively on highly parallel computers and various GPU accelerators. In this talk, we discuss recent improvements and additions to the Trilinos linear solver capabilities. One addition allows mixed precision solver and preconditioner combinations. Another recent improvement provides an abstract interface for small dense matrices in the linear solvers, eliminating extra data movement for GPU-based computers. We will demonstrate potential performance gains with use of the new linear solvers features.
[04769] A rational preconditioner for multi-dimensional Riesz fractional diffusion equations
Format : Online Talk on Zoom
Author(s) :
Mariarosa Mazza (University of Insubria)
Lidia Aceto (University of Eastern Piedmont)
Abstract : Starting from a rational approximation of the Riesz operator expressed as the integral of the standard heat diffusion semigroup, we propose a rational preconditioner for solving linear systems arising from the finite difference/element discretization of multi-dimensional Riesz fractional diffusion equations. We show that, despite the lack of clustering just as for the Laplacian, for fractional orders close to 1 our preconditioner provides better results than the Laplacian itself, while sharing the same computational complexity.
[02906] Some step-size independent theoretical bounds for preconditioning techniques of discrete PDEs
Format : Talk at Waseda University
Author(s) :
Xuelei Lin (Harbin Institute of Technology Shenzhen)
Abstract : It is well-known that the condition number of coefficient matrices arising from discretization of differential equations increases as the grid gets refined, because of which iterative solvers converge slowly for the linear systems when the grid is dense. In this talk, preconditioning techniques for discretization of some differential equations are introduced, with which some Krylov subspace solvers for the preconditioned systems are proven to have a linear convergence rate independent of the stepsizes. Numerical results are also reported.
MS [00719] Recent Advances in Numerical PDE and Scientific Machine Learning
room : E702
[03076] Deep neural operator for learning transient response of composites subject to dynamic loading
Format : Online Talk on Zoom
Author(s) :
Zhen Li (Clemson University)
Minglei Lu (Clemson University)
Ali Mohammadi (Clemson University)
Zhaoxu Meng (Clemson University)
Gang Li (Clemson University)
Abstract : Deep neural operator (DNO) is used learn the transient response of composites as surrogate of physics-based finite element analysis (FEA). We consider a 3D composites beam formed by two metals with different Young's modulus subject to dynamic loads. DNO is trained using sequence-to-sequence learning with incremental learning methods based on 5000 FEA data, leading to a 100X speedup. Results show that DNO can predict the transient mechanical response of composites at an accuracy of 97%.
[05598] Analysis of the derivative-free method for solving PDEs using neural networks
Format : Talk at Waseda University
Author(s) :
Jihun Han (Dartmouth College)
Yoonsang Lee (Dartmouth College)
Abstract : The derivative-free loss method (DFLM) uses a stochastic (Feynman-Kac) formulation to solve a certain class of PDEs using neural networks. The method avoids the derivative calculation from neural networks, using statistical information of local walkers to represent the solution. This work analyzes the effect of the time step and the number of walkers in DFLM. The analysis shows a lower bound for the time step to guarantee a certain accuracy, which contrasts the standard numerical methods with an upper bound. We also show a linear dependence of the walker in the accuracy.
[03762] Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
Format : Talk at Waseda University
Author(s) :
Seungchan Ko (Inha University)
Seok-Bae Yun (Sungkyunkwan University)
Youngjoon Hong (Sungkyunkwan University)
Abstract : In this talk, I will discuss the convergence analysis of unsupervised Legendre-Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial differential equations (PDEs). Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Using the fact that the corresponding loss function is equivalent to the residual induced by the linear algebraic system depending on the choice of basis functions, we prove that the minimizer of the discrete loss function converges to the weak solution of the PDEs. Numerical evidence will also be provided to support the theoretical result. Key technical tools include the variant of the universal approximation theorem for bounded neural networks, the analysis of the stiffness and mass matrices, and the uniform law of large numbers in terms of the Rademacher complexity.
[04540] Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs
Format : Talk at Waseda University
Author(s) :
Lei Ma (Shanghai normal university)
Abstract : Mathematical models considering nonlocal interactions with uncertainty quantification can be formulated as stochastic fractional partial differential equations (SFPDEs). There are many challenges in solving SFPDEs numerically, especially for long-time integration. Here, we combine the bi-orthogonal (BO) method for representing stochastic processes with physics-informed neural networks (PINNs) for solving partial differential equations to formulate the bi-orthogonal PINN method (BO-fPINN) for solving time-dependent SFPDEs. We demonstrate the effectiveness of the BO-fPINN method for different benchmark problem.
MS [00974] Finite element complexes and multivariate splines
room : E703
[05202] The strain Hodge Laplacian and discretisation of the incompatibility operator
Format : Talk at Waseda University
Author(s) :
Francis Raul Anthony Aznaran (University of Oxford)
Kaibo Hu (University of Oxford)
Abstract : Motivated by the physical relevance of many Hodge Laplace PDEs from the FEEC, we analyse the Hodge Laplacian arising from the strain space $H(\mathrm{inc};\mathbb{R}^{d\times d}_{\mathrm{sym}})$, $\mathrm{inc} := \mathrm{rot}\circ\mathrm{rot}$, in the elasticity complex. We propose an adaptation of $C^0$-interior penalisation for the incompatibility, using the Regge element to discretise the strain. Building on pioneering work by van Goethem, we discuss promising connections between functional analysis of the $\mathrm{inc}$ operator and Kröner's intrinsic theory of defect elasticity.
[02874] Nonconforming finite elements for the Brinkman Problems and Quad-curl Problems on Cubical Meshes
Format : Talk at Waseda University
Author(s) :
Qian Zhang (Michigan Technological University)
Abstract : In this talk, I will present two families of nonconforming elements on cubical meshes: one for the quad-curl problem and the other for the Brinkman problem. The element for the quad-curl problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the parameter nu. The lowest-order elements for the quad-curl and the Brinkman problems have 48 and 30 degrees of freedom, respectively. The two families of elements, as a nonconforming approximation to H((gradcurl)) and H1, can form a discrete Stokes complex together with the Lagrange element and the DG element.
[05642] Distributional finite element BGG complexes
Format : Talk at Waseda University
Author(s) :
Jay Gopalakrishnan (Portland State University)
Kaibo Hu (University of Oxford)
Ting Lin (Peking University)
Joachim Schöberl (TU Wien)
Qian Zhang (Michigan Technological University)
Abstract : Distributional finite elements generalize classical concepts by allowing measures (Dirac deltas) as shape functions. Distributional elements were used to derive equilibrated residual error estimators (Braess, Schöberl 2008) and discretization of the stress-displacement formulation of linear elasticity (Pechstein, Schöberl 2011, TDNNS). Regge calculus from discrete relativity can be interpreted as a finite element version of metric with distributional curvature (Christiansen 2008). In this talk, we review the concept of distributional elements and discuss progress in discretizing Bernstein-Gelfand-Gelfand (BGG) diagrams and sequences.
contributed talk: CT092
room : E704
[02377] Accurate approximation of layer potentials evaluated near surfaces of spherical topology
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Layer potentials, integrals representing the solution of a PDE when solved using boundary integral methods, are notoriously difficult to accurately evaluate close to the boundary of the domain due to a rapidly varying integrand. The presented quadrature method resolves this key challenge by factoring the integrand into a smooth and a simpler nearly singular part, then efficiently expanding the smooth part in a new basis and treating the remaining nearly singular integrals analytically.
Anna-Karin Tornberg (KTH Royal Institute of Technology)
[01016] Approximate formula for indefinite convolutions by the DE-Sinc method
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Approximate formula for indefinite convolutions by means of the Sinc approximation has been proposed by Stenger. The formula is based on his Sinc indefinite integration formula combined with the single-exponential transformation. Recently, the Sinc indefinite integration formula was improved by replacing the single-exponential transformation with the double-exponential transformation. Based on the improved formula, this study proposes a new approximate formula for indefinite convolutions.
[00225] Multidimensional WENO-AO Reconstructions Using A Simplified Smoothness Indicator
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Finite volume, weighted essentially non-oscillatory (WENO) schemes using the simple smoothness indicator $\sigma= 1/(L-1) \sum_{j} (u_{j} - u_{m})^2$, are presented, where $L$ is the number of mesh elements in the stencil, $u_j$ is the local function average over $j$th element, and index $m$ gives the target element. We develop a modification of WENO-Z weighting that gives a reliable and accurate reconstruction of adaptive order. Convergence results are proved. Numerical experimental results are also provided.
[02664] Numerical compression of QMC rules for integration
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : We introduce an algorithm for Tchakaloff-like compression of Quasi-Monte Carlo (QMC) volume or surface integration of bivariate and trivariate compact domains.
The key tools of the algorithm are Davis-Wilhelmsen theorem on the so-called “Tchakaloff sets” for positive linear functionals on polynomial spaces, and Lawson-Hanson algorithm for NNLS.
We provide various examples, focusing, in particular, on the compression of volume and surface integration on union of balls.
[00591] Convergence rate of RBSDE by penalisation and its financial applications
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : In this paper, we study the convergence of numerical solution of Reflected Backward Stochastic Equations (RBSDEs) by the penalisation approach and we apply this on the pricing problem of American option. Usually the obstacle-related problem is studied by Snell Envelope and penalisation is used on proving existence. Here we fill the gap between penalisation and numerical solution. As result, we proved successfully the convergence rate for both continuous and discrete penalised solution.
MS [00555] Advanced Numerical Methods for PDEs with Applications
room : E705
[02041] Numerical Methods for PDEs and Mesh Generation
Format : Talk at Waseda University
Author(s) :
Justin Wan (University of Waterloo)
Connor Tannahill (University of Waterloo)
Abstract : We will start with an overview of the mini-symposium. Then, in this talk, we will present a novel optimization-based approach for variational mesh adaptation based on MMPDE methods, combined with recent techniques for solving large-scale nonlinear constraint problems in parallel. The resulting method resembles meshing algorithms based on the spring analogy while producing high-quality adaptive meshes. We demonstrate the advantages of our method over standard MMPDE methods for generating two and three-dimensional meshes in parallel.
[01595] PDAEs redux
Format : Talk at Waseda University
Author(s) :
Uri Michael Ascher (University of BC)
Abstract : We re-examine computational principles for solving constrained PDEs in large applications.
One involves simulation of friction and contact effects in deformable object motion arising in graphics and robotics.
The need to flexibly engage such constraints in differentiable models prompts introducing penalty methods,
despite some additional complexity and minor potential instability.
The other project investigates, in the context of neural ODEs,
different stabilization methods for differential equations with invariants arising from elimination of algebraic constraints.
Ronald Haynes (Memorial University of Newfoundland)
Steven Ruuth (Simon Fraser University)
Abstract : We consider the convergence of optimized Schwarz iterations for the surface intrinsic positive Helmholtz equation $(c−∆_S)u=f, c>0$, for smooth, simple closed 1-manifolds where periodicity is inherent in the geometry. We prove convergence results for the unequal-sized subdomain case with an arbitrary number of subdomains, and find an explicit formula for the optimal Robin parameter. Connections to a particular discretization, the closest point method, are provided as are numerical experiments verifying our results.
[02719] DD approaches for surface PDEs solved by the closest point method
Format : Online Talk on Zoom
Author(s) :
Ronald Haynes (Memorial University of Newfoundland and Labrador)
Abstract : The solution of surface intrinsic PDEs using the closest point method will be proposed. For efficiency we have designed and analyzed domain decomposition solvers and preconditioners to solve the resulting discrete system of equations. Numerical results for model test examples will be presented.
MS [01088] Differential Equations meet Data: Scientific Machine Learning for Cardiovascular Applications
room : E708
[05201] Accelerating hemodynamic predictions via machine learning
Format : Online Talk on Zoom
Author(s) :
Noelia Grande Gutierrez (Carnegie Mellon University)
Abstract : Image-based computational blood flow simulations allow quantifying patient-specific hemodynamics with applications for personalized diagnosis, risk stratification, and treatment selection. However, the clinical translation of these methods is limited due to their high computational cost. We propose machine learning super-resolution to accelerate hemodynamic predictions. For upsampling simulation results, we combine physics-based simulations on a coarse mesh with a graph neural network. Unstructured data (mesh) can be directly transformed into a graph representation, minimizing information loss.
[04443] The fibrotic kernel signature: simulation-free prediction of atrial fibrillation
Format : Online Talk on Zoom
Author(s) :
Francisco Sahli Costabal (Pontificia Universidad Católica de Chile)
Simone Pezzuto (Università di Trento)
Lia Gander (Università della Svizzera Italiana)
Tomás Banduc (Pontificia Universidad Católica de Chile)
Abstract : We propose a fast classifier that is able to predict atrial fibrillation inducibility in patient-specific cardiac models. This is achieved by training the classifier on a variant of the Heat Kernel Signature, which includes information about the fibrosis. These features are fast to compute, when compared to standard cardiac models. The classifier is able to predict the inducibility of single points and also the overall inducibility of the model.
[05176] Learning Reduced-Order Models for Blood Flow Simulations Using Graph Neural Networks
Format : Talk at Waseda University
Author(s) :
Luca Pegolotti (Stanford University)
Martin Pfaller (Stanford University)
Natalia Rubio (Stanford University)
Rita Brugarolas Brufau (Intel )
Ke Ding (Intel)
Eric Darve (Stanford University)
Alison Marsden (Stanford University)
Abstract : We develop one-dimensional reduced-order models for simulating blood flow dynamics in complex cardiovascular geometries using a graph neural network trained on 3D hemodynamic data. Our method, which is a modified version of MeshGraphNet, accurately and efficiently predicts pressure and flow rate with errors below 2% and 3%, respectively, outperforming traditional physics-based models while maintaining high inference efficiency. Our findings demonstrate the potential of this approach in handling diverse anatomies and boundary conditions in physiological settings.
MS [00837] Particle Methods for Bayesian Inference
room : E709
[05135] Improving Ensemble Kalman Filter performance by adaptively controlling the ensemble
Format : Talk at Waseda University
Author(s) :
Ruben Harris (FU Berlin)
Claudia Schillings (FU Berlin)
Abstract : Efficient strategies to improve the performance of the Ensemble Kalman Inversion by adaptively controlling the ensemble.
Due to their low computational costs and straightforward implementation, filtering methods such as the Ensemble Kalman Filter have become very popular for inverse problems over the last few years. They have been demonstrated to work well even for highly nonlinear, complex models. We discuss variants of the Ensemble Kalman Inversion (EKI) aiming to improve the accuracy of the estimate by adaptively choosing the particles in the ensemble.
[03030] Ensemble-based gradient inference for particle methods in optimization and sampling
Format : Talk at Waseda University
Author(s) :
Philipp Wacker (University of Canterbury)
Claudia Schillings (FU Berlin)
Claudia Totzeck (University of Wuppertal)
Abstract : We discuss how some ensemble-based methods for optimization and sampling can be augmented by inexact estimates of the gradient of a potential function, approximated in a straightforward way from pointwise evaluation of the potential in the ensemble. This approximated gradient can be inserted in place of an exact gradient in the context of sampling methods derived from Langevin dynamics, and it can be used as an additional term in global optimization methods like Consensus-based optimization
[05138] Less interaction with forward models in Langevin dynamics: Enrichment and Homotopy
Format : Talk at Waseda University
Author(s) :
Robert Gruhlke (FU Berlin)
Martin Eigel (WIAS Berlin)
David Sommer (WIAS Berlin)
Abstract : Ensemble methods like EKS and ALDI are widely used for Bayesian inference problems but suffer from a large number of forward calls and possible lack of convergence for multimodal distributions. We propose adaptive ensemble enrichment strategies to reduce the total number of forward calls. The method is extended for more complex distributions using adapted Langevin dynamics based on a homotopy formalism. Numerical investigations on benchmark problems demonstrate the method's advantages over state-of-the-art Langevin samplers.
MS [00919] Recent Advances in Hybridizable Discontinuous Galerkin Methods and Applications
room : E710
[04456] Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems
Author(s) :
Manuel Sanchez (Pontificia Universidad Catolica de Chile)
Bernardo Cockburn (University of Minnesota)
Shukai Du (University of Wisconsin-Madision)
Abstract : We provide a short introduction to the devising of a special type of methods for numerically approximating the solution of Hamiltonian partial differential equations. These methods use Galerkin space-discretizations which result in a system of ODEs displaying a discrete version of the Hamiltonian structure of the original system. The resulting system of ODEs is then discretized by a symplectic time-marching method. This combination results in high-order accurate, fully discrete methods which can preserve the invariants of the Hamiltonian defining the ODE system. We restrict our attention to linear Hamiltonian systems, as the main results can be obtained easily and directly, and are applicable to many Hamiltonian systems of practical interest including acoustics, elastodynamics, and electromagnetism. After a brief description of the Hamiltonian systems of our interest, we provide a brief introduction to symplectic time-marching methods for linear systems of ODEs which does not require any background on the subject. We consider the case of finite-element space discretizations. The emphasis is placed on the conservation properties of the fully discrete schemes.
[04720] Multigrid for HDG
Author(s) :
Guosheng Fu (University of Notre Dame)
Wenzheng Kuang (University of Notre Dame)
Abstract : We present optimal geometric and algebraic multigrid preconditioners for low-order and high-order HDG schemes for diffusion and Stokes problems. The algebraic multigrid is based on Jinchao Xu's auxiliary space preconditioning framework, while the geometric multigrid is based on the close connection between the lowest-order HDG scheme with the nonconforming Cruzeix-Raviart method. This is a joint work with Wenzheng Kuang from Notre Dame.
[04725] HDG method for elliptic interface problems and industrial application
Author(s) :
Masaru Miyashita
Norikazu Saito (The University of Tokyo)
Abstract : We propose a hybridized discontinuous Galerkin (HDG) method to solve the interface problem for elliptic equations. We succeed in deriving optimal order error estimates in both the HDG norm and the L2 norm under low regularity assumptions for solutions such as $u|_{Ω_1} ∈ H^{1+s}(Ω_1)$ and $u|_{Ω_2} ∈ H^{1+s}(Ω_2)$ for some $s ∈ (1/2, 1]$. Numerical examples support our theoretical results. Then, we show an example of developing plasma equipment using the proposed method.
[04892] A C0 interior penalty method for mth-Laplace equation
Author(s) :
Weifeng Qiu (City University of Hong Kong)
Huangxin Chen (Xiamen University)
Jingzhi Li (SUSTech)
Abstract : I will talk about a C0 interior penalty method for the mth-Laplace equation.
contributed talk: CT114
room : E711
[00899] Unlocking the Secrets of Locking
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E711
Type : Contributed Talk
Abstract : For nearly incompressible linear elastic materials, such as rubber, finite element methods sometimes exhibit suboptimal convergence rates for the energy and/or stresses. This type of behavior, termed “locking”, is still not completely understood. This talk reviews the concept of locking and recent results that show that conforming high order finite elements provide optimal convergence for both the energy and stresses with respect to the mesh size and polynomial degree. Robust preconditioners will also be presented.
[00611] Deformations of linear elastic bodies computed using the RBF-PU method
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E711
Type : Contributed Talk
Abstract : In this talk we will present numerical solutions to boundary value problems of linear elasticity, computed using the Radial Basis Function Partition of Unity (RBF-PU) method in the least squares formulation. Specifically, we will show deformations of 3D geometries, including a thin plank under bending and a reconstructed human diaphragm under ventilation conditions. Convergence studies and a comparison of the RBF-PU method to the standard Galerkin Finite Element method (GFEM) will be presented.
[01118] Finite Element Analysis of a Non-equilibrium Model for Hybrid Nano-Fluid
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E711
Type : Contributed Talk
Abstract : A theoretical and computational finite element study of modified Navier-Stokes
Equations coupled with energy conservation governing the flow and heat transfer
in complex domain with hybrid nanofluid is carried out. The apriori error
estimates providing the convergence analysis for the finite element scheme is
derived in the H1-norm. The effect of hybrid nano-particle’s volume fraction,
Rayleigh Number, Prandtl Number, Darcy number, porosity are analyzed to trace
the physics related to flow and heat transfer.
SANGITA DEY (Ph.D Student of Indian Institute of Technology Kanpur)
Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
[00821] ADAPTIVE QUADRATIC DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE UNILATERAL CONTACT PROBLEM
Session Time & Room : 4C (Aug.24, 13:20-15:00) @E711
Type : Contributed Talk
Abstract : The proposed title of my talk will be ADAPTIVE QUADRATIC DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE UNILATERAL CONTACT PROBLEM . In the talk, I will be discussing about employing discontinuous Galerkin methods (DG) for the finite element approximation of frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We shall analyze a posteriori error estimates in the DG norm wherein, the reliability and efficiency of the proposed a posteriori error estimators will be addressed. Further we will show that numerical results substantiate the theoretical findings,
MS [02109] Recent Advances on Numerical Analysis of Integral and Integro-differential Equations
room : E802
[02677] An hp-version of the discontinuous Galerkin method for fractional integro-differential equations with weakly singular kernels
Format : Talk at Waseda University
Author(s) :
Yanping Chen (South China Normal University)
Abstract : In this talk, an hp-discontinuous Galerkin method is developed for the fractional integro-differential equations with weakly singular kernels. The key idea of our method is to first convert the fractional integro-differential equations into the Volterra integral equations, and then solve the equivalent integral equations using the hp-discontinuous Galerkin method. The prior error bounds for the proposed method are established in the L2-norm. Numerical results are presented to demonstrate the effectiveness of the proposed method.
[03691] Implicitly Linear Jacobi Spectral-Collocation Methods for Weakly Singular Volterra-Hammerstein Integral Equations
Format : Talk at Waseda University
Author(s) :
Qiumei Huang (Beijing University of Technology)
Huitinh Yang (Beijing University of Technology)
Abstract : Weakly singular Volterra integral equations of the second kind typically have nonsmooth solutions near the initial point of the interval of integration, which seriously affects the accuracy of spectral methods. We present Jacobi spectral-collocation method to solve two-dimensional weakly singular Volterra-Hammerstein integral equations based on smoothing transformation and implicit linear method. The solution of the smoothed equation is much smoother than the original one after smoothing transformation and the spectral method can be used. For the Hammerstein nonlinear term, the implicitly linear method is applied to simplify the calculation and improve the accuracy. Convergence analysis in the L∞−norm is carried out and the exponential convergence rate is obtained. Finally, we demonstrate the efficiency of the proposed method by numerical examples.
[03565] A collocation based approach for the numerical solution of singular fractional integro-differential equations
Format : Talk at Waseda University
Author(s) :
Kaido Latt (University of Tartu)
Arvet Pedas (University of Tartu)
Abstract : We consider a class of fractional integro-differential equations with certain type of singularities at the origin. We reformulate the original problem as a cordial Volterra integral equation and study the existence, uniqueness, and regularity of the exact solution. We also construct a collocation based numerical method for finding the approximate solution of the original problem and present some numerical examples.
[02147] Solutions of second kind Fredholm integral equations by discrete projection methods
Format : Talk at Waseda University
Author(s) :
Gobinda Rakshit (Rajiv Gandhi Institute of Petroleum Technology, Jais Campus, Amethi, Uttar Pradesh 229304)
Abstract : We are interested in approximate solutions of the integral equation $x(s)−\int_{0}^{1} \kappa(s, t, (x(t)) dt =f(s)$, where $f$ and the kernel $\kappa$ are given. A class of projection methods are available for obtaining approximate solutions to the above integral equation. Modified projection method is recently proposed and it exhibits higher orders of convergence as compared to the Galerkin/collocation (projection) methods. Here, we define and analyze a discrete version of the above projection methods.
MS [00704] Numerical Software Libraries Enabling Benefits to Scientific Applications
room : E803
[01915] MFEM: Accelerating Efficient Solution of PDEs at Exascale
Format : Talk at Waseda University
Author(s) :
Tzanio Kolev (Lawrence Livermore National Laboratory)
Veselin Dobrev (Lawrence Livermore National Laboratory)
John Camier (Lawrence Livermore National Laboratory)
Vladimir Tomov (Lawrence Livermore National Laboratory)
Julian Andrej (Lawrence Livermore National Laboratory)
Will Pazner (Portland State University)
Abstract : Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in PDE-based simulations to expose fine-grain parallelism and maximize arithmetic intensity. In this talk we present an overview of MFEM $\mathrm{(\href{https://mfem.org}{mfem.org})}$, a library for high-order finite element methods, which powers HPC applications in a wide variety of fields. We review recent advancements in MFEM’s discretization solver, and GPU-accelerated algorithms, and demonstrate their impact in several large-scale applications from the US Department of Energy.
[01650] Exascale-Ready Adaptive Mesh Refinement Applications with AMReX
Format : Talk at Waseda University
Author(s) :
Andrew Myers (LBNL)
Abstract : AMReX is a block-structured adaptive mesh refinement library that supports a variety of advanced GPU and CPU architectures. I will describe AMReX and its associated ecosystem of application codes, spanning scientific domains such as astrophysics, plasma physics, wind farm modeling, epidemiology, and more. I will demonstrate how AMReX enables these codes to implement novel modeling capabilities involving a range of computational motifs and to run efficiently on some of the largest supercomputers in the world.
[01911] Supporting Applications with the Chombo Framework
Format : Talk at Waseda University
Author(s) :
Daniel Francis Martin (Lawrence Berkeley National Laboratory)
Abstract : Many scientific and industrial applications solve systems of partial differential equations, and can often benefit from algorithmic strategies like adaptive mesh refinement $(AMR)$, higher-order mapped grids, and linear and nonlinear solvers. These are often difficult to implement accurately and efficiently; software frameworks leverage this effort across many applications. We present case studies demonstrating how the modular design of the Chombo software framework supports performant applications, which then feed improved capabilities back into Chombo.
[01456] Firedrake: Math to Supercomputer
Format : Talk at Waseda University
Author(s) :
Koki Sagiyama (Imperial College London)
David A. Ham (Imperial College London)
Abstract : Firedrake is an open-source Python package for solving PDEs using finite element methods.
Using the UFL language originally developed for the FEniCS project and other packages in the Firedrake's ecosystem,
Firedrake generates efficient finite element codes automatically from the math expressions provided by the users, allowing them to move from one idea to another quickly.
It also provides a transparent access to the linear/nonlinear solvers in the PETSc library.
Here, we will show some recent developments in Firedrake.
MS [00047] Combining Machine Learning and Stochastic Methods for Modeling and Forecasting Complex Systems
room : E804
[05245] semi-supervised active learning on graphs
Format : Online Talk on Zoom
Author(s) :
Andrea Bertozzi (UCLA)
Abstract : Similarity graphs are a popular technique for semi-supervised machine learning. They have an advantage over more modern neural network methods in that they can perform well with a modest amount of training data. I will present an active learning framework in which additional training data is introduced through a human in the loop. This approach can outperform prior state of the art on several remote sensing problems such as object recognition in sythetic aperture radar and multispectral and hyperspectral imagery.
[04307] Integrating the spectral analyses of neural networks and nonlinear physics for explainability, generalizability, and stability
Format : Talk at Waseda University
Author(s) :
Pedram Hassanzadeh (Rice U)
Ashesh Chattopadhyay (PARC)
Yifei Guan (Rice U)
Adam Subel (NYU)
Abstract : I will introduce a new framework that combines the spectral (Fourier) analyses of NNs and nonlinear physics, and leverages recent advances in theory and applications of deep learning, to move toward rigorous analysis of deep NNs for applications involving dynamical systems. I will use examples from subgrid-scale modeling of 2D turbulence and Rayleigh-Bernard turbulence and forecasting extreme weather to show how this framework can be used to systematically address challenges about explainability, generalizability, and stability.
[03737] Shock trace prediction by reduced models for a viscous stochastic Burgers equation
Format : Talk at Waseda University
Author(s) :
Fei Lu (Johns Hopkins University)
Abstract : Can data-driven reduced models predict extreme events in nonlinear multiscale systems? Using stochastic Burgers equation's random shocks as a prototype of extreme events, we demonstrate that although large-scale dominating dynamics-focused reduced models cannot represent shocks, they can accurately predict shock trace—the timing and locations of shocks —with relatively low false prediction rates. The data-driven closure terms are critical in capturing unresolved small-scale dynamics' effects on resolved ones.
[01386] A Multi-Fidelity Ensemble Kalman Filter with Adaptive Reduced-Order Models
Author(s) :
Francesco Attilio Bruno Silva (Eindhoven University of Technology)
Cecilia Pagliantini (Eindhoven University of Technology)
Karen Veroy (Eindhoven University of Technology)
Abstract : Recently there has been an increased interest in combining model order reduction techniques and ensemble-based methods for state estimation of complex systems. Data assimilation algorithms have been proposed to jointly use low and high-fidelity ensembles, e.g., the MFEnKF. The construction of low-fidelity models in the offline stage, however, leads these methods into a trade-off between accuracy and computational costs. In our research, we developed adaptive reduced-basis techniques with online modified approximation spaces to mitigate this issue.
MS [00184] Recent advances in data-driven methods for inverse problems
room : E811
MS [00638] Minisymposium on Interaction between Harmonic Analysis and Data Science
room : E812
[04107] Proximal neural networks and Plug-and-Play methods
Format : Talk at Waseda University
Author(s) :
Gabriele Steidl (TU Berlin Berlin)
Johannes Hertrich (TU Berlin)
Sebastian Jonas Neumayer (EPFL)
Abstract : We introduce stable tight frame proximal neural networks (PNNs)
which are by construction averaged operators.
For the training of PNNs, we propose a stochastic gradient descent on (a submanifold of) the Stiefel manifold.
First, we apply cPNN based denoisers within a Plug-and-Play framework and provide convergence results
for the corresponding PnP forward-backward splitting algorithm based on an oracle construction.
Second, we use the averagedness property of PNNs to construct a new architecture within
residual flows.
[03587] The Bayesian Learning Rule
Format : Talk at Waseda University
Author(s) :
Mohammad Emtiyaz Khan (RIKEN Center for AIP)
Abstract : Humans and animals have a natural ability to autonomously learn and quickly adapt to their surroundings. How can we design machines that do the same? In this talk, I will present Bayesian principles to bridge such gaps between humans and machines. I will show that a wide-variety of machine-learning algorithms are instances of a single learning-rule derived from Bayesian principles. The rule unravels a dual perspective yielding new mechanisms for knowledge transfer in learning machines. My hope is to convince the audience that Bayesian principles are indispensable for an AI that learns as efficiently as we do.
[02888] Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
Format : Talk at Waseda University
Author(s) :
Nicole Mücke (TU Brunswick)
Abstract : We consider the problem of learning a linear operator between two Hilbert
spaces from empirical observations, which we interpret as least squares regression in infinite
dimensions. We show that this goal can be reformulated as an inverse problem with the
feature that its forward operator is generally non-compact.
We prove that this inverse problem is equivalent to the known compact inverse
problem associated with scalar response regression.
Our framework allows for obtaining dimension-free rates for generic learning
algorithms. They hold for a variety of practically-
relevant scenarios in functional regression as well as nonlinear regression with operator-
valued kernels and match those of classical kernel regression with scalar response.
[02915] A Non-Asymptotic Analysis of Dropout in the Linear Model
Format : Talk at Waseda University
Author(s) :
Gabriel Clara (University of Twente)
Sophie Langer (University of Twente)
Johannes Schmidt-Hieber (University of Twente)
Abstract : We investigate the statistical behavior of iterates generated by gradient descent with dropout in a linear model. Non-asymptotic convergence rates for expectations and covariance matrices of the iterates are presented. Difficulties arising from the interaction between gradient descent dynamics and the variance added by dropout are examined. The results motivate and support discussion of statistical aspects of dropout, focusing on optimality of the variance.
MS [02349] Deep Implicit and Explicit Models for Inverse Problems: Hybrid Data-Driven Models, Neural ODEs, PDEs and Beyond
room : E817
[03463] Learning pair-wise homeomorphic image registration in a conformal-invariant hyperelastic setting
Format : Talk at Waseda University
Author(s) :
Noémie DEBROUX (Université Clermont Auvergne)
Jing Zou (The Hong Kong Polytechnic University)
Lihao Liu (University of Cambridge)
Angelica Aviles-Rivero (University of Cambridge)
Jing Qin (The Hong Kong Polytechnic University)
Carola-Bibiane Schönlieb (University of Cambridge)
Abstract : Deformable image registration is a fundamental task in medical image analysis and plays a crucial role in a wide range of clinical applications. Recently, deep learning-based approaches have been widely studied for deformable medical image registration and achieved promising results. However, existing deep learning image registration techniques
do not theoretically guarantee physically-meaningful transformations and usually require a lot of training data. In order to overcome these drawbacks, we propose a novel framework for pair-wise deformable image registration in a deep-learning framework. Firstly, we introduce a novel regulariser in the loss function based on conformal-invariant properties in a nonlinear elasticity setting. It theoretically guarantees that the obtained deformations are homeomorphisms and therefore preserve topology. Secondly, we boost the performance of our regulariser through coordinate MLPs, where one can view the to-be-registered images as continuously differentiable entities. We evaluate our model through extensive numerical experiments.
[03252] Spherical Image Inpainting with Frame Transformation and Data-driven Prior Deep Networks
Format : Talk at Waseda University
Author(s) :
Tieyong Zeng (The Chinese University of Hong Kong)
Abstract : Spherical image processing has been widely applied in many important fields. In this talk, we focus on the challenging task of spherical image inpainting with deep learning-based regularizer. We employ a fast directional spherical Haar framelet transform and develop a novel optimization framework based on a sparsity assumption. Furthermore, by employing progressive encoder-decoder architecture, a new and better-performed deep CNN denoiser is carefully designed and works as an implicit regularizer. Finally, we use a plug-and-play method to handle the proposed optimization model, which can be implemented efficiently by training the CNN denoiser prior. Numerical experiments are conducted and show that the proposed algorithms can greatly recover damaged spherical images and achieve the best performance over purely using deep learning denoiser and plug-and-play model. This is a joint work with Jianfei Li, Chaoyan Huang, Raymond Chan, Han Feng, and Michael Ng.
[05441] Learning to solve inverse problems with unsupervised nonlinear models
Format : Talk at Waseda University
Author(s) :
Rihuan Ke (University of Bristol)
Carola-Bibiane Schönlieb (University of Cambridge)
Abstract : Deep learning methods have recently demonstrated remarkable achievements in solving inverse problems. At the core of these methods lies the learning tasks of finding effective inverse problem solvers from a parameterised operator space, which is typically high dimensional. In the context of supervised learning, these learning tasks can be effectively tackled with sufficient supervised data, consisting of paired measurements and ground truth solutions. However, when the ground truth solutions are unknown, these learning tasks can be as challenging as solving the inverse problems themselves. In this talk, we present a hybrid method that addresses the learning tasks in an unsupervised learning setting for denoising and inverse problems more generally, where access to high-quality supervised data is restrictive or unavailable. We highlight a class of nonlinear operators that can be learned from noisy data and offer close approximations to the optimal solutions. Based on these nonlinear operators, we introduce a learning algorithm for solving inverse problems with limited knowledge of the underlying ground truth solutions and noise distributions.
[04181] A learning framework for mapping problems via Quasiconformal geometry
Author(s) :
Ronald Lok Ming LUI (The Chinese University of Hong Kong)
Qiguang Chen (The Chinese University of Hong Kong)
Abstract : Many imaging problems can be formulated as a mapping problem. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems are often inefficient and can sometimes get trapped in local minima. An extra challenge arises when the optimal mapping is required to be diffeomorphic. In this talk, we address the problem by proposing a deep-learning based framework based on the Quasiconformal (QC) Teichmüller theories. The main strategy is to learn the Beltrami coefficient (BC) that represents a mapping as the latent feature vector in the deep neural network. The BC measures the geometric distortions under the mapping. As such, the proposed network based on QC theories is explainable. Another crucial advantage of the proposed framework is that once the network is successfully trained, the optimized mapping corresponding to each input data information can be obtained in real time. In this talk, we will illustrate our framework by applying it to solve the diffeomorphic image registration problem. The developed network, called the quasiconformal registration network (QCRegNet), outperforms other state-of-the-art image registration models. This work is supported by HKRGC GRF (Project IDs: 14305919, 14306721,14307622).
MS [00951] Steps Toward Robust and Stable Artificial Intelligence
room : E818
[03891] Stochastic Separation Theorems for making AI Safe, Adaptive, and Robust
Format : Talk at Waseda University
Author(s) :
Ivan Y Tyukin (King's College London)
Alexander N Gorban (University of Leicester)
Abstract : In this talk we discuss the issues around stability and robustness of modern AI systems to data and structure perturbations. We show that determining robust generalisation may involve computational costs which are exponential in the dimension of AI feature spaces. As a potential way to mitigate the issue we discuss a set of results, termed stochastic separation theorems, which could be used to efficiently “patch” instances of instabilities as soon as they are identified.
[05438] Advancements in Autodiff
Format : Talk at Waseda University
Author(s) :
Elizabeth Cristina Ramirez (Columbia University)
Abstract : The reliance of backpropagation and other gradient-based algorithms on derivative calculations is well-known. Automatic differentiation, a powerful computational tool that often remains overlooked, allows for the efficient computation of gradients, surpassing the limitations of numerical differentiation. In this presentation, we aim to provide a concise overview of the inner workings of autodiff, as implemented in frameworks like TensorFlow, PyTorch, and JAX. Moreover, we will shed light on recent developments that enhance stability and expedite convergence.
MS [01136] Advances in Variational Models and PDEs for Images
room : E819
[03732] Algorithms for Variational Segmentation of Regions and Boundaries
Format : Talk at Waseda University
Author(s) :
Gunay Dogan (National Institute of Standards and Technology)
Abstract : We propose several algorithms for variational segmentation of regions and boundaries in images. The algorithms come in Lagrangian and Eulerian flavors, and optimize variational models incorporating boundaries and region statistics, as well as various geometric regularizers. We demonstrate the advantages of each algorithm on several examples. Our algorithms are available in the open-source Python package scikit-shape.
[04275] Individual Tooth Segmentation in Human Teeth Images Using Pseudo Edge-Region Obtained by Deep Neural Networks
Format : Talk at Waseda University
Author(s) :
Chang-Ock Lee (KAIST)
Seongeun Kim (KAIST)
Abstract : In human teeth images taken outside the oral cavity with a general optical camera, it is difficult to segment individual tooth due to common obstacles such as weak edges, intensity inhomogeneities and strong light reflections. In this talk, we propose a method for segmenting individual tooth in human teeth images. The key to this method is to obtain pseudo edge-region using deep neural networks.
[05117] Joint solution of multi-task problems in imaging
Format : Talk at Waseda University
Author(s) :
Doga Gursoy (Argonne National Laboratory)
Abstract : Imaging in challenging conditions, such as with limited and uncertain data, typically involves solving multiple tasks, including image denoising, registration, segmentation, and various other reconstruction tasks. While the traditional approach has been to address these problems one at a time, solving them jointly with minimal manual hyperparameter setting can provide significant benefits in terms of image quality and acquisition time. In this presentation, I will explore the use of distributed optimization techniques to tackle these challenges and offer examples from my experience in the field of x-ray imaging.
[01799] Counting Objects by Diffused Index: geometry-free and training-free approach
Format : Talk at Waseda University
Author(s) :
Maryam Yashtini (Georgetown University)
Abstract : Counting objects is a fundamental but challenging problem. In this talk, I propose diffusion-based, geometry-free, and learning-free methodologies to count the number of objects in images. The main idea is to represent each object by a unique index value regardless of its intensity or size, and to simply count the number of index values. First, I place different vectors, referred to as seed vectors, uniformly throughout the mask image. The mask image has boundary information of the objects to be counted. Secondly, the seeds are diffused using an edge-weighted harmonic variational optimization model within each object. I propose an efficient algorithm based on an operator splitting approach and alternating direction minimization method, and theoretical analysis of this algorithm is given. An optimal solution of the model is obtained when the distributed seeds are completely diffused such that there is a unique intensity within each object, which I refer to as an index. For computational efficiency, I stop the diffusion process before a full convergence, and propose to cluster these diffused index values. I refer to this approach as Counting Objects by Diffused Index (CODI). I explore scalar and multi-dimensional seed vectors. For Scalar seeds, I use Gaussian fitting in histogram to count, while for vector seeds, I exploit a high-dimensional clustering method for the final step of counting via clustering. The proposed method is flexible even if the boundary of the object is not clear nor fully enclosed. I present counting results in various applications such as biological cells, agriculture, concert crowd, and transportation. Some comparisons with existing methods are presented.
MS [01138] Advances in embedded and Eulerian methods for fluid-structure interaction
room : E820
[05651] A fully Eulerian FSI framework: introduction
Format : Talk at Waseda University
Author(s) :
Thomas Milcent (I2M Bordeaux)
Michel Bergmann (Inria - centre de l'université de Bordeaux)
Abstract : In the fully Eulerian framework, both the fluid and the solid are described
by an Eulerian approach. The fluid-structure problem is
recast as a complex flow: the fluid equations with
an elastic source term is coupled with a transport equation
on the Eulerian interface and deformation. In this presentation we will present
this approach in the case where the elastic media (bulk or/and membrane) is immersed in an incompressible or
compressible flow.
[05652] A fully Eulerian FSI framework: numerical approach and applications
Format : Talk at Waseda University
Author(s) :
Michel Bergmann (Inria - centre de l'université de Bordeaux)
Thomas Milcent (I2M Bordeaux)
Antoine Fondaneche (NUREA)
Abstract : A quadtree-based fully Eulerian finite volume approach for the simulation of fluid-structure interaction problems is presented. The discretization stencils are limited to the first layer of neighbors thus enhancing the efficiency of the parallel computations while limiting the numerical order of the finite volume discretizations that can be reached. To illustrate the versatility of the numerical model presented, a biomedical application, the axisymmetric simulation of a blood flow in a cardiac pump, is presented.
[02558] Embedded Methods for Floating Offshore Structures
Format : Talk at Waseda University
Author(s) :
Jan Modderman (Delft University of Technology)
Oriol Colomés (Delft University of Technology)
Abstract : In this talk we will present a single-phase FE approach for free surface flows, where only the wave-structure interaction is accounted for, in combination with an unfitted floating structure with arbitrary geometry. In this work we propose a monolithic coupling with block preconditioning, ensuring robustness and efficiency of the solution. We will demonstrate the capabilities of the proposed framework with a series of tests for wave-structure interaction problems, assessing accuracy and conservation properties.
[03927] FULLY EULERIAN MODELS FOR FLUID-STRUCTURE INTERACTION: APPLICATION TO CAPSULES
Format : Talk at Waseda University
Author(s) :
Mirco Ciallella (ENSAM - I2M)
Thomas Milcent (ENSAM - I2M)
Abstract : Capsules have an important potential in the fields of biotechnologies but many scientific aspects, related to their modeling and simulation, are still challenging. In this context, eulerian models for fluid-structure interaction are a very promising tool to understand their behavior when interacting with complex geometries. In this talk, we will present a novel numerical tool to analyze complex applications of deformable capsules by introducing a solid bulk within the membrane.
MS [00435] Multiscale Numerical Methods for Complex Fluids
room : D101
[05277] Multi-Physics Simulations of Flow, Friction, and Reactions in Solid/Liquid Interface
Format : Talk at Waseda University
Author(s) :
Momoji Kubo (Tohoku University)
Abstract : In recent years, due to strong demands for energy saving and carbon neutrality, maximizing energy utilization efficiency in automobiles, airplanes, etc. is required. Therefore, it is essential to establish the technologies for the super-low friction. In the present study, we employed our supercomputer “MASAMUNE-IMR” and successfully applied our large-scale molecular dynamics code “Laich” to clarifying the multi-physics processes of the flow, friction, and chemical reactions in the solid/liquid interfaces for realizing the super-low friction system.
[02346] Numerical modeling of viscoelastic flows with high elasticity
Format : Talk at Waseda University
Author(s) :
Laura Moreno (Universita degli Studi di Padova)
Joan Baiges (Universitat Politecnica de Catalunya)
Ramon Codina (Universitat Politecnica de Catalunya)
Abstract : Computing the viscoelastic fluid flow involves a wide range of difficulties, in particular when elasticity becomes dominant. These difficulties are considered one of the biggest challenges in computational rheology; this is known as the High Weissenberg Number Problem.This work presents different strategies to deal with the shortcomings that appear when the fluid is particularly elastic. These are carried out in the Finite Element framework and by using the Variational Multiscale formulation as a stabilization approach.
[02354] DPD Simulation of Ultrasound Propagation through Liquid Water
Format : Talk at Waseda University
Author(s) :
Petra Papež (National Institute of Chemistry, Ljubljana)
Matej Praprotnik (National Institute of Chemistry, Ljubljana)
Abstract : We present a dissipative particle dynamics simulation of ultrasound propagation through liquid water. The effects of frequency and thermostat parameters are studied and discussed. We show that frequency and thermostat parameters affect not only the attenuation but also the computed speed of sound. The present study paves the way for development and optimization of a virtual ultrasound machine for large-scale biomolecular simulations.
[04595] Machine-Learning for Accelerated Multi-Scale Polymer Flow Simulations
Format : Talk at Waseda University
Author(s) :
John Jairo Molina (Kyoto University)
Souta Miyamoto (Kyoto University)
Yoshiki Ueno (Kyoto University)
Takashi Taniguchi (Kyoto University)
Abstract : We develop a Bayesian Machine-Learning approach, based on a Gaussian Process Regression, to accelerate Multi-Scale Simulations (MSS) of polymer melt flows. In particular, we are able to learn the constitutive relation of entangled polymer melts (within the Doi-Takimoto model), which are then used within macroscopic flow solvers, drastically reducing the computational cost. We also show how ML can be used to reduce the statistical variance of a full MSS, significantly enhancing its computational efficiency.
MS [01024] Multiscale modeling and simulation methods of inhomogeneity in defected systems
room : D102
[05384] An IBVP of a model for motion of grain boundaries
Format : Talk at Waseda University
Author(s) :
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.
[04942] Stochastic Continuum Models for High–Entropy Alloys with Short-range Order
Format : Talk at Waseda University
Author(s) :
Luchan Zhang (Shenzhen University)
Yahong Yang (Hong Kong University of Science and Technology)
Yang Xiang (Hong Kong University of Science and Technology)
Abstract : High entropy alloys (HEAs) are a class of novel materials that exhibit superb engineering properties. It has been demonstrated by extensive experiments and first principles/atomistic simulations that short-range order in the atomic level randomness strongly influences the properties of HEAs. In this talk, we present stochastic continuum models for HEAs with short-range order from atomistic models. A proper continuum limit is obtained such that the mean and variance of the atomic level randomness together with the short-range order described by a characteristic length are kept in the process from the atomistic interaction model to the continuum equation. The obtained continuum model with short range order is in the form of an Ornstein–Uhlenbeck (OU) process, which validates our previous continuum model adopting the OU process phenomenologically for HEAs with short range order. We derive such stochastic continuum models with short-range order for both elasticity in HEAs without defects and HEAs with dislocations (line defects). The obtained stochastic continuum models are based on the energy formulations, whose variations lead to stochastic partial differential equations.
[03918] GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
Format : Talk at Waseda University
Author(s) :
Cheng Yuan (Wuhan University)
Abstract : With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs can efficiently handle high-dimensional problems, but the accuracy is relatively low, especially for highly irregular problems. Inspired by the idea of adaptive finite element methods and incremental learning, we propose GAS, a Gaussian mixture distribution-based adaptive sampling method for PINNs. During the training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which are then trained together with historical data to speed up the convergence of the loss and achieve higher accuracy. Several numerical simulations on 2D and 10D problems show that GAS is a promising method that achieves state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers.
[05016] An Elastic Interaction-Based Loss Function in Image Segmentation and Detection
Format : Talk at Waseda University
Author(s) :
Yaxin FENG (Hong Kong University of Science and Technology)
Yuan Lan (Huawei Theory Lab)
Yang Xiang (Hong Kong University of Science and Technology)
Luchan Zhang (Shenzhen University)
Abstract : Deep learning techniques have shown their success in image processing since they are easy to manipulate and robust to various types of datasets. The commonly used pixel-wise loss functions result in a bottleneck to achieve high precision for complicated structures in biomedical and autonomous driving science images. For example, the predicted small blood vessels in retinal images are often disconnected or even missed under the supervision of the pixel-wise losses, and the existence of lanes needed to be inferred even when they are occluded by cars or human. This long-range elastic interaction-based training strategy addresses these problem. In this strategy, convolutional neural network (CNN) learns the target region under the guidance of the elastic interaction energy between the boundary of the predicted region and that of the actual object. Under the supervision of the proposed loss, the boundary of the predicted region is attracted strongly by the object boundary and tends to stay connected.
MS [00781] Physical and Mathematical Research on Transport on Slippery Surfaces
room : D401
[04287] Laminar drag reduction in surfactant-contaminated superhydrophobic channels
Format : Talk at Waseda University
Author(s) :
Samuel Tomlinson (University of Manchester)
Frédéric Gibou (University of California, Santa Barbara)
Paolo Luzzatto-Fegiz (University of California, Santa Barbara)
Fernando Temprano-Coleto (Princeton University)
Oliver Jensen (University of Manchester)
Julien Landel (University of Manchester)
Abstract : Although superhydrophobic surfaces (SHSs) show promise for drag reduction (DR) applications, their performance can be compromised by traces of surfactant. This question is addressed for a three-dimensional laminar flow in a periodic channel with SHSs along both walls, in the presence of soluble surfactant. The system exhibits multiple regimes where asymptotic solutions can be constructed, which compare favourably with numerics. This analysis provides a guide for designing surfactant-contaminated SHSs to maximise the DR for applications.
[04901] Hypermobilization of superhydrophobic microchannels using light
Format : Talk at Waseda University
Author(s) :
Michael Mayer (Imperial College London)
Marc Hodes (Tufts University)
Xiaozhe Hu (Tufts University)
James Adler (Tufts University)
Abstract : This talk seeks to reframe the role of superhydrophobic surfaces, transforming them from passive lubricants to sources of active flow control. Utilizing a new model for the transport of photosurfactants, chemicals that can reversibly switch between two different states under differing light wavelengths, we show that it is possible to use light to generate surface tension gradients across menisci on superhydrophobic surfaces large enough to pump stationary fluid or even “hypermobilize” pressure driven flow.
[04001] Analysis of surface diffusion on steady "stagnant caps'' of surfactant
Format : Talk at Waseda University
Author(s) :
Anna Elizabeth Curran (Imperial College London)
Darren Crowdy (Imperial College London)
Abstract : We present a detailed analytical study, based on complex variable methods, which examines the remobilizing effects of surface diffusion on the structure of steady "stagnant caps'' on a surfactant-loaded interface between a viscous fluid and a constant pressure region. Both insoluble and soluble surfactants are considered. We demonstrate mathematically how, in the presence of a convergent flow, stagnant caps can immobilize interfaces leading to sharp edges which can then be smoothed out by surface diffusion.
[04344] Slip flow enhanced by Marangoni Stresses at a superhydrophobic air-water interface
Format : Online Talk on Zoom
Author(s) :
dong song (Northwestern Polytechnical University)
Baowei Song (Northwestern Polytechnical University)
guang pan (Northwestern Polytechnical University)
Abstract : Surfactant-induced Marangoni stress at an air-water interface would balance the shearing stress which causes the collapse of drag reduction of superhydrophobic surfaces, whereas few solutions have been proposed to overcome the adverse influence due to the difficulty in removing surfactant from water. In this work, we demonstrate that, by changing the orientation or shape of the air-water interface with respect to the bulk flow, the balance between Marangoni stress and shear stress can serve as a driving force of an apparent slip flow without the external input of surfactant. The theoretical model agrees well with the experiments.
MS [00253] Modelling and Simulation of Lithium-Ion Batteries
room : D403
[03631] Asymptotic methods for lithium-ion battery models
Format : Talk at Waseda University
Author(s) :
Ferran Brosa Planella (University of Warwick)
Abstract : Lithium-ion batteries have become an essential in our lives, and to develop better and safer batteries we need accurate and fast models. Current models are often posed in an ad hoc way, which usually leads to inconsistencies. In this talk we will provide an overview of battery modelling, and show how asymptotic methods can help us obtain simple and consistent models that help us design and manage the next generation of batteries.
[05237] Topology Optimization for Li-ion batteries
Format : Talk at Waseda University
Author(s) :
Thomas Roy (Lawrence Livermore National Laboratory)
Hanyu Li (Lawrence Livermore National Laboratory)
Nicholas Brady (Lawrence Livermore National Laboratory)
Giovanna Bucci (Lawrence Livermore National Laboratory)
Tiras Lin (Lawrence Livermore National Laboratory)
Daniel Tortorelli (Lawrence Livermore National Laboratory)
Marcus Worsley (Lawrence Livermore National Laboratory)
Abstract : Typical porous electrodes are homogeneous, stochastic collections of small-scale particles offering few opportunities for engineering higher performance. To leverage recent breakthroughs in advanced and additive manufacturing, we use topology optimization to design electrodes for energy storage devices. Energy density is maximized, leading to non-trivial geometries that outperform monolithic electrodes. These geometries facilitate ionic transport and lead to better electrode utilization. We consider simultaneous optimization of cathode and anode, which can lead to interdigitated designs. LLNL-ABS-847750
[04263] Homogenisation and Modelling of a Silicon nanowire Li-ion battery anode
Format : Talk at Waseda University
Author(s) :
Emma Elizabeth Greenbank (MACSI, University of Limerick)
Michael Vynnycky (MACSI, University of Limerick)
Doireann O'Kiely (MACSI, University of Limerick)
Abstract : We consider a battery anode composed of an array of copper nanowires, coated with Li-carrying copper silicide and surrounded by Li-alloying electrolyte. This anode design alleviates degradation arising from extreme volumetric changes of silicon during lithiation. The governing equations for the electric and concentration fields inside the nanowire array structure are homogenised, and solutions of the homogenised problem are used to predict the transport of lithium through the anode.
[02731] A continuum model for lithium plating and dendrite formation in lithium-ion batteries.
Format : Talk at Waseda University
Author(s) :
Smita Sahu (University of Portsmouth)
Abstract : This work presents a novel physics-based model for lithium plating and dendrite formation in lithium-ion batteries. The formation of Li metal is an undesirable side-effect of fast charging and a primary contributor to cell degradation and failure. The model distinguishes between three types of plated Li metal, namely: (a) Li metal plated within the pores of the solid electrolyte interphase (assumed to be electronically connected to the anode and therefore recoverable); (b) dendrites protruding outside the SEI that remain electronically connected (and are therefore dangerous, potentially leading to a short circuit), and (c) electronically disconnected/“dead” Li metal outside the SEI contributing to capacity fade. The model is validated against two independent experiments. First, measurements of: (i) the cell voltage and current during a constant-current–constant-voltage charge and subsequent discharge, and (ii) the Li metal intensities (derived from operando NMR) which directly quantifies the time-resolved quantity of Li metal in the cell during use. Second, against voltage measurements during galvanostatic discharge at a range of C-rates and temperatures. Favourable agreement is demonstrated throughout; particularly in terms of the proportions of reversible and irreversible plating. We also demonstrate that the model reproduces the well-documented trends of being more prevalent at increased C-rate and/or decreased temperature.
MS [00372] Recent advances on computational wave propagation
room : D404
[02737] Highly Efficient Iterative Method with High Order ABC for Acoustic Scattering
Format : Talk at Waseda University
Author(s) :
Vianey Roman Villamizar (Brigham Young University)
Tahsin Khajah (University of Texas at Tyler)
Jonathan Hale (University of Wisconsin)
Abstract : In this paper, we have developed a highly efficient numerical method for acoustic multiple scattering. This novel method consists of a high order local absorbing boundary condition combined with an isogeometric finite element and finite differences methods. By employing high order NURB basis, a globally high order method results. In our numerical experiments, we obtain errors close to machine precision by appropriate implementation of p- and h-refinement. We include numerical results which demonstrate the improved accuracy and efficiency of this new formulation compared with similar methods.
[02916] The effect normal electric fields on the flow structure beneath waves
Format : Talk at Waseda University
Author(s) :
Roberto Ribeiro Santos Junior (Universidade Federal do Parana)
Marcelo V. Flamarion (Rural Federal University of Pernambuco)
Tao Gao (University of Essex)
Alex Doak (University of Bath)
Abstract : Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric fields and vorticity is of significant research interest. In this talk, we present numerical results on the effect of normal electric fields on the flow structure beneath periodic and solitary rotational waves. By using a combination of conformal mapping techniques and pseudo-spectral numerical methods, we show how variations in voltage potential can affect particle trajectories and the pressure within the bulk of the fluid
MS [00605] Recent advances in theory and application of quantum computing technology
room : D405
[03620] QUBO encoding of inequality constraints in Quantum Minimum Fill-in algorithm
Format : Talk at Waseda University
Author(s) :
Tomoko Komiyama (University of Yamanashi)
Tomohiro Suzuki (University of Yamanashi)
Abstract : Expressing constraints with complex conditions in terms of inequalities in solving optimization problems is common. When solving problems with quantum annealing, inequality constraints must be transformed into an unconstrained quadratic form that does not contain inequalities. There are various methods for this transformation, which vary in the number of auxiliary variables to be added and the total number of solutions that will be optimal. We compare these transformation methods and discuss which is suitable for quantum annealing.
[02807] Approximate block diagonalization of symmetric matrices using a quantum annealing
Format : Talk at Waseda University
Author(s) :
Koshi Teramoto (The University of Electro-Communications)
Masaki Kugaya (The University of Electro-Communications)
Shuhei Kudo (The University of Electro-Communications)
Yusaku Yamamoto (The University of Electro-Communications)
Abstract : Approximate block diagonalization is an efficient preprocessing technique for accelerating the block Jacobi method to solve the symmetric eigenvalue problem.
The aim of this study is to speed up this process using quantum annealing.
To achieve this, we formulated it as a combinatorial optimization problem and expressed it in Quadratic Unconstrained Binary Optimization (QUBO) that can be dealt with by D-Wave's quantum annealing system.
Numerical experiments on small matrices using D-Wave Advantage show that optimal approximate block diagonalization that minimizes the off-diagonal norm can be obtained with high probability.
[03304] Performance evaluation of quantum-inspired machine and quantum simulator
Format : Talk at Waseda University
Author(s) :
Makoto Morishita (Nagoya University)
Takahiro Katagiri (Nagoya University)
Satoshi Ohshima (Kyusyu University)
Tetsuya Hoshino (Nagoya University)
Toru Nagai (Nagoya University)
Abstract : The purpose of this research is to construct a heterogeneous environment in which next-generation computers that quantum computers are equipped as an accelerator specialized for specific calculations (e.g., solving QUBO).
The performance of annealing-base and gate-base by benchmarks is evaluated as a preliminary result. In particular, we evaluated the performance of solving QUBO by the annealing-base such as digital annealers, and by the gate-base of quantum circuits implementing QAOA.
Hyperparameters such as coefficients of constraint terms appearing in the QUBO formula, and the number of unitary gates in QAOA, are tuned by utilizing Optuna in our experiment.
[03892] Use of digital annealer for HPC applications
Format : Talk at Waseda University
Author(s) :
Masatoshi kawai (Nagoya University)
Abstract : In some high-performance applications, combinatorial optimization problems (COPs) are solved in unique methods. However, solving these COPs with more constraint conditions and complex evaluation functions may improve the performance of the applications. In this study, we discuss the performance improvement obtained by using Digital Annealing to solve the complex COPs derived from lattice H-matrices with dynamic load balancing and the parallelized incomplete Cholesky conjugate gradient method using a multi-coloring technique.
MS [00449] Atomistic simulations in the exascale era
room : D407
[01608] Quantum Materials Simulations at the Nexus of Exascale Computing, Artificial Intelligence, and Quantum Computing
Format : Talk at Waseda University
Author(s) :
Aiichiro Nakano (University of Southern CaliforniaUniversity of Southern California)
Abstract : Computing landscape is evolving rapidly. Exascale computers have arrived, and quantum supremacy has been demonstrated for several problems, while artificial intelligence (AI) is transforming every aspect of science and engineering. Atomistic simulations at the exa-quantum-AI nexus are revolutionizing quantum materials research. I will describe research and education on atomically thin two-dimensional and other quantum materials using our AI and quantum-computing enabled exascale materials simulator (AIQ-XMaS). Specifically, I will describe (1) self-assembly of layered material metastructures for scalable and robust manufacturing of quantum emitters for future quantum information science and technology; and (2) excited-state neural-network quantum molecular dynamics (NNQMD) trained by first-principles nonadiabatic quantum molecular dynamics (NAQMD) to prove the exciting concept of picosecond optical, electrical and mechanical control of symmetric breaking in topological ferroelectric skyrmion and skyrmionium for emerging ultralow-power polar topotronics. This research was supported by NSF Future Manufacturing Program, Award 2036359, NSF Cybertraining Program, Award 2118061, and Sony Research Award. Simulations were performed at Argonne Leadership Computing Facility under DOE INCITE and Aurora Early Science programs and at Center for Advanced Research Computing of the University of Southern California.
[01950] Large scale quantum chemistry with Tensor Processing Units
Format : Online Talk on Zoom
Author(s) :
Ryan Pederson (University of California, Irvine)
John Kozlowski (University of California, Irvine)
Ruyi Song (Duke University)
Jackson Beall (SandboxAQ)
Martin Ganahl (SandboxAQ)
Markus Hauru (Alan Turing Institute)
Adam Lewis (SandboxAQ)
Shrestha Basu Mallick (Google LLC)
Volker Blum (Duke University)
Guifre Vidal (Google LLC)
Abstract : We demonstrate the use of Googles cloud-based Tensor Processing Units $\text{(TPUs)}$ to accelerate and scale up conventional $\text{(cubic-scaling)}$ density functional theory $\text{(DFT)}$ calculations. Utilizing $512$ TPU cores, we accomplish the largest such DFT computation to date, with $247,848$ orbitals, corresponding to a cluster of $10,327$ water molecules with $103,270$ electrons, all treated explicitly. Our work thus paves the way toward accessible and systematic use of conventional DFT, free of any system-specific constraints, at unprecedented scales.
[02042] Quantum molecular dynamics using Tensor cores
Format : Talk at Waseda University
Author(s) :
Joshua Finkelstein (Los Alamos National Laboratory)
Emanuel H Rubensson (Uppsala)
Susan M Mniszewski (Los Alamos National Laboratory)
Christian F. A. Negre (Los Alamos National Laboratory)
Anders M Niklasson (Los Alamos National Laboratory)
Abstract : Tensor cores represent a new form of hardware acceleration specifically designed for deep neural network calculations. They provide extraordinary speed and efficiency but were designed for low-precision tensor contractions. Despite this, we demonstrate how Tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations.
[02949] Recent algorithmic improvements in parallel long-time molecular dynamics
Format : Talk at Waseda University
Author(s) :
Danny Perez (Los Alamos National Laboratory)
Abstract : The temporal reach of molecular dynamics is limited by poor parallel strong-scaling: even on exascale computers, direct simulation is expected to remain limited to microseconds. We explore alternative time-wise parallelization schemes that target long-time simulations where multiple trajectory segments are evolved simultaneously and assembled into a unique dynamically correct trajectory. We discuss recent speculative execution and resource-allocation schemes that suggest significant potential scalability enhancements, leading to increased simulation timescales when deployed on massively-parallel computers.
MS [01622] Mathematics for Prediction and Control of Complex Systems
room : D408
[02814] Noise Calibration for the Stochastic Rotating Shallow Water Equations
Format : Talk at Waseda University
Author(s) :
Alexander Lobbe (Imperial College London)
Oana Lang (Imperial College London)
Dan Crisan (Imperial College London)
Peter Jan van Leeuwen (Colorado State University)
Roland Potthast (Deutscher Wetterdienst DWD)
Abstract : We introduce a new method of noise calibration of the Stochastic Rotating Shallow Water (SRSW) model which is rigorously derived from a model reduction technique. The method is generic and can be applied to arbitrary stochastic models. In the (SRSW) case, we calibrate the noise by using the pressure variable of the model, as this is an observable easily obtainable in practical application.
[03049] Machine learning-based estimation of state-dependent forecast uncertainty
Format : Talk at Waseda University
Author(s) :
Juan Jose Ruiz (University of Buenos Aires)
Maximiliano Sacco (National Meteorological Service of Argentina)
Manuel Pulido (Universidad Nacional del Nordeste)
Pierre Tandeo (IMT Atlantique)
Abstract : Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. State dependent uncertainty quantification in numerical weather prediction is a computation intensive task which has been performed using different approaches such as monte carlo sampling (ej. ensemble Kalman filter) and variational approaches (ej. adjoint based model sensitivity). Machine learning techniques consist of trainable statistical models that can represent complex functional dependencies among different groups of variables given a large enough dataset. In this talk we will describe the use of a machine learning approach based on neural networks for the estimation of forecast uncertainty. In particular, we will discuss the estimation of the forecast error covariance matrix, which is at the center of probabilistic forecasting and data assimilation systems. In addition, we will present a hybrid data assimilation method that combines the optimal interpolation technique and a convolutional neural network to estimate the state dependent forecast error covariance matrix.
[03126] Observability of continuous-time Markov model and filter stability
Format : Talk at Waseda University
Author(s) :
JIN WON KIM (University of Potsdam)
Abstract : In control theory, estimation and control are considered as dual problems. A fundamental relationship is the duality between controllability and observability, and it extends to Kalman filter and a linear quadratic control problem. Our contribution is to extend the duality to nonlinear models. I will review the classical duality and present the dual optimal control problem. The dual formulation is used to analyze the stability of the nonlinear filter, similar to the linear Gaussian case.
[03024] On random feature maps in prediction
Format : Talk at Waseda University
Author(s) :
Nicholas Cranch (University of Sydney)
Georg A. Gottwald (University of Sydney)
Sebastian Reich (University of Potsdam)
Abstract : Random feature maps (RFs) can be viewed as a single hidden layer network in which the weights of the hidden layer are fixed. We show how the choice of the internal weights effects performance and generalisation. We propose how to best choose the internal weights. We show that RFs allow for sequential learning when combined with data assimilation, and can be used to learn subgridscale parametrizations and to detect critical transitions.
MS [00625] Mathematical Modeling and Combinatorial Optimization
room : D501
[02230] Sports Scheduling: Number of Trips in the Traveling Tournament Problem
Format : Talk at Waseda University
Author(s) :
Takaki Ono (Chuo University)
Shinji Imahori (Chuo University)
Abstract : This talk deals with the traveling tournament problem, which is a well-known benchmark problem in the field of sports scheduling. We propose a new technique to improve the efficiency of an existing algorithm for the problem. We also design a new method to improve the quality of solutions. Our method first solves an integer programming problem to compute a round-robin tournament, and constructs a double round-robin tournament with smaller number of trips.
[04421] Efficient allocation of demand to facilities on road networks
Format : Talk at Waseda University
Author(s) :
Ken-ichi Tanaka (Keio University)
Mutsunori Yagiura (Nagoya University)
Abstract : We focus on road networks in which some facilities exist and demand for deliveries arises along the edges of the network. We consider the problem of assigning a subset of edges to each facility so that the total facility-demand delivery distances are minimized with the constraint that each facility addresses almost the same amount of demand. We propose an approach to obtain simple and geographically compact service areas by iteratively solving integer optimization problems.
[01600] Optimal UAV Flight Path Planning for Herding Sheep
Format : Talk at Waseda University
Author(s) :
I-Lin Wang (Professor)
Ying-Ting Lin (Ph.D. student)
Abstract : We will first introduce how literature solves the shepherding problem by autonomous agents. All the previous research designed heuristic algorithms to collect the sheep when they are too dispersed and then drive them to the destination after aggregating them. We, on the other hand, propose an innovative framework based on graph theory and integer programming models. Our approaches have a significant performance improvement and provide a new viewpoint on how this problem can be solved.
[02992] Formulations and algorithms for a square independent packing problem
Format : Talk at Waseda University
Author(s) :
Wei Wu (Shizuoka University)
Hiroki Numaguchi (Tokyo University of Science)
Jotaro Kuno (Nagoya University)
Yannan Hu (Tokyo University of Science)
Vitor Mitsuo Fukushige Hama (Nagoya University)
Mutsunori Yagiura (Nagoya University)
Abstract : Given a set of squares and a strip with a fixed width, we consider a square independent packing problem (SIPP) that minimizes the strip height such that all squares are packed into cells by setting vertical and horizontal dividers that pass through the entire strip. We show that the SIPP is NP-hard. To solve the SIPP, we design three mathematical formulations based on different solution representations, and then we propose a fully polynomial-time approximation scheme.
MS [00467] Volatility modeling in finance
room : D502
[05137] Volatility is (Mostly) Path-Dependent
Author(s) :
Julien Guyon (Ecole des Ponts ParisTech)
Jordan Lekeufack Sopze (University of California, Berkeley)
Abstract : Using data, we show that volatility is mostly path-dependent: 90% of the implied volatility of equity indexes is explained endogenously by past index returns thanks to a simple linear model that combined weighted sums of past daily returns and squared returns with different time-shifted power-law weights. It thus suggests a continuous-time Markovian path-dependent volatility model. This model captures key stylized facts of volatility, and fits SPX and VIX smiles well, solving joint SPX/VIX smile calibration problem.
[05626] The 4-Factor Path-Dependent Volatility Model
Author(s) :
Julien Guyon (Ecole des Ponts ParisTech)
Abstract : The natural Markovian continuous-time version of the empirical path-dependent volatility (PDV) uncovered in [Guyon and Lekeufack, Volatility Is (Mostly) Path-Dependent, 2022] is the 4-Factor PDV model. Two factors describe the short and long dependence of volatility on recent returns (trend), while the two other factors describe the short and long dependence of volatility on recent returns squared (historical volatility). We show that this model, which is inferred from the empirical joint behavior of returns and volatility, captures all the important stylized facts of volatility: leverage effect, volatility clustering, large volatility spikes followed by a slower decrease, roughness at the daily scale, very realistic SPX and VIX smiles, joint calibration, Zumbach effect and time-reversal asymmetry. Being Markovian in low dimension, the model is very easy and fast to simulate. It can easily be enhanced with stochastic volatility (PDSV) to account for exogenous shocks. This is joint work with Jordan Lekeufack.
[01960] A theoretical analysis of Guyon's toy volatility model
Format : Talk at Waseda University
Author(s) :
Ofelia Bonesini (Imperial College London)
Antoine Jacquier (Imperial College London)
Chloé Lacombe (Morgan Stanley)
Abstract : We provide a thorough analysis of a path-dependent volatility model introduced by Guyon,
proving existence and uniqueness of a strong solution, characterising its behaviour at boundary points,
providing asymptotic closed-form option prices as well as deriving small-time behaviour estimates.
[05614] Prediction through Path Shadowing Monte-Carlo
Format : Online Talk on Zoom
Author(s) :
Rudy Morel (École Normale Supérieure)
Stéphane Mallat (Collège de France)
Jean-Philippe Bouchaud (CFM)
Abstract : We introduce a Path Shadowing Monte-Carlo method, which provides prediction of future paths, given any generative model. At a given date, it averages future quantities over generated price paths whose past history matches, or “shadows”, the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called “Scattering Spectra”. This model promotes diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on volatility roughness. Our method yields state-of-the-art predictions for future realized volatility. It also allows one to determine conditional option smiles for the S&P500. These smiles depend only on the distribution of the price process, and are shown to outperform both the current version of the Path Dependent Volatility model and the option market itself.
MS [02612] Mathematical modeling of biofilm systems and applications
room : D514
[03848] Simulation of ultrasonic biofilm detachment in membrane aerated bioreactors
Author(s) :
Maryam Ghasemi (University of Waterloo)
Sheng Chang (University of Guelph)
Sivabal Sivaloganathan (University of Waterloo)
Abstract : Controlling biofilm thickness in an aerated membrane biofilm reactor (MBfR) has been recognized as a key for MBfRs to achieve a long-term stable performance. In this context, acoustic cavitation is an effective strategy that can be used for controlling biofilm thickness. However, to maintain the biofilm thickness at an optimum value, it is necessary to understand the effect of acoustic parameters and cavitation bubble distribution on biofilm detachment and establish a link between biofilm detachment and regrowth. The purpose of this study is to provide an integrated mathematical model that describes biofilm development in an aerated membrane biofilm reactor using a nonlinear reaction-diffusion model and its response to mechanical stress generated from acoustic cavitation. The simulation results show that amplitude and frequency of transducer are two key factors that affect biofilm detachment. Moreover, uniform distribution of cavitation along the biofilm surface is critical to achieve an even biofilm thickness. Furthermore, periodic cavitation detachment with an appropriate resting time in between is important for maintaining the biofilm thickness at a desired value. Therefore, the proposed integrated modeling approach can be used to optimize acoustic cavitation parameters and achieve effective biofilm thickness control in MBfRs.
[04151] Bacterial Biofilms across scales and applications
Format : Online Talk on Zoom
Author(s) :
Nicholas Cogan (Florida State University)
Abstract : This talk will describe mathematical modeling of biofilm dynamics in general. This should set the stage for the talks in this session that include models that focus on the physics of fluids, materials, and biology. Applications range from environmental to engineering as well as scales from millimeters to meters and time scales that range from seconds to weeks. Because of the wide variety in scales and applications, mathematical aspects must be both flexible and precise. This tension has driven an explosion in interest in biofilm models in the past 30+ years and there are a handful of broadly studied models which will be discussed in this talk.
[04177] Microbially-influenced transport in sea ice
Author(s) :
Isaac Klapper (Temple University)
Abstract : Sea ice, which covers a significant portion of the earth's surface, is an interestingly complicated material consisting of a mixture of solid ice and liquid brine phases which are coupled by thermodynamic considerations, It also is a platform for microbial life. A model will be presented that hypothesizes that, in turn, the sea ice resident microbial population
might impact ice sheet structure and, in particular, its transport properties including notably heat transport.
[04844] Computational simulations of biofouling on ship hulls
Author(s) :
Rosalind Allen (Friedrich Schiller University Jena)
Patrick Sinclair (University of Edinburgh)
Jennifer Longyear (AkzoNobel)
Kevin Reynolds (AkzoNobel)
Alistair Finnie (AkzoNobel)
Chris Brackley (University of Edinburgh)
Martin Carballo Pacheco (University of Edinburgh)
Abstract : We use computer simulations to investigate two coating technologies for ship hulls. Simulating microbial colonization of a surface that releases a biocidal chemical we find intrinsic stochasticity with an important role for immigration of biocide-resistant species. Further, computational fluid dynamics simulations of flow across a textured (riblet) surface show that removal of biofouling by flow may be ineffective if the flow is not well aligned. Simulations can help understand marine biofouling on advanced surface coatings.
MS [00471] Recent Advancements in Electrical Impedance Tomography
room : D515
[04879] A Multithreaded Implementation of the D-bar Algorithm for 2D Functional EIT Imaging
Format : Talk at Waseda University
Author(s) :
Melody Alsaker (Gonzaga University)
Abstract : D-bar algorithms for Electrical Impedance Tomography have high computational complexity. Previous attempts at fast D-bar implementations had some limitations: these methods used a parallelization strategy which caused a time delay between data acquisition and reconstruction, and they used coarse spatial meshes with large numbers of CPU cores. Furthermore, data acquisition speed of modern EIT systems has increased, making previously published runtimes out-of-date. In this talk, we present a new multithreaded solution which addresses these problems.
[02729] New insight into EIT reconstruction using virtual X-rays
Format : Talk at Waseda University
Author(s) :
Siiri Rautio (University of Helsinki)
Abstract : We introduce a new reconstruction algorithm for EIT, which provides a connection between EIT and X-ray tomography. We divide the ill-posed and nonlinear inverse problem of EIT into separate steps. We start by calculating “virtual” X-ray projection data from the DN map. Then, we perform algebraic operations and integration, ending up with a blurry Radon sinogram. We use neural networks to deconvolve the sinogram and finally, we compute a reconstruction using the inverse Radon transform.
[04009] Combining electrical impedance tomography and machine learning for stroke classification
Format : Talk at Waseda University
Author(s) :
Juan Pablo Agnelli (National University of Córdoba)
Abstract : There are two main types of stroke: ischemic and hemorrhagic. In both cases the symptoms are the same, but treatments very different, so a cost-effective and portable classification device is needed.
In (Agnelli et al. 2020) a methodology for classifying stroke was proposed. The methodology combines the use of EIT data, the computation of VHED functions (Greenleaf et al. 2018) that have a geometric interpretation of the EIT data and finally machine learning applied to these VHED functions for the stroke classification. In this talk we continue this research line and extend the previous results to a more realistic scenario.
[03129] Recent developments on integral equation approaches for Electrical Impedance Tomography
Format : Talk at Waseda University
Author(s) :
Cristiana Sebu (University of Malta)
Abstract : The talk is focused on recent developments of reconstruction algorithms that can be used to approximate admittivity distributions in Electrical Impedance Tomography. The algorithms are non-iterative and are based on linearized integral equation formulations to allow reconstructions of the conductivity and/or permittivity distributions of two and three-dimensional domains from boundary measurements of both low and high-frequency alternating input currents and induced potentials. Reconstructions from noisy simulated data are obtained from single-time, time-difference and multiple-times data.
MS [00509] Recent developments in stochastic optimization
room : A201
[05112] Convex stochastic optimization
Format : Talk at Waseda University
Author(s) :
Teemu August Pennanen (King's College London)
Ari-Pekka Perkkiö (Ludwig-Maximilian University of Munich)
Abstract : We study dynamic programming, duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in the 70s. We give a general formulation of the dynamic programming recursion and derive an explicit dual problem in terms of two dual variables, one of which is the shadow price of information while the other one gives the marginal cost of a perturbation much like in classical Lagrangian duality. Existence of primal solutions and the absence of duality gap are obtained without compactness or boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity condition of the utility function. We extend classical portfolio optimization duality theory to problems of optimal semi-static hedging. Besides financial mathematics, we obtain several new results in stochastic programming and stochastic optimal control.
MS [00521] Recent advances on non-convex optimization in inverse problems, imaging and machine learning
room : A206
[04380] Proximal methods for nonsmooth and nonconvex fractional programs: when sparse optimization meets fractional programs
Format : Talk at Waseda University
Author(s) :
Guoyin Li (University of new south wales )
Radu Ioan Bot (University of Vienna)
Minh Dao (Royal Melbourne Institute of Technology)
Abstract : Nonsmooth and nonconvex fractional programs are ubiquitous and also highly challenging. It includes the composite optimization problems studied extensively lately, and encompasses many important modern optimization problems arising from diverse areas such as the recent proposed scale invariant sparse signal reconstruction problem in signal processing, the robust Sharpe ratio optimization problems in finance and the sparse generalized eigenvalue problem in discrimination analysis. In this talk, we will introduce extrapolated proximal methods for solving nonsmooth and nonconvex fractional programs and analyse their convergence behaviour. Interestingly, we will show that the proposed algorithm exhibits linear convergence for sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraints. This is achieved by identifying the explicit desingularization function of the Kurdyka-Lojasiewicz inequality for the merit function of the fractional optimization models. Finally, if time permits, we will present some preliminary encouraging numerical results for the proposed methods for sparse signal reconstruction and sparse Fisher discriminant analysis.
[03321] Error bounds based on facial residual functions
Format : Talk at Waseda University
Author(s) :
Bruno Lourenço (Institute of Statistical Mathematics)
Scott B. Lindstrom (Curtin University)
Ting Kei Pong (The Hong Kong Polytechnic University)
Abstract : In this talk, we overview some recent error bound results obtained under the framework of facial residual functions.
This includes new tight error bounds for optimization problems with constraints involving
exponential cones, p-cones and others. Time allowing, we will briefly illustrate the applications of such results in
proving precise convergence rates of certain algorithms and in determining automorphism groups of cones.
[02798] Doubly majorized algorithm for sparsity-inducing optimization problems with regularizer-compatible constraints
Format : Talk at Waseda University
Author(s) :
Tianxiang Liu (Tokyo Institute of Technology )
Ting Kei Pong (The Hong Kong Polytechnic University)
Akiko Takeda (The University of Tokyo)
Abstract : We consider a class of sparsity-inducing optimization problems whose constraint set is regularizer-compatible. By exploiting absolute-value symmetry and other properties in the regularizer, we propose a new algorithm, called the Doubly Majorized Algorithm (DMA). Without invoking any commonly used constraint qualification conditions, we show that the sequence generated by DMA clusters in a new stationary point inspired by the notion of L-stationarity. Finally, numerical performance of DMA on variants of ordered LASSO is also illustrated.
contributed talk: CT169
room : A207
[00433] Markov Decision Processes under Model Uncertainty
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting.
By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure.
Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data.
It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.
[02519] Intensity modulated radiotherapy planning through a fuzzy approach
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : In radiotherapy treatment, is it possible to vary the radiation intensity, achieving a dose distribution with superior compliance. An individualized treatment plan comprises information on how the dose is distributed within a patient. The dose distribution problem translates into optimizing the total radiation dose applied to the patient. Fuzzy optimization is used to deal with inaccurate prescription. Interior point methods are applied to determine optimal solutions with less dose distribution in critical organs.
[01669] Generalising Quasi-Newton Updates to Higher Orders
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : At the heart of all quasi-Newton methods is an update rule that enables us to gradually improve the Hessian approximation using the already available gradient evaluations. Theoretical results show that the global performance of optimization algorithms can be improved with higher-order derivatives. This motivates an investigation of generalizations of quasi-Newton update rules to obtain for example third derivatives (which are tensors) from Hessian evaluations. Our generalization is based on the observation that quasi-Newton updates are least-change updates satisfying the secant equation, with different methods using different norms to measure the size of the change. We present a full characterization for least-change updates in weighted Frobenius norms (satisfying an analogue of the secant equation) for derivatives of arbitrary order. Moreover, we establish convergence of the approximations to the true derivative under standard assumptions and explore the quality of the generated approximations in numerical experiments.
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : Most real-world optimization problems have a hierarchical structure. In mathematical optimization, hierarchical optimization problems are often known as multilevel programming problems. A particular case of multilevel problems with just two decision-makers is called a bilevel programming problem. In the formal framework of bilevel programming problems, two decision-makers are involved, a leader and a follower, at two different levels, each striving to minimize their objective functions while constrained by several interconnected constraints.
Shivani Saini (Thapar Institute of Engineering and Technology, Patiala, Punjab)
MS [00961] Reinforcement Learning for Financial Modeling
room : A208
[03063] Reinforcement learning for mean field games and mean field control problems, with applications to finance
Format : Talk at Waseda University
Author(s) :
Mathieu Lauriere (NYU Shanghai)
Abstract : Mean field games have been introduced to study Nash equilibria in large populations of strategic agents, while mean field control problems aim at modeling social optima in large groups of cooperative agents. These frameworks have found a wide range of applications, from economics and finance to social sciences and biology. In the past few years, the question of learning equilibria and social optima in a mean field setting has attracted a growing interest. In this talk, I will discuss several model-free methods based on reinforcement learning. Numerical experiments on stylized examples of financial models will be presented.
[03255] Learning Risk Aversion with Inverse Reinforcement Learning via Interactive Questioning
Format : Talk at Waseda University
Author(s) :
Ziteng Cheng (University of Toronto)
Anthony Coache (University of Toronto)
Sebastian Jaimungal (University of Toronto)
Abstract : This paper proposes a novel framework for identifying an agent's risk aversion using interactive questioning. We assume that the agent's risk aversion is characterized by a spectral risk measure chosen from a finite set of candidates. We show that asking the agent to choose from a finite set of random costs, which may depend on their previous answers, is an effective means of identifying the agent's risk aversion. Specifically, we prove that the agent's risk aversion can be identified as the number of questions tends to infinity, and the questions are randomly designed. We also develop an algorithm for designing optimal questions and provide empirical evidence that our method learns risk aversion significantly faster than randomly designed questions in a simulated environment. Our framework has important applications in robo-advising and provides a new approach for identifying an agent's risk preferences.
[04804] Fisher-Rao Gradient Descent for Stochastic Control Problems.
Format : Talk at Waseda University
Author(s) :
Lukasz Szpruch (University of Edinburgh/The Alan Turing Institute )
David Siska (University of Edinburgh )
Bekzhan Kerimkulov (University of Edinburgh )
Abstract : We study the convergence of Gradient and Mirror Descent schemes for approximating solutions to stochastic control problems with measure-valued controls in continuous time. By exploiting Pontryagin Optimality Principle, these rely on solving forward and backward (adjoint) equations and performing static optimisation problems regularised with Bregman divergence and can be interpreted as implicit and explicit discretisations of Fisher-Rao gradient flow. In the general (non-convex) case, we show that the objective function decreases along the gradient step. Moreover, in the (strongly) convex case, when Pontryagin Optimality Principle provides a sufficient condition for optimality, we prove that the objective converges at the (exponential) linear rate to its optimal value. The main technical difficulty is to show that stochastic control problem admits suitable relative smoothness and convexity properties. These are obtained by utilising the theory of Bounded Mean Oscillation (BMO) martingales required for estimates on the adjoint Backward Stochastic Differential Equation (BSDE).
[05398] Risk Budgeting Allocation for Dynamic Risk Measures
Format : Talk at Waseda University
Author(s) :
Sebastian Jaimungal (University of Toronto)
Silvana Manuela Pesenti (University of Toronto)
Yuri Saporito (FGV)
Rodrigo Targino (FGV)
Abstract : We develop an approach for risk budgeting allocation -- a risk diversification portfolio strategy -- where risk is measured using time-consistent dynamic risk measures. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. Moreover, we prove that, for the class of dynamic coherent distortion risk measures, the risk allocation problem may be recast as a sequence of convex optimisation problems and, leveraging the elicitability of dynamic risk measures, develop an actor-critic approach to solve for risk budgeting strategy using deep learning.
MS [02445] Advances in Optimization II
room : A502
[05126] On Some Optimization-Related Issues In Deep Learning
Format : Talk at Waseda University
Author(s) :
Yin Zhang (The Chinese University of Hong Kong (Shenzhen))
Abstract : Despite many great advances achieved by deep learning, our understandings of it remain sorely limited. In this talk, we discuss a few optimization-related issues in deep learning, including model trainability, gradient stability, over-parameterization, quality of (globally optimal) solutions, interpolation versus extrapolation. We will introduce a new neural-layer architecture using Householder weighting and Absolute-value activating that has a low complexity but guarantees gradient stability and 1-Lipschitz continuity. We empirically evaluate the capacities of the proposed new layer and demonstrate its potential usefulness.
[03071] Creating Collaborative Data Representations Using Matrix Manifold Optimization
Format : Talk at Waseda University
Author(s) :
Keiyu Nosaka (University of Tsukuba)
Akiko Yoshise (University of Tsukuba)
Abstract : The trade-off between performance and privacy is a pain in the neck for centralized machine learning methods. Fed-DR-Filter and Data Collaboration Analysis (DCA) can overcome this difficulty through Collaborative Data Representation (CDR). We propose an alternative algorithm for CDR creation, utilizing matrix manifold optimization. We devise machine learning models in the DCA setting to evaluate algorithms. The results show that our algorithm outperforms the state-of-the-art approach in mean recognition performance within acceptable computation time.
[03047] Accelerated and Sparse Algorithms for Approximate Personalized PageRank
Format : Talk at Waseda University
Author(s) :
David Martinez-Rubio (Zuse Institute Berlin)
Elias Wirth (Zuse Institute Berlin)
Sebastian Pokutta (Zuse Institute Berlin)
Abstract : It has recently been shown that ISTA, an unaccelerated optimization first-order method, presents sparse updates for the $\ell_1$-regularized personalized PageRank problem, leading to cheap iteration complexity.
In this talk I'll explain our work on accelerated optimization algorithms for this problem that also perform sparse updates leading to faster convergence for certain parameter regimes.
Further, we design a conjugate directions algorithm that achieves an exact solution while exploiting sparsity.
Our findings apply beyond PageRank and work for any quadratic objective whose Hessian is a positive-definite $M$-matrix.
[04893] Optimal Composition Ordering for Linear Functions
Format : Talk at Waseda University
Author(s) :
Kazuhisa Makino (Kyoto Univ.)
Abstract : We outline the composition ordering problem of linear functions, i.e.,
given $n$ linear functions $f_1,\dots,f_n:\mathbb{R}\to\mathbb{R}$
and a constant $c\in\mathbb{R}$, we construct a permutation $\sigma:[n]\to[n]$ that
minimizes $f_{\sigma(n)}\circ f_{\sigma(n-1)}\circ\dots\circ f_{\sigma(1)}(c)$, where $[n]=\{1,\dots,n\}$.
We discuss structual properties of optimal solutions for the problem as well as the current status of the complexity issue. We also consider the multiplication ordering of $n$ matrices.
MS [00114] Computational Biology
room : A508
[03648] Mathematical investigation into the mechanism of hair follicle morphogenesis
Format : Talk at Waseda University
Author(s) :
Masaharu Nagayama (Hokkaido University)
Makoto Okumura (Konan University)
Yasuaki Kobayashi (Hokkaidio Universiy)
Hironobu Fujiwara ( Institute of Physical and Chemical Research)
Abstract : Long-term 3D live imaging of hair follicle morphogenesis during development was shown by Fujiwara et al. During hair follicle morphogenesis, basal cells, basement membrane, and mesenchyme were found to undergo dynamic changes. Fujiwara et al. proposed a telescopic model of hair follicle formation based on these results. In this study, to realize this telescope model, we will construct a mathematical model that reproduces 3D cylindrical compartments and investigate by what mechanism the cylindrical compartments are actively formed.
[03506] Parameter estimation of the compartmental model of systemic circulation describing the Glucose, Insulin and C peptide dynamics
Format : Talk at Waseda University
Author(s) :
Yueyuan Gao (Hokkaido University)
Hiroshi Suito (Tohoku University)
Hayato Chiba (Tohoku University)
Masaharu Nagayama (Hokkaido University)
Hideki Katagiri (Tohoku University)
Abstract : In this talk, we explain the construction of the mathematical compartmental model of systemic circulation describing the Glucose, Insulin and C peptide dynamics and we present the application of Markov chain Monte Carlo method to estimate the parameters of the model from clinical data.
[02898] Effective nonlocal kernels on Reaction-diffusion networks
Format : Talk at Waseda University
Author(s) :
Shin-Ichiro Ei (Hokkaido University)
Abstract : A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called ‘‘effective equation’’ in the convolution type.
MS [00739] Inequalities and entropy with applications
room : A510
[02362] Refined Hermite-Hadamard inequalities and their applications to some n variable means
Format : Talk at Waseda University
Author(s) :
Kenjiro Yanagi (Josai University)
Abstract : It is well known that the Hermite-Hadamard inequality $($called the HH inequality$)$ refines the definition of convexity of function $f(x)$ defined on $[a,b]$ by using the integral of $f(x)$ from $a$ to $b$. There are many generalizations or refinements of the HH inequality. Futhermore the HH inequality has many applications to several fields of mathematics, including numerical analysis, functional analysis and operator inequality. Recently we gave several types of refined HH inequalities and obtained inequalities which were satisfied by weighted logarithmic means. In this talk, we give $n$ variable HH inequality and apply to some $n$ variable means. Finally we compare these means.
[02747] Generalization of Hermite-Hadamard Mercer Inequalities for Certain Interval Valued Functions
Format : Talk at Waseda University
Author(s) :
Asfand Fahad (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan)
Abstract : Due to its significance in economics, optimization and different fields, convex analysis theory has experienced various advancements and extensions over time. A modern development is the use of cr-convex functions to construct equivalent optimality conditions for constrained and unconstrained nonlinear optimization problems using interval-valued objective functions. By keeping in mind the relationships between convex functions and mathematical inequalities involving the convex functions, we investigated generalizations of well-known Hermite-Hadamard Mercer Inequalities for new types of cr-convex functions. We include several well-known consequences as special cases.
[01760] Generalized spectral radius of operators and related inequalities
Format : Talk at Waseda University
Author(s) :
Kais Feki (University of Monastir)
Abstract : In this talk, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $\mathcal{H}$, which are bounded with respect to the seminorm induced by a positive operator $A$ on $\mathcal{H}$. We denote this new concept by $r_A(\cdot)$. In this presentation, several basic properties and inequalities involving $r_A(\cdot)$ are investigated. Moreover, we study the connection between the notions of $A$-spectral radius and $A$-spectrum for $A$-bounded operators.
[03970] $q$-deformation of Böttcher-Wenzel inequality
Format : Talk at Waseda University
Author(s) :
Hiromichi Ohno (Shinshu University)
Abstract : The Böttcher-Wenzel inequality states that the 2-norm of the commutator of matrices $A$ and $B$ is less than or equal to $\sqrt{2}$ times the product of the 2-norms of $A$ and $B$. In this talk, we discuss $q$-deformation of the Böttcher-Wenzel inequality in which the commutator is replaced by a q-commutator.
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.
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.
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.
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.
[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.
MS [00955] Incorporating Immune System and Heterogeneous Dynamics into Infectious Disease Modeling
room : A512
[04150] Immunological variables as structure variables of epidemic models
Format : Talk at Waseda University
Author(s) :
Fabio Augusto Milner (Arizona State University)
Abstract : We present some ways to structure epidemic models with infection and immune response as structure variables. The infected class is modeled using a divergence-form partial differential equation with the boundary conditions incorporating the new infections. Some theoretical results are derived, as well as some examples form HIV-infection. Open theoretical and numerical problems will be described.
[01323] Approximations and parameter inference of stochastic models in infectious disease epidemiology
Format : Online Talk on Zoom
Author(s) :
Wasiur KhudaBukhsh (University of Nottingham)
Abstract : In this talk, we will consider stochastic compartmental models in infectious disease epidemiology. We will discuss when the stochastic models agree with their deterministic counterparts in some limiting regimes and when one stochastic model can be approximated in some precise mathematical sense by another. We will also consider the problem of parameter inference of such systems using notions of dynamical survival analysis (DSA).
[04927] Intelligent immunity: wet labs, fat data, and machine learning
Format : Online Talk on Zoom
Author(s) :
Kaitlyn Martinez (Los Alamos National Laboratory)
Abstract : Developing a universal diagnostic is a long standing challenge. However, the human immune system is able to distinguish pathogens and mounts response quickly, perhaps acting as a guide for design of improved, more general diagnostic development. In collaboration with lab scientists, we use data from hundreds of experiments along with both machine learning and mechanistic models to show the potential for determining the presence of bacteria from markers of a human immune response.
[03423] Why do most sexually transmitted infections not produce long-term immunity?
Format : Talk at Waseda University
Author(s) :
Joel C Miller (La Trobe University)
Abstract : Diseases that are classified as "Susceptible-Infected-Recovered" (SIR) are unable to reinfect previously infected individuals. In small communities outbreaks are short-term and the disease is unable to persist. Long-term persistance of an SIR disease requires a large community or many connected small communities, so that new births replenish the susceptible community. The spread of sexually transmitted infections is heavily influenced by the significant heterogeneity of contact rates within the population. We will show that this increases the required "critical community size" for an SIR infection to persist in sexual transmission networks.
contributed talk: CT180
room : A601
[01630] Analysis of blood flow through multiple stenoses in a narrow artery
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
Type : Contributed Talk
Abstract : A study of the effects of blood flow parameters in narrow arteries having multiple stenoses is made here, where the blood is considered as a non-Newtonian Kuang-Luo (K-L) fluid model, with no-slip conditions at the arterial wall. In fact, the main properties of K-L fluid model are that the plasma viscosity and yield stress play a very important role. These parameters make this fluid remarkably similar to blood, however, when we change these parameters the flow characteristics change significantly. We have derived a numerical expression for the blood flow characteristics such as resistance to blood flow, blood flow rate, axial velocity, and skin friction. These numerical expressions have been solved by MATLAB 2021 software and discussed graphically. Furthermore, these results have been compared with Newtonian fluid and observation made that resistance to blood flow and skin friction is decreased when blood is changed from non-Newtonian to Newtonian fluid.
[01463] Chemical Signalling and Pattern Formation in Predator-Prey Models
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
Type : Contributed Talk
Abstract : Random movement of species is well documented to put forward Turing instability in predator-prey models . On the other hand recent studies suggest that directed movement of species known as direct taxis leads to stabilization of steady state and no patterns emerge. However the importance of chemical cues in predator-prey interactions is still a topic of contention among ecologists. Source of chemicals to which prey species respond often originate as cues released by the predators which lead to directed movement of prey individuals opposite to the concentration of chemicals. This movement of prey individuals opposite to the gradient of chemical is known as indirect predator taxis. This talk will introduce an advection-reaction-diffusion mathematical model to understand the impact of chemical induced anti-predation defense in a special class of predator-prey system. The reaction part considers Schoener's model of intraguild-predation which has no periodic solution. We will discuss uniqueness and existence of classical solutions, linear stability analysis results and conditions for the pattern formation. We will show that random diffusion forces constant steady state to be stable and only directed movement of prey individuals has ability to destabilizes the constant steady state and spatio-temporal patterns emerge. We numerically show emergence of spatio-temporal patterning that depicts the tendency to spatio-temporal separation between prey and predators.
Purnedu Mishra (Norwegian University of Life Sciences Norway)
Prof. Darius Wrzosek (Norwegian University of Life Sciences)
[00931] The vaginal microbiota and its association with Chlamydia infection
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
Type : Contributed Talk
Abstract : Chlamydia trachomatis is the most common bacterial sexually transmitted infection in the U.S. While genital chlamydia infection can beget devastating pathologies, it is unclear why some women are more likely to develop severe infections but others are asymptomatic or remain uninfected after exposure to C. trachomatics. We use mice as a model organism, seek to evaluate the potential impact of the time of day of pathogen exposure on the genital tract microbiome in chlamydia infection.
[02680] An analysis of a model of fear in disease transmission
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
Type : Contributed Talk
Abstract : A model for disease transmission has been proposed that includes fear response both to disease and vaccine. It has been shown numerically that public health restrictions can create a bifurcation in the final size of the epidemic. In this talk we analyze this model to determine analytic conditions for stability and bifurcations to final disease size. We modify the model with additional terms such as adverse reactions from disease and a double-fear compartment.
Rebecca Tyson (University of British Columbia Okanagan)
Avneet Kaur (University of British Columbia Okanagan)
[01734] Towards A Modeling Framework For Pediatric Sickle Cell Pain
Session Time & Room : 4C (Aug.24, 13:20-15:00) @A601
Type : Contributed Talk
Abstract : Sickle cell pain presents in acute episodes in pediatric patients, as opposed to the chronic pain observed in adults. This episodic nature necessitates a distinct approach from those used to model adult pain. Statistical studies have examined interactions between sleep actigraphy measurements and pain levels in pediatric populations, and we propose a dynamic model of pediatric pain that incorporates sleep effects over varying time windows. Our aim is to determine markers of future pain episodes.
MS [00498] Approximation and modeling with manifold-valued data
room : A615
[05470] Implicit integration along the low-rank manifold for stiff and nonlinear equations
Format : Online Talk on Zoom
Author(s) :
Aaron Charous (MIT)
Pierre F. J. Lermusiaux (MIT)
Abstract : We introduce a family of implicit integration methods for the dynamical low-rank approximation: the alternating-implicit dynamically orthogonal Runge-Kutta (ai-DORK) schemes. By alternating over the row and column space of the approximate solution, an efficient iterative low-rank linear solver is developed. To evaluate nonlinearities, we propose a local/piecewise polynomial approximation with adaptive clustering, and on-the-fly reclustering may be performed efficiently in the coefficient space. We demonstrate the proposed schemes on ill-conditioned, nonlinear, and realistic systems.
[04268] Stochastic modeling of model uncertainties through Riemannian reduced-order representations
Format : Online Talk on Zoom
Author(s) :
Hao Zhang (Duke University)
Johann Guilleminot (Duke University)
Abstract : Molecular Dynamics (MD) simulations are widely used in computational materials science to explore the conformational space of atomistic systems, to analyze microscopic processes, and to evaluate macroscopic properties of interest. At the core of all MD simulations stands the selection of interatomic potentials, which can be calibrated by means of first-principles calculations or by solving inverse problems based on experimental observations. Such potentials are not uniquely defined in general, which raises the question of model uncertainties and their impact on MD-informed multiscale predictions. In this work, we propose a new probabilistic framework that enables the seamless integration of model-form uncertainties in atomistic computations. The approach relies on a stochastic reduced-order model involving a randomized Galerkin projection operator. An information-theoretic probabilistic model is specifically constructed on the tangent space to the manifold, taking advantage of Riemannian projection and retraction operators. We also explore statistical inference with a view toward inverse identification. We show, in particular, that the Fréchet mean can be constrained by solving a quadratic programming problem. Various applications are finally presented to demonstrate the relevance of the method, including toy examples in the Euclidean space and multiscale simulations on single layer graphene sheets. The proposed method offers key advantages, including a simple and interpretable low-dimensional parameterization, the ability to constraint the mean on the underlying manifold, and ease of implementation and propagation through multiscale operators.
[05113] On approximation and representation of manifold-valued functions
Format : Talk at Waseda University
Author(s) :
Nir Sharon (Tel Aviv University)
Abstract : Recent years have given rise to exciting developments in methods for approximating manifolds and manifold-valued objects. This talk will review recent work concerning manifold-valued approximation via refinement and quasi-interpolation operators and their close connection to multiscaling.