MS and CT list / Aug. 22, 13:20-15:00.

contributed talk: CT002

room : G301

[00017] Modified Operational Laws for Neutrosophic Numbers in Decision-Making Problems

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G301
• Type : Contributed Talk
• Abstract : This presented work results from the study of the existing basic operational laws of neutrosophic numbers which had some shortcomings clearly stating that these are the special type of neutrosophic numbers and not applicable in every practical situation. To overcome this limitation the general basic operational laws of neutrosophic numbers are proposed in this paper and a numerical example from a real-life situation has been solved optimally to show the validity of the proposed neutrosophic numbers laws.
• Classification : 03B52, 03B52, 15B15, 28E10
• Format : Talk at Waseda University
• Author(s) :
  • Akanksha Singh (Chandigarh University)

[00092] The explicit formulae for the distributions of words

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G301
• Type : Contributed Talk
• Abstract : The distributions of the number of words play key roles in information theory, statistics, and DNA analysis. Bassino et al. 2010, Regnier et al. 1998, and Robin et al. 1999 showed generating functions of the distributions in rational forms. However, we can not expand rational functions except for simple cases and do not have explicit formulae for the distributions from them. 
We show the explicit formulae for the distributions of words for the Bernoulli models.
• Classification : 05A05, 05A15, 60C05, 62E15
• Format : Talk at Waseda University
• Author(s) :
  • Hayato Takahashi (Random Data Lab. Inc. )

[02538] Probabilistic proofs for some important combinatorial identities

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G301
• Type : Contributed Talk
• Abstract : Combinatorial identities involving binomial coefficients are very useful in various areas of applied mathematics, especially in discrete mathematics. Using a probabilistic approach, we present simple proofs for some important combinatorial identities involving moments of the gamma, normal, and chi-squared random variates. Some generalizations and interpretations are also given.
• Classification : 05A19, 05A10, 33B15, 60C05, 62E15
• Format : Online Talk on Zoom
• Author(s) :
  • Ashok Kumar Pathak (Central University of Punjab, Bathinda)

[02359] A Weighted Max-Min Model for Stochastic Fuzzy Multi-Objective Supplier Selection in a Supply Chain

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G301
• Type : Contributed Talk
• Abstract : This research is focused on the study of Nonsymmetrical Stochastic Fuzzy Multi-Objective Supplier Selection Linear Programming (SFMOSSLP) with objective and constraint functions containing fuzzy parameters and random variables. This study aimed to develop an algorithm to transform the SFMOSSLP into a Deterministic Single-Objective Linear Programming (DSOLP) using the weighted max-min method so it can be easy to solve using the simplex method. In the end, we showcase the algorithm's performance and discuss its practicality.
• Classification : 03B52, 03E72, 90C05, 90C15, 60G07
• Author(s) :
  • Grandianus Seda Mada (Universitas Gadjah Mada)
  • Nugraha K. F. Dethan (Universitas Timor)
  • Julius Aloysius Nenoharan (Universitas Timor)

contributed talk: CT198

room : G304

[02063] Modeling Uncertainty and Optimizing Control in Philippines COVID-19 Vaccination

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G304
• Type : Contributed Talk
• Abstract : We developed a mathematical model considering vaccination in the country. We incorporated stochastic terms to capture uncertainty. Results show the importance of booster shots that increases the vaccine-induced immunity duration. We then consider the problem of distributing a limited vaccine supply over a time period considering that the country is divided into regions. Simulations showed that the strategy solved from our formulation is better at minimizing infections than a discussed alternative strategy.
• Classification : 92D30, 37N25, 34F05, 49K15, 37H10
• Format : Talk at Waseda University
• Author(s) :
  • Randy L. Caga-anan (MSU-Iligan Institute of Technology)
  • Jayrold P. Arcede (Caraga State University)
  • Joey Genevieve T. Martinez (MSU-Iligan Institute of Technology)

[02271] Enumerate All Routes on a Doughnut

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G304
• Type : Contributed Talk
• Abstract : We consider a following doughnut routing problem. Given a matching $M=(U \cap V,E)$ as a bipartite graph, two concentric circles, the cyclic ordering of the vertices in $U$ and $V$ , we wish to draw $M$ with the minimum number of edge crossings so that the vertices in $U ($resp. $V)$ are on the smaller $($resp. larger$)$ circle with the given cyclic ordering. We propose an enumerate algorithm for all optimal solutions of the problem.
• Classification : 05C38
• Format : Talk at Waseda University
• Author(s) :
  • Yasuko Matsui (Tokai University)
  • Shin-ichi Nakano (Gunma University)

[01193] Cost-effectiveness and Public Health Impact of HPV Vaccination Strategies with consideration of cross-immunity in Japan

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G304
• Type : Contributed Talk
• Abstract : We assessed the epidemiological and economic impact of potential health advantages of the HPV vaccination in Japan among girls and boys of ages 12–16. An age-structured mathematical model of HPV transmission was constructed. Compared to halted vaccination, girls-only vaccination programs with either 4vHPV or 9vHPV are cost-effective, but gender-neutral vaccination programs are less so. Adding boys to an existing successful girls-only program is not cost-effective since men are protected by herd immunity.
• Classification : 92B05
• Format : Talk at Waseda University
• Author(s) :
  • Wongyeong Choi (Soongsil University)
  • Eunha Shim (Soongsil University)

[00095] Low Reynolds number hydrodynamics of a slip-stick sphere

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G304
• Type : Contributed Talk
• Abstract : Low Reynolds number hydrodynamics of spherical particles with non-uniform surface roughness show potential applications in microfluidic situations like swimming micro-organisms and emulsions. In this work, we study the hydrodynamics of spherical slip-stick particle models; namely, i) axisymmetric cap/strip model and ii) non-axisymmetric patch model, suspended in an unbounded arbitrary Stokes flow whose surface is partitioned into two different slip regions. We evaluate the optimum configurations for migrational and rotational motion of the slip-stick spherical particle.
• Classification : 76D07, 35A25
• Format : Talk at Waseda University
• Author(s) :
  • Shiba Biswas (Indian Institute of Technology Kharagpur, India-721302)
  • Poornachandra Sekhar Burada (Indian Institute of Technology Kharagpur, India-721302)
  • Raja Sekhar G P (Indian Institute of Technology Kharagpur, India-721302)

MS [01071] Recent Advances on Groebner Bases and Their Applications

room : G305

• [01758] Parametric Ideal Operations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Ishihara (Tokyo University of Science)
  • Abstract : We present several algorithms for parametric ideal operations of polynomial ideals. Let $K[X]=K[x_1,\ldots,x_n]$ be the polynomial ring over a filed $K$ and $K[A,X]$ the parametric polynomial ring with parameters $A=\{a_1,\ldots,a_m\}$. Let $\varphi_\alpha$ be the homomorphism from $K[A,X]$ to $K[X]$ by $\varphi_\alpha(f(A,X))=f(\alpha,X)$ for $\alpha\in K^m$. For an ideal operation $F$ and parametric ideals $I_1,…,I_r$, we compute a set of pairs $\{(A_i,G_i)\}_{i=1}^s$ s.t. $\bigcup_{i=1}^s A_i=K^m$ and $\varphi_\alpha(G_i)$ is a Groebner basis of $F(\varphi_\alpha(I_1),…,\varphi_\alpha(l_r))$ for any $\alpha\in A_i$.
• [01892] On the complexity of Groebner basis computation
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuhiro Yokoyama (Rikkyo University)
  • Abstract : The complexity of computation of Groebner basis is heavily related to the syzygy of given generating set. We will discuss this relation for generic case, where coefficients of generating set can be considered as parameters.
• [01851] On Parametric Border Basis and Comprehensive Gröbner System
  • Format : Talk at Waseda University
  • Author(s) :
    • Yosuke Sato (Tokyo University of Science)
  • Abstract : A border basis is an alternative tool to a Gröbner basis for handling a polynomial ideal. One of the most important properties of a border basis is its stability. Though this property is cited by many researchers, its precise definition has not been given anywhere yet. We give its rigorous definition in terms of a parametric polynomial ideal and introduce several properties which enable us to have a simple representation of a parametric polynomial ideal.
• [01843] Universal Analytic Gröbner bases, Tate Algebras and toward Tropical Analytic Geometry
  • Format : Talk at Waseda University
  • Author(s) :
    • Tristan Vaccon (Limoges University)
    • Thibaut Verron (Johannes Kepler University)
  • Abstract : Tate algebras are defined as multivariate formal power series over a $p$-adic field, with a convergence condition. We will present the concept of Universal Analytic Gröbner Basis for a polynomial ideal: a finite polynomial basis of an ideal such that it is a Gröbner basis in any of the completions into Tate algebras for any (rational) convergence radius. We will present how to compute it and its relation with tropical varieties.

MS [02392] Low-Rank Models in Data Science

room : G306

• [02769] Low-rank models in data science: Applications and optimization challenges
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dominik Stöger (KU Eichstätt-Ingolstadt)
  • Abstract : Low-rank matrix models have emerged as a powerful tool in data science with applications ranging from recommender systems to computational physics. In this overview talk, we first highlight some applications where low-rank models arise. Next, we discuss which statistical and optimization challenges arise. Moreover, we highlight several advances which have been made in recent years to circumvent these issues.
• [05455] Low Rank Matrix Recovery from Column-wise Projections: Fast and Communication-Efficient Solutions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Namrata Vaswani (Iowa State University)
  • Abstract : We study the following lesser-known low rank (LR) recovery problem: recover an n × q rank-r matrix, $X^* = [ x^*_1 , x^*_2 ,..., x^*_q]$, with $r << min(n, q)$, from m independent linear projections of each of its $q$ columns, i.e., from $y_k := A_k x^*_k , k \in [q]$, when $y_k$ is an m-length vector with m < n . The matrices $A_k$ are known and mutually independent for different k. We introduce a novel gradient descent (GD) based solution called AltGD-Min. We show that, if the $A_k$'s are i.i.d. with i.i.d. Gaussian entries, and if the right singular vectors of $X^*$ satisfy the incoherence assumption, then \epsilon-accurate recovery of X* is possible with order $(n + q) r^2 log(1/\epsilon)$ total samples and order $mqnr log(1/\epsilon)$ time. Compared with existing work, this is the fastest solution, and in most practical settings, it also has the best sample complexity. For a federated implementation, it is also communication-efficient with a cost of only order $nr$ per node per iteration. A simple extension of AltGD-Min also provably solves the LR Phase Retrieval problem, which is a magnitude-only measurements' extension of the above problem.
• [04491] Tensor-Norm Approaches to Low-Rank Matrix Recovery by Convex Program
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kiryung Lee (Ohio State University)
  • Abstract : Low-rank models have been shown effective for solving various inverse problems from classical system identification to modern matrix completion and sketching in signal processing and statistics. If each observation is a linear combination of a subset of matrix entries, the reconstruction is feasible only for a class of matrices incoherent to the measurement process. We propose an estimator that prefers a solution with low rankness and incoherence by a regularizer given by a pair of norms on the tensor product of two Banach spaces. The resulting optimization is cast as a convex semidefinite program and provides a near-optimal error matching the corresponding minimax bound in a low signal-to-noise ratio regime. We illustrate the efficacy of the estimator over selected applications in signal processing. We also present a scalable numerical optimization algorithm and study its empirical performance over large-scale synthesized data.
• [04277] Algorithmic approaches to recovering sparse and low-rank matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Johannes Maly (Ludwig-Maximilians-Universität München)
  • Abstract : In this talk, I consider the problem of recovering an unknown sparse and low-rank matrix X from measurements gathered in a linear measurement process. I discuss the challenges that come with leveraging several structures simultaneously and present two new algorithmic strategies to efficiently approach the problem. Both strategies come with local convergence guarantees.

MS [00170] Integrable systems, orthogonal polynomials and asymptotics

room : G401

• [05493] Welcome and Introduction
  • Format : Talk at Waseda University
  • Author(s) :
    • Nalini Joshi (The University of Sydney)
  • Abstract : This talk will provide an overview of recent developments in integrable systems, orthogonal polynomials and asymptotics and the topics underlying the talks in this minisymposium.
• [02937] Lagrangian multiform structure of discrete and semi-discrete KP typequations
  • Format : Talk at Waseda University
  • Author(s) :
    • Frank Willem Nijhoff (University of Leeds)
  • Abstract : A brief review of of Lagrangian multiform theory for integrable discrete and continuous equations will be presented. As specific examples I will discuss the recently established 3-form structure of the KP hierarchy, and its discrete and semi-discrete counterparts.
• [03500] Charge-conserving solutions to the constant Yang-Baxter equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jarmo Hietarinta (University of Turku)
    • Paul Martin (University of Leeds)
    • Eric C. Rowell (Texas A&M University)
  • Abstract : The Yang-Baxter equation is difficult to solve even in the constant form $R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}$ and a complete solution is known only for rank two. For further progress it is important to make a meaningful ansatz. Recently Martin and Rowell proposed charge-conservation as an effective constraint (arXiv:2112.04533). We explore the results obtained by a slightly different charge-conservation rule.
• [04990] Deformed orthogonal functions and integrable lattices
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiangke Chang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Since the 1990s, the theory of orthogonal polynomials has been increasingly playing an important role in the studies of Toda type lattices, peakon dynamical systems of the Camassa-Holm type, as well as specific Painlevè equations. These integrable lattices can be derived according to deformations of orthogonal functions, directly or indirectly. This talk is devoted to exploring some of related works with focus on our recent results for some new orthogonality.

MS [02541] Biochemical reaction network reduction methods & multiple timescale dynamics

room : G402

• [04793] The relationship between deterministic and stochastic quasi-steady-state
  • Format : Talk at Waseda University
  • Author(s) :
    • Jae Kyoung Kim (KAIST)
  • Abstract : The quasi steady-state approximation (QSSA) is frequently used to reduce de- terministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used as propensities of Gillespie algorithm. Despite the popularity of this heuristic stochastic simulations, it remains unclear when such stochastic reductions are valid. In this talk, I will present conditions under which the stochastic models with the non-elementary propensity functions accurately approximate the full stochastic models. If the validity condition is satisfied, we can perform accurate and computationally inexpensive stochastic simulation without converting the non-elementary functions to the elementary functions (e.g. mass action kinetics).
• [04404] Noise attenuation and ultrasensitivity in biological oscillators utilizing the multiple transcriptional repression mechanism
  • Format : Talk at Waseda University
  • Author(s) :
    • Eui Min Jeong (Institute for Basic Science (IBS))
    • Jae Kyoung Kim (Institute for Basic Science (IBS))
    • Yun Min Song (KAIST)
  • Abstract : In many biological systems, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems. This raises the question of what advantages arise from utilizing multiple repression mechanisms. Here, by deriving Fano factors and equations describing the multiple repression mechanisms, we find that their combination can reduce noise in the transcription while generating an ultrasensitive transcription response and thus, strong oscillation. This rationalizes why multiple repression mechanisms are used in various biological oscillators.
• [04800] Reduction of Chemical Reaction Networks with Approximate Conservation Laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Ovidiu Radulescu (University of Montpellier)
    • Aurelien Desoeuvres (University of Montpelleir)
    • Alexandre Iosif (Rey Juan Carlos University of Madrid)
    • Christopher Lueders (University of Bonn)
    • Hamid Rahkooy (University of Oxford)
    • Matthias Seiss (University of Kassel)
    • Thomas Sturm (CNRS )
  • Abstract : Singular perturbation methods are used to reduce multiple timescale chemical reaction networks, but their practical applicability is limited by the manual identification of the small parameters required by the theory. Recently, we have shown that tropical geometry provides ways to rescale CRNs and to identify the small parameters used by singular perturbation theories. Here we consider the case when the fast subsystem has first integrals, not covered by our previous results.
• [04454] A deep dive into the quasi-steady-state approximation to the Michaelis-Menten system
  • Format : Online Talk on Zoom
  • Author(s) :
    • Justin Spaulding Eilertsen (American Mathematical Society)
  • Abstract : Although the quasi-steady state approximation (QSSA) is justifiable from singular perturbation theory, the results addressing its accuracy rely on heuristic timescale estimates. We take a different approach. By combining phase plane analysis with differential inequalities, we obtain rigorous bounds on the accuracy of the QSSA. Moreover, under the assumption the QSSA is valid at the onset of the reaction, we obtain an error estimate that is order one in the Segel--Slemrod parameter.

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

room : G404

• [04297] The Impact of Time Delays on Synchrony in a Neural Field Model
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sue Ann Campbell (University of Waterloo)
    • Isam Al-Darabsah (Jordan University of Science and Technology)
    • Bootan Rahman (University of Kurdistan Hewler (UKH))
    • Wilten Nicola (University of Calgary)
    • Liang Chen (University of Waterloo)
  • Abstract : We consider a network of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. Without delay, the system exhibits rich dynamics including oscillations, mixed-mode oscillations, and chaos. We show that Hopf bifurcations induced by the excitatory coupling, the connectivity structure and the delay lead to different phase-locked oscillations: both synchronized and desynchronized. We show that interaction between different Hopf bifurcations can lead to complex solutions, such as intermittent synchronization.
• [03295] Stability analysis of coupled feedback in hematopoiesis
  • Format : Talk at Waseda University
  • Author(s) :
    • Jacques Bélair (Université de Montréal)
  • Abstract : Hematopoiesis, the production of mammalian blood cells, involves an intertwined network of physiological processes, with nonlinear, delayed feedback control mechanisms. We consider a simplified model of the coupled regulation of erythrocytes (red blood cells) and thrombocytes (platelets). Equilibrium solutions are determined, their stability established and the nature of the oscillations when instability occurs are investigated. The mathematical part of the analysis revolves around a transcendental characteristic equation of second order with two delays.

MS [01188] Recent Developments in Fluid Dynamics

room : G405

• [04609] Recent progress on singularity formation in incompressible fluids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jiajie Chen (New York University)
    • Thomas Y Hou (California Institute of Technology)
  • Abstract : I will talk about recent progress on singularity formation in incompressible fluids with smooth data.
• [04708] Gravity Unstable Muskat Bubbles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Neel Patel (University of Maine)
    • Siddhant Agrawal (ICMAT)
    • Sijue Wu (University of Michigan)
  • Abstract : The Muskat problem describes the evolution of the interface between two fluids in porous media. Neglecting surface tension, the well-posedness of this problem depends on the Rayleigh-Taylor condition. For fluids of differing densities, it is required that the denser fluid is below. Otherwise, the system is gravity unstable. We will discuss the stability of a closed curve interface, or a bubble, in which the Rayleigh-Taylor condition cannot hold.
• [04950] Whitham’s highest cusped wave
  • Format : Talk at Waseda University
  • Author(s) :
    • Bruno Vergara (Brown University)
  • Abstract : Whitham’s equation is a nonlinear, nonlocal, very weakly dispersive shallow water wave model in one space dimension. As in the case of the Stokes wave for the Euler equation, non-smooth traveling waves with greatest height between crest and trough have been shown to exist for this model. In this talk I will discuss the existence of a unique cusped, convex and monotone traveling wave solution to the Whitham equation. Our results follow a strategy that combines different ideas from classical analysis and rigorous computer verification methods. Joint work with Alberto Enciso and Javier Gómez Serrano.
• [03258] On the (in)stability of smooth self-similar solutions to the compressible Euler equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Anxo Farina Biasi (Ecole Normale Superieure-Paris)
  • Abstract : In this talk, I am going to describe recent progress in smooth self-similar solutions to the compressible Euler equations. I will explain how these solutions, initially found by Merle-Raphael-Rodnianski-Szeftel (2019), arise in the family of Guderley self-similar solutions (1942), how their (in)stability is studied under smooth perturbations, and which are some endpoints of unstable directions. The topic will be introduced making a contrast between its states during the 20th and 21st centuries.

MS [00278] Nonlocal Modeling, Analysis, and Computation

room : G406

• [02501] Coarse-Graining and Nonlocality
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stewart A Silling (Sandia National Laboratories)
  • Abstract : The most intuitive applications of nonlocal modeling arise when long-range interactions, such as electrostatic fields, are present in a physical system. However, nonlocal descriptions are also produced by the homogenization or coarse-graining of heterogeneous, small-scale systems. In this talk, it is shown that the coarse-graining of molecular systems or of local, elastic, heterogeneous systems leads to the peridynamic nonlocal linear momentum balance. Examples demonstrate the discovery of nonlocal material models applicable to a coarse-grained description.
• [00366] Wellposedness, regularity, and convergence of nonlocal solutions to classical counterparts
  • Format : Talk at Waseda University
  • Author(s) :
    • Petronela Radu (University of Nebraska-Lincoln)
  • Abstract : The successful employment of nonlocal models in a variety of applications relies on a deep understanding of mathematical properties and analysis of the underlying integral operators and associated systems of equations. In this talk I will present some recent results on nonlocal frameworks systems based on some existing, as well as newly introduced, nonlocal operators. The studies include a series of results on nonlocal versions of integration by parts theorems, boundary conditions (both, Dirichlet and Neumann), Helmholtz-Hodge type decompositions, as well as convergence of operators to their classical equivalents as the interaction horizon vanishes.
• [00370] Coupling of an atomistic model and peridynamic model using an extended Arlequin framework
  • Author(s) :
    • Jieqiong Zhang (Northwest University )
    • Fei Han (Dalian University of Technology)
  • Abstract : A general nonlocal coupling technique between an atomistic (AM) model and the bond-based peridynamic (PD) model is proposed, based on the Arlequin framework. This technique applies the complementary weight function and constraint conditions to transmit energies through the overlapping region between the AM and PD regions. We extend the original Arlequin framework to discrete cases by redefining constraint conditions by the peridynamic differential operator, which enables the interpolation and corresponding derivative of scattered data. Besides, the preconditioning of calibration for the PD effective micromodulus is implemented to guarantee the equilibrium of energy. One-dimensional benchmark tests investigate the coupling effects influenced by several key factors, including the coupling length, weight function, grid size and horizon in the PD model, and constraint conditions. Two- and three-dimensional numerical examples are provided to verify the applicability and effectiveness of this coupling model. Results illustrate this AM–PD coupling model takes the mutual advantages of the computational efficiency of PD model and the accuracy of AM model, which provides a flexible extension of the Arlequin framework to couple particle methods.
• [00445] Local and nonlocal energy-based coupling models
  • Format : Talk at Waseda University
  • Author(s) :
    • Julio D. Rossi (Buenos Aires Univ.)
  • Abstract : In this talk we will present two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this talk we extend these ideas to deal with local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics. joint work with G. Acosta and F. Bersetche.

MS [00656] Multiscale Pattern Formation

room : G501

• [02507] Front propagation in a multi-variable morphogenetic model of branching
  • Format : Talk at Waseda University
  • Author(s) :
    • Edgar Knobloch (University of California at Berkeley)
    • Arik Yochelis (Ben-Gurion University of the Negev)
  • Abstract : We study the existence and stability of propagating fronts in the Meinhardt model of branching in 1D. We identify a sniper bifurcation of fronts that leads to episodic front propagation in the parameter region below propagation failure and show that this state is stable. We show that propagation failure is a consequence of a T-point in a spatial dynamics description and identify additional T-points responsible for a large multiplicity of different traveling front-peak states.
• [02105] CONTROL OF ENGULFMENT FOR BINARY POLYMER PARTICLES
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Teramoto (Asahikawa Medical University)
  • Abstract : Engulfment configurations with separated phases occur in the nanoparticles of a binary polymer mixture. Numerical investigations of the Cahn-Hilliard model with the boundary contact energy show the relationships between the free energies and two types of configurations within confined spheres in three-dimensions. These results are consistent with experimental observations. A Janus-type configuration forms a spherical-cap-shaped interface inside a particle. In the core-shell configuration, one of polymer phases completely engulfs another phase to form concentric interfaces with inner and outer phases. We consider the sharp interface limit of equilibrium configurations and derive the stability condition that each configuration becomes the only minimizer when the contact angle changes between the three phases.
• [03494] Instability of Planar Interfaces in Reaction-Diffusion-Advection Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Paul Carter (University of California, Irvine)
  • Abstract : We consider planar interfaces between stable homogeneous rest states in singularly perturbed 2-component reaction diffusion advection equations, motivated by the appearance of fronts between bare soil and vegetation in dryland ecosystems, as well as multi-interface solutions, such as vegetation stripes. On sloped terrain, one can find stable traveling interfaces, while on flat ground, one finds that sideband instabilities along the interface can lead to labyrinthine Turing-like patterns. To explore this behavior, using geometric singular perturbation methods, we analyze instability criteria for planar interfaces in reaction diffusion advection systems, focussing on a specific Klausmeier-type model, and examine the effect of terrain slope on the stability of the interfaces.
• [04510] Patterns on patterns
  • Format : Online Talk on Zoom
  • Author(s) :
    • Martina Chirilus-Bruckner (Leiden University)
    • Jolien Kamphuis (Leiden University)
  • Abstract : The formation of patterns on top of spatially varying background states in the context of reaction-diffusion systems with spatially varying coefficients (such as the extended Klausmeier model) is motivated by the study of vegetation patterns on changing topographies. We present two regimes: (i) At onset when the background state loses stability and small amplitude modulations occur and (ii) in the long wavelength limit where the patterned state is composed of highly localized individual pulses.

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

room : G502

• [05476] On the lower spectrum of heterogeneous acoustic operators
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mitia Duerinckx (Université Libre de Bruxelles)
  • Abstract : In this talk, we describe a quantitative link between homogenization and Anderson localization for heterogeneous acoustic operators: we draw consequences on the spatial spreading of eigenstates in the lower spectrum (if any) from the long-time homogenization of the wave equation, through dispersive estimates. This yields an alternative proof (avoiding Floquet theory) that the lower spectrum of the acoustic operator is purely absolutely continuous in case of periodic coefficients, and it further provides nontrivial quantitative lower bounds on the spatial spreading of potential eigenstates in case of quasiperiodic and random coefficients. This is based on joint work with Antoine Gloria.
• [03179] Boundary effects in radiative transfer of acoustic waves in a randomly-fluctuating medium delimited by boundaries
  • Format : Talk at Waseda University
  • Author(s) :
    • Adel Messaoudi (Aix-Marseille université)
    • Régis Cottereau (CNRS)
    • Christophe Gomez (Aix-Marseille université)
  • Abstract : This presentation discusses the derivation of radiative transfer equations for acoustic waves propagating in a randomly-fluctuating half-space and slab in the weak-scattering regime, and the study of boundary effects. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on an asymptotic analysis of the Wigner transform of the wave solution and the method of images.
• [05197] Bloch analysis extended to weakly disordered periodic media
  • Format : Online Talk on Zoom
  • Author(s) :
    • Régis Cottereau (CNRS)
    • Yilun Li (CentraleSupélec)
    • Bing Tie (CNRS)
  • Abstract : The dispersion properties of periodic metamaterials can be tailored in order to obtain desirable effects, for instance band gaps over chosen frequency ranges. However, these patterns are sometimes completely destroyed by the small (random) defects introduced by the manufacturing processes, and the induced loss of periodicity of the metamaterials. This contribution explores the extension of the classical Bloch-Floquet theory to problems that are weakly non-periodic, using asymptotic analysis and a random mapping of the properties to a periodic reference.

contributed talk: CT032

room : G601

[01233] A Study of the Spectra-Cutoff Imaging Method of Multiple Scattering in Isotropic Point-Like Discrete Random Media

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
• Type : Contributed Talk
• Abstract : Imaging in random media is an important and interesting subject of inverse problems, relevant to a wide range of physical and engineering contexts, such as seismic imaging, remote sensing, medical imaging, wireless communications, and nondestructive testing. In this talk, we show that imaging becomes difficult to perform in random media when multiple scattering is too strong to cause image distortion arising from the underlying interactions of multiply scattered waves at resonance frequencies. The Foldy-Lax-Lippmann-Schwinger, (FLLS), formalism, which is employed for the multiply scattered waves, in the frequency domain, in the case of an ensemble of randomly distributed point-like scatterers. The scattering matrix representing the (FLLS) formalism is a non-Hermitian Euclidean random matrix. According to the eigenvalue distribution of the scattering matrix, we present our approach to restore the distorted images by cutting off the sharp frequency responses in the resonance regime due to strong multiple scattering. Finally, we show the use of this approach for imaging in discrete random media with numerical simulations and also discuss the limitations and future research direction.
• Classification : 35J05, 35P15, 35P25, 47B06, 78A46
• Format : Talk at Waseda University
• Author(s) :
  • Ray-Hon Sun (Stanford University (while working on this research))

[00958] Existence results and numerical approximation for a quasilinear elliptic system

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
• Type : Contributed Talk
• Abstract : We analyse, in the context of anisotropic Sobolev spaces, the existence and the numerical simulation of a capacity solution to a coupled nonlinear elliptic system. We consider the case of a non-uniformly elliptic problem with a quadratic growth in the gradient. The system may be regarded as a generalization of the so-called thermistor problem.
• Classification : 35J47, 35J70, 47H05, 46E35, 65N12
• Format : Online Talk on Zoom
• Author(s) :
  • Hajar Talbi (Moulay Ismail University)
  • Mohamed Rhoudaf (Moulay Ismail University)
  • Francisco Ortegón Gallego (Universidad de Cádiz)

[01754] Spectral-Cutoff for Imaging of Multiple Scattering in Isotropic Point-Like Discrete Random Media

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
• Type : Contributed Talk
• Abstract : To image objects in the discrete random medium composed of isotropic point-like scatterers, the resonances with multiple scattering in the medium can interfere with imaging and result in poor quality of images. To solve this problem, we present a spectral-cutoff method, which is derived based on the random matrix theory, to filter out the undesired responses in the resonance regime to recover the damaged images. Finally, we demonstrate this method for boosting imaging with numerical simulations.
• Classification : 35J05, 35P15, 47B06, 78A46, 94A12
• Author(s) :
  • Ray-Hon Sun (Stanford University)
  • Ray-Hon Sun (Stanford University)

MS [00923] PDEs and variational computational methods in image processing, analysis and classification

room : G602

• [03551] Mathematical models and computational algorithms for 3D and 4D image processing in developmental biology and medicine
  • Format : Talk at Waseda University
  • Author(s) :
    • Karol Mikula (Slovak University of Technology in Bratislava)
  • Abstract : We present mathematical models and numerical algorithms based on nonlinear advection-diffusion equations used for image filtering, segmentation and tracking in 3D+time microscopy images leading to automated reconstruction of the cell lineage tree during the first hours of embryogenesis. To achieve that goal, we discretize the nonlinear partial differential equations by the finite volume method, natural to image processing applications, and develop efficient and stable numerical schemes suitable for massively parallel computer architecture.
• [04223] Fractional graph Laplacian for image reconstruction
  • Format : Talk at Waseda University
  • Author(s) :
    • Marco Donatelli (University of Insubria)
    • Alessandro Buccini (University of Cagliari)
  • Abstract : We consider $\ell^2-\ell^q$ regularization with $0
• [03561] Mathematical models for segmentation of Natura 2000 habitats in NaturaSat software
  • Format : Talk at Waseda University
  • Author(s) :
    • Michal Kollár (Algoritmy:SK s.r.o. and Slovak University of Technology in Bratislava)
    • Martin Ambroz (Slovak University of Technology in Bratislava)
    • Aneta Alexandra Ozvat (Slovak University of Technology)
    • Karol Mikula (Slovak University of Technology in Bratislava)
    • Lucia Čahojová (Slovak Academy of Sciences)
    • Mária Šibíková (Slovak Academy of Sciences)
  • Abstract : The contribution presents an overview of numerical methods and mathematical models designed for the NaturaSat software. The application allows botanists, environmentalists and nature conservationists across Europe to explore protected areas of Natura 2000 habitats using the Sentinel-2 optical data. The presented methods are designed for accurate area identification - semi-automatic and automatic segmentation of European protected habitats and monitoring of their spatio-temporal distribution and quality.
• [03205] NatNet - forward-backward diffusion classification tool
  • Format : Talk at Waseda University
  • Author(s) :
    • Aneta Alexandra Ozvat (Slovak University of Technology)
    • Karol Mikula (Slovak University of Technology in Bratislava)
    • Michal Kollar (Slovak University of Technology)
    • Martin Ambroz (Slovak University of Technology)
    • Maria Sibikova (Slovak Academy of Sciences)
    • Jozef Sibik (Slovak Academy of Sciences)
  • Abstract : The presentation introduces a novel method for PDE-based data classification using satellite optical data. The Natural Numerical Network (NatNet) is based on the numerical solution of the nonlinear forward-backward diffusion equation on a semi-complete directed graph. Partial differential equations on the directed graph are solved by a finite volume approach considering the balance of diffusion fluxes in the vertices of the graph. The presented natural numerical network is applied to Earth biodiversity modelling.

MS [00854] Control and stabilization of PDEs: recent advances and applications

room : G605

• [02524] Quantitative rapid stabilization of some PDE models
  • Format : Talk at Waseda University
  • Author(s) :
    • Shengquan Xiang (Peking University)
  • Abstract : Quantitative stabilization is an active research topic in PDEs’ control theory, namely to construct explicit feedback laws as a control to make the closed-loop system stable together with quantitative estimates. In this presentation, we will talk about some recent progress in this topic including the Frequency Lyapunov method for the stabilization of Navier-Stokes equations and the Fredholm backstepping method for the stabilization of water waves.
• [02863] Generalized Fredholm-backstepping transformation
  • Format : Talk at Waseda University
  • Author(s) :
    • Ludovick Gagnon (Inria Nancy)
    • Christophe Zhang (Inria Nancy)
    • Amaury Hayat (Ecole des Ponts Paristech)
    • Shengquan Xiang (Peking University)
    • Swann Marx (CNRS)
  • Abstract : The backstepping method for PDEs, introduced over 20 years ago, is a powerful method to prove the rapid stabilisation of linear PDEs. The Fredholm alternative, introduced by Coron and Lü, quickly proved to provide a systematic approach to the backstepping method based on the spectral behaviour of the PDE as well as controllability assumptions. We present in this talk recent advances on sufficient conditions for the Fredholm-backstepping method in an abstract setting.
• [02944] Indirect controllability of linear constant coefficients parabolic-transport systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre Lissy (Université Paris-Dauphine)
  • Abstract : I will present controllability properties of mixed systems of linear parabolic-transport equations, with possibly nondiagonalizable diffusion matrix, on the 1D torus, coupled by constant coupling terms. The distributed control acts through a constant matrix, with possibly less controls than equations. In small time or for not regular enough initial data, these systems are never controllable, whereas in large time, null-controllability holds, for regular initial data, iff a spectral Kalman rank condition is verified.
• [03571] Optimal Control of Moving Sets
  • Format : Talk at Waseda University
  • Author(s) :
    • Maria Teresa Chiri (Queen's University)
  • Abstract : We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. We first analyze the optimal control of 1-dimensional traveling wave profiles. Using Stokes’ formula, explicit solutions are obtained, which in some cases require measure-valued optimal controls. Then we introduce a family of optimization problems for a moving set and show how these can be derived from the original parabolic problems, by taking a sharp interface limit. Assuming that the initial contaminated set is convex, we prove that an eradication strategy is optimal if an only if at each given time the control is active along the portion of the boundary where the curvature is maximal. We then consider the eradication problem with geographical constraints, and derive necessary and sufficient conditions for the existence of a solution.

MS [00529] Numerical approximation of geophysical flows

room : G606

• [01400] Vertical discretizations of Euler systems and application to bedload problems
  • Format : Talk at Waseda University
  • Author(s) :
    • José Garres-Díaz (Universidad de Córdoba)
    • Tomas Morales de Luna (Universidad de Malaga)
    • Cipriano Escalante Sanchez (Universidad de Málaga)
    • Manuel Castro Díaz (Universidad de Málaga)
  • Abstract : Shallow water type systems are very popular in numerical simulation of geophysical flows, mainly due to their low computational cost. However, these systems share an important drawback: the vertical information of the flow is lost. In this talk, we present a general framework for vertical discretizations of free-surface Euler system, that generalizes the moment and multilayer techniques. It is called multilayer-moment approach. Several tests are presented, pointing out advantages/disadvantages of each approach, and their efficiency.
• [01507] Numerical methods for viscoplastic flows : balancing precision and acceleration
  • Format : Talk at Waseda University
  • Author(s) :
    • Clément Berger (UMPA CNRS UMR 5669, ENS de Lyon)
  • Abstract : We consider here equations for yield stress flows formulated as variational inequalities. The reason is that it allows the best numerical computation of the interfaces between fluid zones and rigid zones. In this talk, we compare multiple optimization methods, from proximal algorithms to second-order cone programming. The compromise between precision and speed differs from one method to another. We will also comment on each associated convergence criteria.
• [01504] Digital Twins (DT) on geophysical extreme hazards. Using Tsunami-HySEA numerical model as DT for tsunami hazards.
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose Manuel Gonzalez-Vida (Dpt. Applied Mathematics. University of Malaga)
    • Jorge Macías (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
    • Manuel J. Castro (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
    • Alex González (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
  • Abstract : A Digital Twin (DT) for GEOphysical extremes (DT-GEO) is an European project that aims to analyse and forecast the impact of tsunamis, earthquakes, volcanoes, and anthropogenic seismicity. This work address tsunami hazard phenomena to conduct precise data-informed early warning systems, forecasts, and tsunami-hazard assessments across multiple time scales.
• [01513] Novel schemes for overdetermined thermodynamically compatible hyperbolic systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Saray Busto (Universidade de Vigo)
    • Michael Dumbser (University of Trento)
  • Abstract : We introduce a novel efficient general class of thermodynamically compatible, HTC, semi-discrete finite volume and discontinuous Galerkin schemes for overdetermined HTC systems. The approach is based on the discretization of the entropy being the total energy conservation a direct consequence of the HTC discretization. The obtained schemes are provably marginally stable in the energy norm, satisfy a discrete entropy inequality by construction and are assessed using classical benchmarks for turbulent shallow water and compressible flows.

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

room : G701

• [00564] On a uniqueness property of harmonic functions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dmitry Khavinson (University of South Florida)
  • Abstract : This is not a new result, yet the paper was dedicated to Walter Hayman and the main question , raised there is still unanswered. The paper was the joint work with late Harold S. Shapiro. We shall discuss the problem of uniqueness for functions u harmonic in a domain G in R^n and vanishing on some parts of the intersection V {not necessarily connected} of G with a line m. The question originated more than two decades ago with N. Nadirashvili {private communication}. For example, let G be a spherical shell, i.e., the region between two concentric spheres, and m is a line through the origin. Does u vanish on both segments along which m intersects G if it does so on one of them? To illustrate the cunning depth of the question note that if you let G to be the annulus with a sector cut out, the function u= arg z in the plane does vanish on the positive part of the real axis, but not on the whole intersection. What happens if G is a spherical shell but m does NOT pass through the center? What if we replace harmonic functions by polyharmonic functions, or, more generally, solutions of analytic elliptic equations, or even worse, by linear combinations of Riesz potentials that satisfy no PDE altogether? The answers are by no means obvious and, in many cases, may be judged as surprising.
• [00367] Factorization of Neumann-Poincare operator
  • Format : Talk at Waseda University
  • Author(s) :
    • Mihai Putinar (University of California)
  • Abstract : It is well known that the Neumann-Poincare operator (double layer potential) is symmetrizable. We will discuss a factorization of this singular integral operator which explains this essential spectral feature.
• [00452] The quasi-static plasmonic problem for polyhedra
  • Format : Talk at Waseda University
  • Author(s) :
    • Karl-Mikael Perfekt (NTNU)
  • Abstract : I will present a characterization of the essential spectrum of the plasmonic problem for polyhedra in $\mathbb{R}^3$. The description is particularly simple for convex polyhedra and relative permittivities $\varepsilon < -1$. The results are obtained through detailed analysis of the double layer potential for polyhedral cones and polyhedra. Based on joint work with Marta de León-Contreras.

MS [00048] Interfaces between kinetic equations and many-agent social systems. Part I

room : G702

• [03361] Multi Agent System for Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Herty (RWTH Aachen University)
  • Abstract : We are interested in the construction of numerical methods for constrained high-dimensional constrained nonlinear optimization problems by gradient free techniques. Gradients are replaced by particle approximations and recently different methods have been proposed, e.g. consensus-based, swarm-based or ensemble Kalman based methods. We discuss recent extensions to the constrained and the parametric case as well as their corresponding mean field descriptions in the many particle  limit. Those allow to show convergence as well as the analysis of properties of the new algorithm. Several numerical examples, also in high dimensions, illustrate the theoretical findings as well as the performance of those methods.
• [03822] Parameter estimation for macroscopic pedestrian dynamics models using microscopic data
  • Format : Talk at Waseda University
  • Author(s) :
    • Susana Gomes (University of Warwick)
  • Abstract : I will present a framework for estimating relevant parameters for pedestrian dynamics by fitting a macroscopic model for crowd dynamics using data from pedestrian trajectories. The model couples a density dependent stochastic differential equation, to a nonlinear partial differential equation for the density via the fundamental diagram. I will discuss identifiability of the parameters, introduce optimisation and Bayesian methods to perform the identification, and analyse the performance of the proposed methodology in various realistic situations.
• [03518] Navigation system based routing strategies in traffic flows on networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Adriano Festa (Politecnico di Torino)
  • Abstract : Navigation choices play an important role in modeling and forecasting traffic flows on road networks. We introduce a macroscopic differential model coupling a conservation law with a Hamilton-Jacobi equation to respectively model the nonlinear transportation process and the strategic choices of users. Furthermore, the model is adapted to the multi-population case, where every population differs in the level of traffic information about the system.
• [02357] Uncertainty quantification in vehicular traffic models
  • Format : Talk at Waseda University
  • Author(s) :
    • Elisa Iacomini (University of Ferrara, Department of Mathematics and Computer Science)
  • Abstract : Traffic models have been widely studied, however limitations for obtaining reliable forecasts are still present. Recently it has been pointed out how traffic is exposed to the presence of uncertainties. In this talk, starting from the hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models. Connections between the scales will be presented in the stochastic scenario and numerical simulations will be performed.

MS [02562] Recent development in data-driven modeling, data assimilation, and applications: meteorology, oceanography ionosphere, hydrology, environment

room : G703

• [04758] Data driven modelling and EnKF for spatial-temporal forecasting: Ozone and PM forecasting in China
  • Format : Talk at Waseda University
  • Author(s) :
    • Fangxin Fang (Imperial College London)
    • Meiling Cheng (Imperial College London)
    • Shengjuan Cai (Imperial College London)
    • Christopher Pain (Imperial College London)
    • Yanghua Wang (Imperial College London)
    • Michael I Navon (Florida State University)
    • Jiang Zhu (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Jie Zhu (Institute of Urban Environment)
    • Jinxi Li (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Xiaofei Wu (Chengdu University of Information Technology)
  • Abstract : Spatiotemporal forecasting involves generating temporal forecasts for system state variables across spatial regions. Data-driven methods, such as Convolutional Long Short-Term Memory (ConvLSTM) and deep convolutional generative adversarial network (DCGAN), are effective in capturing both spatial and temporal correlations. To further improve the predictive accuracy, the data assimilation EnKF is introduced to data driven modelling. Here, the performance of the data driven models has been demonstrated in hourly and daily spatiotemporal pollutant forecasting in China. The results have been compared to monitoring measurements and physical modelling results.
• [05103] Prediction of Swirling Fluid Flow Pattern in a River
  • Format : Talk at Waseda University
  • Author(s) :
    • Haradhan Maity (Rishi Bankim Chandra Evening College)
  • Abstract : Swirling of water in a river occurs when rocks, holes, obstacles, or sudden changes in the river channel obstruct the flow of the water. The swirl is characterized by turbulent parameters (velocities and Reynolds stresses) and corresponding factors associated with turbulence. The main objective of this study is to obtain the governing equations for swirling flow and to predict the flow pattern. The proposed theoretical models show very good agreement with experimental data.
• [05293] A fast, high resolution pluvial flood model for risk assessment and real-time flood prediction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Steven Cocke (Florida State University)
    • Dong-Wook Shin (Florida State University)
  • Abstract : A high resolution, computationally efficient pluvial flood model has been developed to provide flash flood inundation estimates due to heavy precipitation events. The need for a computationally fast model is critical for estimating flood risk, where a large number of flood scenarios are needed to obtain a reliable probability distribution of flood depths and extents, as well as for real-time prediction where sufficient advance warning must be given to the public.
• [05285] Machine learning for data assimilation and predictability to the atmospheric models
  • Format : Talk at Waseda University
  • Author(s) :
    • Haroldo Fraga de Campos Velho (INPE: National Institute for Space Research)
    • Rosangela Cintra (INPE: National Institute for Space Research)
    • Steven Cocke (FSU: Florida State University)
    • Vinicius Albuquerque Almeida (UFRJ: Federal University of Rio de Janeiro)
    • Juliana Aparecida Anochi (INPE: National Institute for Space Research)
    • Vinicius Monego (INPE: National Institute for Space Research)
  • Abstract : Data assimilation is one of the most important challenges for the computational effort of the operational centers for weather and climate predictions. In this talk, the use of machine learning approaches will be shown for numerical weather models. Techniques for data assimilation for global and regional models are addressed by artificial neural networks. The analysis computed by self-configuring a supervised neural network for the COAPS-FSU global model is designed to emulate the Local Ensemble Transform Kalman filter. A deep learning neural network is applied to the WRF-NCAR regional model as a new method for data assimilation, where the 3D-Var scheme is employed as a reference to the machine learning approach. Our numerical experiments show a significant reduction in the CPU-time to calculate the analysis maintaining the precision of the forecasting for both models. Finally, another important issue is to evaluate how good is the prediction, in other words, how we can calculate the forecasting confidence interval. The standard procedure to compute the confidence interval is to apply the ensemble prediction. A novelty approach to estimate the prediction uncertainty quantification is addressed by using machine learning algorithms: neural networks, and decision tree formulations.

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

room : G704

• [03383] Smooth Navier-Stokes Solutions
  • Format : Talk at Waseda University
  • Author(s) :
    • James Glimm (Stony Brook University)
  • Abstract : Smooth Navier-Stokes solutions require a non-physical choice of entropy minimization, achieved constructively as a mean value relative to turbulent fluctuations. Other solutions are not smooth. Drivers of the proof are a turbulence analogue of renormalized perturbation theory, adapted from Quantum Field theory, and shown to be Borel resummable convergent on a dense set of turbulent states, together with the Foias theory of Young measures.
• [03969] Exact solutions to nonlinear difference equations associated with Henon maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Chihiro Matsuoka (Osaka Metropolitan University)
    • Koichi Hiraide (Osaka Metropolitan University)
  • Abstract : We present exact solutions in non-integrable systems, taking the Henon map as an example. The obtained solutions describe the stable and unstable manifolds at saddle fixed points and make it possible to calculate such invariant manifolds with complex structures. Using the obtained functions, we visualize the hyperbolic system encircling KAM tori and the Henon attractor, in which chaotic orbits are captured accurately.
• [03735] Can environmental and intrinsic mechanisms of quantum mixing be distinguished experimentally?
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Y Klimenko (The university of Queesnland)
    • Alexander Y. Klimenko (The university of Queesnland)
  • Abstract : This presentation considers the possibility of quantum experiments that can, at least in principle, allow us to distinguish intrinsic and environmental mechanisms of decoherence. This experiment can be interpreted as a quantum-mechanical version of non-equilibrium mixing between two volumes separated by a thin interface. Decoherence is understood here as a general process that does not involve any significant exchanges of energy and is governed by a particular class of Kraus operators. This presentation considers different regimes of quantum tunnelling in the presence of different types of decoherence and shows that, at least under some conditions, intrinsic and environmental types of decoherence affect the tunnelling rates differently and, therefore, can be distinguished experimentally.

MS [02533] Reliable and Efficient Numerical Computation of Nonlocal Models

room : G709

• [03174] The Effect of Domain Truncation for Nonlocal Models and Asymptotically Compatible Schemes in Numerical Computation
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaobo Yin (Central China Normal University)
    • Qiang Du (Columbia University)
    • Hehu Xie (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Jiwei Zhang (Wuhan University)
  • Abstract : Many nonlocal models have adopted a finite and radially symmetric nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such interaction neighborhoods. A crucial question is, to what extent such approximations affect the nonlocal operators and the corresponding nonlocal solutions. While recent works have analyzed this issue for nonlocal operators in the case of a fixed horizon parameter, the question remains open in the case of a small or vanishing horizon parameter, which happens often in many practical applications and has significant impact on the reliability and robustness of nonlocal modeling and simulations. In this report, we are interested in addressing this issue and establishing the convergence of new nonlocal solutions by polygonal approximations to the local limit of the original nonlocal solutions. Our finding reveals that the new nonlocal solution does not converge to the correct local limit when the number of sides of polygons is uniformly bounded. On the other hand, if the number of sides tends to infinity, the desired convergence can be shown. We also apply this finding to discuss of the aysmptotically compatible property of the numerical schemes.
• [03775] Global well-posedness of one new class of initial-boundary value problem on incompressible Navier-Stokes equations and the related models
  • Format : Talk at Waseda University
  • Author(s) :
    • Shu Wang (Beijing University of Technology)
  • Abstract : The global well-posedness of the initial-boundary value problem on incompressible Navier-Stokes equations and the related models in the domain with the boundary is studied. The global existence of a class of weak solution to the initial boundary value problem to two/three-dimensional incompressible Navier-Stokes equation with the pressure-velocity relation at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case is also established. Some extends to the corresponding incompressible fluid models such as Boussinesq equation/MHD equations and FSI models etc. are given.
• [04201] High performance implementation of 3D FEM for nonlocal Poisson problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • JIWEI ZHANG (Wuhan University )
  • Abstract : Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of queries and invoke operations on the meshes. Besides, the interactions are usually limited to Euclidean balls, so direct numerical integrals often introduce numerical errors. The issues of interactions between the ball and finite elements have to be carefully dealt with, such as using ball approximation strategies. In this talk, an efficient representation and construction methods for approximate balls are presented based on combinatorial map, and an efficient parallel algorithm is also designed for assembly of nonlocal linear systems. Specifically, a new ball approximation method based on Monte Carlo integrals, i.e., the fullcaps method, is also proposed to compute numerical integrals over the intersection region of an element with the ball.
• [03599] Asymptotical compatibility of a class of numerical schemes for a nonlocal traffic flow model
  • Format : Talk at Waseda University
  • Author(s) :
    • Kuang Huang (Columbia University)
    • Qiang Du (Columbia University)
  • Abstract : This talk presents a study of numerical schemes for a nonlocal conservation law modeling traffic flows with nonlocal inter-vehicle interactions. We demonstrate the asymptotical compatibility of a class of finite volume schemes with suitable discretizations of the nonlocal integral. The numerical solutions produced by the schemes converge to the weak solution of the nonlocal model with a fixed nonlocal horizon and to the weak entropy solution of the respective local model as the mesh size and nonlocal horizon parameter go to zero simultaneously. Our findings provide insight into the development of robust numerical schemes for nonlocal conservation laws.

contributed talk: CT049

room : G710

[02638] A note on contribution of finite difference methods for fractional diffusion equations

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G710
• Type : Contributed Talk
• Abstract : Since the last two decades, extensive research has been carried out on the numerical solution of fractional diffusion equations, particularly in finite difference methods. The finite difference schemes play a crucial role in obtaining the solution of fractional diffusion equations. The most popular are the explicit finite difference method, implicit finite difference method, and Crank-Nicolson finite difference method. This article focuses on developing finite difference schemes for fractional diffusion equations. Also, the stability and convergence of finite difference methods will be discussed by using the matrix norm method. Moreover, it will compare methods in the sense of accuracy and rate of convergence of these schemes. The last section will be devoted to the test problems.
• Classification : 35R11, 65M06, 65M12
• Format : Talk at Waseda University
• Author(s) :
  • GUNVANT ACHUTRAO BIRAJDAR (Department of Mathematics, Institute of Chemical Technology, Mumbai)

[00875] Deep learning based reduced ensemble Kalman inversion for microscopic parameter estimation

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G710
• Type : Contributed Talk
• Abstract : In the scope of nonlinear multiscale problems, estimating the macroscopic distribution of the microscopic geometrical parameters given macroscopic measurements is of interest. In general, inverse estimation is challenging due to the need of derivatives of the complex forward model and the high cost of the forward solver. We introduce derivative-free ensemble Kalman inversion and deep-learning based model reduction to tackle the aforementioned challenges, and assess the performance of the proposed method on a hyper-elastic problem.
• Classification : 35R30, 65N21, 74G75, 65N75, 62F86
• Format : Talk at Waseda University
• Author(s) :
  • Yankun Hong (Eindhoven University of Technology)
  • Harshit Bansal (Eindhoven University of Technology)
  • Karen Veroy (Eindhoven University of Technology)

[01079] Higher order numerical scheme to approximation generalized Caputo fractional derivatives and its application

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G710
• Type : Contributed Talk
• Abstract : In this paper, a high-order numerical scheme is established to approximate the generalized Caputo fractional derivative using Lagrange interpolation formula. Order of convergence for this scheme is obtained as (4 − α), where α ∈ (0, 1) is the order of generalized Caputo fractional derivative. The local truncation error of the approximation is also obtained. Further, the developed scheme is used to solve the generalized fractional advection-diffusion equation. Stability and convergence are also discussed for the difference scheme. In the last, numerical examples are discussed to illustrate the theoretical results.
• Classification : 35R11, 26A33, 65R10
• Format : Online Talk on Zoom
• Author(s) :
  • Sarita kumari (Indian Institute of technology (Banaras Hindu University))
  • Dr. Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)

[01551] Observer-based Nonlinear Fault-tolerant Control Design for Fractional-order Parabolic PDE Systems

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @G710
• Type : Contributed Talk
• Abstract : The problem of robust stabilization for fractional-order parabolic PDE systems with nonlinear actuator faults is considered. The main aim of this work is to design an observer-based nonlinear fault-tolerant controller for obtaining the required results. Then, a set of conditions are derived with the aid of Lyapunov-based approach for the stabilization analysis. Further, the theoretical results are verified through the numerical example with graphical results.
• Classification : 35R11, 93Dxx, 93Cxx, 37Mxx, 37N35
• Format : Online Talk on Zoom
• Author(s) :
  • Sweetha Senthilrathnam (Bharathiar university)
  • Sakthivel Rathinasamy (Bharathiar University)

MS [00164] Recent Advances in Direct and Inverse Problems in Mathematical Materials Science

room : G801

• [00473] Bloch Waves in High Contrast Electromagnetic Crystals
  • Author(s) :
    • Silvia Jimenez Bolanos (Colgate University)
    • Robert Lipton (Louisiana State University)
    • Robert Viator (Swarthmore College)
    • Abiti Adili (University of Massachusetts Lowell)
  • Abstract : In this talk, we present the derivation of analytic representation formulas and power series describing the band structure inside non-magnetic periodic photonic crystals, made from high dielectric contrast inclusions. We identify a resonance spectrum for quasi-periodic source-free modes, which are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high-contrast media. A convergent power series for the Bloch wave spectrum is obtained from the representation formulas and explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum.
• [00483] An axisymmetric problem for a nano-sized material surface on a boundary of an elastic semi-space
  • Author(s) :
    • Anna Zemlyanova (Kansas State University)
  • Abstract : An axisymmetric problem for a nano-sized penny-shaped material surface attached to the boundary of an elastic isotropic semi-space is considered. The surface is modeled using the Steigmann-Ogden form of surface energy. The problem is solved by using the Boussinesq potentials and Hankel transforms. The problem can be reduced to a system of two singular integral equations. This is a joint work with Lauren M. White.
• [00569] Clusters of Bloch waves in three-dimensional periodic media
  • Author(s) :
    • Yuri Godin (University of North Carolina at Charlotte)
  • Abstract : We consider acoustic wave propagation through a periodic array of small inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion relation for general frequencies and show that there are exceptional frequencies for which the solution is a cluster of waves propagating in different directions with different frequencies so that the dispersion relation cannot be defined uniquely. The results are illustrated by an example of a medium with a simple cubic lattice of spherical inclusions where we derived the dispersion relation, determine the parameters of the effective medium, and provided examples of some clusters. This is joint work with B. Vainberg.
• [00588] Modeling sea ice as a multiscale composite material
  • Author(s) :
    • Kenneth Morgan Golden (University of Utah)
  • Abstract : Sea ice exhibits composite structure on length scales ranging over many orders of magnitude. Forward and inverse homogenization are central to modeling sea ice and its role in climate and ecosystems. We’ll tour recent advances, from the fractal geometry of millimeter-scale brine inclusions and meter-scale melt ponds, to the homogenized dynamics of the marginal ice zone on the scale of the Arctic Ocean. We’ll also explore spectral representations for effective parameters in several contexts.

MS [01178] On the Interplay between Kinetic Theory and Quantum Dynamics

room : G802

• [04305] Emergent phenomena in an interacting Bose gas
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael Hott (University of Minnesota)
    • Thomas Chen (The University of Texas at Austin)
  • Abstract : The study of kinetic equations describing collisions between a BEC and the surrounding normal fluid go back to Kirkpatrick and Dorfmann '83, '85 and Eckern '84. Ever since, this subject has attracted a lot of attention as it relates to condensation. In this context, mathematicians have studied the quartic quantum Boltzmann equation in the presence of a BEC. In this talk, we will discuss some of the progress made on the PDE level of the quantum Boltzmann equation. Then, we will focus on the validity of the kinetic equations. We will describe the crucial scale separations needed to extract a Boltzmann equation from the quantum dynamics. Moreover, we will see how the interference of sound waves can produce some surprising effects if a Bose gas is trapped in a volume of unit size. This is based on joint work with Thomas Chen.
• [05382] Fluid limits from Quantum Boltzmann equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Ning Jiang (Wuhan University)
  • Abstract : In his 2015 Ecole Polytechnique thesis, T.Zakrevskiy formally derived some fluid dynamics from quantum Boltzmann equation (Fermi-Dirac statistics). We rigorously justify two types of limits: incompressible Navier-Stokes-Fourier and compressible Euler (then acoustic) systems, by establishing some new nonlinear estimates on triple terms, and uniform estimates with respect to Kundsen number. A particular novelty is that the compressible Euler system derived from the quantum Boltzmann equation has a pressure law which is different and more general with that from the classical Boltzmann equation.
• [04436] An explicit coercivity estimate of the linearized quantum Boltzmann operator
  • Format : Talk at Waseda University
  • Author(s) :
    • YULONG ZHOU (Sun Yat-Sen University)
  • Abstract : The Boltzmann-Bose-Einstein equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular singularity. We present a coercivity estimate of the linearized Boltzmann-Bose-Einstein operator for such kernel. The estimate may not be sharp but explicitly reveals the dependence on the fugacity parameter. Joint work with Prof. Tong Yang.
• [04331] Frozen Gaussian Approximation for open quantum system
  • Format : Talk at Waseda University
  • Author(s) :
    • Geshuo Wang (National University of Singapore)
    • Zhenning Cai (National University of Singapore)
    • Siyao Yang (National University of Singapore)
  • Abstract : We study the system-bath dynamics for open quantum systems applying frozen Gaussian approximation, which proposes an approximated ansatz for the wave function, converting the direct calculation of the Schrödinger equation into some ODEs of the parameters in the ansatz. We then derive the Dyson series under such approximation. To further improve the computational efficiency, we develop a fast algorithm known as the inchworm algorithm for the current framework.

MS [00178] Theoretical and Computational Progress on PDE-based Inverse Problems with Applications

room : G808

• [00556] Deterministic-Statistical Approach for Inverse Problems with Partial Data
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jiguang Sun (Michigan Technological University)
  • Abstract : We propose a deterministic-statistical approach for inverse problems with partial data. Certain deterministic method is first used to obtain useful (qualitative) information for the unknowns. Then the inverse problem is recast as a statistical inference problem and the Bayesian inversion is employed to obtain more (quantitative) information of the unknowns. Several examples are presented for demonstration. Furthermore, we introduce new statistical estimators to characterize the non-unique solutions of several inverse problems.
• [00553] Quantitative PAT with simplified PN approximation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yimin Zhong (Auburn University)
    • Hongkai Zhao (Duke University)
  • Abstract : The photoacoustic tomography (PAT) is a hybrid modality that combines the optics and acoustics to obtain high resolution and high contrast imaging of heterogeneous media. In this work, our objective is to study the inverse problem in the quantitative step of PAT which aims to reconstruct the optical coefficients of the governing radiative transport equation from the ultrasound measurements. In our analysis, we take the simplified P N approximation of the radiative transport equation as the physical model and then show the uniqueness and stability for this modified inverse problem. Numerical simulations based on synthetic data are presented to validate our analysis.
• [02856] Adaptive Mesh-free Approach for Gravity Inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • Yan Liu (Chinese Academy of Geological Sciences)
  • Abstract : We proposes a method of gravity inversion based on an adaptive mesh-free approach by using a modified radial basis function. As the subsurface space is generally discretized into regular grid cells, and this unstructured nodal discretization bring the expensive mesh generation and manipulation, we use a mesh-free discretization strategy to establish a mapping of subsurface grid cells to a cloud of discrete points. The nodes are adaptively refined during the inversion process to better recover abnormal bodies. In addition, the hybrid basis function and the modified radial basis function are used to improve the accuracy and stability of the solution.
• [00358] A neural network method for inverse source problem with limited-aperture data
  • Format : Talk at Waseda University
  • Author(s) :
    • Weishi Yin (Changchun University of Science and Technology)
    • Ping Zhang (Changchun University of Science and Technology)
    • Pinchao Meng (Changchun University of Science and Technology)
    • Hongyu Liu ( City University of Hong Kong)
  • Abstract : This talk is concerned with an inverse moving source problem, that is, one identifies and predicts the trajectory of a moving point source by measuring the corresponding wave field. First, for the practical consideration,the dynamical wave field data are collected in a limited aperture and full aperture respectively. Second, we design a parameter inversion model by neural network to reconstruct the trajectory of the moving point source. This model solves the problem of information loss caused by data acquisition in limited aperture and has certain robustness with respect to noise. Third, we consider the trajectory prediction of the moving point source for the inverse source problem associated with the novel input/instruction approach, and construct a trajectory prediction model by neural network to predict the trajectory of the moving point source. Numerical experiments show that the proposed device works effectively and efficiently in some practical scenarios.

MS [01935] Advances in Inverse Problems and Imaging

room : G809

• [04564] An Inverse Problem for Nonlinear Time-dependent Schrodinger Equations with Partial Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Ting Zhou (Zhejiang University)
    • Ru-Yu Lai (University of Minnesota)
    • Xuezhu Lu (Northeastern University)
  • Abstract : In this talk, I will present some recent results on solving inverse boundary value problems for nonlinear PDEs, especially for a time-dependent Schrodinger equation with time-dependent potentials with partial boundary Dirichlet-to-Neumann map. After a higher order linearization step, the problem will be reduced to implementing special geometrical optics (GO) solutions to prove the uniqueness and stability of the reconstruction. This is a joint work with my PhD student Xuezhu Lu and Prof. Ru-Yu Lai.
• [04099] Inverse scattering problems with incomplete data
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaodong Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Inverse scattering problems aim to determine unknown scatterers with wave fields measured around the scatterers. However, from the practical point of views, we have only limited information, e.g., limited aperture data phaseless data and sparse data. In this talk, we introduce some data retrieval techniques and the applications in the inverse scattering problems. The theoretical and numerical methods for inverse scattering problems with multi-frequency spase measurements will also be mentioned.
• [03745] Imaging of penetrable locally rough surfaces from phaseless total-field data
  • Format : Talk at Waseda University
  • Author(s) :
    • Haiwen Zhang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Long Li (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Jiansheng Yang (Peking University)
    • Bo Zhang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : This talk is concerned with inverse scattering by a two-layered medium with a locally rough interface in 2D. We propose a direct imaging method to reconstruct the penetrable locally rough surface from phaseless total-field data. The theoretical analysis is mainly based on the results in our recent work (L. Li, J. Yang, B. Zhang and H. Zhang, arXiv:2208.00456) on the uniform far-field asymptotics of the scattered field for acoustic scattering in a two-layered medium.
• [04075] A new approach to an inverse source problem for the wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Haibing Wang (Southeast University)
  • Abstract : Consider an inverse problem of reconstructing a source term from boundary measurements for the wave equation. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small particles, enjoying a high contrast, into the medium. For this purpose, we first derive the asymptotic expansion of the wave field, based on the time-domain Lippmann-Schwinger equation. The dominant term in the asymptotic expansion is expressed as an infinite series in terms of the eigenvalues of the Newtonian operator (for the pure Laplacian). Such expansions are useful under a certain scale between the size of the particles and their contrast. Second, we observe that the relevant eigenvalues appearing in the expansion have non-zero averaged eigenfunctions. By introducing a Riesz basis, we reconstruct the wave field, generated before injecting the particles, on the center of the particles. Finally, from these last fields, we reconstruct the source term. A significant advantage of our approach is that we only need the measurements for a single point away from the support of the source. This is a joint work with Prof. Mourad Sini from RICAM.

MS [00436] Coupled dynamical systems: from data analysis to biomathematics

room : F308

• [03097] Fractal dimension of multidimensional biological recordings
  • Format : Talk at Waseda University
  • Author(s) :
    • Valeri A. Makarov (Universidad Complutense de Madrid)
  • Abstract : A linear mixture model can describe multisite LFPs, EEG, and MEG recordings. The fractal dimension (FD) of such multidimensional data can measure the complexity of different brain states. However, the local stationarity, the data's high dimension, and noise limit the assessment of FD from raw data. We discuss theoretical principles and methods derived from the model enabling accurate estimation of the FD, and illustrate them on synthetic and biological data.
• [03895] Lyapunov-like characterization of ghost and weak attractors in complex dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ivan Y Tyukin (King's College London)
    • Alexander N Gorban (University of Leicester)
    • Roqaiah Alsolami (University of Leicester)
    • Tatiana Tyukina (University of Leicester)
  • Abstract : In this talk we discuss the problem of identifying and formally characterizing ghost and weak attractors in complex dynamical systems governed by systems of coupled nonlinear ordinary differential equations. We present a set of conditions enabling to determine if an equilibrium is a weak attractor in terms of the corresponding Jacobian and Hessian matrices. We show how these results can be used to constructively define and determine the existence of ghost attractors in such systems.
• [03442] Flip-flip bifurcations in mathematical cardiac systems with and without symmetry
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Kitajima (Kagawa University)
  • Abstract : We study the intersection of double-flip (period-doubling) bifurcations in a parameter plane. We derive normal forms for discrete-time and continuous-time systems. Using these normal forms, we clarify the bifurcation structure around the flip-flip bifurcation point. We apply these analytical results to a system of coupled ventricular cell models. We make the simplest model for generating discordant alternans and clarify that two parameters play key roles in generating discordant alternans.
• [03235] Generation of early afterdepolarizations in cardiomyocytes: Fast-slow and bifurcation analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Roberto Barrio (University of Zaragoza, Spain)
    • Jorge Jover-Galtier (University of Zaragoza)
    • M. Angeles Martinez (University of Zaragoza)
    • Lucia Perez (University of Oviedo)
    • Sergio Serrano (University of Zaragoza)
    • Esther Pueyo (University of Zaragoza)
  • Abstract : We analyze the dynamical mechanisms underlying the formation of arrhythmogenic early afterdepolarizations (EADs) in the cardiomyocyte models of Sato et al. (a biophysically detailed model of dimension 27) and Luo-Rudy (dimension 3). Based on a comparison of the two models, with detailed bifurcation analysis using continuation techniques and using a fast-slow decomposition in the simple model and numerical explorations in the complex model, we propose a conjectured scheme of the formation of EADs that fits well with electrophysiological experimental data on EAD generation.

MS [02023] Theory and applications of random/no-autonomous dynamical systems part IV

room : F309

• [05589] Physical applications of infinite ergodic theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Eli Barkai (Bar Ilan University)
  • Abstract : We show how non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a single Brownian particle in an asymptotically flat potential. Similar tools are applicable for a gas of sub-recoiled laser cooled atoms and weakly chaotic non-linear oscillators.
• [03122] Transition to Anomalous Dynamics in A Simple Random Map
  • Format : Talk at Waseda University
  • Author(s) :
    • Jin Yan (Max Planck Institute for the Physics of Complex Systems)
    • Moitrish Majumdar (International Centre for Theoretical Sciences - TIFR)
    • Stefano Ruffo (SISSA Trieste)
    • Yuzuru Sato (Hokkaido University)
    • Christian Beck (Queen Mary University of London)
    • Rainer Klages (Queen Mary University of London)
  • Abstract : A random dynamical system consists of a setting where different types of dynamics are sampled randomly in time. Here we consider a simple yet universal example, where an expanding or a contracting map is randomly selected at each discrete-time with probability $p$ or $1-p$, respectively. By continuously varying $p$ between zero and one, we found anomalous behaviour characterised by an infinite non-normalisable invariant density, weak ergodicity breaking, and a power-law decay in correlations.
• [05573] Arcsine law for random dynamics with a core
  • Format : Talk at Waseda University
  • Author(s) :
    • Yushi Nakano (Tokai University)
    • Fumihiko Nakamura (Kitami Institute of Technology)
    • Hisayoshi Toyokawa (Kitami Institute of Technology)
    • Kouji Yano (Osaka University)
  • Abstract : The arcsine law is a characterization of intermittent dynamics in infinite ergodic theory. A well-known model of intermittent dynamics is an interval with two increasing surjective branches being uniformly expanding except for indifferent fixed points at the boundary. We show that the arcsine law holds for random dynamics with a core, which is a class of random iterations of two interval maps without indifferent periodic points but "indifferent in average" at the boundary.
• [05570] Infinite ergodic theory in physics
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuma Akimoto (Tokyo University of Science)
  • Abstract : Infinite ergodic theory provides a distributional behavior of time-averaged observables in dynamical systems. We show that the infinite ergodic theory plays an important role in physics. In particular, we show several distributional limit theorems for time-averaged observables in non-stationary stochastic processes that are models of anomalous diffusion and laser-cooled systems.

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

room : F310

• [01969] Frequency-time Green function acceleration for simulation, optimization and design
  • Format : Talk at Waseda University
  • Author(s) :
    • Oscar P Bruno (Caltech)
  • Abstract : We present a novel "Interpolated Factored Green Function" method (IFGF), including a massively parallel implementation, for the accelerated evaluation of the integral operators in scattering theory and other areas. The IFGF algorithm runs on a small memory footprint, and it is better suited than other methods for efficient distributed-memory parallelization. A variety of applications will be mentioned, including frequency- and time-domain scattering in interior and exterior domains, atmospheric propagation and metamaterial design.
• [03041] Analysis of scattering matrix algorithm
  • Format : Talk at Waseda University
  • Author(s) :
    • Andreas Rathsfeld (Weierstrass Institute for Applied Analysis and Stochastics, Berlin)
  • Abstract : The scattering matrix algorithm is a popular numerical method for the diffraction of optical waves by periodic surfaces. The computational domain is divided into horizontal slices and, by a clever recursion, an approximated operator, mapping incoming into outgoing waves, is obtained. Combining this with numerical schemes inside the slices, methods like RCWA and FMM have been designed. The key for the analysis is the scattering problem with special radiation conditions for inhomogeneous cover materials.
• [04576] On the coupling schemes of finite element and boundary integral equation methods solving the acoustic/elastic scattering problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Liwei Xu (University of Electronic Science and Technology of China)
  • Abstract : In this talk, we introduce two coupling schemes of finite element and boundary integral equation methods solving the acoustic/elastic scattering problems. The first one is the coupling of finite element and Fourier series based boundary integral solving the exterior time-harmonic elastic scattering problem. The second is the coupling of discontinuous Galerkin finite element and boundary integral equations solving the fluid-structure interaction problem. Well-posedness of the approximate problems, analysis on the accuracy and stability of numerical schemes, and numerical results will be presented.
• [03004] Fast multipole method in layered media: from Helmholtz to Maxwell's equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Bo Wang (LCSM(MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China.)
  • Abstract : In this talk, a fast multipole method (FMM) for the dyadic Green’s function of Maxwell’s equations in layered isotropic media is presented. As in the homogeneous media, layered dyadic Green’s function (LDGF) of Maxwell’s equation is shown closely related to the Green’s function of Helmholtz equation in layered media. Actually, there are only two essential components in the LDGF.By following the theory developed for the Green’s function of Helmholtz equation, we derive multipole expansions (MEs) and local expansions (LEs) as well as the multipole-to-local translation (M2L) operators for all the reaction field components of the LDGF. Then, the FMMs for the LDGF is implemented with the target particles and equivalent polarization sources associated with the reaction field components. Numerical results validate the fast convergence of the MEs and the O(N) complexity of the FMM for N particle problem in 3-D layered media.

MS [00063] Recent Advances on Nonlocal Interaction Models

room : F311

• [00152] Patterns in tri-block copolymers: droplets, double-bubbles and core-shells.
  • Format : Talk at Waseda University
  • Author(s) :
    • Stan Alama (McMaster Univ)
    • Lia Bronsard (McMaster University)
    • Xin Yang Lu (Lakehead Univ)
    • Chong Wang (Washington and Lee Univ)
  • Abstract : We study the Nakazawa-Ohta ternary inhibitory system, which describes domain morphologies in a triblock copolymer as a nonlocal isoperimetric problem for three interacting phase domains. The free energy consists of two parts: the local interface energy measures the total perimeter of the phase boundaries, while a longer-range Coulomb interaction energy reflects the connectivity of the polymer chains and promotes splitting into micro-domains. We consider global minimizers on the two-dimensional torus, in a limit in which two of the species have vanishingly small mass but the interaction strength is correspondingly large. In this limit there is splitting of the masses, and each vanishing component rescales to a minimizer of an isoperimetric problem for clusters in 2D. Depending on the relative strengths of the coefficients of the interaction terms we may see different structures for the global minimizers, ranging from a lattice of isolated simple droplets of each minority species to double-bubbles or core-shells. This represents work with S. Alama, X. Lu, and C. Wang.
• [00113] Ground states for aggregation-diffusion models on Cartan-Hadamard manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Hansol Park (Simon Fraser University)
  • Abstract : We investigate the existence of ground states of a free energy functional defined on Cartan-Hadamard manifolds. There are two competing effects in the free energy: repulsion modelled by linear diffusion and attraction modelled by a nonlocal interaction term. Nonexistence of energy minimizers can occur if either the diffusion is too strong (spreading) or attraction is dominant (blow-up). Variational approaches have been used to provide sufficient conditions of the attractive interaction to prevent the two scenarios from happening, and thus establishing the existence of global minimizers of the free energy.
• [00101] Well-posedness and asymptotic behaviour of an interaction model on Riemannian manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Razvan C Fetecau (Simon Fraser University)
  • Abstract : We consider a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions and study the long-time behaviour of solutions. For the latter, the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. The analytical results are illustrated with numerical experiments that exhibit various asymptotic patterns.
• [00131] Mean field games with aggregating interaction potentials of nonlocal type
  • Format : Talk at Waseda University
  • Author(s) :
    • Annalisa Cesaroni (University of Padova)
  • Abstract : We discuss existence/non existence of solutions to ergodic mean field game systems in the whole space with interactions of aggregative Riesz type, in dependance on the strength of the interaction term. Moreover, we present qualitative properties of the solutions and concentration phenomena, as the diffusion term vanishes. Finally we discuss some open problems related to stability of equilibria.

contributed talk: CT064

room : F312

[00648] Bounds for effective conductivity of multimaterial composites

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
• Type : Contributed Talk
• Abstract : The paper discusses the exact bounds for the effective properties of multimaterial composites. We refine Hashin-Shtrikman bounds in the region where the last ones are loose. We show that fields in optimal structures vary in restricted domains, modify the Translation method, and obtain new exact bounds and optimal structures. Different volume fractions of components correspond to topologically different types of optimal structures.
• Classification : 49K20
• Format : Talk at Waseda University
• Author(s) :
  • Andrej Cherkaev (University of Utah)

[01946] Optimal Control of Stationary Doubly Diffusive Flows on Lipschitz Domains

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
• Type : Contributed Talk
• Abstract : Doubly diffusive flows involve coupled incompressible flow and double diffusion transport, which models physical problems like bacteria bioconvection, exothermic flows in oceanography and more. We study a distributed optimal control problem governed by doubly diffusive flows under minimal regularity on 2D and 3D bounded Lipschitz domains and establish its well-posedness. First and second-order optimality conditions are derived. Furthermore, a discretization of the control problem based on $H(\mbox{div})$-conforming discontinuous Galerkin finite elements for the state and adjoint variables and piecewise constant finite elements for the control variable is discussed. Optimal apriori error estimates are proven in suitable norms. Numerical experiments are performed using a semi-smooth Newton strategy verifying the theoretical findings.
• Classification : 49K20, 65N30, 76S05, 76R50, 49K27
• Format : Talk at Waseda University
• Author(s) :
  • Jai Tushar (Indian Institute of Technology Roorkee)
  • Arbaz Khan (IIT Roorkee)
  • Manil T. Mohan ( IIT Roorkee)

[01247] Gradient-push algorithm for distributed optimization with event-triggered communications

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
• Type : Contributed Talk
• Abstract : Decentralized optimization problems consist of multiple agents connected by a network. The agents have each local cost function, and the goal is to minimize the sum of the functions cooperatively. In this work, we propose a gradient-push algorithm involving event-triggered communication on a directed network. The convergence of the algorithm is established under suitable decays and summability conditions on a stepsize and triggering threshold.
• Classification : 47Nxx, 65Kxx, Decentralized Optimization
• Format : Talk at Waseda University
• Author(s) :
  • jimyeong kim (Sungkyunkwan University)
  • Woocheol Choi (Sungkyunkwan Univeristiy)

[00997] A Normal Map-Based Perspective on Second Order Theory for Composite Problems: Second Order Conditions, Metric Regularity, and Nonsingularity

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
• Type : Contributed Talk
• Abstract : Strong metric subregularity and strong metric regularity of the natural residual and the normal map are of particular importance in the convergence analysis of first-order and second-order algorithms for composite-type optimization problems. In this talk, we characterize the strong metric subregularity of the natural residual and the normal map for a general class of nonsmooth nonconvex composite functions and establish the equivalence between these conditions, the strong metric subregularity of the subdifferential, and the quadratic growth condition. Furthermore, if the nonsmooth part of the objective function has a strictly decomposable structure, then strong metric regularity of the subdifferential is shown to be equivalent to strong metric regularity of natural residual and the normal map and to a counterpart of the so-called strong second-order sufficient conditions. Finally, we provide a link of these conditions to nonsingularity of the generalized Jacobians of the normal map and natural residual.
• Classification : 47Nxx, 47Nxx, 47Nxx, 47Nxx, 47Nxx, Variational Analysis
• Format : Online Talk on Zoom
• Author(s) :
  • Wenqing Ouyang (The Chinese University of HongKong(Shenzhen))
  • Andre Manfred Milzarek (The Chinese University of Hong Kong, Shenzhen)

MS [00640] Variational Analysis: Theory and Applications

room : F401

• [01802] Fixed point strategies for sparsity aware inverse problems and hierarchical convex optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Isao Yamada (Tokyo Institute of Technology)
    • Masao Yamagishi (Tokyo Institute of Technology)
  • Abstract : We present central ideas behind the recently developed fixed point strategies for a nonconvexly regularized sparse least squares model and a hierarchical convex optimization problem. Related advancements for nonconvex optimization and signal processing will also be introduced briefly.
• [02724] The splitting algorithms by Ryu, by Malitsky-Tam, and by Campoy applied to normal cones of linear subspaces converge strongly to the projection onto the intersection
  • Format : Talk at Waseda University
  • Author(s) :
    • Heinz H Bauschke (University of British Columbia Okanagan)
    • Shambhavi Singh (University of British Columbia Okanagan)
    • shawn xianfu wang (University of British Columbia Okanagan)
  • Abstract : Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that the resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford algorithm. However, when dealing with three or more operators, one must work in a product space with as many factors as there are operators. In groundbreaking recent work by Ryu and by Malitsky and Tam, it was shown that the number of factors can be reduced by one. A similar reduction was achieved recently by Campoy through a clever reformulation originally proposed by Kruger. All three splitting methods guarantee weak convergence to some solution of the underlying sum problem; strong convergence holds in the presence of uniform monotonicity. In this paper, we provide a case study when the operators involved are normal cone operators of subspaces and the solution set is thus the intersection of the subspaces. Even though these operators lack strict convexity, we show that striking conclusions are available in this case: strong (instead of weak) convergence and the solution obtained is (not arbitrary but) the projection onto the intersection. Numerical experiments to illustrate our results are also provided.
• [02977] Fixed Point Algorithms: Convergence, stability and data dependence results
  • Format : Talk at Waseda University
  • Author(s) :
    • Javid Ali (Aligarh Muslim University, Aligarh)
  • Abstract : {\bf Abstract.} In this talk, we discuss a newly introduced two step fixed point iterative algorithm. We prove a strong convergence result for weak contractions. We also prove stability and data dependency of a proposed iterative algorithm. Furthermore, we utilize our main result to approximate the solution of a nonlinear functional Volterra integral equation. Some numerical examples are also furnished. If time permits, then we will discuss Image recovery problem as well.

MS [00418] Nonlinear PDE: beyond the well-posedness theory

room : F402

• [01572] Hessian Riemannian flows in mean-field games
  • Format : Talk at Waseda University
  • Author(s) :
    • Diogo Gomes (KAUST)
  • Abstract : Hessian Riemannian flows are a powerful tool for the construction of numerical schemes for monotone mean-field games that have their origin in constrained optimization problems. In this talk, we discuss the general construction of these flows for monotone mean-field games, their existence and regularity properties, and their asymptotic convergence.
• [02413] Homogenization of Reactions in Random Media
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuming Paul Zhang (Auburn University)
    • Andrej Zlatos (University of California, San Diego)
  • Abstract : Homogenization is a general phenomenon when physical processes in periodic or random environments exhibit homogeneous long time dynamic due to large space averaging of the variations in the environment. While this area of Mathematics saw a slew of remarkable developments in the last 20 years, the progress in the case of reaction-diffusion equations has been somewhat limited due to the homogenized dynamic involving discontinuous solutions to different (first-order) equations. In this talk I will discuss stochastic homogenization for reaction-diffusion equations in several spatial dimensions. These include the cases of both time-independent and time-dependent reactions, with the later proof employing a new subadditive ergodic theorem for time-dependent environments. This talk is based on joint works with Andrej Zlatoš.
• [02535] Continuum limit of dislocations with annihilation in one dimension
  • Format : Talk at Waseda University
  • Author(s) :
    • Norbert Pozar (Kanazawa University)
  • Abstract : In this talk I discuss the many-particle limit for a system of particles in one dimension. The particles carry a signed charge, interact via a Newtonian potential and when two particles with opposite charges meet, they annihilate and are removed from the system. This serves as a simplified model of dislocation dynamics in a crystalline lattice. This talk is based on joint work with Mark Peletier and Patrick van Meurs.
• [04586] Quantitative periodic homogenization of a front propagation model in dynamic environments
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenjia Jing (Tsinghua University)
  • Abstract : In this talk we review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly with respect to the absolute value of the momentum variable. We focus on the case of dynamic environment where the Hamiltonian has highly oscillations in time as well as in space. We present some key steps in the proof of the qualitative homogenization theory and in the quantification of the convergence rate in the periodic setting. The talk is based on several joint works with Souganidis, Tran and Yu.

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

room : F403

• [05439] The convergence problem in mean field control
  • Format : Online Talk on Zoom
  • Author(s) :
    • Joe Jackson (The University of Texas at Austin)
    • Samuel Daudin (Université Côte d'Azur)
    • François Delarue (Université Côte d'Azur)
  • Abstract : This talk will be about a recent joint work with Samuel Daudin and François Delarue concerning the convergence problem in mean field control. When the data is convex and sufficiently smooth, the (optimal) rate of convergence (of the $N$-player value function towards the limiting value function) is known to be $1/N$. The goal of our work is to identify the optimal rate of convergence in the more subtle non-convex setting.
• [05419] Markov $alpha$-Potential Game
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xinyu Li (UC Berkeley)
    • Xin Guo (UC Berkeley)
    • Chinmay Maheshwari (UC Berkeley)
    • Manxi Wu (Cornell University)
    • Shankar Sastry (UC Berkeley)
  • Abstract : We propose a new framework to study multi-agent interaction in Markov games: Markov α-potential games. Markov potential games are special cases of Markov α-potential games, so are two important and practically significant classes of games: Markov congestion games and perturbed Markov team games. In this paper, α-potential functions for both games are provided and the gap α is characterized with respect to game parameters. Two algorithms – the projected gradient-ascent algorithm and the sequential maximum improvement smoothed best response dynamics – are introduced for approximating the stationary Nash equilibrium in Markov α-potential games. The Nash-regret for each algorithm is shown to scale sub-linearly in time horizon. Our analysis and numerical experiments demonstrates that simple algorithms are capable of finding approximate equilibrium in Markov α-potential games.
• [05421] MF-OMO: An Optimization Formulation of Mean-Field Games
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xin Guo (UC Berkeley)
    • Anran Hu (University of Oxford)
    • Junzi Zhang (Citadel Securities)
  • Abstract : The literature on theory and computation of mean-field games (MFGs) has grown exponentially recently, but current approaches are limited to contractive or monotone settings, or with an a priori assumption of the uniqueness of the Nash equilibrium (NE). In this talk, we present MF-OMO (Mean-Field Occupation Measure Optimization), a mathematical framework that analyzes MFGs without these restrictions. MF-OMO reformulates the problem of finding NE solutions in MFGs as a single optimization problem. This formulation thus allows for directly utilizing various optimization tools, algorithms and solvers to find NE solutions of MFGs in practice. We also provide convergence guarantees for finding (multiple) NE solutions using popular algorithms like projected gradient descent. For MFGs with linear rewards and mean-field independent dynamics, solving MF-OMO can be reduced to solving a finite number of linear programs, hence solved in finite time.

contributed talk: CT070

room : F411

[02111] Geometric visual model for linear derivation of elliptical orbits in 3-dimensional space

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F411
• Type : Contributed Talk
• Abstract : If visual space is defined as a 3-dimensional complex vector space, linear perspective is expressed as an L1-norm constraint with the scale. The vanishing point represents the boundary of visual space, and the L2-norm constraint indicates that visual space is a sphere. A geometric visual model that satisfies these constraints allows linear derivation of elliptical orbits. The solution is simple because it does not involve an infinite series.
• Classification : 51K05
• Format : Talk at Waseda University
• Author(s) :
  • Hiroyuki Nishimoto (Kochi University)

[02473] Applications of Bures-Wasserstein geometry of HPD matrices to signal detection

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F411
• Type : Contributed Talk
• Abstract : Autocovariance matrices can describe characteristic of time series data. If the data follow the stationary process, the corresponding autocovariance matrix is Hermitian positive definite (HPD). In this talk, we introduce Riemannian geometry of the HPD matrix spaces equipped with the Bures–Wasserstein (BW) metric and propose a detection method by utilizing the geodesic distance to define BW mean and median of HPD matrices. Robustness of the proposed mean and median will also be analyzed.
• Classification : 53B20, 60G35, 32M15
• Format : Talk at Waseda University
• Author(s) :
  • Yusuke Ono (Keio University)
  • Linyu Peng (Keio University)

[01548] Quadratically Regularized Bilevel Optimal Transport

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F411
• Type : Contributed Talk
• Abstract : We study the effect of an $L^2$ regularization to an optimal control problem that is constrained by the Kantorovich problem of optimal transport. We present a class of possible applications by means of a toy problem. Using a reverse approximation argument, we discuss the approximability of solutions of the unregularized problem by a sequence of solutions of the regularized problems.
• Classification : 49Q22, 90C08, 49J45
• Format : Talk at Waseda University
• Author(s) :
  • Sebastian Hillbrecht (Technische Universität Dortmund)
  • Christian Meyer (Technische Universität Dortmund)
  • Paul Manns (Technische Universität Dortmund)

[02087] Best Approximation in Euclidean Space: A Supply Distribution Efficiency Model

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @F411
• Type : Contributed Talk
• Abstract : In this paper, we developed a mathematical model for supply distribution efficiency using inverse best approximation by considering Euclidean distance in a Euclidean space. Given a sequence $\langle S_i\rangle_{i=1}^k$ of closed convex subsets of a Euclidean space $E$ and a sequence of natural numbers $\langle n_i\rangle_{i=1}^k$, we determined the best location of a convex set $S$ in $E$ such that the Euclidean distance from $S$ to $S_i$ is at most $n_i$ for each $i\in \{1,2,\ldots,k\}$.
• Classification : 51K05, 41A45, 41A29
• Format : Talk at Waseda University
• Author(s) :
  • Rosalio Jr Gaid Artes (Mindanao State University - Tawi-Tawi College of Technology and Oceanography)

MS [00534] Topological and geometric data analysis: theory and applications

room : F412

• [01514] Vietoris-Rips persistent homology, injective metric spaces, and the filling radius
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunhyuk Lim (Max Planck Institute for Mathematics in the Sciences)
    • Facundo Memoli (The Ohio State University)
    • Osman Berat Okutan (Florida State University)
  • Abstract : In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information from metric spaces. In this paper, we consider a different, more geometric way of generating persistent homology of metric spaces which arises by first embedding a given metric space into a larger space and then considering thickenings of the original space inside this ambient metric space. In the course of doing this, we construct an appropriate category for studying this notion of persistent homology and show that, in a category theoretic sense, the standard persistent homology of the Vietoris-Rips filtration is isomorphic to our geometric persistent homology provided that the ambient metric space satisfies a property called injectivity. As an application of this isomorphism result we are able to precisely characterize the type of intervals that appear in the persistence barcodes of the Vietoris-Rips filtration of any compact metric space and also to give succinct proofs of the characterization of the persistent homology of products and metric gluings of metric spaces. Our results also permit proving several bounds on the length of intervals in the Vietoris-Rips barcode by other metric invariants, for example the notion of spread introduced by M. Katz. As another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres which follow from work of M. Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence barcodes which follow from work of F. Wilhelm. Finally, we establish a sharp version of Hausmann’s theorem for spheres which may be of independent interest.
• [01746] Reeb Order Method and its Application to Topological Flow Data Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoki UDA (Tohoku University)
  • Abstract : Sakajo and Yokoyama have classified the topology of streamlines and characterised them by unique tree representations, called Cyclically Ordered rooted Tree (COT) representations. The author realised the practical application of their theory to data science, called Topological Flow Data Analysis (TFDA), utilising Reeb graphs and their discretised version, Reeb order. In this talk, we briefly introduce TFDA theory and its application to meteorology and oceanography.
• [04575] Topological Node2vec: Graph Embeddings via Persistent Homology
  • Format : Talk at Waseda University
  • Author(s) :
    • Killian Meehan (Kyoto University)
  • Abstract : Node2vec is a machine learning framework which specializes in transforming graph into euclidean data. However, we demonstrate that with very simple examples we see a high destruction of topological information during the embedding process. Our project builds on top of the original Node2vec framework and introduces a topological loss function derived from optimal transport which forces this new machine learning network to maximally preserve graph information while checking topological loss at every step.
• [04694] Data, Geometry, and homology
  • Format : Talk at Waseda University
  • Author(s) :
    • Wojciech Chacholski (KTH, Royal Institute of Technology)
    • Jens Agerberg (KTH, Royal Institute of Technology and Ericsson)
    • Ryan Ramanujam (Karolinska Institutet (Dept. of Clinical Neuroscience) and Datanon Corporation)
    • Francesca Tombari (KTH, Royal Institute of Technology)
  • Abstract : For a successful analysis a suitable representation of data by objects amenable for statistical methods is fundamental. There has been an explosion of applications in which homological representations of data played a significant role. I will present one such representation called stable rank and introduce various novel ways of using it to encode geometry, and then analyse, data. I will provide several illustrative examples of how to use stable ranks to find meaningful results.

contributed talk: CT078

room : E501

[00514] Diffusion approximation of a Markov-modulated infinite-server queue

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E501
• Type : Contributed Talk
• Abstract : In a queue, overdispersion nature of arrivals and stochastic nature of service times can be captured by incorporating modulation into the queue dynamics. We discuss stochastic approximations for an infinite-server queue, where the stochastic arrival and service rates are determined by a Markovian environment. The incorporation of modulation leads to an Ornstein-Uhlenbeck process as its diffusion approximation with the variance parameter capturing the stochastic variations of both modulating and modulated processes.
• Classification : 60K25, 60K37
• Format : Talk at Waseda University
• Author(s) :
  • Selvaraju Natarajan (Indian Institute of Technology Guwahati, India)
  • Ankita Sen (Indian Institute of Technology Guwahati, India)

[02573] Local convergence analysis of modified King's family for multiple roots

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E501
• Type : Contributed Talk
• Abstract : We Introduce a new optimal King-like family of methods to solve nonlinear equations when the multiplicity of the root is known in advance. Local convergence of fourth order modified King's family, defined by first two steps of the new scheme is also studied. Radius of convergence balls of fourth order scheme are computed and compared with the existing methods. Comparison of these results show the superiority of our schemes over the existing ones.
• Classification : 65A05, 65Gxx, 65H05, 65G99
• Format : Talk at Waseda University
• Author(s) :
  • Saurabh Bhatia (Panjab University Chandigarh)

[01146] Steady-State Analysis of a Single Server Queueing System Subject to Differentiated Vacations and N-Policy

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E501
• Type : Contributed Talk
• Abstract : An M/M/1 queueing system subject to differentiated vacations and N-policy is studied. When there are no customers, the server takes a vacation and returns to the system if N or more customers are found. Still, if the number of customers in the system is less than “N,” the server takes another vacation type. The explicit expression for steady-state probabilities of the system size is obtained. The exact solutions for some performance measures are also derived.
• Classification : 60K25, 68M20, 90B22, Queueing theory
• Format : Online Talk on Zoom
• Author(s) :
  • SURANGA SAMPATH MIYANAWATHURA IHALA GAMAGE (Wayamba University of Sri Lanka)

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

room : E502

• [03377] Modeling and learning methods applied to collective motion in biology
  • Format : Talk at Waseda University
  • Author(s) :
    • James Greene (Clarkson University)
    • Ming Zhong (Illinois Institute of Technology)
  • Abstract : From groups of cells to groups of humans, collective motion is ubiquitous in biological systems . Inspired by phototaxis, we develop minimal mathematical models that exhibit the emergence of social structure in Cucker-Smale type pairwise interaction models. Numerical and analytical results are provided, which show the emergence of linear spatial structures. We also present methods by which local interaction rules may be learned from trajectory data, and apply these techniques to cancer migration models.
• [03399] Neural architectures for identifying stochastic differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Ali Hasan (Duke University)
    • Joao Pereira (Instituto Nacional de Matemática Pura e Aplicada)
    • Haoming Yang (Duke University)
    • Sina Farsiu (Duke University)
    • Vahid Tarokh (Duke University)
  • Abstract : In this work, we will describe a variational framework to recover the parameters of a latent stochastic differential equation (SDE) from high dimensional observations. We prove that, in the limit of infinite data, the true parameters can be recovered up to an isometry and numerically illustrate the efficacy of the method. We finally discuss connections to McKean-Vlasov SDEs when using neural network parameterizations of SDEs and present numerical examples in machine learning applications.
• [02129] Emergent Short-range Memory in Stochastic Gradient Noise and Its Implications on Generalization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jiangshe Zhang (Xi‘an Jiaotong University)
  • Abstract : Investigating stochastic gradient descent (SGD) from the perspective of stochastic differential equations (SDEs) is quite popular in the deep learning community. In this talk, I will present an analytical result on modeling SGD with SDEs driven by fractional Brownian motion, which reveals the escaping efficiency when trapped in local minima. From the optimization point of view, I will further show how we can relate the smoothness of the optimization pathway to the generalization ability.

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

room : E503

• [05558] Gaussian likelihoods for non-Gaussian data
  • Format : Talk at Waseda University
  • Author(s) :
    • Heikki Haario (University of Lappeenranta)
  • Abstract : Various modelling situations – chaotic dynamics, stochastic differential equations, random patterns by the Turing reaction-diffusion systems, cellular automata– share the analogy that a fixed model parameter corresponds to a family of solutions rather than a fixed deterministic one. This may be due to extreme sensitivity with respect to the initial values, randomized or unknown initial values, or explicit stochasticity of the system. Standard methods based on directly measuring the distance between model and data are no more available. We discuss a unified construction of Gaussian likelihoods for such ‘intractable’ situation, where the raw data is far from Gaussian. Examples cover the cases in the above list of modelling situations.
• [05515] Multi-output multilevel best linear unbiased estimators via semidefinite programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Matteo Croci (University of Texas at Austin)
    • Karen E. Willcox (University of Texas at Austin)
    • Stephen J. Wright (University of Wisconsin - Madison)
  • Abstract : Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this talk we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. We demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.
• [03923] Simulating rare events with Stein variational gradient descent
  • Format : Talk at Waseda University
  • Author(s) :
    • Max Ehre (Technical University of Munich)
    • Iason Papaioannou (Technical University of Munich)
    • Daniel Straub (Technical University of Munich)
  • Abstract : Stein variational gradient descent (SVGD) is an approach to sampling from Bayesian posterior distributions. We repurpose SVGD for simulating rare events with probabilities 10^{-5} -- 10^{-12}. We employ a tempered version of SVGD to sample from an approximately optimal importance sampling density. Several examples are used to benchmark the efficacy of our approach against state-of-the-art methods for estimating rare event probabilities.

MS [00897] Nonlinear and nonlocal models: analysis and numerics

room : E504

• [04670] Energy gap for nonlocal model
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Kh. Balci (University of Bielefeld, Germany)
  • Abstract : The essential feature of many models with non-standard growth is the possible presence of Lavrentiev gap and related lack of regularity, non-density of smooth functions in the corresponding energy space. Finding assumptions for the presence of Lavrentiev phenomena is in particular important for regularity theory. We show that nonlocal and local-nonlocal models enjoy the presence of energy gap. We obtain the optimal conditions separating the regular case from the one with Lavrentiev gap for the different types of nonlocal and mixed local-nonlocal double phase models. The obtained conditions show the sharpness of resent regularity results for nonlocal double-phase problems.
• [04387] Kacanov Iteration
  • Format : Talk at Waseda University
  • Author(s) :
    • Lars Diening (Bielefeld University)
    • Anna Kh. Balci (Bielefeld University)
    • Johannes Storn (Bielefeld University)
  • Abstract : The p-Laplace equation is one of the model equations for non-linear problems. Due to its non-linearity it is quite challenging to approximate its solution numerically in particular in the degenerate/singular case. Standard methods like gradient descent or Newton's method have significant problems to approximate the solution. We present an iterative, linear method that allows to solve the p-Laplace equation efficiently both for small and large exponents.
• [04258] Regularity results for fractional nonlocal equation with nonstandard growth and differentiability
  • Format : Talk at Waseda University
  • Author(s) :
    • Jihoon Ok (Sogang University)
  • Abstract : We discuss on nonlocal problems with nonstandard growth and differentiability. In particular, we introduce local boundedness and Hölder continuity for nonlocal double phase problems and nonlocal problems with variable growth and differentiability, by identifying sharp assumptions on parameters and functions characterizing these nonlocal problems.
• [05242] BBM-type theorem for fractional Sobolev spaces with variable exponents
  • Format : Talk at Waseda University
  • Author(s) :
    • Minhyun Kim (Hanyang University)
  • Abstract : A Bourgain–Brezis–Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in general.

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

room : E505

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

room : E506

MS [00831] Randomization for Simplified Machine Learning: Random Features and Reservoir Computers

room : E507

• [02997] Scalable Gaussian Process Regression with Quadrature-based Features
  • Format : Talk at Waseda University
  • Author(s) :
    • Paz Fink Shustin (Tel Aviv University)
  • Abstract : Gaussian processes provide a powerful probabilistic kernel learning framework, which allows high-quality nonparametric learning via methods such as Gaussian process regression. Nevertheless, its learning phase requires unrealistic massive computations for large datasets. In this talk, we present a quadrature-based approach for scaling up Gaussian process regression via a low-rank approximation of the kernel matrix. The low-rank structure is utilized to achieve effective hyperparameter learning, training, and prediction. Our Gauss-Legendre features method is inspired by the well-known random Fourier features approach, which also builds low-rank approximations via numerical integration. However, our method is capable of generating high-quality kernel approximation using a number of features that is poly-logarithmic in the number of training points, while similar guarantees will require an amount that is at the very least linear in the number of training points when using random Fourier features. The utility of our method for learning with low-dimensional datasets is demonstrated using numerical experiments.
• [03226] Advances in Time Series Analysis With Reservoir Computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Braden John Thorne (University of Western Australia)
    • Michael Small (University of Western Australia)
    • Débora Cristina Corrêa (University of Western Australia)
    • Ayham Zaitouny (University of Doha for Science and Technology)
  • Abstract : Reservoir computers have proven to be powerful embedding machines for dynamical systems. However, bridging the gap from their machine learning origins to time series analysis is still relatively new, with great potential for novel discoveries. In this talk, we will outline what reservoir time series analysis is and why one should care about it amidst the ecosystem of other embedding-based techniques. We will then present some use cases and applications to motivate future work.
• [03272] Error analysis of random feature neural networks for Black-Scholes-type PDEs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lukas Gonon (Imperial College London)
  • Abstract : We mathematically analyse the learning performance of random feature neural networks for learning solutions to a class of PDEs which includes the Black-Scholes PDE as special case. In contrast to other existing mathematical results on neural network-based PDE-learning, in our context it is possible to obtain a full error analysis addressing all error components (approximation, generalization and optimization) with the derived bounds (convergence rates and constants) not suffering from the curse of dimensionality.
• [04091] Theoretical advances for learning functions and operators with random features
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicholas H. Nelsen (California Institute of Technology)
  • Abstract : This talk provides a complete error analysis of operator learning with random features (RF). The theoretical results are developed in a fully general infinite-dimensional input-output setting. The highlights include strong consistency of RF estimators under model misspecification and minimax optimal convergence rates. This work also contributes theory for rigorous uncertainty quantification by establishing (i) new pointwise error bounds for vector-valued Gaussian process (GP) regression and (ii) strong consistency of RF estimators of GPs.

MS [00911] Sparse Linear Solvers for Computational Science at Extreme Scales

room : E508

• [04144] Scalable domain decomposition solvers for cardiac reaction-diffusion cell-by-cell models
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Franco Pavarino (University of Pavia)
    • Ngoc Mai Monica Huynh (University of Pavia)
    • Simone Scacchi (University of Milano)
    • Fatemeh Chegini (Zuse Institute Berlin)
    • Martin Weiser (Zuse Institute Berlin)
  • Abstract : Scalable preconditioners are constructed and analyzed for the iterative solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. These models lead to large-scale ill-conditioned discrete systems which have discontinuous global solutions across cells (subdomains) boundaries. A scalable convergence rate bound is proved for dual-primal cell-by-cell preconditioned operators. Numerical tests validate this bound and investigate its dependence on the discretization parameters.
• [04292] Adapting Patch-based Relaxation to Generalized MHD Systems Within An Algebraic Multigrid Solver
  • Format : Talk at Waseda University
  • Author(s) :
    • Raymond Tuminaro (Sandia National LaboratoriesWe discuss a multigrid algorithm for generalized magnetohydrodynamics (GMHD). This GMHD system has two different PDE terms that can each generate a large near null space, complicating the linear solution process. One expre)
    • Michael Crockatt (Sandia National Laboratories)
    • Graham Harper (Sandia National Laboratories)
    • Allen Robinson (Sandia National Laboratories)
  • Abstract : We discuss multigrid solvers for generalized magnetohydrodynamics. This system has two PDE terms that each generate a large near null space. One expression contains the curl operator while the other arises from generalized Ohm's law. We propose a geometric multigrid algorithm based on Arnold-Falk-Winther relaxation. We then adapt the Rietzinger/Schoberl AMG scheme to the generalized system. We apply the resulting preconditioner to two test problems to illustrate its effectiveness.
• [04198] An immersed approach to fluid-structure-contact interaction
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Zulian (Università della Svizzera italiana)
    • Maria Giuseppina Chiara Nestola (Università della Svizzera italiana)
    • Rolf Krause (Università della Svizzera italiana)
  • Abstract : We presents an immersed technique for solving fluid-structure interaction (FSI) problems using dual Lagrange multipliers, which enables the resampling of discrete fields with standard matrix-vector multiplication within the nonlinear solution procedure. The fluid and structure are coupled in the overlapping volume, while different structures in contact are coupled on the surface using mortar-based techniques.
• [02685] GMRES+AMG Navier-Stokes Pressure Projection Solvers with RAS and ORAS Smoothers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stephen Thomas (Advanced Micro Devices)
    • Amik St-Cyr (Shell)
    • Erika Strakova (IT4-innovations Ostrava)
    • Allison Baker (National Center for Atmospheric Research)
  • Abstract : PeleLM is a Navier-Stokes combustion model. Extremely ill-conditioned problems arise for incompressible and reacting flows in the low Mach flow regime, particularly for cut-cell meshes in complex geometries, Prenter (2020) improved convergence rates for cut-cells by employing PCG-AMG with Schwarz smoothers. We combine ILU smoothers using iterative triangular solves with RAS and ORAS smoothers adapted to hypre for a new low-synch MGS-CGS GMRES. The iteration counts tend to remain constant and these smoothers reduce run times on many-core GPU's in the strong-scaling limit.

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

room : E603

• [05381] Nonlinear spectral graph theory: an overview of graph properties
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Tudisco (Gran Sasso Science Institute)
    • Dong Zhang (Peking University)
    • Piero Deidda (Gran Sasso Science Institute)
  • Abstract : It is well-known that a variety of combinatorial graph quantities are approximated by the spectrum of relevant graph matrices, such as the Laplacian or the adjacency matrix. While very useful and widely used, these approximations are far from being tight. A generalization of the graph spectrum can be defined by considering nonlinear eigenvalue problems defined in terms of pairs of homogeneous convex functions. For quadratic functions, this definition boils down to the standard linear (matrix) eigenvalue problem. In this talk, we review several basic definitions and properties of nonlinear eigenproblems defined in terms of generic homogeneous pairs, and we then show how the corresponding eigenvalues can be used to provide tight approximations to fundamental graph quantities, including the multi-way Cheeger constant, the graph packing radius, the graph's max and min cuts, and graph's modularity.
• [05445] Solving Non-Convex Problems without Relaxation: Unexpected Usefulness of NEPv on Optimization Theory
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jeonghun Park (Yonsei University)
  • Abstract : Non-convex optimization problems arise in many applications of wireless communications and signal processing. To solve this, one typical principle is relaxing the original problem, obtaining a "convexified" solution, and repeat the process until convergence. In this talk, breaking away from this conventional approach, we develop an unorthodox method called spectral method. We also show that in some applications, this new approach offers significantly better performances with less complexity.
• [05390] Trace Minimization Principles on Matrix Manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Liang (Tsinghua University)
    • Ren-Cang Li (University of Texas at Arlington)
    • Li Wang (University of Texas at Arlington)
    • Leihong Zhang (Soochow University)
  • Abstract : This talk is concerned with establishing a trace minimization principle for two Hermitian matrix pairs: when is $\inf_X{\rm trace}(\widehat AX^{\rm H}AX)$ subject to $\widehat BX^{\rm H}BX=I$ finite? Sufficient and necessary conditions are obtained and, when the infimum is finite, an explicit formula for it is presented in terms of the finite eigenvalues of the matrix pairs.
• [05272] Bound states in the continuum for a class of infinite matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Ya Yan Lu (City University of Hong Kong)
  • Abstract : For certain infinite matrix $A$, the equation $Ax=\lambda x$ may represent a boundary value problem (BVP) for $\lambda$ in a real interval $C$. Such an equation models the scattering of incident waves by some objects. Without the incident waves, $Ax=\lambda x$ is still an eigenvalue problem. A bound state in the continuum (BIC) is a special eigenpair with the eigenvalue $\lambda \in C$. In that case, the BVP for the same $\lambda$ has no uniqueness. A nonlinear version is $(A + D(x)) x = \lambda x$, where $D(x)$ is a diagonal matrix with the $(i,i)$ entry being $d_i |x_i|^2$. In this talk, we discuss linear and nonlinear BICs for a class of infinite matrices.

MS [02448] Verified Numerical Computations and Applications

room : E604

• [02902] High relative accuracy computing with the Cauchon algorithm
  • Format : Talk at Waseda University
  • Author(s) :
    • Juergen Garloff (University Konstanz)
    • Mohammad Adm (Palestine Polytechnic University Hebron)
    • Fatima Rasheed (Palestine Polytechnic University Hebron)
  • Abstract : We present the condensed form of the so-called Cauchon Algorithm and reformulate the computations in such a way that they can be performed without any subtraction of numbers of equal sign. This provides the basis for an algorithm needing O(n³) arithmetic operations for the computation of all eigenvalues of an n-by-n nonsingular totally nonnegative matrix, i.e., a matrix having all its minors nonnegative, with guaranteed high relative accuracy, independently of the condition number of the matrix.
• [03658] Floating-point matrices with specified solutions for linear algebra problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Katsuhisa Ozaki (Shibaura Institute of Technology)
    • Yuki Uchino (Shibaura Institute of Technology)
    • Takeshi Terao (Kyushu University)
  • Abstract : This research aims to rigorously verify the accuracy of the numerical results for numerical linear algebra problems. If an exact solution to a problem is known in advance, we can observe the relative error of the computed result. We proposed methods that generate a test problem based on an error-free transformation of floating-point numbers. We focus on liner systems, eigenvalue decomposition, singular value decomposition, and least squares problems with specified solutions.
• [05571] Adaptive precision sparse matrix-product and application to Krylov solvers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stef Graillat (LIP6, Sorbonne Université)
    • Fabienne Jezequel (LIP6, Sorbonne Université)
    • Theo Mary (Sorbonne Université, CNRS, LIP6)
    • Romeo Molina (Sorbonne Université, CNRS)
  • Abstract : We introduce a mixed precision algorithm for computing sparse matrix-vector products and use it to accelerate the solution of sparse linear systems by iterative methods. Our approach is based on the idea of adapting the precision of each matrix element to their magnitude: we split the elements into buckets and use progressively lower precisions for the buckets of progressively smaller elements. We carry out a rounding error analysis of this algorithm that provides us with an explicit rule to decide which element goes into which bucket and allows us to rigorously control the accuracy of the algorithm. We implement the algorithm on a multicore computer and obtain significant speedups (up to a factor 7×) with respect to uniform precision algorithms, without loss of accuracy, on a range of sparse matrices from real-life applications. We showcase the effectiveness of our algorithm by plugging it into various Krylov solvers for sparse linear systems and observe that the convergence of the solution is essentially unaffected by the use of adaptive precision.
• [05577] Iterative refinement for an eigenpair subset of real symmetric matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Terao (Kyushu University)
    • Toshiyuki Imamura (RIKEN Center for Computational Science)
    • Katsuhisa Ozaki (Shibaura Institute of Technology)
  • Abstract : Numerical computation for eigenvalue decomposition plays a crucial role in many scientific fields, and highly accurate eigenpairs are required in certain domains. A novel method was proposed in this study for the iterative refinement of the eigenpair of a real symmetric matrix, which is based on the Ogita-Aishima method and uses compact WY representation. The proposed method can refine the accuracy of a partial eigenpair without using a full eigenvector matrix.

MS [00687] Recent advances in deep learning-based inverse and imaging problems

room : E605

• [05273] Data-driven parameter optimization for some inverse problems with sparsity-based priors
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Carlos De los Reyes (MODEMAT)
  • Abstract : In recent years, novel ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different parameters of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based on a training set is used. When confronted with inverse problems with sparsity-based regularizers, however, the bilevel optimization problem structure becomes quite involved to be analyzed, as classical nonlinear or bilevel programming results cannot be directly utilized. In this talk, I will discuss on a strategy to overcome these difficulties, leading to a reformulation of the bilevel problems as mathematical programs with complementarity constraints. This enables to obtain sharp first-order optimality conditions, but at the price of lifting the problems to a higher dimension. Some ideas on how to reduce the dimension of the problems back will also be presented, together with the different challenges that these problems pose, when dealing with large training sets.
• [03185] Data-driven Joint Inversion for PDE Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Kui Ren (Columbia University)
  • Abstract : The task of simultaneously reconstructing multiple physical coefficients in partial differential equations from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. We characterize the impact of learning uncertainty on the joint inversion results for two typical model inverse problems. This is based on a joint work with Lu ZHang.
• [02972] A scalable deep learning approach for solving high-dimensional dynamic optimal transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Zuoqiang Shi (Tsinghua University)
  • Abstract : The dynamic formulation of optimal transport has attracted growing interests. In this talk, we propose a deep learning based method to solve the dynamic optimal transport in high dimensional space based on carefully designed representation of the velocity field, the discretization along the characteristics, and the computation of high dimensional integral by Monte Carlo method. Numerical experiments show that our method could give more accurate results in high dimensional cases and has very good scalability.
• [04688] Learning nonlinearities in time-dependent PDEs from data
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Aarset (University of Göttingen)
    • Martin Holler (University of Graz)
    • Tram Thi Ngoc Nguyen (Max-Planck Institute for Solar System Research, Göttingen)
  • Abstract : We introduce and analyze an all-at-once approach for learning parts of a partial-differential-equation-based model from data. More specifically, we consider the learning of a non-linearity in the model, which acts pointwise on the state, from indirect, noisy measurements. We provide a function-space analysis of the corresponding learning problem and of the resulting PDE with learned components in a general setting. Furthermore, we show numerical experiments that confirm the practical feasibility of the proposed method.

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

room : E606

MS [00959] Numerical modeling and analysis in electromagnetic applications

room : E701

• [03708] Recent Advances in Finite Element Methods for Electromagnetic Analysis on Integrated Circuits
  • Author(s) :
    • Woochan Lee (Incheon National University)
  • Abstract : The finite element method plays a significant role in the electromagnetic analysis of integrated circuits (IC) in electrical engineering. As IC structures constitute a very large-scale problem, the resources required for finite element modeling and analysis increase exponentially, making high-speed electromagnetic analysis an essential factor. This talk reviews recent trends in accelerating electromagnetic analysis, including the fundamental application of time- and frequency-domain finite element methods, high-speed techniques utilizing brick element characteristics, and parallel processing techniques.
• [03728] Forced field continuity condition of object interface for the vector wave equation
  • Author(s) :
    • Hyesun Na (Yonsei University)
  • Abstract : Electromagnetic wave scattering problem is considered when perfect electric conductor is coated with several dielectric layers. Solving the scattering problem using finite element method requires huge number of degrees of freedom. Insufficient degrees of freedom may not be able to capture the information about abrupt changes in the interface. This work proposes to force a field continuity condition on the functional to overcome the difficulty.
• [03748] A three-dimensional NEGF development using finite element method in the presence of heterogeneous quantum dots
  • Author(s) :
    • URANCHIMEG DORLIGJAV (Yonsei university )
  • Abstract : In this work, we propose an algorithm to calculate electron density and space charge effect in 3D nanoscale device containing heterogeneous quantum dots. We begin by formulating the nonequilibrium Green’s function (NEGF) approach to calculate electron density and apply a nonlinear solver for Poisson equation using the finite element method.
• [04959] A Moving Mesh Method for Nano-Rod Electro-Osmosis
  • Author(s) :
    • Richard James (Samsung Display)
    • Jahoon Koo (Samsung Display)
    • Sunyoung Oh (Samsung Display)
    • Hyunguk Cho (Samsung Display)
    • Sung-Chan Jo (Samsung Display)
  • Abstract : Modelling the hydrodynamics of charged colloids within ionic fluids is a challenging multi-physics problem. Rigid body particle motion is resisted by drag due to the viscosity of the fluid. Furthermore, ionic impurities give rise to electrical-double layers that can in turn induce flow of the solvent. In this paper, a moving mesh method for nano-rod electro-osmosis is introduced and applied to analyse particle trajectories in response to external electric fields.

contributed talk: CT102

room : E702

[00513] The perfectly matched layer for elastic waves in layered media

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E702
• Type : Contributed Talk
• Abstract : The perfectly matched layer (PML) is widely used to truncate domains in large-scale simulation of wave propagation in open boundaries. PML absorbs outgoing waves without reflection and significantly improves computational efficiency. However, it is very challenging to prove stability of PML models. In this talk, I present our recent contribution on the stability analysis of PML models for the elastic wave equation in layered media modeling seismic wave propagation in the Earth layers.
• Classification : 65M06, 65M12, 86-08
• Format : Talk at Waseda University
• Author(s) :
  • Siyang Wang (Umeå University)

[00999] High-order energy stable schemes for the phase-field model by the Convex Splitting Runge-Kutta methods

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E702
• Type : Contributed Talk
• Abstract : The Convex Splitting Runge-Kutta method is a high-order energy stable scheme for gradient flow which is a combination of the well-known convex splitting method and the multi-stage Runge-Kutta method. In this talk, we will discuss the applications and challenges of CSRK via extensive examples of the phase-field model.
• Classification : 65M06, 65M12, 65M70, Phase-field model, Convex splitting method, Runge-Kutta method
• Format : Talk at Waseda University
• Author(s) :
  • Jaemin Shin (Chungbuk National University)
  • Hyun Geun Lee (Kwangwoon University)
  • June-Yub Lee (Ewha Womans University)

[01005] Nonlinear Disturbance Observer-Based Control Design for Markovian Jump Systems

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E702
• Type : Contributed Talk
• Abstract : This paper addresses the anti-disturbance control problem for time-delayed Markovian jump nonlinear systems with modeled and unmodeled disturbances. Specifically, the modeled disturbance is generated by a nonlinear exogenous system and estimated using a nonlinear disturbance observer. A mode-dependent asymmetric Lyapunov-Krasovskii functional is used to derive sufficient conditions for the existence of the proposed controller and disturbance observer. A numerical example is included to demonstrate the efficacy of the theoretical results developed.
• Classification : 93D05, 93D15, 93E15, LYAPUNOV STABILITY; SYSTEMS AND CONTROL THEORY
• Format : Online Talk on Zoom
• Author(s) :
  • KAVIARASAN BOOMIPALAGAN (CHUNGBUK NATIONAL UNIVERSITY)
  • OH-MIN KWON (CHUNGBUK NATIONAL UNIVERSITY)

[01012] Uncertainty and disturbance estimator design for interval type-2 fuzzy systems

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E702
• Type : Contributed Talk
• Abstract : This article investigates the uncertainty and disturbance estimator-based control problem for the interval type-2 fuzzy systems. By designing the appropriate filter, the proposed control designs can estimate system uncertainties and external disturbances accurately. By using the Lyapunov-Krasovskii stability theorem, the required stability conditions and the control gain matrices for the system under consideration are obtained. Finally, an illustrative example is demonstrated to verify the feasibility of the proposed control method.
• Classification : 93D05, 93D09, 93D15, Lyapunov Stability, Systems and Control Theory, Fuzzy Systems
• Format : Online Talk on Zoom
• Author(s) :
  • KAVIKUMAR RAMASAMY (CHUNGBUK NATIONAL UNIVERSITY)
  • KWON OH-MIN (CHUNGBUK NATIONAL UNIVERSITY)

[01014] Fault detection asynchronous filter design for Markovian jump fuzzy systems under cyber attacks

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @E702
• Type : Contributed Talk
• Abstract : This work is concerned with the issue of fault detection asynchronous filter design for a class of discrete-time Markovian jump fuzzy systems with cyber attacks. Precisely, the cyber attacks phenomenon in the network environment satisfies the Bernoulli distribution. Finally, the applicability and usefulness of the proposed filter design method is verified through a practical example.
• Classification : 93D05, 93D09, 93D20, Lyapunov Stability of control systems
• Format : Online Talk on Zoom
• Author(s) :
  • Sakthivel Ramalingam (Chungbuk National University)
  • Oh-Min Kwon (Chungbuk National University)

MS [00673] Recent advances in discontinuous Galerkin methods and the related applications

room : E703

• [03246] Bound preserving DG methods for multi-species flow with chemical reactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Jie Du (Tsinghua University)
  • Abstract : For multispecies chemical reactive flows, the solutions have some physical bounds. The mass fraction does not satisfy a maximum principle and hence it is not easy to preserve the upper bound. Also, most of the bound-preserving techniques available are based on Euler forward method. For problems with stiff source, the time step will be significantly limited. In this work, we will construct third order conservative bound-preserving DG methods to overcome all these difficulties.
• [03960] Staggered discontinuous Galerkin methods for the Stokes problem on rectangular grids
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyea Hyun Kim (Kyung Hee University)
    • Thien Binh Nguyen (Vietnamese-German University)
    • Gung-Min Gie (University of Louisville)
    • Chang-Yeol Jung (UNIST)
  • Abstract : A staggered DG (Discontinous Galerkin) method, that was originally developed on triangular meshes, is extended to rectangular grids for the second order elliptic problems in the first, second, and fourth authors' previous work. On the rectangular grids, the higher order polynomials in higher dimensions can be easily formed without the need for meshing the physical domain. In this talk, we present the extension of our previous staggered DG method to the Stokes system and provide the optimal error estimate for the given polynomial order. Compared to the triangle based DG methods, we also obtain a better inf-sup stability result for the rectangular based DG methods. Numerical results are presented to confirm our optimal error estimate results.
• [02857] A mass conservative scheme for the coupled flow and transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Lina Zhao (City University of Hong Kong)
    • Shuyu Sun (KAUST)
  • Abstract : In this talk, I will present a mass conservative scheme for the coupled Brinkman flow and transport, where the flow equations are discretized using staggered DG method and mixed FEM. As such, the interface conditions are naturally incorporated into the formulation. Then the transport equation is discretized using unwinding staggered DG methods. The optimal convergence error estimates for all the variables are carried out. Several numerical experiments are carried out to demonstrate the performance.
• [03078] hp-Multigrid preconditioner for a divergence-conforming HDG scheme for the incompressible flow problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Guosheng Fu (University of Notre Dame)
    • Wenzheng Kuang (University of Notre Dame)
  • Abstract : In this study, we present an hp-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming simplicial meshes in two- and three-dimensions. The hp-multigrid algorithm is a multiplicative auxiliary space preconditioner that employs the lowest-order space as the auxiliary space, and we developed a geometric multigrid method as the auxiliary space solver. For the generalized Stokes problem, the crucial ingredient of the geometric multigrid method is the equivalence between the condensed lowest-order divergence-conforming HDG scheme and a Crouzeix-Raviart discretization with a pressure-robust treatment as introduced in Linke and Merdon (Comput. Methods Appl. Mech. Engrg., 311 (2016)), which allows for the direct application of geometric multigrid theory on the Crouzeix-Raviart discretization. The numerical experiments demonstrate the robustness of the proposed $hp$-multigrid preconditioner with respect to mesh size and augmented Lagrangian parameter, with iteration counts insensitivity to polynomial order increase. Inspired by the works by Benzi & Olshanskii (SIAM J. Sci. Comput., 28(6) (2006)) and Farrell et al. (SIAM J. Sci. Comput., 41(5) (2019)), we further test the proposed preconditioner on the divergence-conforming HDG scheme for the Navier-Stokes equations. Numerical experiments show a mild increase in the iteration counts of the preconditioned GMRes solver with the rise in Reynolds number up to 10^3.

MS [00232] Theoretical foundations and algorithmic innovation in operator learning

room : E704

• [03323] BelNet: basis enhanced learning, a mesh-free neural operator
  • Format : Online Talk on Zoom
  • Author(s) :
    • zecheng zhang (Carnegie Mellon University)
    • Wing Tat Leung (City University Hong Kong)
    • Hayden Schaeffer (UCLA)
  • Abstract : Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions, allows for the input and output functions to be on different domains, and is able to have different grids between samples. We propose a mesh-free neural operator for solving parametric partial differential equations. The basis enhanced learning network (BelNet) projects the input function into a latent space and reconstructs the output functions. In particular, we construct part of the network to learn the ``basis'' functions in the training process. This generalized the networks proposed in Chen and Chen's universal approximation theory for the nonlinear operators to account for differences in input and output meshes. Through several challenging high-contrast and multiscale problems, we show that our approach outperforms other operator learning methods for these tasks and allows for more freedom in the sampling and/or discretization process.
• [01354] The curse of dimensionality in operator learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Samuel Lanthaler (California Institute of Technology)
  • Abstract : Neural operator architectures employ neural networks to approximate operators between Banach spaces of functions. We show that for general classes of operators, which are characterized only by their Lipschitz- or $C^r$-regularity, operator learning with neural operators suffers from a curse of dimensionality related to the infinite-dimensional input and output function spaces. This curse, made rigorous in this work, is characterized by an exponential lower complexity bound: in order to achieve approximation accuracy $\epsilon$, the number of tunable parameters generally has to scale exponentially in $\epsilon^{-1}$. This negative result is applicable to a wide variety of existing neural operators, including DeepONet, the Fourier neural operator and PCA-Net. It is then shown that the general curse of dimensionality can be overcome for operators possessing additional structure, going beyond regularity. This is illustrated for the solution operator of the Hamilton-Jacobi equation.
• [05247] Score-based Diffusion Models in Function Space
  • Format : Talk at Waseda University
  • Author(s) :
    • Nikola Kovachki (NVIDIA)
  • Abstract : We present a generalization of score-based diffusion models to function space by perturbing functional data via a Gaussian process at multiple scales. We obtain an appropriate notion of score by defining densities with respect to Guassian measures and generalize denoising score matching. We then define the generative process by integrating a function-valued Langevin dynamic. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost that is independent of the data discretization.
• [04771] Deep Learning Theories for Problems with Low–Dimensional Structures
  • Format : Talk at Waseda University
  • Author(s) :
    • Hao Liu (Hong Kong Baptist University)
    • Minshuo Chen (Princeton University)
    • Siawpeng Er (Georgia Institute of Technology)
    • Haizhao Yang (University of Maryland College Park)
    • Tong Zhang (he Hong Kong University of Science and Technology)
    • Tuo Zhao (Georgia Institute of Technology)
    • Wenjing Liao (Georgia Institute of Technology)
  • Abstract : Deep neural networks have demonstrated a great success on many applications, especially on problems with high-dimensional data sets. However, most existing theories are cursed by data dimension. To mitigate the curse of dimensionality, we exploit the low-dimensional structures of data set and establish theoretical guarantees with a fast rate that is only cursed by the intrinsic dimension of the data set. This presentation addresses our recent work on function approximation and operator learning.

MS [00201] Data-Driven Methods for Rough PDEs

room : E705

• [04969] Operator Learning by Regressing PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Bamdad Hosseini (University of Washington)
  • Abstract : In this talk we will discuss a new approach towards operator learning by regression or discovery of the functional form the PDE. A simple, three step approach will be discussed that can be implemented using convenient, off-the-shelf kernel regression tools. Our approach naturally includes PDEs with unknown and variable coefficients and obtains competitive accuracy when training data is very scarce.
• [05235] Neural Operator for Discovering Physical Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Paul Bogdan (USC)
    • Xiongye Xiao (USC)
    • Gaurav Gupta (USC)
    • Radu Victor Balan (UMD)
  • Abstract : We develop a multiwavelet-based neural operator learning architecture that compresses the associated operator’s kernel using fine-grained multiwavelets. For the initial value problems, we propose an exponential neural operator scheme for efficiently learning the map between the initial condition and the activities at later times. To solve coupled partial differential equations, we propose the coupled multiwavelets operator learning scheme by decoupling the coupled integral kernels during the decomposition and reconstruction procedures in the Wavelet space.
• [05013] Neural Option Pricing for Rough Bergomi Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Guanglian Li (HKU )
  • Abstract : This research investigates pricing financial options based on the rough Bergomi model by neural SDEs. We propose an efficient approximation of sample paths using the sum of exponentials and implement the Wasserstein distance as a loss function for network training. The option pricing is entirely based on the traditional martingale theory. Our experimental results indicate that the error of the option price can be bounded by the very Wasserstein distance attained during training.
• [05221] One shot learning of stochastic differential equations with kernel methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthieu Darcy (California Institute of Technology )
    • Boumediene Hamzi (Johns Hopkins University)
    • Giulia Livieri (Scuola Normale Superiore)
    • Houman Owhadi (California Institute of Technology)
    • Peyman Tavallali (Jet Propulsion Lab, NASa)
  • Abstract : We consider the problem of learning a Stochastic Differential Equations from one sample trajectory, a challenging problem as a single trajectory only provides indirect information on the unknown functions. We propose a kernel-based method that recovers the drift function $f$ and the diffusion function $\sigma$ via Maximum a Posteriori Estimation given the data. Additionally, we learn the kernels from data with randomized cross-validation. Numerical examples illustrate the efficacy and robustness of our method.

MS [00736] Modeling and Computation for Interface Dynamics in Fluids and Solids

room : E708

• [02231] Competition between viscous flow and diffusion in pinch-off dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiezheng Qian (Hong Kong University of Science and Technology)
  • Abstract : We employ the Cahn-Hilliard-Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous fluid. A characteristic length scale is introduced to measure the competition between diffusion and viscous flow. This length scale is adjustable in the model and can approach micrometer scale for aqueous two-phase systems close to the critical point. Numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively.
• [02273] A phase field model of vesicle growth or shrinkage
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuwang Li (Illinois Institute of Technology)
    • Xiaoxia Tang (Illinois Institute of Technology)
    • Steven Wise (University of Tennessee)
  • Abstract : We present a diffuse interface model for vesicle growth or shrinkage induced by an osmotic pressure. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard equation describing the evolution of concentration field. We establish control conditions for expanding or shrinking vesicles via a common tangent construction. Numerical experiments reveal that the model can capture the main feature of dynamics: formation of circle-like (expanding) and finger-like (shrinking) vesicles.
• [03394] A symmetrized parametric finite element method for anisotropic surface diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • YIFEI LI (National University of Singapore)
  • Abstract : In this talk, we introduce an energy-stable numerical scheme for 2D closed curve motion under anisotropic surface diffusion using a general anisotropic surface energy γ(n). We propose a symmetric surface energy matrix Z_k(n), derive a symmetrized variational formulation, and discretize it using an structure-preserving parametric finite element method (SP-PFEM). The SP-PFEM is proven unconditionally energy-stable under mild conditions on γ(n). Finally, we report the high performance through numerical results.
• [02478] On a diffuse interface model for incompressible viscoelastic two-phase flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Yadong Liu (University of Regensburg)
    • Dennis Trautwein (University of Regensburg)
  • Abstract : This talk concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where the two components are partially mixed. Considering the elasticity of both components, one ends up with a coupled Oldroyd-B/Cahn--Hilliard type system, which describes the behavior of two-phase viscoelastic fluids. We prove the existence of weak solutions to the system in two dimensions for general (unmatched) mass densities, variable viscosities, different shear moduli, and a class of physically relevant and singular free energy densities that guarantee that the order parameter stays in the physically reasonable interval. The proof relies on a combination of a novel regularization of the original system and a new hybrid implicit time discretization for the regularized system together with the analysis of an Oldroyd-B type equation.

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

room : E709

• [03094] Arbitrary high-order fully-decoupled numerical schemes for phase-field models of two-phase incompressible flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Ruihan Guo (Zhengzhou University)
  • Abstract : Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows, it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations. One popular and efficient strategy is adding an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them. The resulting numerical methods are only first-order accurate in time, and it seems extremely difficult to generalize the idea of stabilization to the second-order version or higher. In this talk, we employ the spectral deferred correction method to improve the temporal accuracy, based on the first-order decoupled and energy stable scheme constructed by the stabilization idea. The novelty lies in how decoupling and linear implicit properties are maintained to improve efficiency. Within the framework of the spatially discretized local discontinuous Galerkin method, the resulting numerical schemes are fully decoupled, efficient, and high-order accurate in both time and space. Numerical experiments are performed to validate the high order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
• [03096] Accuracy-enhancement of discontinuous Galerkin methods for PDEs containing high-order spatial derivatives
  • Format : Talk at Waseda University
  • Author(s) :
    • Qi Tao (Beijing University of Technology)
    • Liangyue Ji (Milton Keynes College)
    • Jennifer K. Ryan (KTH Royal Institute of Technology in Stockholm)
    • Yan Xu (University of Science and Technology of China)
  • Abstract : In this talk, we shall first introduce the accuracy-enhancement of discontinuous Galerkin (DG) methods for solving PDEs with high-order spatial derivatives. It is well known that there are highly oscillatory errors for finite element approximations to PDEs that contain hidden superconvergence points. To exploit this information, a Smoothness-Increasing Accuracy Conserving (SIAC) filter is used to create a superconvergence filtered solution. This is accomplished by convolving the DG approximation against a B-spline kernel. We then present theoretical error estimates in the negative-order norm for the local DG (LDG) and ultra-weak local DG (UWLDG) approximations to PDEs containing high order spatial derivatives. Numerical results will be shown to confirm the theoretical results.
• [03105] A discontinuous Galerkin method for the Camassa-Holm-Kadomtsev-Petviashvili type equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Qian Zhang (Harbin Institute of Technology, Shenzhen )
    • Yan Xu (University of Science and Technology of China)
    • Yue Liu (The University of Texas at Arlington)
  • Abstract : This paper develops a high-order discontinuous Galerkin (DG) method for the Camassa-Holm-Kadomtsev-Petviashvili (CH-KP) type equations on Cartesian meshes. The significant part of the simulation for the CH-KP type equations lies in the treatment for the integration operator $\partial^{-1}$. Our proposed DG method deals with it element by element, which is efficient and applicable for most solutions. Using the instinctive energy of the original PDE as a guiding principle, the DG scheme can be proved as an energy stable numerical scheme. In addition, the semi-discrete error estimates results for the nonlinear case are derived without any priori assumption. Several numerical experiments demonstrate the capability of our schemes for various types of solutions.

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

room : E710

• [04578] Conservative and robust methods for the Biot-Brinkman equations in vorticity form
  • Format : Talk at Waseda University
  • Author(s) :
    • Alberto Francisco Martin Huertas (Australian National University)
    • Ruben Caraballo-Diaz (Universidad del Bio-Bio)
    • Chansophea Wathanak In (Monash University)
    • Ricardo Ruiz-Baier (Monash University)
  • Abstract : In this talk we present a new formulation, a suitable finite element method, along with robust/mesh-independent preconditioners, for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. Apart from the well-posedness of the different formulations, and optimal error estimates, our mathematical analysis confirms robustness of the different methods presented in the case of large Lam\'e parameters and small permeability and storativity coefficients. A few representative numerical examples are presented to back up the analysis.
• [04697] A five-field mixed formulation for stationary magnetohydrodynamic flows in porous media
  • Format : Talk at Waseda University
  • Author(s) :
    • Jessika Camaño (Universidad Católica de la Santísima Concepción)
  • Abstract : We introduce a new mixed variational formulation for a stationary magnetohydrodynamic flows in porous media problem, whose governing equations are given by the steady Brinkman-Forchheimer equations coupled with the Maxwell equations. Unique solvability of the continuous and discrete systems has been proven. Stability, convergence, and optimal a priori error estimates for the associated Galerkin scheme are obtained. Numerical tests illustrate the theoretical results.
• [04964] Domain decomposition solvers for problems with strong interface perturbations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Miroslav Kuchta (Simula Research Laboratory)
  • Abstract : Operators formed by an elliptic part in the bulk domain and a parameter weighted interface perturbation arise in coupled multiphysics systems as solution operators or as part of their preconditioners. Such systems are often not amenable to off-the-shelf methods if robustness with respect to the coupling is to be retained. In this talk we develop robust and scalable solvers for interface-perturbed operators based on domain/subspace decomposition. We demonstrate performance of the algorithms for single and multiphysics problems such as the EMI and Darcy-Stokes equations.
• [04995] Numerical solution of the Biot/elasticity interface problem using virtual element methods
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nitesh Verma (Indian Institute of Technology Bombay)
    • Ricardo Ruiz Baier (Monash University)
    • David Mora (Universidad del Bio-Bio)
    • Sarvesh Kumar (Indian Institute of Space Science and Technology)
  • Abstract : We propose, analyse and implement a virtual element discretisation for an interfacial poroelasticity/elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure and total pressure, and the elasticity equations are written in the displacement-pressure formulation. The construction of the virtual element scheme does not require Lagrange multipliers to impose the transmission conditions (continuity of displacement and total traction, and no flux for the fluid) on the interface. We show the stability and convergence of the virtual element method for different polynomial degrees, and the error bounds are robust with respect to delicate model parameters (such as Lame constants, permeability, and storativity coefficient). Finally, we provide numerical examples that illustrate the properties of the scheme.

MS [02423] Non-standard finite element methods

room : E711

• [04214] A posteriori error estimation for a C1-virtual element method of Kirchhoff plates
  • Author(s) :
    • Jianguo Huang (Shanghai Jiao Tong University)
  • Abstract : A residual-type a posteriori error estimation is developed for a $C^1$-conforming virtual element method (VEM) to solve a Kirchhoff plate bending problem. As an outcome of the error estimator, an adaptive VEM is introduced using the mesh refinement strategy with the one-hanging-node rule. A series of numerical results are performed to verify the efficiency of the method. This is a joint work with Mingqing Chen and Sen Lin from Shanghai Jiao Tong University.
• [03654] Stabilization-Free Virtual Element Methods
  • Author(s) :
    • Xuehai Huang (Shanghai University of Finance and Economics)
  • Abstract : Stabilization-free virtual element methods (VEMs) in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM in arbitrary dimension and a conforming VEM in two dimensions. The key is to construct local $H(\div)$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these stabilization-free VEMs. Numerical experiments are provided to test the stabilization-free VEMs.
• [03806] Discontinuous Galerkin methods for magnetic advection-diffusion problems
  • Author(s) :
    • Jindong Wang (Peking University)
    • Shuonan Wu (Peking University)
  • Abstract : We devise and analyze a class of the primal discontinuous Galerkin methods for magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we find a new mechanism under the vector case that provides more flexibility in constructing the schemes. For the more general Friedrichs system, we show the stability and optimal error estimate, which boil down to two core ingredients -- the weight function and the special projection -- that contain information of advection. Numerical experiments are provided to verify the theoretical results.
• [03492] Some finite element divdiv complexes in three dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Rui Ma (Beijing Institute of Technology)
  • Abstract : This talk will present two families of finite element divdiv complexes on tetrahedral grids and one family on cuboid grids. They can be used to discretize the linearized Einstein-Bianchi system.

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

room : E802

• [02611] An efficient parallel interpolation algorithm with applications to multi-physics simulation of cardiac radiofrequency ablation
  • Format : Talk at Waseda University
  • Author(s) :
    • Massimiliano Leoni (Johann Radon Institute for Computational and Applied Mathematics)
    • Argyrios Petras (RICAM-Johann Radon Institute for Computational and Applied Mathematics)
    • Luca Gerardo-Giorda (JKU and RICAM)
  • Abstract : In this talk we discuss modelling and simulation of Cardiac Radiofrequency Ablation, a clinical procedure used to treat some forms of cardiac arrhythmia by accessing the patient's heart with a catheter and burning it locally to make it electrically insulating. By its nature, this problem requires a complex multi-physics approach, which in turn yields many computational challenges. In particular, we will focus on parallel interpolation, a trivial-looking step that is crucial to a performant implementation
• [04831] A nonlinear preconditioning strategy for solving phase-field fracture problems in a constrained minimization framework
  • Format : Talk at Waseda University
  • Author(s) :
    • Hardik Kothari (Università della Svizzera Italiana)
    • Alena Kopaničáková (Brown Universitty)
    • Rolf Krause (Università della Svizzera Italiana)
  • Abstract : The phase-field approach to fracture allows one to model crack propagation, branching, and merging. Despite its robust modeling properties, solving this problem is computationally challenging due to the non-convex, non-smooth, highly nonlinear, and ill-conditioned nature of the underlying energy function. We propose a field-split-based additive/multiplicative Schwarz preconditioned Newton method to solve the fracture problem by employing a right preconditioner that can handle inequality constraints. The robustness of the method will be shown using numerical examples.
• [04801] Multi-scale modelling and simulation: EMI models, 3D-1D transport, and DG methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Rami Masri (Simula Research Laboratory)
    • Marius Zeinhofer (Simula Research Laboratory)
    • Miroslav Kuchta (Simula Research Laboratory)
    • Marie Rognes (Simula Research Laboratory )
  • Abstract : In this presentation, we discuss several of our findings on a variety of multi-scale models and their discretizations. First for the EMI equations which are used to model excitable tissue, we formulate and analyse discontinuous Galerkin interior penalty formulations. The practical advantages of such an approach are that (i) it can be implemented in any finite element library without additional multimesh/mixed-dimensional features, and that (ii) black box multigrid solvers perform well. Second, we formulate coupled time dependent 3D-1D models of transport used to model a variety of phenomena. The modeling and the discretisation errors for finite element approximations are discussed.
• [04846] SCALABLE SOLVERS FOR BULK-SURFACE MATERIALS UNDERGOING SPINODAL DECOMPOSITION
  • Format : Talk at Waseda University
  • Author(s) :
    • stefano zampini (KAUST)
    • Luis Espath (University of Nottingham)
    • Luca Heltai (SISSA)
    • Hector Gomez (Purdue University)
  • Abstract : In this work, we present numerical results for two- and three-dimensional bulk-surface materials undergoing spinodal decomposition. The emphasis will be on the numerical implementation using the deal.II framework, and on the solution of the nonlinear equations using the PETSc library.

MS [00760] Improving Reproducibility, Trustworthiness and Fairness in Machine Learning

room : E803

• [02574] A tale of two crises: COVID-19 and ML reproducibility
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Thomas Roberts (University of Cambridge)
  • Abstract : Machine learning, like many fields before it, is suffering from a reproducibility crisis. In this talk we will give an overview of four different domains in which issues have been identified: (a) imaging, (b) missing data imputation, (c) learning at scale and (d) engineering of codebases. We also present solutions to problems identified.
• [02265] Leakage and the reproducibility crisis in ML-based science
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sayash Kapoor (Princeton University)
    • Arvind Narayanan (Princeton University)
  • Abstract : As quantitative fields adopt ML methods, it is important to ensure reproducibility. We show that data leakage is a widespread problem and has led to severe reproducibility failures. Through a literature survey of research in communities that adopted ML methods, we show that errors have been found in 17 fields, collectively affecting hundreds of papers and leading to wildly overoptimistic conclusions. We propose model info sheets to detect and prevent leakage in ML-based science.
• [02088] A critical look: overly optimistic results on the TPEHGDB dataset
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gilles Vandewiele (IDLab, Ghent)
  • Abstract : I will discuss the overly optimistic prediction results that arise when applying oversampling on data before partitioning into a train and test set. Specifically, I will present a case study on predicting preterm birth using the TPEHG database where many studies report near-perfect predictive performances due to making a fundamental mistake. After correcting this mistake, the predictive power of the models becomes similar to a coin toss.
• [01993] Classification of datasets with imputed missing values: does imputation quality matter?
  • Format : Talk at Waseda University
  • Author(s) :
    • Tolou Shadbahr (University of Helsinki)
    • Michael Thomas Roberts (University of Cambridge)
    • Jan Stanczuk (University of Cambridge)
    • Julian Gilbey (University of Cambridge)
    • Philip Teare (AstraZeneca)
    • Sören Dittmer (University of Cambridge)
    • MAtthew Thorpe (University of Manchester)
    • Ramon Vinas Torne (University of Cambridge)
    • Evis Sala (University of Cambridge)
    • Pietro Lio (University of Cambridge)
    • Mishal Patel (AstraZeneca)
    • James H.F. Rudd (University of Cambridge)
    • Tuomas Mirtti (university of Helsinki)
    • Antti Sakari Rannikko (universiity of Helsinki)
    • John Aston (University of Cambridge)
    • Jing Tang (University of Helsinki)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : Classifying samples in incomplete datasets is a common non-trivial task. Missing data is commonly observed in real-world datasets. Missing values are typically imputed, followed by classification of the now complete samples. Often, the focus is to optimize the downstream classification performance. In this talk, we highlight the serious consequences of using poorly imputed data, demonstrate how the common quality measures for measuring imputation quality are flawed, and introduce an improved class of imputation quality measures.

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

room : E804

• [03345] Approximation Theory for Sequence Modelling
  • Format : Talk at Waseda University
  • Author(s) :
    • Qianxiao Li (National University of Singapore)
  • Abstract : In this talk, we present some recent results on the approximation theory of deep learning architectures for sequence modelling. In particular, we formulate a basic mathematical framework, under which different popular architectures such as recurrent neural networks, dilated convolutional networks (e.g. WaveNet), encoder-decoder structures, and transformers can be rigorously compared. These analyses reveal some interesting connections between approximation, memory, sparsity and low rank phenomena that may guide the practical selection and design of these network architectures.
• [03154] Finite Expression Method: A Symbolic Approach for Scientific Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Haizhao Yang (University of Maryland College Park)
  • Abstract : Machine learning has revolutionized computational science and engineering with impressive breakthroughs, e.g., making the efficient solution of high-dimensional computational tasks feasible and advancing domain knowledge via scientific data mining. This leads to an emerging field called scientific machine learning. In this talk, we introduce a new method for a symbolic approach to solving scientific machine learning problems. This method seeks interpretable learning outcomes in the space of functions with finitely many analytic expressions and, hence, this methodology is named the finite expression method (FEX). It is proved in approximation theory that FEX can avoid the curse of dimensionality in discovering high-dimensional complex systems. As a proof of concept, a deep reinforcement learning method is proposed to implement FEX for learning the solution of high-dimensional PDEs and learning the governing equations of raw data.
• [01880] Discretization Invariant Operator Learning for Solving Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Zheng Ong (National University of Singapore)
  • Abstract : Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as inputs and/or outputs of a learning model. This talk presents a novel deep learning framework based on integral autoencoders, IAE-Net, for discretization invariant learning. Using IAE-Net, an adaptive training scheme is proposed with different loss functions to train the model. The proposed model is tested with various applications.
• [03159] Deep Adaptive Basis Galerkin Method for Evolution Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yiqi Gu (University of Electronic Science and Technology of China)
  • Abstract : We study deep neural networks (DNNs) for solving high-dimensional evolution equations. Unlike other existing methods (e.g., the least square method) that simultaneously deal with time and space variables, we propose a deep adaptive basis approximation structure. On the one hand, orthogonal polynomials are employed to form the temporal basis to achieve high accuracy in time. On the other hand, DNNs are employed to form the adaptive spatial basis for high dimensions in space.

MS [00389] Randomized methods for solving linear systems and eigenvalue problems

room : E811

• [03670] Making the Nystrom method highly accurate for low-rank approximations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jianlin Xia (Purdue University)
  • Abstract : The Nystrom method is a convenient method to quickly obtain a low-rank approximation to a kernel matrix with low or modest accuracies. In this work, we propose a type of Nystrom methods that can reach high accuracies. The methods (called high-accuracy Nystrom methods) treat the Nystrom method and a skinny rank-revealing factorization as a fast pivoting strategy in a progressive alternating direction refinement process. A rank expansion strategy based on fast subset updates is further proposed and can quickly advance the sizes of the basis matrices. A fast randomized accuracy control strategy is also given. Different versions of high-accuracy Nystrom methods are derived and can produce low-rank approximations with prespecified accuracies, sometimes with near SVD quality.
• [04016] Superfast iterative refinement of Low Rank Approximation of a Matrix
  • Format : Online Talk on Zoom
  • Author(s) :
    • Victor Pan (CUNY)
  • Abstract : Every superfast (aka sublinear cost) Low Rank Matrix Approximation (LRA) algorithm -- involving much fewer flops and memory cells than matrix has entries -- cannot work on ANY input, failing even with randomization, but our LRA algorithms are efficient or nearly optimal for MANY (large class of) inputs. Moreover, we propose, analyze, and test novel superfast algorithms for iterative refinement of any crude but sufficiently close LRA, according to both formal study and numerical tests.
• [00881] Relaxation in low-rank updates of Schur complement preconditioners in fluid flow problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Sabine Le Borne (Hamburg University of TechnologyHamburg University of Technology)
  • Abstract : In the simulation of fluid dynamic problems we often have to solve large-scale saddle-point systems. Low-rank updates can adapt standard preconditioners and accelerate convergence. We consider a low-rank correction for pressure Schur complement preconditioners and introduce a relaxation of the initial preconditioner which can improve the update scheme. Numerical results for the linearized Navier-Stokes equations illustrate the action of the update scheme.
• [00530] Randomized low-rank approximations beyond Gaussian random matrices
  • Format : Online Talk on Zoom
  • Author(s) :
    • Arvind Krishna Saibaba (North Carolina State University)
    • Agnieszka Miedlar (Virginia Tech)
  • Abstract : Randomized algorithms have been a revolutionary force in the field of low-rank approximations. A key step in these randomized algorithms is the randomized range finder which involves products with random matrices. The prevalent approach is to take the random matrix to be standard Gaussian which has favorable theoretical properties and is easy to implement in practice. Although several non-Gaussian random matrices have been used and analyzed, there are many open questions on what classes of random matrices are suitable for the randomized range finder. We analyze three different classes of random matrices: independent subgaussian entries, independent subgaussian columns, and independent bounded columns. These bounds provide a unified approach to studying various classes of random matrices and are supported by numerical experiments on test and real-world matrices.

MS [00211] Mathematics of Geometric Deep Learning

room : E812

• [05109] Geometric Deep Learning from a Topological Viewpoint
  • Author(s) :
    • Cristian Bodnar (Microsoft Research)
  • Abstract : The multitude of applications where data is attached to spaces with non-Euclidean structure has driven the rise of the field of Geometric Deep Learning (GDL). Nonetheless, from many points of view, geometry does not always provide the right level of abstraction to study all the spaces that commonly emerge in such settings. For instance, graphs, by far the most prevalent type of space in GDL, do not even have a geometrical structure in the strict sense. In this talk, I will explore how we can take a (more general) topological perspective of the field with a focus on understanding and developing Graph Neural Network models.
• [03727] FoSR: First-order spectral rewiring for addressing oversquashing in GNNs
  • Author(s) :
    • Guido Montufar (UCLA and MPI MiS)
  • Abstract : Graph neural networks (GNNs) are able to leverage the structure of graph data by passing messages along the edges of the graph. While this allows GNNs to learn features depending on the graph structure, for certain graph topologies it leads to inefficient information propagation and a problem known as oversquashing. This has recently been linked with the curvature and spectral gap of the graph. On the other hand, adding edges to the message-passing graph can lead to increasingly similar node representations and a problem known as oversmoothing. We propose a computationally efficient algorithm that prevents oversquashing by systematically adding edges to the graph based on spectral expansion. We combine this with a relational architecture, which lets the GNN preserve the original graph structure and provably prevents oversmoothing. We find experimentally that our algorithm outperforms existing graph rewiring methods in several graph classification tasks. This is work with Kedar Karhadkar and Pradeep Kr. Banerjee.
• [04482] DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs
  • Author(s) :
    • Mengjia Xu (Brown University & MIT)
    • Apoorva Vikram Singh (National Institute of Technology)
    • George Em Karniadakis (Brown University)
  • Abstract : Dynamic graph embedding has gained great attention due to its capability of learning low-dimensional graph embeddings for complex temporal graphs with high accuracy. However, recent advances mostly focus on learning node embeddings as deterministic ``vectors'' for static graphs, hence disregarding the key graph temporal dynamics and the evolving uncertainty associated with node embedding in the latent space. We propose an efficient stochastic dynamic graph embedding method (DynG2G) that applies an inductive feed-forward encoder trained with node triplet energy-based ranking loss. Every node per timestamp is encoded as a time-dependent probabilistic multivariate Gaussian distribution in the latent space. We adopted eight benchmarks of different sizes and evolving dynamics (from slowly changing dynamics to rapidly varying multi-rate dynamics). Our experiments indicate that DynG2G achieves new state-of-the-art performance in capturing the temporal node embeddings and simultaneously predicting the evolving node embedding uncertainty, which plays a crucial role in quantifying the intrinsic dimensionality of the dynamical system over time. We also obtain a “universal” relation of the optimal embedding dimension $L$ versus the effective dimensionality of uncertainty ($D$). The $L$ - $D$ correlation provides a clear path for selecting the optimum embedding size adaptively per timestamp by $L \ge D$.
• [05074] Applied harmonic analysis and particle dynamics for designing neural message passing on graphs
  • Author(s) :
    • Yuguang Wang (Shanghai Jiao Tong University)
  • Abstract : Graph representation learning has broad applications applications from recommendation systems to drug and protein designs. In this talk, I will talk about using harmonic analysis and particle systems to design useful neural message passing with theoretically guaranteed separability and efficient computation. These message passings are proved to have strictly positive lower bounded Dirichlet energy and thus to circumvent the oversmoothing problem appearing in many spatial GNNs, when the node features are indistinguishable as the network deepens.

MS [00774] Applications of machine learning to analyzing time-series and imaging data

room : E817 -> A715 (changed)

• [04949] Introduction to miniymposium session: Applications of machine learning to analyzing time-series and imaging data
  • Format : Talk at Waseda University
  • Author(s) :
    • Kevin Flores (NC State University)
  • Abstract : This talk is an introduction to the minisymposium session on "Applications of machine learning to analyzing time-series and imaging data".
• [05230] Reinforcement Learning in a Digital Twin Framework for the Stabilization of an Inverted Pendulum
  • Format : Talk at Waseda University
  • Author(s) :
    • Hien Tran (North Carolina State University)
  • Abstract : In this talk we benchmark common reinforcement learning algorithms on a modified version of OpenAI Gym's Cartpole: a virtual environment simulating the dynamics of an inverted pendulum. The reinforcement learning algorithms that we used to stabilize the virtual inverted pendulum included the Policy Gradient, Actor-Critic, and Proximal Policy Optimization. We then transferred the trained neural network models from the virtual environment to the real physical inverted pendulum to verify their performances. While all of the reinforcement learning algorithms were able to satisfactorily balance the real inverted pendulum, Actor-Critic is best able to adequately reject disturbances.
• [03788] Predicting Bladder Pressure and Contractions from Non-Invasive Time-Series Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Erica M Rutter (University of California, Merced)
  • Abstract : Symptoms of bladder dysfunction can be alleviated by electrical stimulation of nerves at the start of a contraction. However, determining when a bladder contraction will occur remains an active area of research. Due to the extremely dense time-series data, we employ statistical and machine learning methods to predict bladder pressure from external nerve data. These bladder pressures are used to predict the onset of bladder contractions with high sensitivity and specificity.
• [04294] Leveraging topological data analysis for parameter estimation of an agent-based model of collective motion
  • Format : Talk at Waseda University
  • Author(s) :
    • Kyle Nguyen (North Carolina State University)
    • Carter Jameson (North Carolina State University)
    • John Nardini (The College of New Jersey)
    • Kevin Flores (North Carolina State University)
  • Abstract : Understanding the social interaction between members of groups in the context of collective motion is significant to gain the insights on the link between local and global behaviors. By leveraging topological data analysis, we use dimensional reduction techniques on topological features to visually cluster different time series of collective motion simulations of an agent-based model into groups. We also propose inverse problem approaches for parameter estimation of this particular agent-based model of collective motion.

MS [00768] Recent Advances in Computational Tools of Scientific Machine Learning towards Digital Twins

room : E818

• [03527] Digital Twins and Machine Learning from an Inverse Problem Perspective
  • Author(s) :
    • Mark Asch (Université de Picardie Jules Verne)
  • Abstract : Digital Twins that are exchanging data with their real-world counterparts can be considered as instances of inverse problems—either of parameter identification type (static, or quasi-static), or of data assimilation type (dynamic). Many classical methods exist for solving inverse problems, but inverse problems remain complex, time-consuming and difficult to solve, especially with limited resources. However, machine learning can also be viewed as a parameter identification inverse problem, where for example in a neutral network we seek to identify the weights (parameters) of the network. Moreover, the machine learning community has developed extremely efficient frameworks and tools for solving their inverse problems, such as stochastic gradient, backpropagation, and others. In this talk I will review machine learning methods with respect to the solution of inverse problems and I will present some examples of Digital Twins that have been developed on this basis.
• [03528] Physics-guided data-driven simulations for a digital twin
  • Author(s) :
    • Youngsoo Choi (Lawrence Livermore National Laboratory)
  • Abstract : A computationally expensive physical simulation is a huge bottleneck for a digital twin. Fortunately, many data-driven approaches have emerged to accelerate those simulations, thanks to the recent advance in machine learning (ML) and artificial intelligence. For example, a well-trained 2D convolutional deep neural network can predict the solution of complex Richtmyer–Meshkov instability problem with a speed-up of 100,000x (1). However, the traditional black-box ML models do not incorporate existing governing equations, which embed underlying physics, such as conservation of mass, momentum, and energy. Therefore, the black-box ML models often violate important physics law, which greatly concerns physicists, and require big data to compensate the missing physics information. Additionally, it comes with other disadvantages, such as non-structure-preserving, computationally expensive training phase, non-interpretability, and vulnerability in extrapolation. To resolve these issues, we can bring physics into data-driven framework. Physics can be incorporated in different stages of data-driven modeling, i.e., sampling stage and model-building stage. Physics-informed greedy sampling procedure minimizes the number of required training data for a target accuracy (2). Physics-guided data-driven model better preserves physical structure and more robust in extrapolation than traditional black-box ML models. Numerical results, e.g., hydrodynamics (3,4), particle transport (5), plasma physics, and 3D printing, will be shown to demonstrate the performance of the data-driven approaches. The benefits of the data-driven approaches will also be illustrated in multi-query decision-making applications, such as design optimization (6,7). Reference: (1) Jekel, Charles F., Dane M. Sterbentz, Sylvie Aubry, Youngsoo Choi, Daniel A. White, and Jonathan L. Belof. "Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-meshkov Instabilities." arXiv preprint arXiv:2208.11477 (2022). (2) He, Xiaolong, Youngsoo Choi, William D. Fries, Jon Belof, and Jiun-Shyan Chen. "gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification." arXiv preprint arXiv:2204.12005 (2022). (3) Copeland, Dylan Matthew, Siu Wun Cheung, Kevin Huynh, and Youngsoo Choi. "Reduced order models for Lagrangianhydrodynamics." Computer Methods in Applied Mechanics and Engineering 388 (2022): 114259. (4) Kim, Youngkyu, Youngsoo Choi, David Widemann, and Tarek Zohdi. "A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder." Journal of Computational Physics 451 (2022): 110841. (5) Choi, Youngsoo, Peter Brown, William Arrighi, Robert Anderson, and Kevin Huynh. "Space–time reduced order model for large-scale linear dynamical systems with application to boltzmann transport problems." Journal of Computational Physics 424 (2021): 109845. (6) McBane, Sean, and Youngsoo Choi. "Component-wise reduced order model lattice-type structure design." Computer methods in applied mechanics and engineering 381 (2021): 113813. (7) Choi, Youngsoo, Gabriele Boncoraglio, Spenser Anderson, David Amsallem, and Charbel Farhat. "Gradient-based constrained optimization using a database of linear reduced-order models." Journal of Computational Physics 423 (2020): 109787.
• [03532] Attributing anomalies from black-box predictions
  • Author(s) :
    • Tsuyoshi Ide (IBM Research)
  • Abstract : One of the most important problems with digital twins is how to explain an unusual event observed as a significant discrepancy from the prediction of an AI model. Although this problem encompasses various different scenarios, we are particularly interested in the task of anomaly attribution in the black-box regression setting. The question is how we can quantify the contribution of each input variable in the face of an unexpected deviation between observation and prediction. In this talk, I will first review existing attribution approaches recently developed in the machine learning community, including linear surrogate modeling, Shapley values, and integrated gradient. After summarizing the challenges of these methods in the particular context of anomaly explanation, I will touch upon a newer notion of likelihood compensation as one of the major counterfactual-type explanations. If time permits, I will share some experimental results, including the one conducted for IBM IoT Business Unit.
• [03536] AI Based Medical Twin System: Investigation on Focused Ultrasound Therapeutics
  • Author(s) :
    • Kyungho Yoon (Yonsei University)
  • Abstract : In the huge paradigm shift of 4th industrial revolution driven by AI technique, the medical industry is also pursuing personalized precision medicine through digital transformation and smart transformation from analogue, standard, and empirical medical procedure. At the center of this change, IT technology is acting as key driving force. In particular, personalized digital twin model of human body and therapeutic tool will be the core engine of smart medicine. In this presentation, I will introduce research on the development of artificial intelligence-based medical twin systems for digital/smart therapeutics by convergence of computational science, medical engineering, and artificial intelligence technologies as the core technologies of the 4th medical revolution. In particular, investigation on the focused ultrasound device will be presented, which has recently been emerging as a non-invasive brain stimulation tool.

MS [00065] Recent Advances on Stochastic Hamiltonian Dynamical Systems

room : E819

• [04102] The Hamilton-Jacobi Theory for Stochastic Hamiltonian Systems on Jacobi Manifold
  • Format : Talk at Waseda University
  • Author(s) :
    • Pingyuan Wei (Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China)
    • Qiao Huang (Nanyang Technological University)
  • Abstract : In this talk, we generalize the systems of Hamiltonian diffusions, which were introduced and studied by Bismut, to accommodate arbitrary Jacobi manifolds as phase spaces and general continuous semimartingales as forcing noises. As is well-known, Jacobi structures are the natural generalization of Poisson structure and in particular of symplectic, cosymplectic and Lie-Poisson structures. However, very interesting manifolds like contact and locally conformal symplectic manifolds are also Jacobi but not Poisson. We are interested in the systems such that the phase flows preserve characteristic structures, and develop a Hamilton-Jacobi theory which is regarded as an alternative method for formulating the dynamics. A particular example is the case of thermodynamic dynamics in which we apply our methods on a manifold with its canonical contact form.
• [02876] Homogenization of Dissipative Hamiltonian Systems under L\'evy Fluctuations
  • Format : Talk at Waseda University
  • Author(s) :
    • Zibo Wang (Huazhong University of Science and Technology)
  • Abstract : We study the small mass limit for a class of Hamiltonian systems with multiplicative non-Gaussian L\'evy noise. The limiting equation has a discontinuous noise-induced drift term. First, we show that the momentum in the stochastic Hamiltonian system converges to zero when the kinetic energy has polynomial growth. Then we prove that the stochastic Hamiltonian system with classical kinetic energy converges to the limiting equation in probability with respect to Skorohod topology.
• [02877] The stochastic flocking model with far-field degenerate communication
  • Format : Talk at Waseda University
  • Author(s) :
    • Li Lv (Huazhong University of Science and Technology)
  • Abstract : We reconsider the stochastic kinetic Cucker-Smale model with multiplicative Brownian noise, in which we remove the positive lower bound assumption on the communication. First we prove the emergence of conditional flocking in strong sense. Then, we show that unconditional strong flocking occurs when communication weight decays slowly at the far field. These results imply uniform stability and mean-field limit. In particular, strong stability and mean-field limit in the expectation sense are established in one-dimensional case.
• [04106] The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei Wei (Shanghai Jiao Tong University )
    • Jianyu Hu (Nanyang Technological University)
  • Abstract : Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, we find that the action functional (or rate function) does not involve with the solution of the skeleton equation, which describes unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution-dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.

MS [00685] Mathematical modeling, simulation and optimization in stroke risk assessment

room : E820

• [03136] Hemodynamic modeling of directional shear risk metrics in the carotid artery
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Hundertmark (RPTU Kaiserslautern-Landau)
    • Kevin Richter (RPTU Kaiserslautern-Landau)
    • Tristan Probst (RPTU Kaiserslautern-Landau)
  • Abstract : We present a numerical evaluation of hemodynamic risk metrics and their multi-directional behavior in human stenosed carotid artery. In the FSI model considered, the elastic modulus is strain-dependent in agreement with laboratory compliance measurements. We investigate the multidirectional behavior of wall shear stress (WSS) based on specially constructed longitudinal tangent vectors using centerline projection approach. We present the utility of longitudinal WSS evaluation for the detection of opposing or transverse (injurious) WSS in slow flow.
• [03760] Physiological flow simulations for stroke assessement and importance of distensiblity
  • Format : Talk at Waseda University
  • Author(s) :
    • Kevin Richter (RPTU Landau)
  • Abstract : In the process of bringing hemodynamic simulations to the clinical forefront we present the creation of a database that can offer guidance in the assessement of stroke risks in the carotid bifurcation area. We established a working pipeline for creating CFD simulations for over 100 patient-specific geoemetries. The importance of realistic boundary conditions are highlighted. To incorporate realistic distensibility of the arterial wall, we compared simulations to in vivo experiments.
• [03568] Predicting Stroke Risk with Graph Neural Networks and CFD Simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Rohit Pochampalli (RPTU Kaiserslautern)
    • Nicolas R. Gauger (RPTU Kaiserslautern)
  • Abstract : We propose a novel approach for predicting stroke risk using graph neural networks (GNNs) and computational fluid dynamics (CFD) simulations. GNNs enable us to capture the complex, nonlinear relationships between the geometry of the blood vessel and features such as the distribution of shear stresses on the vessel walls, which are known to influence the development of atherosclerosis. Our approach provides new insights into the relationship between blood flow patterns and stroke risk, potentially enabling more personalized prevention and treatment strategies.
• [03834] Shape optimization in applications of blood flows under uncertainties
  • Format : Online Talk on Zoom
  • Author(s) :
    • Georgios Bletsos (Hamburg University of Technology (TUHH))
    • Michael Hinze (Universität Koblenz)
    • Winnifried Wollner (University of Hamburg)
    • Thomas Rung (Hamburg University of Technology (TUHH))
  • Abstract : The goal of this study is to minimize the expected value and standard deviation of blood damaging metrics of biomedical geometries, by updating their shape while considering uncertainties of the flow or the blood modeling. The robust shape optimization procedure is realized by means of a gradient-descent method. Gradient information is obtained by a hybrid stochastic-deterministic approach or by an adjoint-assisted method in which uncertainty quantification is realized based on the FOSM approach.

MS [02458] Progress and Challenges in Extreme Scale Computing and Big Data

room : D101

• [05569] Innovative Supercomputing in the Exascale Era by Integration of Simulation/Data/Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Kengo Nakajima (The University of Tokyo/RIKEN)
  • Abstract : We propose an innovative method of computational science for sustainable promotion of scientific discovery by supercomputers in the Exascale Era by integrating (Simulation/Data /Learning (S+D+L)), and develop a software platform “h3-Open-BDEC” for integration of (S+D+L) and evaluate the effects of the integration of on heterogenous supercomputer systems. The h3-Open-BDEC is designed for extracting the maximum performance of the supercomputers with minimum energy consumption. Related activities are described in the talk with future perspectives.
• [03388] Task-based hybrid parallel matrix factorization for distributed memory environment
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomohiro Suzuki (University of YamanashiUniversity)
  • Abstract : The task parallel approach provided by OpenMP has achieved great success in shared memory environments. In distributed memory environments, an interoperability issue exists between MPI and OpenMP. Several techniques have been proposed to address the issue. However, these proposed methods require a high level of thread support in MPI, so they can only work in limited environments. In this presentation, basic experimental results performed on the Wisteria-O system will be presented.
• [03651] Accelerating lattice Boltzmann method with GPU and C++ standard parallelization
  • Format : Talk at Waseda University
  • Author(s) :
    • Ziheng Yuan (The University of Tokyo)
    • Takashi Shimokawabe (The University of Tokyo)
  • Abstract : In recent years, with the increasing use of GPUs as accelerators in the HPC platform, using C++ standard parallel language as a GPU programming language has also attracted attention. Compared with traditional parallel programming languages, C++ standard parallel language for programming has advantages such as readability and maintainability of the code. This talk intends to introduce the application of C++ standard parallel language in fluid simulation using the lattice kinetic scheme (LKS), an extended lattice Boltzmann method (LBM), and discusses its performance.
• [05041] GPU-accelerated viscoelastic crustal deformation analysis with data-driven method
  • Format : Talk at Waseda University
  • Author(s) :
    • Sota Murakami (The University of Tokyoyo)
    • Kohei Fujita (The University of Tokyo)
    • Tsuyoshi Ichimura (The University of Tokyo)
    • Takane Hori (Japan Agency for Marine-Earth Science and Technology)
    • Muneo Hori (Japan Agency for Marine-Earth Science and Technology)
    • Maddegedara Lalith (The University of Tokyo)
    • Naonori Ueda (RIKEN)
  • Abstract : We developed a viscoelastic analysis solver with data-driven method on GPUs for fast computation of highly detailed 3D crustal structure models. Here, the initial solution is obtained with high accuracy using a data-driven predictor based on previous time-step results, which reduces the number of multi-grid solver iterations and thus reduces the computation cost. The algorithm is designed to be suitable for GPUs. The developed GPU-based solver attained 8.6-fold speedup from the state-of-art GPU-based multi-grid solver.

MS [00707] Theoretical and Numerical Challenges in the Modelling of Fluid Motion

room : D102

• [03903] Paradigm and Long-Time Evolution of Localized Solutions of Wave Systems: Consistency vs Integrability
  • Format : Talk at Waseda University
  • Author(s) :
    • Michail Todorov (Technical University of Sofia)
  • Abstract : Boussinesq’s equation was the first model for the propagation of surface waves over shallow inviscid fluid layer. He proved that the balance between the steepening effect of the nonlinearity and the flattening effect of the dispersion maintains the shape of the wave - so termed ‘Boussinesq Paradigm.’ Apart from the significance for the shallow water flows, this paradigm is very important for understanding the particle-like behavior of nonlinear localized waves. As it should have been expected, most of the physical systems are not fully integrable (even in one spatial dimension) and only a numerical approach can lead to unearthing the pertinent physical mechanisms of the interactions. A different approach to removing the incorrectness is by changing the spatial fourth derivative to a mixed fourth derivative, which resulted into an equation know nowadays as the Regularized Long Wave Equation or Benjamin–Bona–Mahony equation - known as the ‘Linear Impedance Relation’. The latter has produced innumerable instances of unphysical results.
• [05180] Modelling of tsunami generated by submarine volcanic eruptions in statified oceans.
  • Format : Talk at Waseda University
  • Author(s) :
    • Manish kanojia (Trinity College Dublin)
  • Abstract : We present a novel mathematical model for the generation of tsunamis by submarine volcanic eruptions in stratified oceans. Unlike current models, our model accounts for the complex stratification of the ocean, providing a more accurate representation of the tsunami generation process.
• [01814] Pressure distribution on seawalls due to wave effects
  • Format : Talk at Waseda University
  • Author(s) :
    • Paul Suman (Indian Institute of Engineering Science and Technology, Shibpur)
    • Aparna Dey Ghosh (Indian Institute of Engineering Science and Technology, Shibpur)
    • Biswajit Basu (Trnity College Dublin)
  • Abstract : A numerical approach to obtain wave forces on seawalls is proposed using Bernoulli’s equation. The nonlinear formulation computes horizontal and vertical velocities, and pressure distribution along the depth, without any restriction on wave height. Forces are obtained on the seawall for nonbreaking travelling waves. The wave force increases for waves of longer time periods. The existing guidelines are found to overestimate the wave forces as compared to the forces obtained from the proposed nonlinear formulation.
• [05211] Physics-informed neural network for computating steady periodic water waves
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lin Chen (Tongji University)
    • Ben Li (Tongji University)
    • Chenyi Luo (ETH Zurich)
  • Abstract : We investigate full-field recovery and computation of rotational flow under nonlinear periodic water waves using physics-informed neural networks (PINNs). Flow characteristics beneath water waves are of interest in various disciplines, e.g., for hydraulic loading analysis. In ocean or water tunnel tests, wave heights, flow velocity, and pressure data are often collected at specific points. It is not feasible to measure the flow with very high spatial resolution, particularly for water waves with a wavelength of over 100 m in practice. Therefore, we develop PINNs for flow recovery taking multiple types of measurement data into account and with the Euler equation governing rotational flow embedded. High-fidelity datasets are obtained using the numerical continuation method which is able to solve nonlinear waves with limiting wave height. Different PINN architectures are proposed and compared based on the numerically computed datasets. Influences of the wave height, vorticity, the volume of datasets, and hyperparameters are discussed in detail.

contributed talk: CT141

room : D401

[01046] Flow past a mounted wedge: The three fold structure

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @D401
• Type : Contributed Talk
• Abstract : This talk is concerned with the simulation of flow past a wedge mounted on a wall for channel Reynolds number $Re_c = 6873$ in accelerated flow medium. All three stages of vortex shedding for the accelerated flow, leading to the exceedingly intricate three-fold structure has been captured very accurately. Transition to turbulence have also been resolved which is indicated by the existence of coherent structures.
• Classification : 76D05, 76D17, 65M06
• Format : Talk at Waseda University
• Author(s) :
  • Jiten C Kalita (Indian Institute of Technology Guwahati)

[00344] Forced convection from an isothermal square cylinder in shear flow

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @D401
• Type : Contributed Talk
• Abstract : Forced convection from an uniformly heated square cylinder placed in linear shear flow of constant properties fluid is numerically investigated at Reynolds number, Re=100, shear rate, K=0.0-0.2 and Prandtl number, Pr=0.5. The two-dimensional mathematical equations of flow motion and energy are solved using a higher order compact (HOC) finite difference scheme on Cartesian grids. The effect of K is investigated on flow and thermal fields in terms of isotherm patterns, Nusselt number distributions etc. The resulting vortex shedding phenomena behind the cylinder is detected and thermal field is determined.
• Classification : 76D05
• Format : Online Talk on Zoom
• Author(s) :
  • Atendra Kumar (National Institute of Technology Srinagar, India)

[01490] RANS modelling of OWC device over the sloping seabed

• Session Time & Room : 2C (Aug.22, 13:20-15:00) @D401
• Type : Contributed Talk
• Abstract : The hydrodynamics of the oscillating water column device placed over the sloping seabed under the influence of irregular incident waves is studied. Reynolds-Averaged Navier-Stokes equations (RANS) with a modified k − w turbulence model was used and the air-water interface was tracked using a volume-of-fluid (VOF) approach. The results demonstrate that the amplitude of the inward and outward velocities via the orifice, free surface elevations, and flow characteristics are greater for higher significant wave heights.
• Classification : 76D05, 76D33, 76F25
• Format : Online Talk on Zoom
• Author(s) :
  • AMYA RANJAN RAY (Birla Institute of Technology and Science, Pilani – Hyderabad Campus)
  • SANTANU KOLEY (Birla Institute of Technology and Science - Pilani, Hyderabad Campus)

MS [00792] Recent Advances of Modeling and Computation of Moving Boundary Problems

room : D402

• [01873] Solving motions of an incompressible interface with bending in Navier-Stokes flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Yunchang Seol (Sungkyunkwan University)
    • Ming-Chih Lai (National Yang Ming Chiao Tung University, Taiwan)
    • Kian Chuan Ong (Fields Institute for Research in Mathematical Sciences)
    • Yongsam Kim (Chung-Ang University)
  • Abstract : We present two numerical approaches in the immersed boundary method for solving motions of an incompressible biological cell membrane, a vesicle structure sharing similar behaviors with red blood cells. In the original problem, the surface tension enforcing the interfacial incompressibility is unknown, so the fluid variables and the tension shall be found together via an iterative method which requires huge computational cost. To overcome this difficulty, we introduce a penalty idea and a projection approach.
• [01918] Convergence of boundary integral methods for interfacial Stokes and Darcy flow with surface tension
  • Format : Online Talk on Zoom
  • Author(s) :
    • David M Ambrose (Drexel University)
  • Abstract : We consider efficient numerical methods for interfacial fluid flow. For interfacial Darcy flow in three space dimensions and interfacial Stokes flow in two space dimensions, we demonstrate convergence of boundary integral methods. The problems are subject to the effect of surface tension and/or elastic membrane forces. The proofs rely on energy estimates. This will include joint work with Yang Liu, Michael Siegel, Svetlana Tlupova, and Keyang Zhang.
• [02287] A Cartesian Grid-Based Boundary Integral Method for Moving Interface Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Han Zhou (Shanghai Jiao Tong University)
    • Wenjun Ying (Shanghai Jiao Tong University)
  • Abstract : Moving interface problems are ubiquitous in natural sciences. Often the interface motion is coupled with PDEs in the bulk domain. This talk will present a Cartesian grid-based boundary integral method for solving moving interface problems. Layer potentials are evaluated by solving simple interface problems on a Cartesian grid to take advantage of fast solvers such as FFTs and the geometric multigrid method. Numerical simulations, including crystal growth and two-phase flows, will be reported.
• [02762] An explicit numerical method for the Cahn-Hilliard equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Junseok Kim (Korea University )
    • Soobin Kwak (Korea University)
  • Abstract : In this talk, I present an explicit conservative numerical method for the Cahn–Hilliard (CH) equation, which is a famous mathematical model for conservative phases. The CH equation has been applied in many important problems and a lot of computational methods were developed to numerically compute the CH equation. So far most of numerical methods were based on implicit numerical methods because of very stiff timestep restriction of the explicit scheme. To overcome this severe time-step restriction of the explicit scheme, we developed an explicit conservative numerical scheme. To demonstrate the superior performance of the proposed scheme, we present the computational experiments.

MS [02212] Modeling, Algorithms and Simulations for Flow and Transport in Porous Media

room : D403

• [03292] Stabilized enhancement for large time computation using exponential spectral process method
  • Author(s) :
    • Xiang Wang (Jilin University)
  • Abstract : We propose an exponential spectral process (ESP) method for time discretization of spatial-temporal equations. The proposed ESP method uses explicit iterations at each time step, which allows us to use simple initializations at each iteration. This method has the capacity to obtain high accuracy (up to machine precision) with reasonably large time step sizes. Theoretically, the ESP method has been shown to be unconditionally energy stable for arbitrary number of iteration steps for the case where two spectral points are used. To demonstrate the advantages of the ESP approach, we consider two applications that have stability difficulties in large-time simulations. ​One of them is the Allen-Cahn equation with the symmetry breaking problem that most existing time discretizations face, and the second one is about the complex Ginzburg-Landau equation, which also suffers from large-time instabilities.
• [03294] A pressure robust solver for Stokes flow based on a lifting operator
  • Author(s) :
    • Ruishu Wang (Jilin University)
  • Abstract : We presents novel finite element solvers for Stokes flow that are pressure-robust due to the use of a lifting operator. Weak Galerkin (WG) finite element schemes are developed for the Stokes problem on quadrilateral and hexahedral meshes. Local Arbogast-Correa or Arbogast-Tao spaces are utilized for construction of discrete weak gradients. The lifting operator lifts WG test functions into 𝐻(div)-subspaces and removes pressure dependence of velocity errors.
• [03331] Numerical Approaches and Analysis for The Generalized Maxwell-Stefan Equations
  • Author(s) :
    • Xiuping Wang (King Abdullah University of Science and Technology)
    • Shuyu Sun (King Abdullah University of Science and Technology)
  • Abstract : This talk presents an analysis of the thermodynamic properties of the generalized Maxwell-Stefan equations for the diffusion process in multi-component systems and proposes a corresponding numerical scheme. Detailed proofs show that the model satisfies Onsager's principle and the second law of thermodynamics. An energy-stable numerical scheme is established by a mixed finite element method and the backward Euler scheme.
• [03419] The Undrained Split Phase Field Method for Modeling Hydraulic Fracture Propagation
  • Author(s) :
    • Tameem Almani (Saudi Aramco)
  • Abstract : In this work, we present and analyze the undrained split iterative coupling scheme for coupling flow with geomechanics applied to the fracture propagation problem. In the undrained split scheme, the mechanics problem is solved first, followed by the flow problem, and the fluid content of the medium (i.e., porosity) is assumed to be constant during the mechanics solve. This sequential coupling approach was shown to be convergent in an earlier work, and has the advantage of being easier to integrate with legacy reservoir simulators compared to the standard fixed-stress split scheme. This is due to the fact that in the undrained split scheme, the regularization terms are added to the mechanics equation and not the flow equation. In this work, we will establish the convergence of this scheme when applied to the fracture prograpation problem using the phase field method. To the best of our knowledge, this is the first time in literature the undrained split scheme is applied to the fracture propagation problem using the phase field method, and the convergence of the combined scheme is established.

MS [00307] Advanced Solver for Computational Poromechanics

room : D404

• [01387] A coupled multi-field model of dynamic poro-elasticity in anisotropic porous media
  • Format : Talk at Waseda University
  • Author(s) :
    • Massimiliano Ferronato (University of Padova)
    • Nico De Marchi (University of Padova)
    • Giovanna Xotta (University of Padova)
    • Valentina Salomoni (University of Padova)
  • Abstract : A fully coupled multi–field model for the dynamic simulation of anisotropic porous materials is presented. The multi-field formulation of the dynamic poro-elastic PDEs is addressed by using inf-sup stable Finite Element spaces and solved in a fully-implicit way. The GMRES convergence of the discrete non-symmetric linearized systems is accelerated by an ad-hoc Multi-Physics Reduction preconditioning technique. A set of dynamic test problems verify the potential and computational efficiency of the proposed numerical model.
• [01468] Space-time finite element multigrid solver for fully dynamic poroelasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Markus Bause (Helmut Schmidt University Hamburg)
    • Mathias Anselmann (Helmut Schmidt University Hamburg)
  • Abstract : Space-time finite element methods ((STFEMs)) allow the natural construction of higher order discretizations and to achieve accurate results on computationally feasible grids. We present and analyze higher order STFEMs for two- and multi-field modelling of poroelastic wave propagation studied, for instance, in computational seismology or biomedicine. To solve the arising complex algebraic systems, geometric multigrid preconditioning with local Vanka-type smoother of GMRES iterations is suggested. The STFEMs performance is investigated for three-dimensional test problems.
• [01676] Multiscale Dynamics in Glioblastoma Growth and Spread within the Fibrous Brain Environment
  • Format : Talk at Waseda University
  • Author(s) :
    • Dumitru Trucu (University of Dundee, Division of Mathematics)
  • Abstract : Despite significant recent advancements, the 3D glioblastoma invasion patterns in the brain are still poorly understood. A particular role in the collective migration of the glioblastoma cells is played by the distribution of both major brain fibres and collagen fibres present at the tumour site. To address this aspect, in this talk we present our recent advances in this direction, focusing on our recent 3D multiscale moving-boundary modelling and computational framework development for glioblastoma invasion.
• [01820] Efficient splitting schemes for poromechanics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Florin Adrian Radu (University of Bergen)
  • Abstract : In this work we will present robust and efficient numerical schemes for poromechanics. Monolithic or splitting solvers will be discusssed. A special focus will be on non-linear poromechanics models, including soft material poromechanics. Splitting ideas will be combined with L-scheme and Anderson acceleratin to design robust and effective numerical schemes. Convergence aspects will be discussed both theoretically and numerically.

MS [00462] Mathematical and applicable studies on quantum walks

room : D405

• [01759] The Ihara expression of graph zeta functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Ayaka Ishikawa (Yokohama National University)
  • Abstract : Konno and Sato showed that the Grover walk corresponds to the Sato zeta function. They also gave the characteristic polynomial of the transition matrix of the Grover walk, using the Ihara expression of the Sato zeta function. We define the graph zeta function related to the Szegedy walk on a finite graph and give the Ihara expression. The Ihara expression will extend Konno-Sato's result to the Szegedy walk.
• [02778] Topological stability of quantum walks and related
  • Format : Talk at Waseda University
  • Author(s) :
    • Chris Bourne (Nagoya University)
  • Abstract : Quantum walks with additional symmetries may possess topologically protected bound states, meaning these bound states are robust against small perturbations and changes. I will give a gentle mathematical introduction to this phenomenon, which borrows ideas from so-called topological phases of matter. I will also explain how the existence of topological bound states can be detected using a winding number-like formula.
• [03296] Spectral mapping theorem for quantum walks on graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kei Saito (Kanagawa University)
  • Abstract : Quantum walks (QWs) are well known as a quantum version of random walks, and their time evolution is described by a unitary operator. Segawa, Suzuki(2019) show that the spectrum of the QW is given by that of a self-adjoint operator on the underlying graph. In this talk we reconsider such a spectral mapping theorem from a different perspective and present a relation between the spectrum of QWs and the weighted line matrix.
• [05096] The Segawa-Suzuki spectral mapping theorem, revisited
  • Format : Talk at Waseda University
  • Author(s) :
    • Yohei Tanaka (Gakushuin University)
  • Abstract : The Segawa-Suzuki spectral mapping theorem for chiral unitaries is particularly useful when studying spectral properties of chiral symmetric quantum walks. For example, it states that topologically protected bound states can be characterised by elements of the so-called birth and inherited eigenspaces. The purpose of this talk is to show that this characterisation has a yet another interpretation in terms of the real part of a chiral unitary.

MS [00134] Evolution Equations for Interacting Species: Applications and Analysis

room : D407

• [05128] Evolution Equations for Interacting Species: Applications and Analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jan-Frederik Pietschmann (University of Augsburg)
    • Markus Schmidtchen (Technische Universität Dresden)
    • Havva Yoldaş (Delft University of Technology)
  • Abstract : This talks provides an overview of the mini-symposium's topic of systems of PDEs arising in the context of interacting particles. Steric effects and interactions between members of opposite or the same species typically lead to systems of nonlocal and cross-diffusion type. The interplay of degenerate parabolicity and nonlocalities leads to a myriad of interesting emergent behaviours including pattern formation and phase separation. At the same time, these systems pose a variety of challenging analytical mathematical problems including the dramatic loss of regularity at the onset of phase separation. Thus, new analytical techniques and reliable numerical methods are needed.
• [05084] A Keller-Segel type approximation to a cell population dynamics model
  • Format : Talk at Waseda University
  • Author(s) :
    • Hideki Murakawa (Ryukoku University)
  • Abstract : We deal with a cell population dynamics model with nonlocal advection term. Approximating non-local advection as a local problem can be useful for analysis and numerical analysis of the problem. In this talk, we present a Keller-Segel type approximation to the cell population dynamics model. The approximation consists only of local terms. We discuss convergence of the approximation and introduce some applications. This is a joint work with Yoshitaro Tanaka.
• [04550] Convergence of position-based dynamics for first-order particle systems with volume exclusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Steffen Plunder (Kyoto University, ASHBi)
    • Sara Merino-Aceituno (University of Vienna)
  • Abstract : To simulate first-order particle systems with volume exclusion, we adapted the position based dynamics (PBD) method from computer graphics. PBD is a simple, fast and explicit time-stepping method which is unconditionally stable. Our contribution is the first convergence proof for PBD for first-order systems. Our proof uses the theory of differential inclusions on uniformly prox-regular sets and a new error estimate for alternating projections. We successfully applied the method in various applications in developmental biology.
• [04803] Graph-to-local limit for the nonlocal interaction equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Georg Heinze (University of Augsburg)
  • Abstract : In this talk I will discuss a proof of existence of solutions for the nonlocal interaction equation in Euclidean space using a graph-based nonlocal approximation. The graph equations are induced by an upwind interpolation, which leads to non-symmetric graph gradient structures that nevertheless converge to a symmetric Wasserstein-type local gradient structure. Furthermore, the flexibility of our graph model allows us to introduce a tensor to modify the geometry underlying the limiting model.

MS [00378] Mathematical Methods in System Reliability

room : D408

• [01347] Domination and multistate systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Arne Bang Huseby (University of Oslo)
  • Abstract : Domination functions has been studied extensively in the context of binary systems, where the structure function is a sum of products of the component states, and with coefficients given by the domination function. Using matroid theory, properties of the domination function can be derived. We generalise these results to multistate systems. The domination is determined by the poset generated by the minimal paths, and two systems with isomorphic posets also have the same domination function.
• [01419] Mathematical analysis of the reliability of stable systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Eduardo Sáenz-de-Cabezón (University of La Rioja)
  • Abstract : One of the main characteristics of coherent systems is redundancy. In this talk we define stability as a way to encode redundancy in a way that generalizes well known systems like k-out-of-n and variants. We furthermore provide a complete algebraic analysis of the reliability of these systems and design based on stability.
• [01422] Algebraic probability: the case of system reliability
  • Format : Online Talk on Zoom
  • Author(s) :
    • Henry Wynn (London School of Economics)
  • Abstract : Algebra arises in probability because of additivity over set disjointness and multiplication with independence. With systems such as those in causal analysis, data analysis and reliability we can have rich algebraic structures. In reliability, under coherence, failure patterns give rise to monomial ideals and from there Betti numbers and Hilbert series lead to efficient identities and bounds for failure probabilities. Structures such as mixed series-parallel systems and multi state systems have special features.
• [01425] Algebraic analysis of importance measures of coherent systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Patricia Pascual-Ortigosa (University of La Rioja)
    • Eduardo Sáenz-de-Cabezón (University of La rioja)
    • Rodrigo Iglesias (University of La Rioja)
  • Abstract : The aim of this talk is to do an analysis of importance measures of coherent systems using an algebraic approach. First of all, we introduce what importance measures are, providing a classification of them and some background for all of them. Then, we will show how Algebra can help us to study structural measures of importance of coherent systems. Finally, we present some examples explaining the advantages and disadvantages of this approach.

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

room : D501

• [02799] Real-time tool path planning using deep learning for subtractive manufacturing
  • Author(s) :
    • Yi-Fei Feng (University of Chinese Academy of Sciences)
    • Li-Yong Shen (University of Chinese Academy of Sciences)
    • Hong-YU Ma (University of Chinese Academy of Sciences)
    • Chun-Ming Yuan (Academy of Mathematics and Systems Sciences, CAS)
    • Xin Jiang (University of Chinese Academy of Sciences)
  • Abstract : Tool path planning is a crucial factor of computer-aided design and manufacturing. To generate suitable tool paths, the previous methods bases on traditional optimization often take to a long computational time. To achieve real-time planning, we propose an efficient neural network-based direct tool path generating method, and the whole process only takes a few microseconds. As an auxiliary result, a new tool path dataset with confined scallop height is first established for tool path training.
• [02796] NeuroPrim: An Attention-based Model for Solving NP-hard Spanning Tree Problems
  • Author(s) :
    • Yuchen Shi (University of Chinese Academy of Sciences)
    • Congying Han (University of Chinese Academy of Sciences)
    • Tiande Guo (University of Chinese Academy of Sciences)
  • Abstract : We define the Markov Decision Process (MDP) for general combinatorial optimization problems on graphs and propose NeuroPrim, a novel framework for reducing the action and state space using the technique of Prim algorithm, which is trained by REINFORCE to solve various spanning tree problems. We apply it to three difficult problems on Euclidean spaces, namely Degree-constrained Minimum Spanning Tree (DCMST) problem, Minimum Routing Cost Spanning Tree (MRCST) problem and Steiner Tree Problem in graphs (STP). Experimental results on literature instances show that our model is able to outperform strong heuristics and obtain small optimality gaps up to 250 vertices. In addition, we find no significant degradation on problem instances as large as 1000, which demonstrates our model has strong generalization ability.
• [02832] Streaming Algorithms for Maximizing the Difference of Submodular Functions
  • Author(s) :
    • Wenguo Yang
    • Cheng LU (UCAS)
    • Suixiang GAO (UCAS)
  • Abstract : In this paper, we study the problem of maximizing the Difference of two Submodular (DS) functions in the streaming model, where elements of the ground set arrive one at a time in an arbitrary order. We present one-pass streaming algorithms for both the unconstrained and cardinality-constrained problems. Our analysis shows that the algorithms we propose are able to pro�duce solutions with provable approximation guarantees. To the best of our knowledge, this is the first theoretical guarantee for the DS maximization problem in the streaming model.
• [03350] Recursive Importance Sketching for Rank Constrained Least Squares
  • Author(s) :
    • Xudong Li (Fudan University)
    • Yuetian Luo (University of Wisconsin-Madison)
    • Anru Zhang (Duke University)
    • Wen Huang (Xiamen University)
  • Abstract : In this talk, we propose a new Recursive Importance Sketching algorithm for rank constrained least squares optimization (RISRO). As its name suggests, the algorithm is based on a new sketching framework, recursive importance sketching. Several existing algorithms in the literature can be reinterpreted under the new sketching framework and RISRO offers clear advantages over them. RISRO is easy to implement and computationally efficient, where the core procedure in each iteration is only solving a dimension reduced least squares problem. Different from numerous existing algorithms with locally geometric convergence rate, we establish the local quadratic-linear and quadratic rate of convergence for RISRO under some mild conditions. In addition, we discover a deep connection of RISRO to Riemannian manifold optimization on fixed rank matrices. The effectiveness of RISRO is demonstrated in two applications in machine learning and statistics: low-rank matrix trace regression and phase retrieval. Simulation studies demonstrate the superior numerical performance of RISRO.

MS [00441] Intersection between financial economics and optimal control

room : D502

• [02868] Debt Maturity Management
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Ying (Chinese University of Hong Kong)
    • Yunzhi Hu (UNC)
    • Felipe Varas (Duke)
  • Abstract : This paper studies how a borrower issues long- and short-term debt in response to shocks to the enterprise value. Our theory highlights the tradeoff between commitment and hedging. Short-term debt protects creditors from future dilution and forces the borrower to reduce leverage after negative shocks. Long-term debt postpones default and allows the borrower time to recover after a downturn, thereby providing hedging in the upturn.
• [05611] Nonlinear Dependence and Households’ Portfolio Decisions over the Life Cycle
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wei Jiang (HKUST)
    • Shize Li (HKUST)
    • Jialu Shen (University of Missouri)
  • Abstract : This paper uncovers the nonlinear relationship between earning risk and stock returns, as measured by the between-squares correlation. By incorporating this between-squares correlation into a life-cycle model, we demonstrate that it lowers households’ participation rate and generates moderate risky asset holdings. We identify two pathways through which the between-squares correlation affects portfolio choices: the skewness and kurtosis channels. The extent to which these channels dominate each other depends on the level of between-squares correlation, leading to a nonlinear relationship between this variable and household decisions. Our empirical studies support the model’s predictions. Moreover, we find that ignoring between-squares correlations leads to substantial welfare loss and contributes to increasing wealth inequality.
• [04014] Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility
  • Format : Online Talk on Zoom
  • Author(s) :
    • Scott Robertson (Boston University)
    • Jerome Detemple (Boston University)
  • Abstract : In this talk, we establish the existence of equilibrium in the presence of both asymmetric information and general preferences for the uninformed agent. Specifically, there is an insider who possesses a private signal about the terminal value of the traded asset, and an uninformed agent who possesses no private signal. While the insider has CARA (exponential) preferences, the uninformed agent’s preferences are described by a general utility function defined for positive wealth. The terminal value of the traded asset is a function of a time homogeneous diffusion. In this setting, and under mild conditions on the diffusion, terminal payoff function, and uninformed preferences, we establish existence of a partially revealing equilibrium, where a market signal is communicated to all agents at time zero. Additionally, the equilibrium is a rational expectations equilibrium in the univariate case. As the uninformed agent preferences are general, we are able to obtain sensitivity of the asset price, volatility, and market price of risk, to the uninformed agent’s initial endowment, as we will show through examples. This is joint work with Jerome Detemple of Boston University.

MS [00715] Recent Trends in Market Design

room : D505

• [01516] Are Simple Mechanisms Optimal when Agents are Unsophisticated?
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiangtao Li (Singapore Management University)
    • Piotr Dworczak (Northwestern University)
  • Abstract : We study the design of mechanisms involving agents that have limited strategic sophistication. We define a mechanism to be simple if—given the assumed level of strategic sophistication—agents can determine their optimal strategy. We examine whether it is optimal for the mechanism designer who faces strategically unsophisticated agents to offer a simple mechanism. We show that when the designer uses a mechanism that is not simple, while she loses the ability to predict play, she may nevertheless be better off no matter how agents resolve their strategic confusion.
• [05446] Strategyproof Mechanisms for Group-Fair Facility Location Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Minming Li (City University of Hong Kong)
    • Houyu Zhou (City University of Hong Kong)
    • Hau Chan (University of Nebraska–Lincoln)
  • Abstract : We study the facility location problems where agents are located on a real line and divided into groups based on criteria such as ethnicity or age. Our aim is to design mechanisms to locate a facility to approximately minimize the costs of groups of agents to the facility fairly while eliciting the agents' locations truthfully. We first explore various well-motivated group fairness cost objectives for the problems and show that many natural objectives have an unbounded approximation ratio. We then consider minimizing the maximum total group cost and minimizing the average group cost objectives. For these objectives, we show that existing classical mechanisms (e.g., median) and new group-based mechanisms provide bounded approximation ratios, where the group-based mechanisms can achieve better ratios. We also provide lower bounds for both objectives. To measure fairness between groups and within each group, we study a new notion of intergroup and intragroup fairness (IIF) . We consider two IIF objectives and provide mechanisms with tight approximation ratios.
• [01738] Optimal allocation with costly verification and distributional constraint
  • Format : Talk at Waseda University
  • Author(s) :
    • Yunan Li (City University of Hong Kong)
  • Abstract : A planner allocates multiple slots $\text{(e.g., a spot in college)}$ among a finite number of agents, each of whom wants one slot and privately knows the value to the planner of assigning one slot to him. The slots are allocated based on the agents’ reports. The planner can choose to inspect an agent’s report at a cost. The constrained efficient mechanism for a planner facing a distributional constraint adds a constant to the values of the agents in the targeted group $\text{(a “flat subsidy”)}$ and specifies a threshold. The slots are first allocated to the agents whose $\text{(adjusted)}$ values are above the threshold. Any remaining slots are randomly allocated among the agents whose $\text{(adjusted)}$ values are below the threshold. For a stringent distributional constraint, the randomization favors the targeted group $\text{(a “quota”)}$.
• [01616] Optimal Dynamic Matching
  • Format : Talk at Waseda University
  • Author(s) :
    • Junpei Komiyama (New York University)
    • Akira Matsushita (The University of Tokyo)
    • Shunya Noda (The University of Tokyo)
  • Abstract : We propose a machine-learning method to construct an approximately optimal algorithm for a general class of dynamic matching problems. We apply our method to several problems and compare an algorithm generated by our method with simplistic ones, such as a greedy algorithm, to illustrate the importance of optimizing allocations in dynamic environments.

MS [00382] Stochastic control and stochastic analysis in finance and insurance

room : D514

• [02210] Lévy bandits under Poissonian decision times
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazutoshi Yamazaki (University of Queensland)
    • Jose Luis Perez (CIMAT)
  • Abstract : We consider a version of the continuous-time multi-armed bandit problem where decision opportunities arrive at Poisson arrival times, and study its Gittins index policy. When driven by spectrally one-sided Lévy processes, the Gittins index can be written explicitly in terms of the scale function, and is shown to converge to that in the classical Lévy bandit of Kaspi and Mandelbaum (1995).
• [02144] Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum
  • Format : Talk at Waseda University
  • Author(s) :
    • Xun LI (The Hong Kong Polytechnic University)
    • Xiang Yu (The Hong Kong Polytechnic University)
    • Zhang Qinyi (The Hong Kong Polytechnic University)
  • Abstract : This talk studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the non-negative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the realization utility with respect to consumption, allowing us to focus on an auxiliary HJB variational in- equality on the strength of concavification principle and dynamic programming arguments. By applying the dual transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in closed-form piecewisely and some thresholds of the wealth variable are obtained. The optimal consumption and investment control of the original problem can be derived analytically in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.
• [02873] On the Entropy martingale optimal transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuoqing Deng (The Hong Kong University of Science and Technology)
    • Erhan Bayraktar (University of Michigan)
    • Dominykas Norgilas (University of Michigan)
  • Abstract : We study the Entropy Martingale Optimal Transport of Doldi and Frittelli (Finance&Stochastics, 2023). Compared with classical MOT, marginal constraints and linear pricing rules are respectively replaced by penalisation on deviations from the reference measures and utility-induced nonlinear rules. Inspired by techniques from classical MOT, we prove the duality with different arguments and weaker conditions. In particular, combining minimax arguments and the optional decomposition theorem, we generalise their duality without continuity requirement for the dynamic strategy.
• [02785] Functional convex order for the McKean-Vlasov equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yating Liu (Paris Dauphine University)
    • Gilles Pagès (Sorbonne University)
  • Abstract : We introduce the functional convex order for two McKean-Vlasov processes X and Y with respective marginal distributions $(\mu_t)_{t\in[0, T]}$ and $(\nu_t)_{t\in[0, T]}$. For a convex functional $G$ defined on the product space involving the path space and its marginal distribution space, we obtain $\mathbb{E}\,G(X, (\mu_t)_{t\in[0, T]}) \leq \mathbb{E}\,G(Y, (\nu_t)_{t\in[0, T]})$ under appropriate conditions. This presentation also includes two applications of the convex order result to mean-field control and mean-field games.

MS [00989] Structure and dynamics in complex biological systems

room : D515

• [01956] Controlling cell fate specification system based on network structure
  • Format : Talk at Waseda University
  • Author(s) :
    • Atsushi Mochizuki (Institute for Life and Medical Sciences, Kyoto University)
    • Kenji Kobayashi (Department of Zoology, Graduate School of Science, Kyoto University)
    • Kazuki Maeda (Faculty of Informatics, The University of Fukuchiyama)
    • Miki Tokuoka (Department of Zoology, Graduate School of Science, Kyoto University)
    • Yutaka Satou (Department of Zoology, Graduate School of Science, Kyoto University)
  • Abstract : Modern biology provided large networks describing regulatory interactions between biomolecules. We developed Linkage Logic theory, which ensures observability and controllability of any long-term dynamics of the whole system by a subset of nodes, that is identified from the network alone as a feedback vertex set (FVS). We applied the theory to gene network for cell-fate specification in ascidian, including 92 genes. By manipulating 6 genes in FVS, all the seven tissues could be induced experimentally.
• [01938] An extension of the Fiedler-Mochizuki theory to time-delay systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Atsushi Kondo (Department of Mathematics, Kyoto University)
  • Abstract : We consider the dynamics of a system of differential equations called a Regulatory Network, which represents complex regulatory relationships such as gene regulatory networks. The paper by Fiedler-Mochizuki et al. (JDDE 2013) showed that it is possible to identify a set of determining nodes that determines the asymptotic dynamics of the Regulatory Network from its network structure alone. We extend this theory to the case where the regulatory network contains time delays.
• [01727] Structure-based and dynamics-based control of biological network models
  • Format : Talk at Waseda University
  • Author(s) :
    • Jorge Gomez Tejeda Zanudo (Harvard Medical School)
    • Reka Albert (Pennsylvania State University)
    • Eli Newby (Pennsylvania State University)
  • Abstract : A task of interest when analyzing mathematical models of intracellular networks is to identify nodes that can provide attractor control in these systems. I will introduce stable motif control and feedback vertex set (FVS) control, two methods we have used to provide control strategies in multiple systems. I will discuss how we used FVS control and structure-based metrics based on signal propagation to identify high-ranking manipulations involving only 1-3 nodes that can provide attractor control.
• [01991] Universal structural requirements for maximal robust perfect-adaptation in biomolecular networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Ankit Gupta (ETH Zürich)
    • Mustafa Khammash (ETH Zürich)
  • Abstract : Living systems survive in unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. This property is called robust perfect adaptation (RPA) and the aim of this talk is to mathematically characterize the structural requirements for biomolecular networks to attain a form of maximal RPA, whereby the network is simultaneously robust to the largest set of disturbances. These results provide a new Internal Model Principle for biomolecular RPA networks.

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

room : A201

• [04488] Integrable equations and Riemann-Hilbert problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Wen-Xiu Ma (University of South Florida)
  • Abstract : This talk covers the zero curvature formulation and the Riemann-Hilbert technique. Nonlocal integrable equations are derived from conducting group reductions. The associated matrix spectral problems are used to build a kind of Riemann-Hilbert problems, whose reflectionless cases generate soliton solutions.
• [04064] A study of 3D generalized nonlinear wave equation in fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Chaudry Masood Khalique (North-West University, South Africa)
  • Abstract : In this talk we study a (3+1)-dimensional generalized nonlinear wave equation of fluids. Using Lie symmetry methods, we transform the underlying equation into a nonlinear ordinary differential equation. We deduce periodic, trigonometric bright soliton together with singular soliton solutions. Moreover, some soliton solutions are secured via the simplest equation method in the form of Jacobi elliptic functions. The dynamics of the solutions are depicted using suitable graphs. Furthermore, we construct conservation laws of the equation by employing Ibragimov's theorem.
• [04126] Burgers' nth Partial Differential Equation Hierarchy
  • Format : Talk at Waseda University
  • Author(s) :
    • Sameerah Jamal (University of the Witwatersrand )
  • Abstract : We present some recent advances of the applications of one-parameter Lie group transformations of famous partial differential equations. In particular, we discuss the Burgers' equation, which are often the benchmarks in the study of differential equations. We exploit the link between the equation and a recursion operator and show how the full hierarchy may be solved.
• [03471] Nonclassical Potential Symmetries for the transient heat transfer equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Mpho Nkwanazana (Sefako Makgatho Health Science Universitye)
    • Raseelo Moitsheki (University of the Witwatersrand)
  • Abstract : In this article we consider the one dimensional transient heat conduction equation. The diffusivity term and internal heat generator are given by the power law. The objective is to employ nonclassical and nonlocal approach to generate nonclassical potential symmetries.

MS [01099] Physics-based and data-driven modeling for digital twins

room : A206

• [03242] Towards smart city digital twins
  • Format : Talk at Waseda University
  • Author(s) :
    • Francisco Chinesta (ENSAM)
    • Daniele Di Lorenzo (ESI)
    • Victor Champaney (ENSAM)
    • Angelo Pasquale (ENSAM)
    • Amine Ammar (ENSAM)
    • Elias Cueto (I3A)
    • Dominique Baillargeat (CNRS@CREATE)
  • Abstract : Smart cities are composed of a number of coupled complex system of systems. Modelling them needs enhancing the traditional physics-based modelling approaches as well as speeding-up the predictions. Artificial intelligence and data-driven models obtained by using physics-informed and physics-augmented learning represents a valuable approach where accuracy and rapidity met. In this presentation advanced methodologies will be used for addressing complex scenarios, enabling real-time diagnosis and prognosis.
• [05203] Digital twins for green carbon processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Benner (MPI for Dynamics of Complex Technical Systems, Magdeburg)
    • Ion Victor Gosea (Max Planck Institute for Dynamics of Complex Technical Systems)
  • Abstract : Recent advances in scientific computing have made digital twins (DTs) increasingly popular in various fields, including process engineering (ProcEng). DTs have the potential to transform ProcEng by enabling real-time monitoring or process optimization. However, their full potential in this area has yet to be realized. We provide an overview of computational tools required for developing DTs in ProcEng. It characterizes models used to develop DTs and discusses the challenges and requirements associated with their implementation. We particularly focus on the development of sustainable chemical production processes in the context of a green carbon society.
• [01503] Hierarchical modeling of electrical machines in the context of digital twins
  • Format : Talk at Waseda University
  • Author(s) :
    • Karim Cherifi (TU Berlin)
    • Volker Mehrmann (TU Berlin)
    • Philipp Schulze (TU Berlin)
  • Abstract : Digital twins of electrical machines require mathematical models that are accurate enough for the design and fast enough to be used for condition monitoring. This leads to a hierarchy of models that are used within the digital twin. These models must in addition incorporate the physical coupling between electrical, mechanical, and thermal phenomena for more accurate computations. In this talk, we present how one can construct this model hierarchy by incorporating physics-based and data-driven modeling.
• [04060] From physics to machine learning and back: Applications to fault diagnostics and prognostics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Olga Fink (EPFL)
  • Abstract : Deep learning requires representative data, but condition monitoring data for complex systems lack labels and representativeness. Integrating physics can help to overcome this. The talk will give some insights into various techniques that combine physics-based and deep learning algorithms, as well as incorporate structural inductive bias for fault diagnostics and prognostics. The focus will be in particular on calibration-based hybrid approaches, physics-enhanced graph neural networks and on transformer-based architectures combined with transfer learning.

MS [00616] Continuous optimization: theoretical and algorithmic trends

room : A207

• [03586] Adaptive Third-Order Methods for Composite Convex Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Geovani Grapiglia (UCLouvain)
    • Yurii Nesterov (UCLouvain)
  • Abstract : In this talk we present adaptive third-order methods for composite convex optimization problems in which the smooth part has Lipschitz continuous third-order derivatives. In our new schemes the regularization parameters are tunned by checking the progress of the inner solver used to compute trial points. In particular, this technique allows us to design an adaptive accelerated method that can find an $\epsilon$-approximate solution using at most $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-\frac{1}{4}}\right)$ iterations of the inner solver.
• [03706] On the globalization of nonlinear programming methods.
  • Format : Talk at Waseda University
  • Author(s) :
    • L. Felipe Bueno (Universidade Federal de São Paulo)
  • Abstract : In this work we identify some very general conditions that guarantee the global convergence of numerical methods to solve constrained nonlinear optimization problems. With that in mind, we show that a range of Inexact Restoration methods fit the presented framework. Furthermore, we propose a particular algorithm in this line, combined with an acceleration process supported by the general theory of convergence. Computational tests attest to the efficiency of the proposed strategy.
• [04137] Proportionality based algorithms for quadratic programming
  • Format : Talk at Waseda University
  • Author(s) :
    • Gerardo Toraldo (Università della Campania "L.Vanvitelli")
    • William W. Hager (University of Florida)
    • Marco Viola (University College Dublin)
  • Abstract : We present a decomposition of the negative gradient on the tangent cone at a feasible point for optimization problems with polyhedral constraints. This decomposition, based on the idea of proportioning, extends the definition of the free and chopped gradient in bound constrained optimization. Such decomposition allows us to generalize the definition of binding variables and to measure complementary aspects of stationarity that can be exploited to design effective switching rules in Gradient Projection two-phase algorithms.

CSIAM

room : A208 -> D604 (changed)

[EM001] Current State and outlook of applied math in China

• Session Date & Time : 2C (Aug.22, 13:20-15:00) @A208
• Type : Talk in Embedded Meeting
• Abstract : Firstly, I will introduce CSIAM: who we are and what we do. Then I will introduce the current state of applied math in China. I will introduce national policies and opportunities for researcher in China. I will share some of my thinking about the outlook of applied math research as well as practical applications.
• Format : Talk at Waseda University
• Author(s) :
  • Pingwen Zhang (Wuhan University)

[EM002] Fluid dynamical system, numerical analysis and its applications in AMSS, CAS

• Session Date & Time : 2C (Aug.22, 13:20-15:00) @A208
• Type : Talk in Embedded Meeting
• Abstract : In this talk, I will briefly introduce recent progress on the fluid dynamical system, numerical analysis and its applications in Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
• Format : Talk at Waseda University
• Author(s) :
  • Feimin Huang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

[EM003] Efficient and Trustworthy AI and its Applications to 5G networks

• Session Date & Time : 2C (Aug.22, 13:20-15:00) @A208
• Type : Talk in Embedded Meeting
• Abstract : As the main workhorse of artificial intelligence, deep neural networks (DNN) have led to spectacular successes in voice/face recognition applications among other things. However, training a good neural network that can generalize well and is robust to data perturbation is quite challenging. This talk will discuss efficient and trustworthy DNN training methods and their applications in 5G networks. In particular, three fundamental research topics will be discussed: theoretical analysis of the most popular DNN training algorithm called ADAM; efficient distributed DNN training algorithms; and understanding why DNNs are fragile and how to obtain robustness. Applications of DNN in modeling and optimization of the performance of 5G networks will be presented. Potential application of other AI techniques such as reinforcement learning to future communication networks will also be discussed.
• Format : Talk at Waseda University
• Author(s) :
  • Zhi-Quan Luo (Shenzhen Research Institute of Big Data/The Chinese University of Hong Kong, Shenzhen)

[EM004] Efficient estimation and computation of parameters and nonparametric functions for semi/non-parametric models

• Session Date & Time : 2C (Aug.22, 13:20-15:00) @A208
• Type : Talk in Embedded Meeting
• Abstract : The efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature. However, efficient estimation of nonparametric functions are still not clear. We study efficient estimators for both parameters and nonparametric functions with distribution known and unknown, including non-parametric models for sparse functional data, and generalized semi-parametric models, which cover commonly used semiparametric models such as partially linear models, partially linear single index models, and two-sample semiparametric models. We propose a (quasi)-likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions. The proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient. Efficient computational algorithms to achieve the maximization are proposed. Extensive simulation experiments show the superiority of the proposed methods. Real data examples are analyzed and presented as an illustration.
• Format : Talk at Waseda University
• Author(s) :
  • Huazhen Lin (Southwestern University of Finance and Economics)

MS [00815] Recent trends in continuous optimization

room : A502

• [04582] Sharp convex exact penalty formulations in statistical signal recovery
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Liheng Wang (Purdue University)
    • Lijun Ding (University of Wisconsin Madison)
  • Abstract : This talk presents a sample complexity vs. conditioning tradeoff in signal recovery problems including sparse recovery, low-rank matrix sensing, and phase retrieval. We introduce condition numbers related to the "sharpness" of these problems and show that they can be used to control the accuracy of the recovery procedure in the presence of noise and the convergence rates of a new first-order method. These condition numbers approach constants a small factor above the statistical thresholds.
• [02314] Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Ching-pei Lee (Institute of Statistical Mathematics)
    • Ling Liang (National University of Singapore)
    • Tianyun Tang (National University of Singapore)
    • Kim-Chuan Toh (National University of Singapore)
  • Abstract : This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth Burer-Monteiro (BM) decomposition, while effectively escapes saddle points and spurious local minima ubiquitous in the BM form to obtain guarantees of fast convergence rates to the global optima of the original nuclear-norm-regularized problem through aperiodic inexact proximal gradient steps on it. The proposed approach adaptively adjusts the rank for the BM decomposition and can provably identify an optimal rank for the BM decomposition problem automatically in the course of optimization through tools of manifold identification. BM-Global hence also spends significantly less time on parameter tuning than existing matrix-factorization methods, which require an exhaustive search for finding this optimal rank. Extensive experiments on real-world large-scale problems of recommendation systems, regularized kernel estimation, and molecular conformation confirm that BM-Global can indeed effectively escapes spurious local minima at which existing BM approaches are stuck, and is a magnitude faster than state-of-the-art algorithms for low-rank matrix optimization problems involving a nuclear-norm regularizer.
• [05168] The Goemans and Williamson Algorithm Extended to Fractional Cut Covering
  • Format : Talk at Waseda University
  • Author(s) :
    • Nathan Benedetto Proença (University of Waterloo)
    • Marcel K. de Carli Silva (University of São Paulo)
    • Cristiane Sato (Federal University of ABC Region)
    • Levent Tunçel (University of Waterloo)
  • Abstract : The fractional cut-covering number is the optimal value of a linear programming relaxation for the problem of covering each edge by a set of cuts. By exploiting the relationship of this problem with the maximum cut problem, we obtain a primal-dual extension to the celebrated work of Goemans and Williamson, including an approximation algorithm and new optimality certificates.
• [01270] Solving graph equipartition SDPs on an algebraic variety
  • Format : Talk at Waseda University
  • Author(s) :
    • Tianyun Tang (National University of Singapore)
    • Kim-Chuan Toh (National University of Singapore)
  • Abstract : In this talk, we focus on using the Burer-Monteiro method to solve the graph equipartition SDP. The constraints of the low rank SDP problem is an algebraic variety with conducive geometric properties which we analyse. This allows us to develop an algorithm based on Riemannian optimization that can escape from a non-optimal singular point. Numerical experiments are conducted to verify the efficiency of our algorithm.

MS [00217] Integration of modeling and data analysis on molecular, cellular, and population dynamics in the life sciences

room : A511

• [01180] Mathematical Models of Plasmid Loss
  • Author(s) :
    • Kresimir Josic (University of Houston)
    • Jayson Cortez (University of Philippines at Los Banos)
    • Amanda Alexander (University of Houston)
    • Charilaos Giannitsis (Rice University)
    • Oleg Igoshin (Rice University)
  • Abstract : Plasmids, extrachromosomal DNA elements, are found in most bacteria and confer benefits to their hosts. Most models suggest that plasmids are lost in barring strong selection. The ubiquity of plasmids thus presents a paradox. We developed a mathematical model of ColE1 plasmid copy number based on experimental findings. This allows us to relate the probability of plasmid loss to properties of the population and provide testable predictions about conditions under which plasmids are lost.
• [00813] Morphology of organoids using a multicellular phase-field model
  • Author(s) :
    • Sakurako Tanida (The University of Tokyo)
    • Kana Fuji (The University of Tokyo)
    • Tetsuya Hiraiwa (The University of Tokyo, National University of Singapore)
    • Makiko Nonomura (Nihon University)
    • Masaki Sano (The University of Tokyo, Shanghai Jiaotong University)
  • Abstract : Organoids are self-organizing cells grown from stem cells in vitro. The organoid morphology is affected not only by genes but also by mechanical constrained due to the geometrical requirements to maintain the cell cluster. In this study, using a multicellular phase-field model, we examined the morphology when changing luminal fluid pressure and the minimum time of the cell cycle. Classifying the patterns by several indices, we discuss the mechanisms which generate the different patterns.
• [00720] Mind the gap:The extra-embryonic space is crucial geometric constraints regulating cell arrangement.
  • Author(s) :
    • Sungrim Seirin-Lee (Kyoto University)
    • Kazunori Yamamoto (Kanagawa Institute of Technology)
    • Akatsuki Kimura (National Institute of Genetics)
  • Abstract : Imagine sitting at a meeting where the shape of the table and your place at it might impact how you get along with the other members. In multicellular systems, cells also communicate with adjacent cells to decide their positions and fates. Cellular arrangement in space is thus important for development. Orientation of cell division, cell-cell interaction, and geometric constraints are the three major factors that define cell arrangement. In particular, the details of geometric constraints are difficult to be revealed only in experiments and the contribution of local contour has been remained elusive. Here we developed a multicellular morphology model based on the phase-field method so that we can incorporate precise geometric constrains. We applied the model to examine cell arrangement in the 4-cell stage embryo of nematodes, and succeeded in reproducing cell arrangements observed in vivo, including an arrangement which has not been explained before. Our cell morphology model predicted that the amount of extra-embryonic space (ES), the empty space within the eggshell not occupied by embryonic cells, affects cell arrangement in a manner dependent on the local contour and the aspect ratio of the eggshell as well as the strength of cell adhesion. The prediction was validated experimentally as increasing the (ES) did change the cell arrangement in the Cenorhabditis elegans embryo. Overall, our analyses characterized the roles of new geometrical contributors, namely the amount of (ES) and the local contour, to cell arrangements. These factors should be considered in all multicellular systems, including human being. Reference S. Seirin-Lee*, K. Yamamoto, A. Kimura, The extra-embryonic space and the local contour are critical geometric constraints regulating cell arrangement (2022) Development. 149, dev200401.
• [03207] Test three different models for the Chlamydia developmental cycle with intrinsic noise
  • Author(s) :
    • Jinsu Kim (POSTECH)
  • Abstract : Chlamydia is an intracellular bacterium that reproduces via an unusual developmental cycle such as late RB-EB conversion and heterogeneity of individual Chlamydia size. A key step is a conversion from a replicating form (RB) to an infectious form (EB), which occurs in a delayed and asynchronous manner. The regulatory mechanisms that control this developmental switch are unknown, but could potentially include extrinsic signals from the host cell or from other chlamydiae, or an intrinsic signal such as chlamydial cell size. In this presentation, we introduce three stochastic models, each based on a different regulatory mechanism. To test the models, we use the intrinsic noise of each model that can be estimated with statistical quantities measured experimentally. We found that all three models successfully reproduced the observed timing of RB-to-EB conversion and the growth curves of the developmental forms within an inclusion. However, only one model, based on the regulation of RB-to-EB conversion by RB size, was able to produce the positive correlation between the number of RBs and EBs and the monotonic time evolution of the coefficient of variation in the RB population.

MS [00643] Stochastic modeling in cell biology

room : A512

• [05399] Stochastic models of DNA methylation, plasticity and drug resistance
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jasmine Foo (University of Minnesota)
  • Abstract : In this talk I will discuss some recent work on modeling stochastic intracellular DNA methylation processes and examine their consequences on population dynamics within a growing tumor.
• [04460] Stochastic modeling of ovarian aging
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sean Lawley (University of Utah)
  • Abstract : Why are women born with up to a million primordial follicles when only a few hundred will ever ovulate a mature egg? What physiological mechanisms trigger menopause? Can the age of natural menopause be predicted? Can menopause be delayed? In this talk, we will describe recent stochastic models of ovarian aging which are aimed at answering these questions.

MS [00309] Population Dynamics in Biology and Medicine

room : A601

• [04328] Population Dynamics in Biology and Medicine
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunmi Lee (Kyung Hee University )
    • Hyo Sun Lee (Kyung Hee University )
  • Abstract : The rapid spread of COVID-19 worldwide has highlighted the importance of non-pharmaceutical interventions. Policies that limit gatherings and enforce social distancing help to mitigate the spread of the disease, but also negatively impact the economy. Consequently, policymakers face the dilemma of whether to slow the outbreak by imposing strict rules or reduce the economic burden. This paper presents a novel framework for designing intervention policies based on deep reinforcement learning.
• [01337] A mathematical model to melanoma growth with macrophages and immunotherapy
  • Format : Talk at Waseda University
  • Author(s) :
    • Paulo F. A. Mancera (UNESP)
    • Jairo G Silva (IFMT)
    • Mostafa Adimy (Inria and UCBL 1, Lyon France)
    • Guilherme Rodrigues (UNESP)
  • Abstract : We present a new mathematical model based on ODE to describe the dynamics of melanoma under an immunotherapeutic treatment. The novelty of the proposed model is the inclusion of the tumor-associated macrophage (TAM) population, enabling the in silico analysis of its influence on the failure of this immunotherapy.
• [02941] A Mathematical Perspective on Resilience and Sustainability in Climate and Biodiversity
  • Format : Talk at Waseda University
  • Author(s) :
    • Michel DE LARA (CERMICS - Ecole des Ponts ParisTech)
  • Abstract : In this talk, I will * scan through the IPCC (climate) and IPBES (biodiversity) international bodies reports, * address theoretical aspects: how can we formalize sustainability and resilience with tools from control theory (including viability) and decision under uncertainty? * present methods: how can we tackle problem solving, once mathematically formalized? * outline examples: biodiversity (fisheries, epidemiology), energy and climate, * raise open questions and challenges, especially for the stochastic optimization community.
• [01827] Potential Impacts of Mass Nutritional Supplementation on Measles Dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Navideh Noori (Institute for Disease Modeling, Bill & Melinda Gates Foundation)
    • Laura A Skrip (School of Public Health, University of Liberia)
    • Assaf P Oron (Institute for Health Metrics and Evaluation, University of Washington)
    • Kevin A McCarthy (Institute for Disease Modeling, Bill & Melinda Gates Foundation)
    • Joshuna L Proctor (Institute for Disease Modeling, Bill & Melinda Gates Foundation)
    • Guillaume Chabot-Couture (Institute for Disease Modeling, Bill & Melinda Gates Foundation)
    • Benjamin M Althouse (Information School, University of Washington)
    • Kevin P.Q. Phelan (The Alliance for International Medical Action (ALIMA))
    • Indi Trehan (Department of Pediatrics, Global Health, and Epidemiology, University of Washington)
  • Abstract : The bidirectional interaction between undernutrition and infection can be devastating to child health. Treatment of acute malnutrition can reverse some of its deleterious effects and reduce susceptibility to infection. To understand how integrating nutrition interventions and vaccination affects a vaccine-preventable disease dynamics, we developed a measles transmission model. We show leveraging mass nutritional supplementation as a contact point with the health system to increase measles vaccination coverage has a synergistic benefit beyond either intervention alone.

MS [00087] Intersection of Machine Learning, Dynamical Systems and Control

room : A615

• [02826] Solving Parametric PDEs by Deep Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Bin Dong (Peking University)
  • Abstract : Deep learning continues to dominate machine learning and has been successful in computer vision, natural language processing, etc. Its impact has now expanded to many research areas in science and engineering. In this talk, I will present a series of our recent works on combining wisdom from traditional numerical PDE methods and machine learning to design data-driven solvers for parametric PDEs and their applications in fluid simulations. This is joint work with Professor Jinchao Xu, my previous Ph.D. student Yuyan Chen, and my colleagues from Huawei MindSpore AI + Scientific Computing team and the Shanghai Aircraft Design and Research Institute of The Commercial Aircraft Corporation of China.
• [02805] Training Deep ResNet with Batch Normalization as a First-order Mean Field Type Problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Phillip Sheung Chi Yam (Department of Statistics, Chinese University of Hong Kong)
  • Abstract : In this talk, we shall discuss a numerical scheme for training Deep Residual Networks that incorporates the popular Batch Normalization technique into the recently proposed extended Method of Successive Approximation in the work of Li, Chen, Tai and E, The Journal of Machine Learning Research (2017), 18: 5998–6026, and its effectiveness has been demonstrated by numerical studies. The convergence of this proposed scheme depends on the first-order mean field theory, namely the resolution of the corresponding generic first-order mean field type problems inherited from the augmented Hamiltonian, and we shall introduce this brand-new fundamental theory behind.
• [02933] Dynamics-Quantified Implicit Biases of Large Learning Rates
  • Format : Talk at Waseda University
  • Author(s) :
    • Molei Tao (Georgia Inistitute of Technology)
  • Abstract : This talk will describe some nontrivial (and pleasant) effects of large learning rates, which are often used in machine learning practice but defy traditional optimization theory. I will first show how large learning rates can lead to quantitative escapes from local minima, via chaos, which is an alternative mechanism to commonly known noisy escapes due to stochastic gradients. I will then report how large learning rates provably bias toward flatter minimizers, which arguably generalize better.
• [04799] An optimal control perspective on diffusion-based generative modeling leading to robust numerical methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Lorenz Richter (Zuse Institute Berlin, dida)
  • Abstract : This talk establishes a connection between generative modeling based on SDEs and three classical fields of mathematics, namely stochastic optimal control, PDEs and path space measures. Those perspectives will be both of theoretical and practical value, for instance allowing to transfer methods from one to the respective other field or leading to novel algorithms for sampling from unnormalized densities. Further, the connection to HJB equations leads to novel loss functions which exhibit favorable statistical properties and result in improved convergence of respective algorithms.

MS [00598] Hyperplane arrangements and enumerative problems

room : A617

• [01887] Coboundary polynomial and related polynomial invariants
  • Format : Talk at Waseda University
  • Author(s) :
    • Norihiro Nakashima (Nagoya Institute of Technology)
  • Abstract : The coboundary polynomial is a polynomial computed by all characteristic polynomials for restriction arrangements to all flats in the intersection poset. It is known that the coboundary polynomial is essentially the same as the weight enumerator and Tutte polynomial. In this talk, we introduce some known results about these relationship and future issues.
• [01889] Generalizations of Tutte-Grothendieck polynomials
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsuyoshi Miezaki (Waseda University)
    • HIMADRI SHEKHAR CHAKRABORTY (Shahjalal University of Science and Technology)
    • CHONG ZHENG (Waseda University)
  • Abstract : A Tutte-Grothendieck polynomial is a graph invariant that satisfies a generalized deletion-contraction formula. In this talk, we introduce the notion of weighted Tutte-Grothendieck polynomial and weighted Tutte-Grothendieck invariant for matroid and discuss some of its properties. Moreover, we show that the weighted Tutte-Grothendieck invariant is stronger than the Tutte-Grothendieck invariant. This is joint work with Himadri Chakraborty (SUST) and Chong Zheng (Waseda University).
• [01791] Characteristic quasi-polynomials of arrangements over algebraic integers
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuhei Tsujie (Hokkaido University of Education)
  • Abstract : Kamiya, Takemura, and Terao initiated the theory of the characteristic quasi-polynomial of an integral arrangement, which is a function counting the elements in the complement of the arrangement modulo positive integers. In this talk, we will discuss arrangements over the rings of integers of algebraic number fields.
• [01780] Counting the regions of hyperplane arrangements related to Coxeter arrangements.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yasuhide Numata (Hokkaido University)
  • Abstract : We consider the Shi and Ish arrangement of type $B_n$. Both are hyperplane arrangements in the real vector space of dimension $n$ containing the Coxeter arrangement of type $B_n$. We discuss combinatorial objects which parametrize the regions, i.e. connected components of complement of the arrangement, of these arrangement.

MS [00400] Bilevel optimization in machine learning and imaging sciences

room : A618

• [03653] Fixed-Point Automatic Differentiation of Forward--Backward Splitting Algorithms for Partly Smooth Functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Sheheryar Mehmood (University of Tuebingen)
    • Peter Ochs (Saarland University)
  • Abstract : A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We consider such structured problems which also depend on a parameter vector and study the problem of differentiating its solution mapping with respect to the parameter which has far reaching applications in sensitivity analysis and parameter learning optmization problems. We show that under partial smoothness and other mild assumptions, Automatic Differentiation (AD) of the sequence generated by proximal splitting algorithms converges to the derivative of the solution mapping. For a variant of automatic differentiation, which we call Fixed-Point Automatic Differentiation (FPAD), we remedy the memory overhead problem of the Reverse Mode AD and moreover provide faster convergence theoretically. We numerically illustrate the convergence and convergence rates of AD and FPAD on Lasso and Group Lasso problems and demonstrate the working of FPAD on prototypical practical image denoising problem by learning the regularization term.
• [05289] A framework for bilevel optimization that enables stochastic and global variance reduction algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Moreau (Inria - MIND)
  • Abstract : Bilevel optimization, the problem of minimizing a value function that involves the arg-minimum of another function, appears in many areas of machine learning. In a large-scale empirical risk minimization setting where the number of samples is huge, it is crucial to develop stochastic methods, which only use a few samples at a time to progress. However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates. To overcome this problem we introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. These directions are written as a sum, making it straightforward to derive unbiased estimates. The simplicity of our approach allows us to develop global variance reduction algorithms, where the dynamics of all variables are subject to variance reduction. This allows to design near-optimal algorithms to solve the bi-level problem.
• [03309] Bilevel Optimization with a Lower-level Contraction: Optimal Sample Complexity without Warm-Start
  • Format : Talk at Waseda University
  • Author(s) :
    • Saverio Salzo (Sapienza Università di Roma)
    • Riccardo Grazzi (Istituto Italiano di Tecnologia)
    • Massimiliano Pontil (Istituto Italiano di Tecnologia)
  • Abstract : We present a stochastic algorithm for a general class of bilevel problems consisting of a minimization problem at the upper-level and a fixed-point equation at the lower-level. This setting includes instances of meta-learning, equilibrium models, and hyperparameter optimization. The main feature of our solution is to avoid using the warm-start procedure at the lower-level, which is not always well-suited in applications, and yet to achieves order-wise optimal or near-optimal sample complexity.
• [02768] Bilevel subspace optimisation in heterogeneous clustering for cryo-EM
  • Format : Talk at Waseda University
  • Author(s) :
    • Willem Diepeveen (University of Cambridge)
    • Carlos Esteve-Yagüe (University of Cambridge)
    • Jan Lellmann (University of Lübeck)
    • Ozan Öktem (KTH Royal Institute of Technology)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : In heterogeneous Cryo-EM we are concerned with retrieving protein conformations from noisy 2D projection images. Attempting to solve this directly is challenging in the absence of a good prior. In recent work, it has been observed that MD simulations live on low-dimensional manifold of conformation space. Although this subspace might not be a perfect reflection of reality, it potentially yields a good prior. In this work we attempt to use this information in Cryo-EM conformation retrieval. In particular, we aim to retrieve conformations and the actual manifold from Cryo-EM data, but we want the manifold to match the MD data. We propose a bilevel optimisation approach to this problem.