MS and CT list / Aug. 21, 15:30-17:10.

MS [00795] Topological data analysis and machine learning

room : G301

• [03657] Generic transitions for flows on surfaces with or without constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoo Yokoyama (Saitama University)
  • Abstract : This talk describes the generic time evolutions of gradient flows and Hamiltonian flows on surfaces with or without physical constraints. Moreover, we show the non-contractibility of connected components of the spaces of such flows, respectively, under the non-existence of creations and annihilations of singular points by using combinatorics and simple homotopy theory.
• [04624] Topological learning for multiscale biology
  • Format : Talk at Waseda University
  • Author(s) :
    • Heather Harrington (University of Oxford)
  • Abstract : Biological processes are multi-scale. Spatial structures and patterns vary across levels of organisation, from molecular to multi-cellular to multi-organism. With more sophisticated mechanistic models and data available, quantitative tools are needed to study their evolution in space and time. The most prominent tool in topological data analysis is persistent homology (PH), which provides a multi-scale summary of data. Here we present extensions to the PH pipeline and highlight its utility with concrete case studies.
• [04715] Topological Data Analysis for Biological Images and Video
  • Format : Online Talk on Zoom
  • Author(s) :
    • Peter Bubenik (University of Florida)
  • Abstract : I will present the results of two projects applying topological data analysis (TDA) and machine learning (ML) to biological data. In the first, we have developed a tool, TDAExplore, that combines TDA and ML to both classify biological images and to provide a visualization that is biologically informative. In the second, we use TDA and ML to classify quasi-periodic biological videos and we apply TDA to such a video to produce synthetic periodic videos.
• [05453] Topological data analysis of music data and AI composition
  • Format : Talk at Waseda University
  • Author(s) :
    • Jae-Hun Jung (POSTECH)
    • Mai Lan Tran (POSTECH)
    • Dongjin Lee (POSTECH)
  • Abstract : We employ topological data analysis to analyze music. Initially, the provided music data is transformed into a graph and we identify embedded cycles within the music using persistent homology. We elucidate how the cycle structure changes based on the metric definition between music nodes, with theoretical justifications. Then, we introduce the overlap matrix, which shows the interconnectedness of these cycles. We explain an AI algorithm utilizing the overlap matrix to facilitate new music compositions.

MS [00444] Complex Systems: Advances in Theory and Applications

room : G304

• [01264] Adaptive Finite-Time Output Consensus for Fractional-Order Complex Networks With Multiple Output Derivative Couplings
  • Format : Talk at Waseda University
  • Author(s) :
    • Chenguang Liu (Beihang University)
    • Qing Gao (Beihang University)
    • Jinhu Lu (Beihang University)
  • Abstract : This paper delves into the adaptive fifinite-time output consensus (FTOC) problem for a multiple output derivative coupled fractional-order complex network (MODCFOCN). Based on the properties of the Gamma function and the fractional derivetive, a FTOC criterion for the MODCFOCN is derived by designing an appropriate adaptive output-feedback controller. Finally, a numerical example is utilized to substantiate the effectiveness of the acquired FTOC results and the devised adaptive output-feedback controller.
• [01255] Optimizing 3D Complex Networks on chip
  • Format : Talk at Waseda University
  • Author(s) :
    • Maciej Ogorzalek (Jagiellonian University)
    • Katarzyna Grzesiaak-Kopec (Jagiellonian University)
  • Abstract : Current generations of integrated circuits can contain billions of transistors and extremely complicated interconnect network the length of which goes into dozens of kilometers – all these placed in an extremely small physical volume. For the correct operation of the circuit placement of elements and building blocks and design of interconnect has to be done in optimal or quasi-optimal way satisfying also several types of constraints. Mathematical models of complex networks can play a significant role in the design and AI-based methodologies can be used for finding good/quasi-optimal solution in reasonable time.
• [01268] Machine Learning for Detecting Internet Traffic Anomalies
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ljiljana Trajkovic (Simon Fraser University )
    • Ljiljana Trajkovic (Simon Fraser University)
  • Abstract : Border Gateway Protocol (BGP) enables the Internet data routing. BGP anomalies may affect the Internet connectivity and cause routing disconnections, route flaps, and oscillations. Hence, detection of anomalous BGP routing dynamics is a topic of great interest in cybersecurity. Various anomaly and intrusion detection approaches based on machine learning have been employed to analyze BGP update messages collected from RIPE and Route Views collection sites. Survey of supervised and semi-supervised machine learning algorithms for detecting BGP anomalies and intrusions is presented. Deep learning, broad learning, and gradient boosting decision tree algorithms are evaluated by creating models using collected datasets that contain Internet worms, power outages, and ransomware events.
• [01280] Model for estimating unconfirmed COVID-19 cases and multiple waves of pandemic progression
  • Format : Talk at Waseda University
  • Author(s) :
    • Choujun Zhan (South China Normal University)
    • Chi K. Tse (City University of Hong Kong)
  • Abstract : The novel coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has unique epidemiological characteristics that include presymptomatic and asymptomatic infections, resulting in a large proportion of infected cases being unconfirmed, including patients with clinical symptoms who have not been identified by screening. These unconfirmed infected individuals move and spread the virus freely, presenting difficult challenges to the control of the pandemic. To reveal the actual pandemic situation in a given region, a simple dynamic susceptible-unconfirmed-confirmed-removed (D-SUCR) model is developed taking into account the influence of unconfirmed cases, the testing capacity, the multiple waves of the pandemic, and the use of nonpharmaceutical interventions. Using this model, the total numbers of infected cases in 51 regions of the USA and 116 countries worldwide are estimated, and the results indicate that only about 40% of the true number of infections have been confirmed. In addition, it is found that if local authorities could enhance their testing capacities and implement a timely strict quarantine strategy after identifying the first infection case, the total number of infected cases could be reduced by more than 90%. Delay in implementing quarantine measures would drastically reduce their effectiveness.

MS [02396] Recent Advances on Polynomial System Solving

room : G305

• [03688] Square-Free Pure Triangular Decomposition of Zero-Dimensional Polynomial Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Haokun Li (Peking University)
    • Bican Xia (Peking University)
    • Tianqi Zhao (Peking University)
  • Abstract : The concepts of pure chains and square-free pure triangular decomposition (SFPTD) of zero-dimensional polynomial systems are defined. We propose an algorithm for computing SFPTD and prove its arithmetic complexity can be single exponential in the square of the number of variables. We show experimentally that, on most examples in the literature, the algorithm is more efficient than a triangular-decomposition method in Maple, and the real solution isolation method based on SFPTD is very efficient.
• [05286] On the bit complexity of roadmap algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Schost (University of Waterloo)
  • Abstract : Roadmaps were introduced by Canny in order to reduce connectivity queries on semi-algebraic sets to similar questions on curves. In the last ten years, with Mohab Safey El Din, we proposed randomized algorithms with an improved complexity - in an algebraic cost model; the bit-complexity analysis remained to be done. I will report on recent work done in this direction with Jesse Elliott.
• [03750] Solving semi-algebraic systems arising in applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Changbo Chen (Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences)
  • Abstract : Semi-algebraic systems, which are systems consisting of polynomial equations and inequalities, naturally appear in many applications. To solve them efficiently, it is important to exploit their particular structures. In this talk, I will present specialized algorithms designed for solving semi-algebraic systems arising in several applications, namely computing the steady states of parametric biological systems, automatic parallelization of loops, and detecting quantum correlations.
• [04993] Root Separation Bounds
  • Format : Talk at Waseda University
  • Author(s) :
    • Vikram Sharma (The Institute of Mathematical Sciences Chennai)
  • Abstract : Root separation bounds are a classical topic in algebraic number theory. They also play an important role in the analysis of algorithms for finding the roots of polynomials. In this talk, we will start with some classical results of Mignotte and Davenport and trace the recent development that has occurred in this area.

MS [01211] Generalized and non-Gaussian Tensor Decompositions

room : G306

• [03326] Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenqiang PU (Shenzhen Research Institute of Big Data)
    • Xiao FU (Oregon State University)
  • Abstract : This talk considers low-rank canonical polyadic decomposition (CPD) under a class of non-Euclidean loss functions that frequently arise in statistical machine learning and signal processing. These loss functions are often used for certain types of tensor data, e.g., count and binary tensors, where the least squares loss is considered unnatural. Compared to the least squares loss, the non-Euclidean losses are generally more challenging to handle. Non-Euclidean CPD has attracted considerable interests and a number of prior works exist. However, pressing computational and theoretical challenges, such as scalability and convergence issues, still remain. This talk offers a unified stochastic algorithmic framework for large-scale CPD decomposition under a variety of non-Euclidean loss functions. Our key contribution lies in a tensor fiber sampling strategy-based flexible stochastic mirror descent framework. Leveraging the sampling scheme and the multilinear algebraic structure of low-rank tensors, the proposed lightweight algorithm ensures global convergence to a stationary point under reasonable conditions. Numerical results show that our framework attains promising non-Euclidean CPD performance. The proposed framework also exhibits substantial computational savings compared to state-of-the-art methods.
• [03666] Generalized Tucker tensor estimation: An optimal statistical and computational framework
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anru Zhang (Duke University)
    • Rungang Han (Duke University)
    • Rebecca Willett (University of Chicago)
  • Abstract : We describe a flexible framework for generalized low-rank tensor estimation problems. The proposed estimator consists of finding a low Tucker rank tensor fit to the data under generalized parametric models. To overcome the difficulty of nonconvexity, we introduce a unified approach of projected gradient descent. We establish both an upper bound on the statistical error and the linear rate of computational convergence. We demonstrate the superiority of the proposed framework on real data.

MS [02067] Recent topics on generalized orthogonal polynomials and their applications

room : G401

• [02693] Christoffel Transformations for (Partial-)Skew-Orthogonal Polynomials and Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Guofu Yu (Shanghai Jiao Tong University)
  • Abstract : In this talk, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transformations can act as spectral problems for discrete integrable hierarchies, and therefore we derive certain integrable hierarchies from these transformations. Some reductional cases are also considered. This is a joint work with Shi-Hao Li.
• [02730] Multiple skew orthogonal polynomials and two-component Pfaff lattice
  • Format : Talk at Waseda University
  • Author(s) :
    • Shi-Hao Li (Sichuan University)
  • Abstract : The relation between orthogonal polynomials and integrable system is a long-standing focus in mathematical physics, and sheds light in many related fields like random matrices, random walks, and so on. Skew orthogonal polynomials, which were proposed in the study of random matrices with orthogonal/symplectic symmetry, were found to be wave functions for integrable systems of DKP type. In this talk, we will generalize this frame by considering multiple skew orthogonal polynomials which involve several different weights. In particular, connections with integrable systems are also considered. Pfaffian expressions, recurrence relations and Cauchy transforms for multiple skew orthogonal polynomials will be performed to give rise to multiple-component Pfaff lattice hierarchy.
• [04996] Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme
  • Format : Talk at Waseda University
  • Author(s) :
    • Satoru Odake (Shinshu University)
  • Abstract : The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the differential or difference operators. Based on other factorizations, we obtain another type of forward and backward shift relations.

MS [00988] Treatment of infinity and finite-time singularities in differential equations

room : G402

• [01810] Traveling wave solutions for certain 1D degenerate parabolic equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yu Ichida (Meiji University)
  • Abstract : In this talk, the speaker will report results on the classification of the traveling wave solutions of the 1D degenerate parabolic equation and porous medium equation, and give observations and suggestions on phenomena corresponding to bifurcations of equilibria at infinity. These are obtained through dynamical systems theory and Poincar\'e compactification. This talk includes a collaborative work with Professor Takashi Sakamoto at Meiji University.
• [02005] Blow-up Rates for Solutions of a Quasi-Linear Parabolic Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Koichi Anada (Waseda University)
    • Tetsuya Ishiwata (Shibaura Institute of Technology)
    • Takeo Ushijima (Tokyo University of Science)
  • Abstract : The motion of curves by the power of their curvatures with positive exponent has been studied. The motion is described by a parabolic equation and some solutions blow up with Type II singularity. In this talk, we discuss the blow-up rates of solutions with Type II singularity. Precisely, we derive an asymptotic expansion of the traveling wave which plays a significant role and then we provide an upper estimate for the blow-up rates.
• [04119] Rigorous numerics for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Akitoshi Takayasu (University of Tsukuba)
    • Toshimasa Ishige (Chiba University)
  • Abstract : In this talk, we present a method for finding monodromy matrices of linear differential equations with finite-dimensional solution spaces via rigorous numerics. We also provide a computational result that gives monodromy matrices, which represent the fundamental group of the differential equation, of Picard-Fuchs differential equations for a certain family of K3 toric hypersurfaces.
• [02492] Computation of collision and near-collision orbits in Celestial Mechanics problems.
  • Format : Talk at Waseda University
  • Author(s) :
    • Shane Kepley (Vrije Universiteit)
    • Jason Desmond Mireles James (Florida Atlantic University)
    • Maciej Capinski (AGH University of Science and Technology)
  • Abstract : Understanding connecting and collision/ejection orbits is central to the study of transport in Celestial Mechanics. Finding and validating connecting orbits can be difficult in general, and is complicated even more by the presence of ejection/collisions which are singularities of the flow. We present a rigorous Levi-Cevita regularization algorithm which, combined with existing analytic continuation techniques, allows us to overcome this obstruction. This regularization is performed dynamically allowing invariant manifolds to be parameterized dynamically and globally, even near singularities.

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

room : G404

• [03461] Asymptotic behaviour for nonautonomous Nicholson equations with mixed monotonicities
  • Format : Talk at Waseda University
  • Author(s) :
    • Teresa Faria (Professor/University of Lisbon)
  • Abstract : A general nonautonomous Nicholson equation with multiple pairs of distinct delays is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds. Imposing an additional condition on the size of some delays, the global attractivity of positive solutions is established. Sharper results are obtained when there exists a positive equilibrium or periodic solution. These results improve on recent literature, due to the generality of the equation and less restrictive constraints.
• [03291] Periodicity and stability in some biological delay models
  • Format : Talk at Waseda University
  • Author(s) :
    • Anatoli F Ivanov (Pennsylvania State University)
  • Abstract : We consider mathematical models of several biological processes which are described by simple form scalar delay differential equations. They include autonomous nonlinear equations as well as equations with periodic coefficients. New criteria for the global asymptotic stability of equilibrium states are proposed. It is proved that the instability of equilibria implies the existence of periodic motions in the models. Explicit examples from applications demonstrating theoretical findings are given.
• [03816] Exponential stability of linear discrete systems with multiple delays
  • Format : Talk at Waseda University
  • Author(s) :
    • Josef Diblik (Brno University of Technology)
    • Josed Diblik (Brno University of Technology)
  • Abstract : The problem of exponential stability of delayed linear discrete systems with multiple delays and with constant matrices is studied. A new degenerated Lyapunov-Krasovskii functional is used to derive sufficient conditions for exponential stability and derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here.
• [03498] On asymptotic stability of equations and systems with distributed, unbounded and infinite delays
  • Format : Talk at Waseda University
  • Author(s) :
    • Elena Braverman (university of Calgary)
    • Leonid Berezansky (Ben-Gurion University of Negev)
  • Abstract : Many differential equations of mathematical biology assume delayed production process and instantaneous mortality. Introduction of delay can destabilize the unique positive equilibrium and even lead to chaos. However, for some types of equations and systems, lags in the reproduction term do not change stability properties. Consideration of variable, unbounded and distributed delays emphasizes robustness of this `absolute stability' property. Influence of an infinite, not just unbounded, delay is also outlined.

MS [00982] Partial Differential Equations in Fluid Dynamics

room : G405

• [04072] Global Finite-Energy Solutions of the Compressible Euler-Poisson Equations for General Pressure Laws with Spherical Symmetry
  • Format : Talk at Waseda University
  • Author(s) :
    • Feimin Huang (Academy of Mathematics and Systems Science, Chinese Academy of Science)
  • Abstract : We are concerned with global finite-energy solutions of the three-dimensional compressible Euler-Poisson equations with gravitational potential and general pressure law, especially including the constitutive equation of white dwarf stars. In this paper, we construct a global finite-energy solution with spherical symmetry of the Cauchy problem for the Euler-Poisson equations as the vanishing viscosity limit of the corresponding compressible Navier-Stokes-Poisson equations. The strong convergence of the vanishing viscosity solutions is achieved through the compensated compactness analysis and uniform estimates in $L^p$ via several new main ingredients. A new key estimate is first established for the integrability of the density over unbounded domains independent of the vanishing viscosity coefficient. Then a special entropy pair is carefully designed via solving a Goursat problem for the entropy equation such that a higher integrability of the velocity is established, which is a crucial step. Moreover, the weak entropy kernel for the general pressure law and its fractional derivatives of the required order near vacuum ($\rho=0$) and far-field ($\rho=\infty$) are carefully analyzed. Owing to the generality of the pressure law, only the $W^{-1,p}_{\mathrm{loc}}$-compactness of weak entropy dissipation measures with $p\in [1,2)$ can be obtained; this is rescued by the equi-integrability of weak entropy pairs which can be established by the estimates obtained above, so that the div-curl lemma still applies. Finally, based on the above analysis of weak entropy pairs, the $L^p$ compensated compactness framework for the compressible Euler equations with general pressure law is established. This new compensated compactness framework and the techniques developed in this paper should be useful for solving further nonlinear problems with similar features.
• [04789] Global-in-time quasi-neutral limit for a two-fluid Euler-Poisson system
  • Format : Talk at Waseda University
  • Author(s) :
    • Yue-Jun Peng (Université Clermont Auvergne)
  • Abstract : We consider Cauchy problem for a two-fluid Euler-Poisson system where the single parameter is the Debye length. When the initial data are sufficiently close to constant equilibrium states, we show the uniform global existence of smooth solutions and justify the convergence of the system to compressible Euler equations with damping as the Debye length tends to zero. We also establish global error estimates of the solutions. A key step of the proof is to control the quasi-neutrality of the velocities by using a projection operator.
• [03623] A compressible two-fluid model with unequal velocities: existence and uniqueness
  • Format : Talk at Waseda University
  • Author(s) :
    • Huanyao Wen (South China University of Technology)
  • Abstract : In this talk, we will introduce our recent works on the existence and uniqueness theory of a compressible two-fluid model with unequal velocities. The viscosity coefficients depend on the density functions, which can be degenerate.
• [04539] On the Stability of Outflowing Compressible Viscous Gas
  • Format : Talk at Waseda University
  • Author(s) :
    • Yucong Huang (University of Edinburgh)
    • Shinya Nishibata (Tokyo Institute of Technology)
  • Abstract : I will discuss the long-time stability of a spherically symmetric motion of outflowing isentropic and compressible viscous gas. The fluid occupies unbounded exterior domain, and it is flowing out from an inner sphere centred at the origin. In this talk, I will show that, for a large initial data, the solution will converge to the stationary solution as time goes to infinity. This is a joint work with S. Nishibata.

MS [00085] Singular Problems in Mechanics

room : G406

• [00288] Evolution equations with complete irreversibility
  • Format : Talk at Waseda University
  • Author(s) :
    • Goro Akagi (Tohoku University)
  • Abstract : In this talk, recent developments of studies on evolution equations with complete irreversibility, i.e., solutions are constrained to be monotone in time, will be reviewed. In particular, such evolution equations often arise from fracture and damage mechanics. From mathematical points of view, they are classified as fully nonlinear PDEs, and therefore, it is in general more difficult to prove their well-posedness and reveal dynamics of their solutions. However, by change of variables, they can be rewritten as doubly-nonlinear evolution equations, whose energy and variational structures are available for the analysis. Moreover, they are sometimes equivalently reformulated as semilinear obstacle problems whose obstacle functions coincide with initial data. It will also give us a clue for the analysis. In this talk, we shall overview recent results on diffusion equations and Allen-Cahn equations with complete irreversibility and also some phase-field systems arising from fracture models.
• [00285] H^2-regularity up to boundary for a Bingham fluid model
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahito Kashiwabara (The University of Tokyo)
  • Abstract : Bingham fluid is a model describing the motion of viscoplastic materials. The problem is formulated by a variational inequality, to which weak solvability in the Sobolev space H^1 is well known. However, regularity in H^2 up to the boundary, unlike its interior counterpart, seems to remain open. In this talk, we present such a result for the homogeneous slip boundary value problem, avoiding the difficulty of being unable to get good pressure estimates.
• [00279] On a generalization Kelvin–Voigt model with pressure-dependent moduli
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiromichi Itou (Tokyo University of Science)
    • Victor Kovtunenko (University of Graz)
    • Kumbakonam Rajagopal (Texas A&M University)
  • Abstract : In this talk, we discuss a generalization Kelvin–Voigt model of viscoelasticity whose material moduli depend on the pressure in which both the Cauchy stress and the linearized strain appear linearly. This model is derived from an implicit constitutive relation, and is well-suited to describe porous materials like concrete, ceramics. We show well-posedness for the corresponding variational problem by thresholding the moduli.
• [00287] A reconstruction problem in nanoscale processing by transverse dynamic force microscopy
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alemdar Hasanov Hasanoglu (Kocaeli University)
  • Abstract : In this study, the dynamic model of reconstruction of the shear force in the transverse dynamic force microscopy (TDFM)-cantilever tip-sample interaction is proposed. For this inverse problem, an input-output operator is introduced and then the compactness of this operator, thus, the ill-posedness of the inverse problems is proved. The least square solution of the inverse problem is introduced through the Tikhonov functional. The Lipschitz continuity of the input-output operator is proved. As a consequence of this, the existence of the least square solution is proved. An explicit formula for the Fr\'{e}chet gradient is derived by making use of the unique solution of the corresponding adjoint problem. This allows us to construct an effective and fast reconstruction algorithm, as the presented computational experiments show.

MS [00656] Multiscale Pattern Formation

room : G501

• [01951] Multiscale pattern formation in space and time
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasumasa Nishiura (Hokkaido University/Chubu University)
  • Abstract : One way to understand the complex dynamics in dissipative systems is to decompose the object into subsystems with different spatiotemporal scales. The resulting subsystems could be unified by singular perturbation, fast-slow method, unfolding of singularities, bifurcation, averaging, and data-driven approaches. I will try to present the state-of-the-art multi-scale pattern formation arising in biology, chemical reaction, fluid dynamics, and materials science in homogeneous and heterogeneous media.
• [01983] Localized spot dynamics: curvature and instability
  • Format : Talk at Waseda University
  • Author(s) :
    • Justin Tzou (Macquarie University)
  • Abstract : For localized spots solutions of singularly perturbed reaction-diffusion systems, we discuss two aspects of slow drift dynamics: the oscillatory instabilities, and effects of domain curvature. The problem with curvature is analyzed within the context of a model of vegetation patterns on a curved terrain, which incorporates advection effects due to flow of water downhill. The stability analysis on flat domains centers on understanding how domain geometry selects dominant modes of oscillation.
• [01901] Spiky patterns in a three-component consumer chain model
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuangquan Xie (Hunan University)
  • Abstract : We study a cooperative consumer chain model with one producer and two consumers, which is a three-component extension of the Schankenberg model. We show that consumers can survive and have a profile of a spike for sufficiently high consumption. We then study the stability of spike solutions. When the consumption constant is further increased to a certain threshold, the system undergoes a Hopf bifurcation and the spiky pattern begins to oscillate. 
• [01941] Emergence of locomotion by autonomous parameter tuning
  • Format : Talk at Waseda University
  • Author(s) :
    • Keiichi Ueda (University of Toyama)
    • Takumi Horita (University of Toyama)
  • Abstract : A peristaltic locomotion model with parameter tuning is presented. The parameter tuning system is described by the dynamical system with selection algorithm. The model autonomously generates stable elongation-contraction wave and finds appropriate anchor timing. We model the parameter tuning system as distributed system in order that the system achieves adaptability to various environmental changes.

MS [00276] Interplay of Numerical and Analytical Methods in Nonlinear PDEs

room : G502

• [01636] Convergent finite element approximation of liquid crystal polymer networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuo Yang (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
    • Ricardo Nochetto (University of Maryland)
    • Lucas Bouck (University of Maryland)
  • Abstract : Liquid crystals polymer networks $(\text{LCN})$ deform spontaneously upon temperature or optical actuation. In this talk, we discuss a $2D$ membrane model of LCN and its properties. We design a finite element discretization for this model, propose a novel iterative scheme to solve the non-convex discrete minimization problem, and prove stability of the scheme and a convergence of discrete minimizers. We present a wide range of numerical simulations.
• [01583] Evolving FEMs with artificial tangential velocities for curvature flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiashun Hu (Hongkong Polytechnic University)
    • Buyang Li (Hongkong Polytechnic University)
  • Abstract : By considering a limiting situation in the method proposed by Barrett, Garcke and Nurnberg, a new artificial tangential velocity is introduced into the evolving finite element methods for mean curvature flow and Willmore flow to improve the mesh quality of the numerically computed surfaces. Stability and optimal-order convergence of the evolving finite element methods are established.
• [03481] Finite element approximation of implicitly constituted non-Newtonian fluids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Endre Suli (University of Oxford)
  • Abstract : The framework of classical continuum mechanics, built upon an explicit constitutive equation for the stress tensor, is too narrow to describe inelastic behaviour of solid-like materials or viscoelastic properties of materials. We present a survey of recent results concerning the mathematical analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids, where the stress tensor and the symmetric part of the velocity gradient are related by a, possibly multi-valued, maximal monotone graph.
• [01330] Error analysis for a local discontinuous Galerkin approximation for systems of p-Navier–Stokes type
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Kaltenbach (University of Freiburg)
  • Abstract : In this talk, we propose a Local Discontinuous Galerkin (LDG) approximation for systems of p-Navier–Stokes type involving a new numerical flux in the stabilization term and a new discretization of the convective term. A priori error estimates are derived for the velocity, which are optimal for all $p>2$ and $\delta\ge 0$. A new criterion is presented that yields a priori error estimates for the pressure, which are optimal for all $p>2$ and $\delta\ge 0$.

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

room : G601

• [04517] Uniqueness in puzzles and puzzle solving
  • Format : Talk at Waseda University
  • Author(s) :
    • David Eppstein (University of California, Irvine)
  • Abstract : Many classical pencil-and-paper puzzles are defined in a way that requires the puzzle to have a unique solution. We explore the theoretical and practical implications of this requirement on the difficulty of puzzle-solving and puzzle generation, and the uses of the assumption of uniqueness in puzzle inference rules for puzzles including Sudoku, Slither Link / Loopy, and Map.
• [04855] The Complexity of Games and Puzzles with Limited Width
  • Format : Talk at Waseda University
  • Author(s) :
    • Tom van der Zanden (Maastricht University)
  • Abstract : When studying the complexity of games and puzzles, we usually consider generalized versions. For example, chess is played on an $8\times 8$ board but when analyzing the complexity, we consider a version played on an $n\times n$ board. What if instead we consider the $n\times k$ variant, where $k$ is a small number? In this talk, we survey some results on the computational complexity of games and puzzles with small width.
• [04898] Mathematical Puzzles for Computer Scientists: Leisure or More?
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirokazu Iwasawa (Waseda University)
  • Abstract : The speaker, a creator of mathematical puzzles including mechanical puzzles, introduces a selection of puzzles that are likely to appeal to computer scientists, chosen from those he has devised in the past. While these puzzles can be enjoyed as leisure, some of them may potentially become subjects of research.
• [05028] One Cycle to Rule Them All
  • Format : Talk at Waseda University
  • Author(s) :
    • Giovanni Viglietta (University of Aizu)
  • Abstract : One of the consequences of the classification of the finite simple groups is that, if $G$ is a primitive permutation group of degree $n$ containing a cycle of length $n-3$ or less, then $G$ is either the symmetric group $S_n$ or the alternating group $A_n$. We will discuss some applications of this result to the theory of token permutation puzzles, as well as some open problems and directions for further research.

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

room : G602

• [05097] Uniform spectral gap in nonlocal-to-local approximations of diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • José Cañizo (Universidad de Granada)
  • Abstract : We consider the nonlocal diffusion equation $\partial_t u = \frac{1}{\epsilon^2} (J_\epsilon * u - u) + \nabla \cdot (x u)$, where $J_\epsilon(x) = \epsilon^{-d} J(x/\epsilon)$, posed for $t \geq 0$ and $x \in \mathbb{R}^d$. This equation approximates the standard Fokker-Planck equation as $\epsilon \to 0$, and serves as a good test ground for several techniques used to study the long-time behaviour of nonlocal PDE. In particular, entropy techniques are not easy to apply here, and lead to functional inequalities which are not well understood. Using probabilistic techniques we show that the above equation has a uniformly positive spectral gap as $\epsilon \to 0$, and we link this to quantitative versions of the central limit theorem. This problem has links to numerical analysis and to some models in mathematical biology, which will also be discussed.
• [03996] Concentration phenomena arising in Aggregation Fast-Diffusion equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Alejandro Fernández-Jiménez (University of Oxford)
  • Abstract : We will discuss about the asymptotic behaviour of the family of Aggregation-Diffusion Equations $$ \partial_t\rho=\Delta\rho^m+div(\rho\nabla (V+W\ast\rho )), $$ for $0 < m < 1$. We rely on compactness arguments, and the gradient flow structure of the problem to obtain convergence of the solutions when $t\to\infty$. Then, we pass to the mass equation and we use viscosity solutions to characterise the limit and discuss the existence of Dirac deltas. The talk presents joint work with Prof. J.A. Carrillo and Prof. D. Gómez-Castro.
• [05394] Sharp uniform-in-time propagation of chaos on the torus
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rishabh Sunil Gvalani (Max Planck Institute for Mathematics in the Sciences)
    • Matías Delgadino (The University of Texas at Austin)
  • Abstract : We prove uniform-in-time propagation of chaos for weakly interacting diffusions with gradient drift on the torus. Our results are sharp both in terms of the rate (i.e. $N^{-\frac 12}$) and validity (they hold in the full subcritical range of temperatures). The proof relies on directly controlling the path-space relative entropy between the $N$ particle system and $N$ i.i.d copies of the synchronously-coupled limiting McKean SDE. This is joint work with Matías Delgadino.
• [04109] Limiting gradient flow structure of deep linear neural networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xavier Fernandez-Real (EPFL)
  • Abstract : We present recent results with L. Chizat, M. Colombo, A. Figalli, on the infinite-width limit of deep linear neural networks initialized with random parameters. We show that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear neural network.

MS [00559] DNB Theory and its Applications

room : G605

• [05648] Early warning signals for multistage transitions in tipping dynamics on networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Neil G. MacLaren (State University of New York at Buffalo)
    • Prosenjit Kundu (State University of New York at Buffalo)
    • Naoki Masuda (State University of New York at Buffalo)
  • Abstract : Complex dynamical systems for which we want to anticipate sudden regime shifts often form a heterogeneous network. We propose methods to select sentinel nodes in a given network to construct informative early warning signals given that the network may be heterogeneous and show multistage transitions. We show that small subsets of nodes can anticipate transitions as well as or even better than using all the nodes under the proposed node selection method. Informative sentinel nodes depend on the direction of regime shifts, which we also highlight in the talk.
• [05646] Deciphering Key Causal Mechanisms for Guided Phenotype and State Transitions
  • Format : Talk at Waseda University
  • Author(s) :
    • Chengming Zhang (The University of Tokyo)
  • Abstract : Understanding and manipulating cell state transitions is pivotal in biology. We introduce CauFinder, an innovative causal decoupling framework leveraging neural networks to emulate biological systems' hierarchical control, pinpointing crucial causal control nodes. Through optimizing information flow and isolating causal elements in latent spaces, CauFinder offers concise, accurate, and causal insights into phenotype and state transitions.
• [05638] The algorithm and application of landscape-DNB in complex disease of single sample
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoping Liu (Hangzhou Institute for Advanced Study)
  • Abstract : A new model-free method has been developed and termed the landscape dynamic network biomarker (l-DNB) methodology. The method is based on bifurcation theory, which can identify tipping points prior to serious disease deterioration using only single-sample omics data. Here, we show that l-DNB provides early-warning signals of disease deterioration on a single-sample basis and also detects critical genes or network biomarkers (i.e. DNB members) that promote the transition from normal to disease states. As a case study, l-DNB was used to predict severe influenza symptoms prior to the actual symptomatic appearance in influenza virus infections. The l-DNB approach was then also applied to three tumor disease datasets from the TCGA and was used to detect critical stages prior to tumor deterioration using an individual DNB for each patient. The individual DNBs were further used as individual biomarkers in the analysis of physiological data, which led to the identification of two biomarker types that were surprisingly effective in predicting the prognosis of tumors. The biomarkers can be considered as common biomarkers for cancer, wherein one indicates a poor prognosis and the other indicates a good prognosis.
• [03348] Modelling single cell multi-omics data
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk I will introduce combinatorial regulon (cRegulon) to model the combinations among TFs, which can better characterize cell types and serves as the driving forces for cell state transitions. By leveraging rapidly accumulated single multi-omics data, we develop an optimization model to systematically infer cRegulons (i.e., the representative TF modules, their associated regulatory elements and target genes formed regulatory network).

MS [00528] High order and well-balanced methods and stability analysis for non-linear hyperbolic systems

room : G606

• [01687] Structure preserving high order discontinuous Galerkin schemes for general relativity
  • Format : Talk at Waseda University
  • Author(s) :
    • Elena Gaburro (Inria)
    • Michael Dumbser (University of Trento)
    • Ilya Peshkov (University of Trento)
    • Olindo Zanotti (University of Trento)
    • Manuel J. Castro (University of Malaga)
  • Abstract : In this talk we present a novel first order hyperbolic reformulation of the coupled Einstein-Euler system allowing robust and long-time stable simulations for the joint evolution of matter and space-time in general relativity. Among our numerical results we have long-time evolution of TOV neutron stars and accretion disks and a black holes collision. This is obtained through high order discontinuous Galerkin schemes endowed with subcell finite volume limiter, well balanced techniques and GLM curl cleaning.
• [01663] Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems
  • Format : Talk at Waseda University
  • Author(s) :
    • José M. Gallardo (University of Málaga)
  • Abstract : This work deals with the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. We present a general strategy for constructing genuinely two-dimensional Riemann solvers, that can be applied for solving systems including source and coupling terms. Two-dimensional effects are taken into account through the approximate solutions of 2d Riemann problems arising at the vertices of the computational mesh. Applications to magnetohydrodynamics and shallow water equations are presented.
• [01841] A fully-well-balanced hydrodynamic reconstruction
  • Format : Talk at Waseda University
  • Author(s) :
    • Christophe Berthon (Nantes Université)
    • Victor Michel-Dansac (INRIA)
  • Abstract : The present work concerns the numerical approximation of the weak solutions of the shallow-water model. To address such an issue, the well-known hydrostatic reconstruction is adopted. Such a relevant technique easily gives numerical schemes able to exactly capture the steady states at rest. Here, necessary conditions are stated on the reconstruction process in order to also capture the moving steady states. An example of suitable hydrodynamic reconstruction is presented and tested.
• [01690] A well-balanced scheme for landslide models
  • Format : Talk at Waseda University
  • Author(s) :
    • Manuel J. Castro (Universidad de Malaga)
    • Cipriano Escalante Sanchez (Universidad de Málaga)
    • José Garres-Díaz (Universidad de Córdoba, Spain)
    • Tomas Morales de Luna (Universidad de Malaga)
  • Abstract : When landslide models in the shallow water framework, special care has to be taken with the stationary solutions. Indeed, motion of the material only begins when the slope of the material is bigger than that of the repose angle. Preserving such steady states is not a trivial task. We present here different strategies to design well-balance high-order finite volume schemes.

MS [00108] Recent Advances on Kinetic and Related Equations

room : G702

• [04112] On BGK-type models with velocity-dependent collision frequency
  • Format : Talk at Waseda University
  • Author(s) :
    • Doheon Kim (Hanyang University)
    • Seok-Bae Yun (Sungkyunkwan University)
  • Abstract : In the original Bhatnagar-Gross-Krook (BGK) model, the collision term in the Boltzmann equation is replaced by a simpler expression, so that the model is easier-to-handle and satisfies the conservation laws and the H-Theorem. This model contains the collision frequency as a parameter independent of the particle velocity. In this talk, I will introduce variants of the BGK model which contain velocity-dependent collision frequency, thereby mimicing the behavior of the Boltzmann equation more closely.
• [02844] Green's function for solving IBVP of evolutionary PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Hung-Wen Kuo (National Cheng Kung University)
  • Abstract : We propose a new method to solve the initial-boundary value problem for hyperbolic-dissipative PDEs based on the spirit of LY algorithm. Utilizing the idea of Laplace wave train and the notions of Rayleigh surface wave operators, we are able to obtain the complete representations of the Green's functions for the convection-diffusion equation and the drifted wave equation in a half space with various boundary conditions.
• [00644] H\"OLDER REGULARITY OF THE BOLTZMANN EQUATION PAST AN OBSTACLE
  • Format : Talk at Waseda University
  • Author(s) :
    • donghyun lee (POSTECH)
    • chanwoo Kim (University of Wisconsin, madison)
  • Abstract : Regularity and singularity of the Boltzmann equation with various shape of domains is a challenging research theme in the Boltzmann theory. In this talk, we discuss about H\"oler regularity of the Boltzmann equation outiside of convex object under specular reflection boundary condition.
• [03811] Solution to the Boltzmann equation without cutoff in $(L^1\cap L^p)_k$
  • Format : Talk at Waseda University
  • Author(s) :
    • Shota Sakamoto (Kyushu University)
    • Renjun Duan (Chinese University of Hong Kong)
    • Yoshihiro Ueda (Kobe University)
  • Abstract : We consider a Cauchy problem of the Boltzmann equation without angular cutoff near the global Maxwellian on the whole space. In this case, the control of the $L^1$ norm on the Fourier side is not sufficient for global existence due to low-frequency terms. Therefore, we employ the $L^p$ norm estimates with respect to the frequency to control such parts. This $L^1\cap L^p$ strategy will close a priori estimates when combined with a time-weighted energy method.

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

room : G703

• [04347] Bounded weak solutions to the 2D quasi-geostrophic equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elaine Cozzi (Oregon State University)
  • Abstract : We outline a proof of global existence of bounded weak solutions to the 2D quasi-geostrophic equation (SQG), building on a result of Marchand. Our proof utilizes a Littlewood-Paley version of a Serfati type of identity for SQG. This is joint work with David Ambrose and Jim Kelliher.
• [02935] On the support of anomalous dissipation measures
  • Format : Online Talk on Zoom
  • Author(s) :
    • Theodore D. Drivas (Stony Brook University)
  • Abstract : By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero-viscosity limit of Navier--Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This is joint work with L. De Rosa and M. Inversi.
• [03059] Kinetic shock profiles for the Landau equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Dallas Albritton (UW-Madison)
  • Abstract : Compressible Euler solutions develop jump discontinuities known as shocks. However, physical shocks are not, strictly speaking, discontinuous. Rather, they exhibit an internal structure which, in certain regimes, can be represented by a smooth function, the shock profile. We demonstrate the existence of weak shock profiles to the kinetic Landau equation. Joint work with Matthew Novack (Purdue University) and Jacob Bedrossian (UCLA).
• [04056] On sharp-crested water waves and finite-time singularity formation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nastasia Grubic (ICMAT, CSIC)
  • Abstract : We show that the 2d gravity water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. These singular points are not rigid; if the initial interface exhibits a corner, it remains a corner but generically its angle changes. Using a characterization of the asymptotic behavior of the fluid near a corner that follows from our a-priori energy estimates, we show the existence of initial data in these spaces for which the fluid becomes singular in finite time.

MS [01532] Recent Trends in Fluid Mechanics and its Applications

room : G704

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

room : G709

• [03228] An information geometric and optimal transport framework for Gaussian processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Minh Ha Quang (RIKEN Center for Advanced Intelligence Project)
  • Abstract : Information geometry (IG) and Optimal transport (OT) have been attracting much research attention in various fields, in particular machine learning and statistics. In this talk, we present results on the generalization of IG and OT distances for finite-dimensional Gaussian measures to the setting of infinite-dimensional Gaussian measures and Gaussian processes. Our focus is on the Entropic Regularization of the 2-Wasserstein distance and the generalization of the Fisher-Rao distance and related quantities. In both settings, regularization leads to many desirable theoretical properties, including in particular dimension-independent convergence and sample complexity. The mathematical formulation involves the interplay of IG and OT with Gaussian processes and the methodology of reproducing kernel Hilbert spaces (RKHS). All of the presented formulations admit closed form expressions that can be efficiently computed and applied practically. The theoretical formulations will be illustrated with numerical experiments on Gaussian processes.
• [03101] Data analysis and optimal transport: some statistical tools
  • Format : Talk at Waseda University
  • Author(s) :
    • Elsa Cazelles (CNRS, Université de Toulouse)
  • Abstract : We focus on the analysis of data that can be described by probability measures supported on a Euclidean space, through optimal transport. Our main objective is to present first and second order statistical analyses in the space of distributions, as a first approach to understand the general modes of variation of a set of observations. These studies correspond to the barycenter and the decomposition into geodesic principal components in the Wasserstein space.
• [02871] Multispecies Optimal Transport and its Linearization
  • Format : Talk at Waseda University
  • Author(s) :
    • Katy Craig (Department of Mathematics at the University of California Santa Barbara)
    • Nicolás García Trillos (Department of Statistics at the University of Wisconsin Madison)
    • Dorde Nikolic (Department of Mathematics at the University of California Santa Barbara)
  • Abstract : The discovery of linear optimal transport by Wang et al. in 2013 improved the computational efficiency of optimal transport algorithms for grayscale image classification. Our main goal is to classify multicolor images arising in collider events. We will introduce the basics of linear optimal transport theory, and the multispecies distance. I will discuss similarities of the multispecies case with the Hellinger-Kantorovich distance, which was linearized in 2021 by Cai et al., via its Riemannian structure.
• [03196] Semi-supervised learning with the p-Laplacian
  • Format : Talk at Waseda University
  • Author(s) :
    • Nadejda Drenska (Louisiana State University)
    • Jeff Calder (University of Minnesota, Twin Cities)
  • Abstract : Semi-supervised learning involves learning from both labeled and unlabeled data. In this talk we apply p-Laplacian regularization to cases of very low labeling rate; in such applications this approach classifies properly when the standard Laplacian regularization does not. Using the two-player stochastic game interpretation of the p-Laplacian, we prove asymptotic consistency of p-Laplacian regularized semi-supervised learning, thus justifying the utility of the p-Laplacian. This is joint work with Jeff Calder.

MS [00038] Frontiers of gradient flows: well-posedness, asymptotics, singular limits

room : G710

• [02587] Weak solutions to gradient flows in metric measure spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose M Mazon (Universitat de Valencia)
  • Abstract : We show how to introduce the notion of weak solutions in metric measure spaces in the model case of the $p$-Laplacian evolution equation, including the borderline case $p = 1$, i.e., the total variation flow. For $p > 1$, it has been previously studied as the gradient flow in $L^2 $of the $p$-Cheeger energy. Using the first-order differential structure on a metric measure space introduced by Gigli, we characterise the subdifferential in $L^2$ of the $p$-Cheeger energy. This leads to a new definition of solutions to the $p$-Laplacian evolution equation in metric measure spaces, in which the gradient is replaced by a vector field, defined via Gigli’s differential structure, satisfying some compatibility conditions.
• [04233] Duality methods for gradient flows of linear growth functionals
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wojciech Górny (University of Vienna; University of Warsaw)
    • Jose M Mazón (University of València)
  • Abstract : We study gradient flows in $L^2$ of general convex and lower semicontinuous functionals with linear growth. Typical examples of such evolution equations are the time-dependent minimal surface equation and the total variation flow. Classical results concerning characterisation of solutions require a special form or differentiability of the Lagrangian; we apply a duality-based method to formulate a general definition of solutions, prove their existence and uniqueness, and reduce the regularity and structure assumptions on the Lagrangian.
• [04556] Convergence of Sobolev gradient trajectories to elastica
  • Format : Talk at Waseda University
  • Author(s) :
    • Shinya Okabe (Tohoku University)
  • Abstract : In this talk we consider the $H^2(ds)$-gradient flow for the modified elastic energy defined on closed immersed curves in $\mathbb{R}^n$. We prove (i) the existence of a unique global-in-time solution to the flow; (ii) the full limit convergence of solutions to elastica without any additional reparametrization and translation. The main ingredients of the proof of (ii) are a Lojasiewicz--Simon's gradient inequality and the completeness of a $H^2(ds)$-Riemannian metric space.
• [05251] Recent advances in Sobolev gradient flows of plane curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Glen Wheeler (University of Wollongong)
  • Abstract : In this talk, we discuss recent progress made alongside Shinya Okabe, Philip Schrader, and Valentina-Mira Wheeler in studying the relationship between the classical curve shortening flow and the triviality of the L^2(ds) metric. Our method is to study gradient flows with different metrics (that give rise to non-trivial metric spaces). Our investigation with global analysis reveals intriguing behavior.

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

room : G801

• [04830] Rogue waves in 1+1 and in 2+1 dimensions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Paolo Maria Santini (Dept. of Physics, University "La Sapienza")
    • Petr Grinevich (Steklov Math. Institute, Moscow)
    • Francesco Coppini (Dept. of Physics, University "La Sapienza")
  • Abstract : We summarize recent results on the theory of rogue waves. 1) Relevant exact rogue wave (RW) solutions of integrable continuous, discrete, and relativistic NLS type field theories in 1+1 and/or 2+1 dimensions. 2) Analytic description of the recurrence of RWs. 3) Stability properties of exact RW solutions. 4) The effect of perturbations of the model on the RW dynamics.
• [04499] Finite-gap approach to the Davey-Stewardson-2 rogue waves
  • Format : Online Talk on Zoom
  • Author(s) :
    • Petr G. Grinevich (Steklov Mathematical Institute, RAS)
    • Paolo Maria Santini (University Roma-1 "La Sapienza", INFT)
  • Abstract : In a recent series of paper we showed that for the 1+1 dimensional soliton systems the finite-gap formulas for solutions describing the generation of rogue waves can be essentially simplified in the leading order. The origin of this simplification is that the Cauchy problem for rogue waves naturally contains a small parameter therefore the spectral curve is a small perturbation of a rational one. We show that this approach can be naturally extended to the focusing Davey-Stewardson 2 equation, which is 2+1 integrable model admitting rogue waves type solutions. Again, in the leading order we obtain elementary formulas for the rogue waves Cauchy problem.
• [04876] Non-commutative soliton equations: some solutions of matrix mKdV equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sandra Carillo (Dip SBAI, SAPIENZA UNIV. & INFN, Sez. IV, MMNLP)
    • Cornelia Schiebold (Sundswall University)
  • Abstract : Solutions of matrix mKdV equation are presented. They can be termed soliton solutions since they exhibit the typical behaviour of solitons. The asymptotics of 2-soliton solutions of the d x d-matrix modified Korteweg de-Vries equation is given under the assumption that the involved spectral matrices are invertible. This work is motivated by explicit solutions by the authors, and bases on an explicit solution formula for the N-soliton solutions previously obtained.
• [05198] Spectral approaches to wave instability
  • Format : Talk at Waseda University
  • Author(s) :
    • Sara Lombardo (Heriot-Watt University)
  • Abstract : Recent spectral techniques to study the stability of nonlinear waves will be reviewed in connection with more established results, with a particular focus on the case of nonlinear evolution equations of integrable type.

MS [00957] Mathematics of thin structures

room : G802

• [04480] Numerical approximation of the deformation of thin plates
  • Format : Talk at Waseda University
  • Author(s) :
    • Andrea Bonito (Texas A&M University)
    • Diane Guignard (University of Ottawa)
    • Angelique Morvant (Texas A&M University)
    • Ricardo H Nochetto (University of Maryland)
    • Shuo Yang (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
  • Abstract : We study the elastic behavior of prestrained and bilayer plates which can undergo large deformations and achieve nontrivial equilibrium shapes. The mathematical model consists of a fourth order minimization problem subject to a nonlinear and nonconvex metric constraint. We introduce a numerical method based on discontinuous Galerkin finite elements for the space discretization and a discrete gradient flow for the energy minimization. We discuss the properties of the method and present several insightful numerical experiments.
• [01792] A reduced model for plates arising as low energy Gamma-limit in nonlinear magnetoelasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Marco Bresciani (University of Erlangen)
    • Martin Kruzik (Czech Academy of Sciences)
  • Abstract : We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider low-energy configurations by rescaling the elastic energy according to the linearized von Kármán regime. First, we identify a reduced model by computing the $\Gamma$-limit of the magnetoelastic energy, as the thickness of the plate goes to zero. Then, we introduce applied loads given by mechanical forces and external magnetic fields and we prove that, under clamped boundary conditions, sequences of almost minimizers of the total energy converge to minimizers of the corresponding energy in the reduced model. Subsequently, we study quasistatic evolutions driven by time-dependent applied loads and a rate-independent dissipation. We prove that energetic solutions for the bulk model converge to energetic solutions for the reduced model and we establish a similar result for solutions of the approximate incremental minimization problem. Both these results provide a further justification of the reduced model in the spirit of the evolutionary $\Gamma$-convergence.
• [04118] A novel dimensional reduction for the equilibrium study of inextensional material surfaces Author links open overlay panel
  • Format : Talk at Waseda University
  • Author(s) :
    • Eliot Fried (Okinawa Institute of Science and Technology)
    • Yi-Caho Chen (University of Houston)
    • Roger Fosdick (University of Minnesota)
  • Abstract : A general framework is developed for finding the equations describing the equilibrium of an inextensional material surface with arbitrary flat reference shape that is deformed by applying tractions or moments to its edge. Euler--Lagrange equations are derived, leading to a complete and definitive set of equilibrium equations, which are a system of ordinary-differential equations for the spatial directrix.
• [01343] Mesoscale modeling of systems of planar wedge disclinations and edge dislocations
  • Format : Talk at Waseda University
  • Author(s) :
    • pierluigi cesana (kyushu university)
  • Abstract : Planar wedge disclinations are rotational mismatches at the level of the crystal lattice entailing a violation of rotational symmetry. Alongside dislocations, disclinations are observed in classes of Shape-Memory Alloys undergoing the austenite-to-martensite transformation and in crystal plasticity. In this talk, I will describe some recent results on the modeling of planar wedge disclinations and edge dislocations via an energy minimization principle. We model disclinations and dislocations as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Our main result is the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. The material of this talk is mainly based on a collaboration with Prof M. Morandotti & L. De Luca https://arxiv.org/abs/2207.02511

MS [02616] Recent Developments in Applied Inverse Problems

room : G808

• [03014] Principles and Examples of Magnetic Resonance Elastography for Distribution Measurement of Viscoelasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Mikio Suga (Chiba University)
  • Abstract : The mechanical property of a tissue is related to physiological and pathological states. Magnetic resonance elastography (MRE) is an imaging technique that can noninvasively measure the physical properties of biological soft tissues by using a magnetic resonance imaging system. Measuring the mechanical properties of tissues is expected to be helpful in diagnosing diseases such as hepatic fibrosis and cancer. In this minisymposium, I will talk about the principles and examples of MRE.
• [04180] Inverse scattering technique for a defect in anisotropic plates
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahiro SAITOH (Gunma University)
  • Abstract : In recent years, plates with anisotropic properties, such as CFRP, have been increasingly used in the engineering industry. In general, it is known that the elastic wave propagation is very complicated in anisotropic plates, due to the anisotropic properties and the generation of some types of wave modes between the incident wave and both upper and lower surfaces. In this study, the author proposes an inverse scattering technique for reconstructing a defect in anisotropic plates.

MS [00876] Inverse Problems in Partial Differential Equations and Graphs

room : G809

• [05146] Density results in the Calderon problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mikko Salo (University of Jyvaskyla)
  • Abstract : We will discuss recent density results for products of harmonic functions, and applications of these results to inverse problems such as the linearized Calderon problem and the Calderon problem for nonlinear partial differential equations. The emphasis will be on the geometric setting that corresponds to anisotropic conductivity coefficients given by a Riemannian metric.
• [03644] Rellich type theorem for lattice Hamiltonians
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Isozaki (University of Tsukuba)
  • Abstract : We announce results for a Rellich type theorem on a locally perturbed periodic lattice containing square, triangular and hexagonal lattices. This is a joint work with K. Ando and H. Morioka.
• [04868] Continuum limits of discrete Schr\"odinger operators on lattices
  • Format : Talk at Waseda University
  • Author(s) :
    • Yukihide Tadano (Tokyo University of Science)
  • Abstract : We consider continuum limit problems of discrete Schr\”odinger operators defined on lattices. We show that the corresponding Schr\”odinger operators on the Euclidean space are obtained as the above continuum limits in the generalized norm resolvent sense. This talk is based on joint work with Shu Nakamura.

MS [00593] Advances in Nonlinear Dynamics

room : F308

• [03886] Understanding how blenders emerge: weaving a carpet from global manifolds
  • Author(s) :
    • Dana C'Julio (University of Auckland)
    • Bernd Krauskopf (University of Auckland)
    • Hinke M Osinga (University of Auckland)
  • Abstract : A blender is a tool for constructing `wild' robust chaotic dynamics in partially hyperbolic systems. We make precise statements about how a blender emerges in a family of 3D Hénon-like maps as parameters are changed. To this end, we employ advanced numerical techniques to determine when the one-dimensional stable manifolds of two saddle points weave through phase space to form an impenetrable carpet, which is the characterising property of a blender.
• [03948] A Dynamical Systems Approach for Most Probable Escape Paths over Periodic Boundaries
  • Author(s) :
    • Emmanuel Fleurantin (George Mason University, University of North Carolina at Chapel Hill)
    • Katherine Slyman (University of North Carolina at Chapel Hill)
    • Blake Barker (Brigham Young University)
    • Christopher K.R.T. Jones (George Mason University, University of North Carolina at Chapel Hill)
  • Abstract : Analyzing when noisy trajectories, in the two dimensional plane, of a stochastic dynamical system exit the basin of attraction of a fixed point is specifically challenging when a periodic orbit forms the boundary of the basin of attraction. Our contention is that there is a distinguished Most Probable Escape Path (MPEP) crossing the periodic orbit which acts as a guide for noisy escaping paths in the case of small noise slightly away from the limit of vanishing noise. It is well known that, before exiting, noisy trajectories will tend to cycle around the periodic orbit as the noise vanishes, but we observe that the escaping paths are stubbornly resistant to cycling as soon as the noise becomes at all significant. Using a geometric dynamical systems approach, we isolate a subset of the unstable manifold of the fixed point in the Euler-Lagrange system, which we call the River. Using the Maslov index we identify a subset of the River which is comprised of local minimizers. The Onsager-Machlup (OM) functional, which is treated as a perturbation of the Friedlin-Wentzell functional, provides a selection mechanism to pick out a specific MPEP. Much of this talk will be focused on the system obtained by reversing the van der Pol Equations in time (so-called IVDP). Through Monte-Carlo simulations, we show that the prediction provided by OM-selected MPEP matches closely the escape hatch chosen by noisy trajectories at a certain level of small noise.
• [04096] On the connectedness and disconnectedness of the Julia set for the Hénon map.
  • Author(s) :
    • Zin Arai (Tokyo Institute of Technology)
  • Abstract : We discuss the connectedness and disconnectedness of the Julia set for the complex Hénon map. To prove the disconnectedness of the Julia set, we develop a topological method that uses the plurisubharmonic nature of the Green function. We also construct a hyperbolic complex Hénon map with a connected Julia set. Consequently, we obtain a certain topological property of the connectedness locus of the map. This is a joint work with Yutaka Ishii (Kyushu Univerisity).
• [04135] Standard piecewise smooth symplectic maps
  • Author(s) :
    • Vered Rom-Kedar (The Weizmann Institute)
    • Michal Pnueli (The Weizmann Institute)
    • Alexandra Zobova (The Weizmann Institute)
  • Abstract : Return maps of near integrable/near quasi-integrable Hamiltonian impact systems are shown to produce piecewise smooth symplectic maps. In the integrable/quasi-integrable limit, these maps reduce to piecewise smooth families of rotations/interval exchange maps. As for the standard map, we introduce simplified models for these return maps and study their dynamics numerically. Regular and singular resonances emerge, as well as transient behavior, leading to conjectures regarding the non-existence of dividing circles in the singularity bands.

MS [02015] Theory and applications of random/non-autonomous dynamical systems part II

room : F309

• [03870] Worked out examples of Random Relaxed Newton's Methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Takayuki Watanabe (Chubu University)
  • Abstract : We give some numerical results on Random Relaxed Newton's Methods which were proposed by Sumi to compute an approximate root of a given polynomial. He proved that this randomized algorithm almost surely works well if large noise is inserted. In this talk, we demonstrate by numerical experiments that even small noise can make the randomized algorithm successful, and discuss a mathematical conjecture.
• [02705] Complex two-dimensional random relaxed Newton's methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroki Sumi (Kyoto University)
  • Abstract : We develop the theory of random dynamical systems of meromorphic maps on the complex two-dimensional projective space and we consider complex two-dimensional random relaxed Newton's methods to find backward images of the origin (0,0) in C^{2} under complex two dimensional regular polynomial maps on C^{2}. We will see the randomness or noise in the systems bring us very nice things, noise-induced order and collapsing of nasty attractors, which cannot hold in deterministic relaxed Newton's methods.
• [02999] New Q-Newton's method and Backtracking line search
  • Format : Talk at Waseda University
  • Author(s) :
    • Tuyen Trung Truong (University of Oslo)
  • Abstract : New Q-Newton's method is a variant of Newton's method which preserves the fast rate of convergence while having the additional good property of being able to avoid saddle points. It works by adding a term into the Hessian, and change the sign of negative eigenvalues. Backtracking line search boosts the convergence guarantee. This talk will describe the algorithm, good experimental performance (including finding roots of meromorphic functions), and good theoretical guarantees.
• [05306] A Universal Fatou Component
  • Format : Talk at Waseda University
  • Author(s) :
    • Mark David Comerford (University of Rhode Island)
  • Abstract : We show that, for the non-autonomous iteration of polynomials with suitably bounded degrees and coefficients, it is possible to obtain the whole of the classical schlicht family of normalized univalent functions on the unit disc as limit functions on a single Fatou component for a single bounded sequence of quadratic polynomials.

MS [02644] Black box methods for efficient learning in high-dimensional scientific computing

room : F310

• [05120] Is Monte Carlo a bad sampling strategy?
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ben Adcock (Simon Fraser University)
    • Simone Brugiapaglia (Concordia University)
  • Abstract : When approximating smooth, high-dimensional functions from limited samples using polynomials, it is common to use Monte Carlo (MC) sampling to lessen the curse of dimensionality. However, it is well known that MC is theoretically suboptimal. This has led to a concerted effort to design improved strategies with near-optimal sample complexities. In this work we demonstrate, both theoretically and numerically, that MC is actually an eminently suitable strategy in sufficiently high dimension despite its apparent suboptimality.
• [05196] CAS4DL: Christoffel Adaptive Sampling for Deep Learning in data-scarce applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ben Adcock
    • Juan M. Cardenas (Simon Fraser University)
    • Nick Dexter (Florida State University)
  • Abstract : Many problems in computational science and engineering require the approximation of a high-dimensional function from data. In many such applications, data is costly to generate: for example, it each sample may require a costly PDE solve. Therefore, it is imperative to develop highly sample efficient algorithms. Recently, deep neural networks and deep learning have shown great promise to provide breakthrough performance in challenging function approximation tasks. In this work, we propose an adaptive sampling strategy, CAS4DL (Christoffel Adaptive Sampling for Deep Learning) to increase the sample efficiency of DL. Our novel approach is based on interpreting the second to last layer of a DNN as a dictionary of functions defined by the nodes on that layer. With this viewpoint, we then define an adaptive sampling strategy motivated by adaptive sampling schemes recently proposed for linear approximation schemes, wherein samples are drawn randomly with respect to the Christoffel function of the subspace spanned by this dictionary. We present numerical experiments comparing CAS4DL with standard Monte Carlo (MC) sampling. Our results demonstrate that CAS4DL often yields substantial savings in the number of samples required to achieve a given accuracy, particularly in the case of smooth activation functions. These results therefore are a promising step towards fully adapting DL towards scientific computing applications.
• [05283] Exploiting the local parabolic landscapes of adversarial losses to accelerate black-box adversarial attack
  • Format : Talk at Waseda University
  • Author(s) :
    • Hoang Anh Tran (Oak Ridge National Laboratory)
  • Abstract : Machine learning models, and convolutional neural networks (CNNs) in particular, have demonstrated remarkable performance in many classification tasks. However, deep learning technology also exposed certain security risks, as they are susceptible to malicious inputs, which are small, human-imperceptible perturbations to the inputs designed to fool the model prediction. In this talk, we present an investigation into the vulnerability of CNN classifiers from the shape of the loss’s landscape perspective. We theoretically and experimentally justify that the adversarial losses of many standard and robust image classifiers behave like parabolas with respect to perturbations in the Fourier domain, but not in the pixel domain. Then, we exploit the parabolic landscape to design a new black-box adversarial attack methods with improved query efficiency, compared to the other state-of-the-art baselines. We demonstrate the efficiency of our method on MNIST, CIFAR-10 and ImageNet datasets for various standard and robust models.
• [05315] A Mathematical Approach Towards Physical Law Learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gitta Kutyniok (LMU Munich)
    • Philipp Scholl (LMU Munich)
    • Aras Bacho (LMU Munich)
    • Holger Boche (TU Munich)
  • Abstract : For most of human history, scientists had to derive physical laws by hand. Recently, due to the data deluge, several learning-based approaches to infer the governing laws from experimental data have been suggested. However, a theoretical foundation is at present missing. In this talk, we will discuss our first stage of a mathematical framework for physical law learning, in particular, how to derive well-definedness of the learning problem, both theoretically and numerically.

contributed talk: CT061

room : F311

[00408] Reducing Complexity of a Population Balance Model for Synthesis of Composite Polymer Particles

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @F311
• Type : Contributed Talk
• Abstract : An accurate prediction of the formation of polymer particles is vital for synthesis of high quality materials, but still not feasible due to its complexity. We present a Population Balance Equations model as a tool targeting the task. Aimed to enhance model performance, we derive a quantitative criterion for locating regions of “slow” aggregation among particles. Within such a regime, the aggregation terms can be neglected and computational efficiency improves by several orders of magnitude.
• Classification : 45Kxx, 70-10, 92Exx
• Format : Talk at Waseda University
• Author(s) :
  • Simone Rusconi (CUNEF Universidad)
  • Christina Schenk (IMDEA Materials Institute)
  • Arghir Zarnescu (Basque Center for Applied Mathematics)
  • Elena Akhmatskaya (Basque Center for Applied Mathematics)

[01651] Coagulation equations for non-spherical clusters

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @F311
• Type : Contributed Talk
• Abstract : We study the long-time asymptotics of a coagulation model describing the evolution of a system of particles characterized by volume and surface area. The aggregation mechanism takes place in two stages: collision and fusion of particles. A particularity of the system is that, for some fusion mechanisms, the particle distribution describes a system of ramified-like particles. Moreover, we prove that we are able to recover the standard coagulation equation in the case of fast fusion.
• Classification : 45K05, 34A34, 35Q92, 35Q70
• Format : Talk at Waseda University
• Author(s) :
  • Iulia Cristian (University of Bonn)
  • Juan J. L. Velázquez (University of Bonn)

[01564] Extended Observer-based Control for Interval-type-2 Fuzzy Systems Under Event-Triggered Scheme

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @F311
• Type : Contributed Talk
• Abstract : The problems of disturbance rejection and fault tolerant control for interval-type-2-fuzzy systems are investigated by utilization of a generalized extended state observer. To be specific, the system states along with disturbances and actuator faults are simultaneously reconstructed by the implemented observer. Besides, an observer-based event-triggered scheme is implemented to mitigate the communication burden. Furthermore, the asymptotic stability criteria for the constructed system are formulated. Consequently, the theoretical declarations are authenticated by prevailing numerical simulation results.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Format : Online Talk on Zoom
• Author(s) :
  • Shobana Nagarajan (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

[01550] Stabilization and State Estimation of Semi-Markovian Cyber-Physical Systems via Time-Triggered Control

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @F311
• Type : Contributed Talk
• Abstract : The issues of input-output finite-time stabilization and state estimation for a class of semi-Markovian switching cyber-physical systems with cyber-attacks are investigated. Primarily, immeasurable states are estimated by designing a mode-dependent observer. Further, based on the observer information, mode-dependent time-triggered controller is developed to ensure that the resultant system is input-output finite-time stable. Finally, the efficacy of proposed result is demonstrated through a numerical example.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Format : Online Talk on Zoom
• Author(s) :
  • Panneerselvam Vellingiri (Bharathiar university)
  • Sakthivel Rathinasamy (Bharathiar university)

MS [01200] New Trends in Optimal Control and Their Applications

room : F312

• Type : Proposal of Minisymposium
• Abstract : This proposal belongs to the area of optimal control for sweeping processes and their applications to optimization-related and control problems, as well as some practical models. By now, the sweeping process has been recognized as a class of nonsmooth dynamical systems involving normal cones to moving sets. The controlled sweeping processes have been studied with applications relating to the theory of plasticity, ferromagnetism, ferroelectricity, and elastoplasticity. Further developments also apply to various problems of hysteresis, phase transitions, modelling systems with contact, friction, and impacts. These systems frequently arise in applications such as mechanical systems, switched electrical circuits, and biological systems.
• Organizer(s) : Leonardo Colombo, Dao Nguyen
• Classification : 47J20, 49J40, 49J53, 65K10, 90C99
• Minisymposium Program : No registered information

MS [00711] Recent Advances in Optimal control and optimization

room : F401

• [03864] Analysis and Control in Poroelastic Systems
  • Author(s) :
    • Lorena Bociu (NC State University)
  • Abstract : We answer questions related to tissue biomechanics via wellposedness, sensitivity analysis, and optimal control problems for fluid flows through deformable porous media. These results are relevant for many applications in biology, medicine and bio-engineering. We focus on the local description of the problem, which involves implicit, degenerate, nonlinear poroelastic systems, as well as scenarios where the global features of the problem are accounted for through a multi-scale coupling with a lumped hydraulic circuit.

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

room : F402

• [03634] Opial property in Wasserstein spaces and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Emanuele Naldi (TU Braunschweig)
  • Abstract : The Opial property is a metric characterization of weak convergence for a suitable class of Banach spaces. It plays an important role in the study of weak convergence of iterates of mappings and of the asymptotic behavior of nets satisfying some metric properties. Since it involves only metric quantities, it is possible to define this property also in metric spaces provided with a suitable notion of weak convergence. This is the case for spaces of probability measures endowed with the Kantorovich-Rubinstein-Wasserstein metric deriving by optimal transport. In particular, in this talk, we present an Opial property in the Wasserstein space of Borel probability measures with finite quadratic moment on a separable Hilbert space. We present applications of this property to convergence of Wasserstein gradient flows of lower semicontinuous and geodesically convex functionals defined on the space of probability measures. We show further application to convergence of sequences generated by the proximal point algorithm and a proximal gradient algorithm when the functional satisfy some additional hypothesis. We conclude with one last application of the property to convergence to a fixed point for iterations of a non-exapansive map defined on a weakly closed set.
• [03671] An Optimal Transport-based approach to Total-Variation regularization for the Diffusion MRI problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Rodolfo Assereto (University of Graz)
    • Kristian Bredies (University of Graz)
    • Marion I. Menzel (GE Global Research, Munich)
    • Emanuele Naldi (TU Braunschweig)
    • Claudio Mayrink Verdun (TU München)
  • Abstract : Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive imaging technique that draws structural information from the interaction between water molecules and biological tissues. Common ways of tackling the derived inverse problem include, among others, Diffusion Tensor Imaging (DTI), High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Spectrum Imaging (DSI). However, these methods are structurally unable to recover the full diffusion distribution, only providing partial information about particle displacement. In our work, we introduce a Total-Variation (TV) regularization defined from an optimal transport perspective using 1-Wasserstein distances. Such a formulation produces a variational problem that can be handled by well-known algorithms enjoying good convergence properties, such as the primal-dual proximal method by Chambolle and Pock. It allows for the reconstruction of the complete diffusion spectrum from measured undersampled k/q space data.
• [04791] A minimization problem in the space of bounded deformations arising in visco-plastic fluid flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Lukas Holbach (Johannes Gutenberg University Mainz)
    • Christian Meyer (TU Dortmund)
    • Georg Stadler (New York University)
  • Abstract : Plasticity and material failure play an important role in Earth's plate motion. These phenomena are commonly modeled by incompressible Stokes flows with visco-plastic rheologies. Weak solutions of these nonlinear equations can be characterized as minimizers of a convex energy functional. While the solution is unique and lies in $H^1$ if a lower-bound regularization on the viscosity is employed, the problem becomes singular without regularization and the solution must be sought in the space of bounded deformations (BD). We present an existence result in BD and show that the regularized solutions converge to a solution of the singular problem with respect to a suitable topology when the regularization parameter tends to zero.

MS [00635] Mean field games and optimal transport with applications in data science and biology

room : F403

• [05294] Towards a mathematical theory of development
  • Format : Talk at Waseda University
  • Author(s) :
    • Geoffrey Schiebinger (University of British Columbia)
  • Abstract : This talk introduces a mathematical theory of developmental biology, based on optimal transport. While, in principle, organisms are made of molecules whose motions are described by the Schödinger equation, there are simply too many molecules for this to be useful. Optimal transport provides a set of equations that describe development at the level of cells. We propose that this optimal transport hypothesis is a fundamental mathematical principle of developmental biology.
• [03712] Applications of Gromov-Wasserstein Distance to Graph and Hypergraph Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Tom Needham (Florida State University)
  • Abstract : Gromov-Wasserstein distances are metrics, inspired by the usual Wasserstein distances of optimal transport, which are designed to handle comparisons between distributions that lie on different spaces. I will overview some recent applications of these metrics to the analysis of graph and hypergraph datasets.
• [03382] Single-cell data integration using optimal transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Ritambhara Singh (Brown University)
    • Pinar Demetci (Brown University)
    • Rebecca Santorella (Brown University)
    • Bjorn Sandstede (Brown University)
    • William Stafford Noble (University of Washington)
    • Ievgen Redko (Jean Monet University, Saint Etienne)
    • Quang Huy Tran (Université Bretagne-Sud, CNRS, IRISA, Vannes)
  • Abstract : Integration of single-cell multi-omic measurements is crucial to understand the underlying biology. However, this is particularly challenging due to the lack of sample-wise or feature-wise correspondence information across single-cell datasets generated from different samples. In this talk, I will present our optimal transport-based integration methods that perform the alignment of different single-cell measurements with minimal supervision. We demonstrate their state-of-the-art performance on simulations and real-world datasets.
• [03962] A mathematical framework of transfer learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Haoyang Cao (Ecole Polytechnique)
  • Abstract : Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. Despite its numerous empirical successes, theoretical analysis for transfer learning is limited. In this talk we introduce for the first time, to the best of our knowledge, a mathematical framework for the general procedure of transfer learning. Our unique reformulation of transfer learning as an optimization problem allows the analysis of its feasibility. Additionally, we propose a novel concept of transfer risk to evaluate transferability of transfer learning. At the end we will demonstrate how this framework can be embedded in both a generic image classification problem and a portfolio optimization problem to demonstrate the potential and benefits of incorporating transfer risk in the evaluation of transfer learning performance.

MS [00966] Theoretical and computational advances in measure transport

room : F411

• [04311] On the Monge gap and the MBO feature-sparse transport estimator.
  • Format : Talk at Waseda University
  • Author(s) :
    • marco cuturi (Apple)
  • Abstract : This talk will cover two recent works aimed at estimating Monge maps from samples. In the first part (in collaboration with Théo Uscidda) I will present a novel approach to train neural networks so that they mimic Monge maps for the squared-Euclidean cost. In that field, a popular approach has been to parameterize dual potentials using input convex neural networks, and estimate their parameters using SGD and a convex conjugate approximation. We present in this work a regularizer for that task that is conceptually simpler (as it does not require any assumption on the architecture) and which extends to non-Euclidean costs. In the second part (in collaboration with Michal Klein and Pierre Ablin), I will show that when adding to the squared-Euclidean distance an extra translation-invariant cost, the Brenier theorem translates into the application of the proximal mapping of that extra term to the derivative of the dual potential. Using an entropic map to parameterize that potential, we obtain the Monge-Bregman-Occam (MBO) estimator, which has the definOn the Monge gap and the MBO feature-sparse transport estimator.ing property that its displacement vectors $T(x) - x$ are sparse, resulting in interpretable OT maps in high dimensions.
• [05300] Simulation-Free Generative Modeling with Neural ODEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Ricky Tian Qi Chen (Meta AI)
  • Abstract : Standard diffusion models offer a simulation-free method of training continuous-time transport maps but are typically restricted to linear stochastic processes. In this talk, I will discuss Flow Matching, a training objective that allows regressing onto the generating vector field instead of the score vector field. This allows more flexibility in the design of probability paths, extends seamlessly to general manifolds, and brings the model closer to optimal transport solutions.
• [04077] Diffusion Schrödinger Bridge Matching
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuyang Shi (Oxford university)
    • Valentin De Bortoli (ENS Ulm)
    • Andrew Campbell (Oxford University)
    • Arnaud Doucet (Oxford University)
  • Abstract : Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g. Denoising Diffusion Models (DDMs) and Flow Matching Models (FMMs) implement such a transport through a Stochastic Differential Equation (SDE) or an Ordinary Differential Equation (ODE). However, while it is desirable in many applications to approximate the deterministic dynamic Optimal Transport (OT) map which admits attractive properties, DDMs and FMMs are not guaranteed to provide transports close to the OT map. In contrast, Schrödinger bridges (SBs) compute stochastic dynamic mappings which recover entropy-regularized versions of OT. Unfortunately, existing numerical methods approximating SBs either scale poorly with dimension or accumulate errors across iterations. In this work, we introduce Iterative Markovian Fitting, a new methodology for solving SB problems, and Diffusion Schrödinger Bridge Matching (DSBM), a novel numerical algorithm for computing IMF iterates. DSBM significantly improves over previous SB numerics and recovers as special/limiting cases various recent transport methods. We demonstrate the performance of DSBM on a variety of problems.
• [05473] Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefano Peluchetti (Cogent Labs)
  • Abstract : The dynamic Schrödinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a reference process. We propose a novel sampling-based iterative algorithm, the iterated diffusion bridge mixture (IDBM) procedure, aimed at solving the dynamic Schrödinger bridge problem. The IDBM procedure exhibits the attractive property of realizing a valid transport between the target probability measures at each iteration. We perform an initial theoretical investigation of the IDBM procedure, and carry out numerical experiments illustrating the competitive performance of the IDBM procedure. Recent advancements in generative modeling employ the time-reversal of a diffusion process to define a generative process that approximately transports a simple distribution to the data distribution. As an alternative, we propose utilizing the first iteration of the IDBM procedure as an approximation-free method for realizing this transport. This approach offers greater flexibility in selecting the generative process dynamics and exhibits accelerated training and superior sample quality over larger discretization intervals.

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

room : F412

• [04676] Persistent cycle registration and topological bootstrap
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yohai Reani (Viterbi Faculty of Electrical Engineering, Technion - Israel Institute of Technology)
    • Omer Bobrowski (Viterbi Faculty of Electrical Engineering, Technion - Israel Institute of Technology)
  • Abstract : In this talk we present a novel approach for comparing the persistent homology representations of two spaces (filtrations) directly in the data space. We do so by defining a correspondence relation between such representations and devising a method, based on persistent homology variants, for its efficient computation. We demonstrate our new framework in the context of topological inference, where we use statistical bootstrap-like methods to differentiate between real phenomena and "noise" in point cloud data.
• [05127] The Density Fingerprint of a Periodic Set and Persistent Homology
  • Format : Online Talk on Zoom
  • Author(s) :
    • Herbert Edelsbrunner (Institute of Science and Technology Austria)
    • Teresa Heiss (Institute of Science and Technology Austria)
    • Vitaliy Kurlin (University of Liverpool)
    • Philip Smith (University of Liverpool)
    • Mathijs Wintraecken (Institute of Science and Technology Austria)
  • Abstract : Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions. The density fingerprint is invariant under isometries, continuous, and complete in the generic case, which are necessary features for reliable comparison of crystals. The fingerprint has a fast algorithm based on Brillouin zones and related inclusion-exclusion formulae, which we have implemented. I will discuss the connection with persistent homology, suggesting a possible extension of the fingerprint.
• [04866] Reconstruction of manifolds from point clouds and inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Matti Lassas (University of Helsinki)
    • Charles Fefferman (Princeton University)
    • Sergei Ivanov (Steklov Institute of Mathematics)
    • Hariharan Narayanan (Tata Institute for Fundamental Research)
    • Jinpeng Lu (University of Helsinki)
  • Abstract : We consider a geometric problem on how a Riemannian manifold can be constructed to approximate a given discrete metric space. This problem is closely related to invariant manifold learning, where a Riemannian manifold $(M,g)$ needs to be approximately constructed from the noisy distances $d(X_j,X_k)+\eta_{jk}$ of points $X_1,X_2,\dots,X_N$, sampled from the manifold $M$. Here, $d(X_j,X_k)$ are the distance of the points $X_j,X_k\in M$ and $\eta_{jk}$ are random measurement errors. The values $d(X_j,X_k)$ can be considered as distance fingerprints of the manifold $M$. We also consider applications of the results in inverse problems encountered in medical and seismic imaging. In these problems, an unknown wave speed in a domain needs to be determined from indirect measurements. Moreover, we discuss a problem analogous to the above one, where distances are measured from points in a small subset $U\subset M$ to points in a discrete subset of $M$ and the errors are deterministic.

MS [02700] Recent developments on Infinite Dimensional Analysis, Stochastic Analysis and Quantum Probability

room : E501

• [02981] Multiplication Operators by White Noise Delta Functions and Associated Differential Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Un Cig Ji (Chungbuk National University)
  • Abstract : We establish explicit forms of the multiplication operators induced by white noise delta functions, which are closely related to the Bogoliubov transformation and a quantum analogue of Girsanov transform. Then we study the differential equations for operators associated with the multiplication operators by the white noise delta functions. This talk is based on a joint work with L. Accardi and K. Saito.
• [03986] Positivity of Q-matrices and quadratic embedding constants of graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Nobuaki Obata (Tohoku University)
  • Abstract : Let $G=(V,E)$ be a graph. Positivity of the Q-matrix $Q=Q_q=[q^{d(x,y)}]$ is essential for q-deformed vacuum state of a graph and q-deformed CLT for a growing graph. Positivity of $Q_q$ is profoundly related to conditional negativity of the distance matrix $D=[d(x,y)]$. It is shown that the positivity region of $Q_q$ contains $[0,1]$ if and only if the quadratic embedding constant (QEC) of $G$ is non-positive. We report some results in this line and discuss open questions.

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

room : E502

• [02123] Transition Phenomena in Non-Gaussian Stochastic Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinqiao Duan (Illinois Institute of Technology and Great Bay University )
  • Abstract : Dynamical systems under non-Gaussian Levy fluctuations manifest as nonlocality at a certain “macroscopic” level. Transition phenomena are special events for evolution from one metastable state to another. Examples for such events are phase transition, pattern change, gene transcription, climate change, abrupt shifts, extreme transition, and other rare events. The most probable transition pathways are the maximal likely trajectory (in the sense of optimizing a probability or an action functional) between metastable states.
• [02120] Föllmer flows: contraction, sampling and generative learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuling Jiao (Wuhan University)
  • Abstract : We construct a unit-time flow on the Euclidean space, termed the F{\"o}llmer flow, whose flow map at time 1 pushes forward a standard Gaussian measure onto a general target measure. We study the well-posedness of the F{\"o}llmer flow and establish the Lipschitz property of the flow map at time 1. We apply the Lipschitz mapping to several rich classes of probability measures on deriving functional inequalities with dimension-free constants,  sampling and generative learning. 
• [02122] Stochastic systems via rough path theory: theory and numerics
  • Format : Talk at Waseda University
  • Author(s) :
    • Hoang Duc Luu (MPI MIS & IMH-VAST)
  • Abstract : This talk presents stochastic differential equations driven by Hoelder noises, which can be solved in the pathwise sense using rough path theory. The asymptotic dynamics of the system can be studied under random dynamical systems, and results on existence of random pullback attractors can be derived for dissipative systems. The numerical attractor of the discrete system is proved to converge to the one of the continuous system as the time step tends to zero.
• [02124] Data-driven method to learn polymer dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoli Chen (National University of Singapore)
  • Abstract : We propose a machine learning approach where we construct reduced thermodynamic coordinates and interpret the dynamics of these coordinates directly from microscopic stochastic trajectory data. Our approach allows the creation of custom thermodynamics that elucidates macroscopic dynamical landscapes and facilitates subsequent analysis and control. We demonstrate our method on a long polymer chain in an externally applied field by showing that only three learnt thermodynamic coordinates are sufficient to build a dynamical landscape of unfolding.

MS [00059] Numerical solutions for differential equations: Probabilistic approaches and statistical perspectives

room : E503

• [00714] Approximating the solutions of delay differential equations via the randomized Euler method
  • Format : Talk at Waseda University
  • Author(s) :
    • Yue Wu (University of Strathclyde)
    • Fabio Difonzo (University of Bari Aldo Moro)
    • Pawel Przybyl (AGH University of Science and Technology)
  • Abstract : In this talk, we consider Caratheodory delay ODEs with time-irregular coefficients, where a randomized Euler scheme is proposed to approximate the exact solution. This is the case when there is a lack of convergence for deterministic algorithms.
• [00186] Posterior error estimates for statistical finite element methods with Sobolev priors
  • Format : Talk at Waseda University
  • Author(s) :
    • Toni Karvonen (University of Helsinki)
    • Fehmi Cirak (University of Cambridge)
    • Mark Girolami (University of Cambridge)
  • Abstract : The statistical finite element, statFEM, approach synthesises measurement data with finite element models and allows for making predictions about the system response. Suppose that noisy measurement data are generated by a deterministic true system response function satisfying a second-order elliptic partial differential equation for an unknown true source term. In this setting, we provide probabilistic error analysis for a prototypical statFEM setup based on a Gaussian process prior whose covariance kernel induces a Sobolev space.
• [04863] The Bayesian approach to inverse Robin problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ieva Kazlauskaite (University of Cambridge)
  • Abstract : In this talk, I will present the Bayesian approach to inverse Robin problems. The problem of interest is a certain elliptic boundary value problem of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the observable part. Such an inverse problem arises naturally in the initialisation of large-scale ice sheet models that are crucial in climate and sea-level predictions. We motivate the Bayesian approach for a prototypical Robin inverse problem by showing that the posterior mean converges in probability to the data-generating ground truth as the number of observations increases. Related to the stability theory for inverse Robin problems, we establish a logarithmic convergence rate for regular Robin coefficients, whereas for analytic coefficients we can attain an algebraic rate. Further, our numerical results demonstrate the effectiveness of the approach in recovering the Robin coefficient for an ice sheet model.
• [02954] Statistical finite elements for misspecified models
  • Format : Talk at Waseda University
  • Author(s) :
    • Connor Duffin (University of Cambridge)
    • Edward Cripps (University of Western Australia)
    • Thomas Stemler (University of Western Australia)
    • Mark Girolami (University of Cambridge)
  • Abstract : I will present a statistical finite element method for nonlinear, time-dependent problems. This is a statistical augmentation of the finite element method which admits model misspecification inside of the governing equations, via Gaussian processes. The method is Bayesian, sequentially updates model mismatch upon receipt of observed data, and ensures scalability through low-rank approximations to the posterior. In this talk I will present statFEM and discuss various case studies with experimental and synthetic data.

MS [00980] Recent Advances in Applied Mathematics including adopting machine learning and deep learning

room : E504

• [01658] A hybrid difference method and its postprocessings for second order elliptic problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Dongwook Shin (Ajou University)
    • Youngmok Jeon (Ajou University)
    • Eun-Jae Park (Yonsei University)
  • Abstract : In this talk, we investigate a new method, the hybrid difference method, proposed by S., Jeon, and Park (Appl. Math. Comput., 2022), for second order elliptic problems. The hybrid difference method is a finite difference method that is based on the hybrid discontinuous Galerkin method introduced by Jeon and Park (SINUM, 2010). The HD method allows arbitrarily high-order approximations, and the local conservation property holds. The HD method allows arbitrarily high-order approximations, and satisfies the local conservation property. Additionally, it can significantly reduce the global degrees of freedom by the static condensation via Schur complement similar to the HDG method. In the recent work, we have extended and improved the HD method by introducing additional conditions. This new generalized method can be seen as the method introduced by Jeon, Park, and S. (Comput. Methods Appl. Math., 2017) with the addition of a simple postprocessing. To increase computational efficiency, we also introduce a residual type error estimator that allows for the use of adaptive algorithms. The proposed method can be extended to more complex domain geometries through simple modifications, although the local conservation property may not hold in these cases and thus requires further postprocessing. Several numerical experiments are presented to show the performance of the proposed method, which support our theoretical findings.
• [05287] Predicting Thermoelectric Material Properties using Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • YunKyong Hyon (National Institute for Mathematical Sciences)
  • Abstract : According to the development of machine learning technologies, the application of machine learning is already very active in all research areas. Material design requires a lot of calculation and computer resources in its classical process, but the process and period of material development can be shortened by using machine learning methodologies. We present a machine learning model that predicts the properties of materials required for the development of thermoelectric materials and its performance.
• [05338] Classification of respiratory sounds using deep learning methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunju Lee (National Institute for Mathematical Sciences (NIMS))
  • Abstract : Auscultation with a stethoscope has been an essential part of diagnosing patients with respiratory diseases and providing first aid. However, accurate interpretation and diagnosis of auscultation sounds relies on the expertise of clinicians, so it is important to develop an artificial intelligence-based diagnosis support system using respiratory sounds. In this talk, we propose a deep-learning based classification model for respiratory sounds recorded in the clinical setting.
• [05339] Interpretable Classification for Multivariate Gait Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Soon-Sun Kwon (Department of Mathematics/Artificial Intelligence, Ajou University, South Korea)
  • Abstract : Motivated by gait data from both the normal and the cerebral palsy (CP) patients group with various gross motor function classification system (GMFCS) levels, we propose a multivariate functional classification method to investigate the relationship between kinematic gait measures and GMFCS levels. A sparse linear functional discrimination framework is utilized to achieve an interpretable prediction model. The method is generalized to handle multivariate functional data and multi-class classification. The method yields superior prediction accuracy and provides easily interpretable discriminant functions. And it will help clinicians to diagnose CP and assign an appropriate GMFCS level in a more consistent and mathematical evidence.

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

room : E505

• [03752] Large Deviations for Model Coarse Graining
  • Format : Talk at Waseda University
  • Author(s) :
    • Tobias Grafke (Warwick Mathematics Institute)
  • Abstract : Systems with time-scale separation allow effective model reduction via averaging and homogenization, where average effects of fluctuating degrees of freedom are as reduced dynamics. In the language of probability theory, this averaging corresponds to a law-of-large numbers, making it natural to ask about expected fluctuations and large deviations. In this talk, I will introduce developments regarding large deviations in the presence of time-scale separation for the computation of rare event probabilities in reduced models.
• [03592] Mean curvature flow as the limit of a spin system
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick van Meurs (Kanazawa University)
  • Abstract : I will present the derivation of a continuum mean-curvature flow as a certain hydrodynamic scaling limit of a stochastic particle system (Glauber-Kawasaki) on the discrete torus in d dimensions. The particles can jump to neighboring vacant sites and there is a creation and annihilation mechanism. Our work combines techniques from probability theory (in particular the relative entropy method), numerical analysis and PDE theory. Collaborators: T. Funaki, S. Sethuraman, K. Tsunoda.
• [04679] Model reduction methods for non-reversible multiscale dynamics: a comparison
  • Format : Talk at Waseda University
  • Author(s) :
    • Lara Neureither (BTU Cottbus)
  • Abstract : In this talk we will compare existing coarse graining methods such as averaging, effective dynamics as well as the normal form approach among others for multiscale dynamics given by a non-reversible Ornstein-Uhlenbeck process driven by degenerate noise. We will address the following questions: which of the methods yields the best approximation to the original dynamics? What causes the differences in the approaches, if there are any?
• [04002] Model Reduction using the Koopman Operator
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiu Yang (Lehigh University)
    • Bian Li (Lehigh University)
    • Yi-An Ma (University of California at San Diego)
    • J. Nathan Kutz (University of Washington)
  • Abstract : We propose the adaptive spectral Koopman (ASK) method to solve nonlinear autonomous dynamical systems. ASK leverages the spectral method and the Koopman operator to obtain the solution. Specifically, this solution is represented by Koopman operator’s eigenfunctions, eigenvalues, and Koopman modes. Numerical experiments demonstrate high accuracy of ASK for solving both ordinary and partial differential equations. Using ASK as a surrogate model, we can design novel efficient uncertainty quantification methods.

MS [00886] Numerical methods for stochastic partial differential equations

room : E506

• [03909] Space-time Discontinuous Galerkin Methods for the $\varepsilon$-dependent Stochastic Allen-Cahn Equation with mild noise
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dimitra Antonopoulou (University of Chester)
  • Abstract : We consider the $\varepsilon$-dependent stochastic Allen-Cahn equation with mild space-time noise posed on a bounded domain in $\mathbb{R}^d$, $d\geq 1$. The noise tends to rough on the sharp interface limit. This equation is numerically approximated by a space-time discontinuous in time nonlinear Galerkin scheme for which we prove existence and uniqueness. A priori and a posteriori error analysis is applied and error estimates are established.
• [05156] Finite differences method for stochastic heat equation with singular drifts.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ludovic Michel Goudenège (CNRS)
    • El Mehdi Haress (Paris-Saclay University)
    • Alexandre Richard (Paris-Saclay University)
  • Abstract : I will present the numerical approximation of the unique solution to a stochastic heat equation in dimension 1 with distributional drifts under Besov regularity and additive space-time white noise. The approximation is based on a tamed Euler finite-difference scheme with mollified drift. The rate of convergence of the numerical approximation towards the unique strong solution is related to the regularity of the drift. When the Besov regularity increases and the drift becomes a bounded measurable function, we recover the rate of convergence 1/2 in space and 1/4 in time. Some numerical simulations of the stochastic heat equation with Dirac drift or penalization drift will be presented.
• [04362] Numerical schemes and related qualitative properties for degenerate PDEs driven by L𝑒́𝑣𝑦 noise.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ananta Kumar Majee (Indian Institute of Technology Delhi)
    • Soumya Ranjan Behera (Indian Institute of Technology Delhi)
  • Abstract : In this talk, we consider an operator splitting scheme and semi-discrete finite difference scheme for fractional degenerate conserva1on laws driven by L𝑒́𝑣𝑦 noise and degenerate parabolic- hyperbolic PDE with L𝑒́𝑣𝑦 noise respectively. By using necessary a-priori bounds for approximate solutions, generated by splitting scheme, and average time continuity of regularized viscous solutions together with a variant of classical Kru𝑧̌kov’s doubling of variables approach, we prove convergence of approximate solutions to the unique BV entropy solution of the underlying problem. Moreover, the convergence analysis is illustrated by several numerical examples. Furthermore, for compactly supported initial data, we prove that the expected value of the 𝐿1 -difference between the unique entropy solution and the approximate solutions, generated by finite difference scheme, converges at a rate of order 1/7.
• [04784] Linear implicit time-stepping schemes for SPDEs with super-linearly growing coefficients
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaojie Wang (Central South University)
    • Mengchao Wang (Central South University)
  • Abstract : The present talk is on strong approximations of stochastic partial differential equations (SPDEs) with polynomially growing nonlinearity and multiplicative trace-class noise. We propose and analyze a spatio-temporal discretization of the SPDEs, by incorporating a standard finite element method in space and a linear implicit Euler-type scheme for the temporal discretization. We recover the strong convergence rates of the fully discrete scheme.​

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

room : E507

• [01326] A Nonlinear B-spline quasi-interpolation method,
  • Format : Talk at Waseda University
  • Author(s) :
    • Francesc Aràndiga (Universitat de València)
  • Abstract : Quasi-interpolation based on B-spline approximation methods are used in numerous applications. However, we observe that the Gibbs phenomenon appears when approximating near discontinuities. We present nonlinear modifications, based on weighted essentially non-oscillatory (WENO) techniques, of well-known quasi-interpolant methods to avoid this phenomena near discontinuities and, at the same time, maintain the high-order accuracy in smooth regions.
• [01853] Edge adaptive schemes and machine learning for image super-resolution
  • Format : Talk at Waseda University
  • Author(s) :
    • Agustin Somacal (Sorbonne University)
  • Abstract : In image processing Edge-adapted methods are used to reconstruct high-resolution images from coarser cell averages. When images are piece-wise smooth functions, interfaces can be approximated by a pre-specified functional class through optimization LVIRA or specific preprocessing ENO-EA. We extend the ENO-EA approach to polynomials, show two methods to treat vertices and compare with learning-based methods in which an artificial neural network is used to attain the same goal.
• [01411] Univariate subdivision schemes based on local polynomial regression
  • Format : Talk at Waseda University
  • Author(s) :
    • Dionisio F. Yanez (UV)
  • Abstract : The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be solved by means of subdivision schemes. They are a powerful tool that allows obtaining new data from the initial one using simple calculations. In some real applications, the initial data are given with noise and interpolatory schemes are not adequate to process them. In this talk, we present some new families of binary univariate linear subdivision schemes using weighted local polynomial regression. We study their properties, such as convergence, monotonicity and polynomial reproduction and show some examples.
• [01410] Linear and nonlinear approximation rules arising from optimal denoising
  • Format : Talk at Waseda University
  • Author(s) :
    • Sergio López-Ureña (Universitat de València)
  • Abstract : We explore the design of new linear filter-like methods based on the minimization of the noise variance. But linear methods, when applied to data with large gradients, may lead to some kind of Gibbs phenomenon. To overcome this problem, we combine some of these linear methods in a WENO style to obtain a nonlinear denoising method which handles properly large gradients in the data. Some examples are performed to validate the theoretical results.

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

room : E508

• [02061] Preconditioners based on random sampling for solving least squares problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Junfeng Yin (Tongji University)
    • Yuxin Ye (Tongji University)
    • Aqin Xiao (Tongji University)
    • Nan Li (Tongji University)
    • Ning Zheng (Tongji University)
  • Abstract : For the solution of large sparse least squares problems, preconditioned Krylov subspace methods are usually the fist choice and the preconditioners play the important roles in accelerating the convergence of the iteration. After the study on incomplete QR decomposition preconditioners based on Givens rotation, we proposed the preconditioners on random sampling and QR decomposition for solving least squares problems. Theoretical analysis and numerical experiments are presented to show the efficiency of the preconditioners, compared with the existing preconditioners.
• [01654] On Convergence Analysis of the Randomized Gauss-Seidel Method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lu Wang (Hebei Normal University)
  • Abstract : The Gauss-Seidel and Kaczmarz methods are two classical iteration methods for solving systems of linear equations, which operate in column and row spaces, respectively. In this report, by utilizing the inner connections between these two methods and the convergence analysis of the randomized Kaczmarz method, we give a new upper bound for the convergence rate of the randomized Gauss-Seidel method. Moreover, these convergence results are extended to the more general extrapolated randomized Gauss-Seidel method.
• [01890] Condition numbers for the total least squares problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Huaian Diao (Jilin University)
  • Abstract : The total least squares problems (TLS) is a generalization of the linear least squares problem and has many applications in linear system theory, computer vision, image reconstruction, system identification, speech and audio processing, modal and spectral analysis, etc. Perturbation analysis and algorithms for TLS have been studied extensively in the past decades. In this talk, I shall report our recent progresses on condition numbers for TLS.
• [02050] Quantum-inspired algorithm for truncated total least squares solution
  • Format : Talk at Waseda University
  • Author(s) :
    • Yimin Wei (Fudan University)
  • Abstract : Compared with the ordinary least squares method, for total least squares (TLS) problem we take into account not only the observation errors, but also the errors in the measurement matrix, which is more realistic in practical applications. For the large-scale discrete ill-posed problem Ax ≈ b, we introduce the quantum-inspired techniques to approximate the truncated total least squares (TTLS) solution.

MS [00404] Large-Scale Eigenvalue Computations and Optimization

room : E603

• [03188] Estimation of the dominant poles of a large-scale descriptor system
  • Format : Talk at Waseda University
  • Author(s) :
    • Emre Mengi (Koc University)
  • Abstract : The dominant poles of the transfer function of a descriptor system are those poles that can cause large frequency response. They can be used to form reduced-order approximations to the system. We describe a subspace framework to estimate the dominant poles of a large-scale descriptor system based on Petrov-Galerkin projections. The projection subspaces are expanded gradually by means of the dominant poles of the projected systems. We argue formally that the framework converges quadratically.
• [03212] Subspace Methods for Nonlinear Eigenvalue Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Rifqi Aziz (Koc University)
    • Emre Mengi (Koc University)
    • Matthias Voigt (UniDistance Suisse)
  • Abstract : We will discuss numerical methods for nonlinear eigenvalue problems that are described by matrices of large dimension. We project the large matrices within an interpolatory framework in order to obtain a reduced nonlinear eigenvalue problem that can be solved more efficiently. Based on the eigenpair residuals, new interpolation points and corresponding projection matrices can be computed in order to obtain a few eigenvalues close to a desired target point.
• [05296] Optimizing orthogonality in large-scale tensor networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Roel Van Beeumen (Lawrence Berkeley National Laboratory)
  • Abstract : Orthogonality plays a key role in eigenvalue computations. In 1D tensor networks such as tensor trains, the orthogonality is maintained by using QR or truncated SVD factorizations. However, this technique does not extend to 2D tensor networks such as projected entangled pair states (PEPS). Moreover, orthogonality inside a PEPS keeps the computational complexity of eigenvalue evaluations bounded. We will discuss and compare several approximate orthogonalization techniques and strategies for orthogonalizing PEPS columns and rows.
• [05462] Linearizability of eigenvector nonlinearities
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elias Jarlebring (KTH Royal Institute of Technology)
  • Abstract : We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear functions of the eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) that contains the exact solutions of the NEPv. Based on the linearization we propose numerical schemes that exploit the structure of the linearization.

MS [02527] AI for Healthcare and Medicine

room : E604

• [02894] Data Collaboration Cox Proportional Hazards Model for Privacy-preserving Survival Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Akira Imakura (University of Tsukuba)
    • Ryoya Tsunoda (University of Tsukuba Hospital)
    • Rina Kagawa (University of Tsukuba)
    • Kunihiro Yamagata (University of Tsukuba)
    • Tetsuya Sakurai (University of Tsukuba)
  • Abstract : In recent years, privacy-preserving machine learning for datasets held by multiple organizations in a distributed manner has been attracted attention. In this study, we focus on privacy-preserving survival analysis for datasets held by multiple medical institutions and propose a data collaboration technique that shares dimensionality-reduced intermediate representations instead of raw data. The proposed DC-COX can calculate the contribution of each feature to survival time and the corresponding p-value. Numerical experiments verify the effectiveness of DC-COX.
• [05307] AI-Enhanced Medical Imaging Analysis: Advancing Precision Treatment for NSCLC Brain Metastases
  • Format : Talk at Waseda University
  • Author(s) :
    • Cheyu Hsu (National Taiwan University Hospital)
  • Abstract : In this talk, we discuss the innovative use of radiomics and deep learning in AI-enhanced medical imaging analysis for managing NSCLC brain metastases. Through automated segmentation, we streamline diagnosis and treatment planning. The presentation delves into predicting local recurrence after radiosurgery, detecting EGFR mutations, and evaluating distant metastases or brain metastases velocity in radiosurgery-treated patients. Our focus on AI-driven methodologies fosters tailored, precision treatment strategies, ultimately enhancing patient outcomes for those with NSCLC brain metastases.
• [05001] Explainability and Fairness of Distributed Data Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Bogdanova (University of Tsukuba)
    • Tetsuya Sakurai (University of Tsukuba)
    • Akira Imakura (University of Tsukuba)
  • Abstract : Ensuring fairness and transparency in machine learning models is critical for their ethical application in the medical field. With the increasing use of distributed machine learning to protect patient privacy, there is a growing need to address the challenges of explainability and fairness in medical data analysis. Machine learning models trained on horizontally or vertically partitioned medical data may present difficulties for explainability, as different participants may have a biased view of the background data or a partial view of the feature space, leading to inconsistencies in the explanations obtained. To address these issues, this paper proposes an Explainable Data Collaboration Framework that combines a model-agnostic additive feature attribution algorithm (KernelSHAP) with a privacy-preserving distributed machine learning method called Data Collaboration. The framework offers three algorithms for various scenarios of explainability in medical data collaboration, which were tested on open-access medical datasets. In addition, we show that our proposed framework can be combined with fairness-sensitive data representation techniques to eliminate data biases at the local level.
• [05362] Mitigating Non-IID Data Challenges in Federated Learning for Healthcare Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Fan Zhang (University of Cambridge)
  • Abstract : Federated Learning has emerged as a promising technique for healthcare applications, enabling collaboration among different healthcare institutions without sharing sensitive data. Data in each healthcare institution usually has a unique distribution, leading to non-IID (independent and identically distributed) data that can impact model performance and convergence in Federated Learning. In this talk, we will present the findings of non-IID challenges in Federated Learning and recommendations for the strategies we evaluated to mitigate these challenges.

MS [00622] Inverse Problems and Imaging

room : E605

• [01577] 3D image reconstruction for cone beam computed tomography using sparsity
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Meaney (University of Helsinki)
    • Samuli Siltanen (University of Helsinki)
  • Abstract : Cone beam computed tomography is an increasingly popular three-dimensional medical imaging technique. However, in many settings it suffers from suboptimal image quality. In this work, we will present a new approach to regularized iterative image reconstruction. Our technique has an in-built automatic choice of the regularization parameter, based on a priori knowledge on gradient sparsity. Combined with a novel primal-dual optimization algorithm, this results in an efficient technique for large-scale reconstruction of improved quality.
• [01591] High Dynamic Range Tomography via Modulo Radon Transform
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthias Beckmann (University of Bremen)
  • Abstract : Recently, practitioners in tomography proposed high dynamic range solutions that are inspired by multi-exposure fusion strategies in computational photography. In this talk, we propose a single-shot alternative based on the novel Modulo Radon Transform, which folds Radon projections via modulo non-linearity into the dynamic range of the sensor to avoid information loss due to saturation. We propose a sequential reconstruction algorithm, which is backed by mathematical guarantees, and illustrate our theoretical results by numerical simulations.
• [01593] A new inversion scheme for elastic diffraction tomography
  • Author(s) :
    • Bochra Mejri (RICAM, Austria Johann Radon Institute for Computational and Applied Mathematics)
    • Otmar Scherzer (University of Vienna)
  • Abstract : We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties, i.e. mass density and elastic Lamé parameters, of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the 2D Fourier transform of scattered waves with the Fourier transform of the scatterer in the 3D spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into four modes. A new two-step inversion process is developed, providing information on the modes first and secondly on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.
• [01606] inverse electromagnetic scattering problems with internal dipoles
  • Format : Talk at Waseda University
  • Author(s) :
    • Yakun Dong (University of Vienna)
    • Otmar Scherzer (University of Vienna)
    • Kamran Sadiq (Radon Institute for Computational and Applied Mathematics)
  • Abstract : We propose a method to reconstruct the optical properties of inverse scattering problems with internal sources. The method is based on macroscopic Maxwell’s equations and achieves super-resolution reconstruction. Applications in single-molecule localization microscopy are shown.

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

room : E606

• [03144] Mittag-leffler stability of Fractional-order Neural Networks with time-varying delays
  • Author(s) :
    • wei ding
    • xiang zhu (Shanghai Normal University)
  • Abstract : This paper mainly studies a kind of fractional-order neural networks with time-varying delays. By using the mean value theorem of integrals, inequality technique and Banach fixed point theorem, the Mittag-leffler stability of the unique equilibrium point of the system can be proved when some satisfied conditions are built.
• [03170] Singular Riemann problems and their applications
  • Author(s) :
    • Aifang Qu (Shanghai Normal University)
  • Abstract : In this talk, we will focus on a class of singular Riemann problems which contain concentration supported at the initial discontinuity. It corresponds to the study of a class of measure partial differential equations. Further, we will briefly introduce some applications of these problems to the study of hypersonic limit flow passing a wedge, fluid-structure interaction problems and conservation laws with discontinuous flux.
• [03270] Gas-liquid Phase Transition Problem for Non-isentropic Compressible Euler Equations
  • Author(s) :
    • Pei-yu Zhang (Shanghai Normal University)
  • Abstract : We study gas-liquid phase transition problem described by one-dimensional non-isentropic Euler equations. For this purpose, we solve the Riemann problem for non-isentropic Euler equations in the class of Radon measure. The difficulty is to find a meaningful solution to Riemann problem that satisfies the occurrence of this gas-liquid phase transformation phenomenon. This provide a new way of thinking for the study of gas-liquid phase transition.
• [03286] Accelerated subgradient-extragradient methods for VIPs and CFPPs implicating countable nonexpansive-operators
  • Author(s) :
    • Yun-ling Cui (shanghai normal university)
  • Abstract : In a real Hilbert space, let the VIP and CFPP denote the variational inequality problem and common fixed-point problem of countable nonexpansive operators and asymptotically nonexpansive operator, respectively. In this paper, we construct two modified Mann-type subgradient extragradient rules with a linear-search process for finding a common solution of the VIP and CFPP. We demonstrate the strong convergence of the suggested rules to a common solution of the VIP and CFPP.

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

room : E701

• [05336] Value function approximation of PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazufumi Ito (North Carolina State University)
  • Abstract : \title{\bf Value function approximation of PDEs} \author{Kazufumi Ito\thanks{Department of Mathematics, North Carolina State University, USA} \noindent {\bf Abstract} In this paper we discuss a value function approximation of a general class of nonlinear system of parabolic equations. Our approach is based on the backward stochastic differential equations of nonlinear expectation. The approach uses the discrete time dynamic programing formulation of the value function update. It results in an operator splitting of the diffusion term and a semi-implicit method for the nonlinear hyperbolic term. It is very easy to implemented and provides an accurate value function approximation. We apply the method several applications including elliptic interface problems, conservation laws and Navier-Stokes equations. We analyze the stability and convergence of the proposed method. Numerical results are presented to demonstrate the applicability
• [03699] A hybrid asymptotic and augmented compact FVM for degenerate interface problem with extreme conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhiyue Zhang (Nanjing Normal University)
  • Abstract : An accurate and efficient numerical method has been proposed for degenerate interface problem with extreme conditions such as very big jump ratio, coefficient blow-up and geometric singularity interface . The scheme combines Puiseux series asymptotic technique with augmented fourth order compact finite volume method for the problem. Error estimates are obtained. Numerical examples confirm the theoretical analysis and efficiency of the method. We also apply this method for solving time dependent problems and 2D problems.
• [03531] A fast front-tracking approach for a temporal multiscale blood flow problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Ping Lin (University of Dundee)
    • Zhenlin Guo (Beijing Computational Science Research Center)
  • Abstract : We consider a blood flow problem (fast system) coupled with a slow plaque growth with memory effect (slow system) at the artery wall. We construct an auxiliary temporal periodic problem and an effective time-average equation to approximate the original problem and analyze the approximation error of the corresponding PDE system, where the front-tracking technique is used to update the moving boundary. An effective multiscale method is then designed and its approximation error is analysed.
• [03479] An Energy Stable Immersed Boundary Method for Deformable Membrane Problem with Non-uniform Density and Viscosity
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dongdong He (The Chinese University of Hong Kong, Shenzhen)
    • Qinghe Wang (The Chinese University of Hong Kong, Shenzhen)
    • Mingyang Pan (Hebei University of Technology)
    • Yu-Hau Tseng (Kaohsiung University)
  • Abstract : Membrane problems commonly encountered in engineering and biological applications involve large deformations and complex configurations. Immersed boundary method, formulated by the fluid equations in which the fluid-structure interaction is described in terms of the Dirac function, is one of the most powerful tools to simulate such problems. However, the IB method suffers from severe time step restrictions to maintain stability if the discretization lacks conservation of energy, especially for two-phase flows. In this paper, we develop an energy stable IB method for solving deformable membrane problems with non-uniform density and viscosity. Unlike the classic IB formulation, the evolution of membrane, including elastic tension and bending force, is controlled by its tangent angle and arc length. After minor modifications, it is shown that the model satisfies the continuous energy law. Thus, for the reformulated model, we proposed an implicit unconditionally energy stable scheme, where the energy of the scheme is proved to be dissipative. The resultant system is solved iteratively and the numerical results show that the proposed scheme is energy stable and capable of predicting the dynamics of extensible and inextensible interface problems with non-uniform density and viscosity.

MS [00952] Numerical methods for emerging flow problems in geosciences

room : E702

• [02375] A stability solver for nonlinear mountain waves
  • Format : Talk at Waseda University
  • Author(s) :
    • Craig Epifanio (Texas A&M University)
    • Prabir Daripa (Texas A&M University)
    • Kevin Viner (Naval Research Lab, Monterey)
  • Abstract : One of the primary sources of clear-air turbulence in the atmosphere is the breaking of internal gravity waves forced by topography, otherwise known as mountain waves. In the present work, the linear stability of nonlinear mountain waves is considered through the application of a steady-state Newton solver combined with a discretized large eigenvalue problem. The results show that mountain waves are subject to instability over a broader range of parameters than previously considered.
• [02890] Coupling numerical solutions of NS and GFD equations for ocean flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Hansong Tang (City College of New York)
  • Abstract : This talk discusses the integration of a solver of the Navier Stokes (NS) equations and a solver for the geophysical fluid dynamics (GFD) equations. In the integrated system, the NS solver is applied to local, fully 3D flow phenomena, and the GFD solver is adopted to simulate the background ocean flows. We will discuss the coupling methods and numerical experiments. The presentation will also discuss the difficulties and topics of future study.
• [02177] A machine learning approach to phytoplankton productivity across the GoM
  • Format : Talk at Waseda University
  • Author(s) :
    • Bailey Armos (Texas A&M University)
    • Shuang Zhang (Texas A&M University)
    • Prabir Daripa (Texas A&M University)
  • Abstract : Although the hypoxia and algal bloom events seen within the Gulf of Mexico (GoM) have been largely linked to nitrogen loading from the Mississippi River, the nutrient inputs from smaller have been largely unexplored. In this study, we built machine learning models from coupled river-ocean data to better understand and quantify the chlorophyll content on multiple timescales in different regions of the GoM. Our study will help mitigation strategies in a changing coastal environment.

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

room : E703

• [03859] Efficient Schwarz Preconditioning Techniques for Nonlinear Problems Using FROSch
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Heinlein (Delft University of Technology (TU Delft))
    • Axel Klawonn (University of Cologne)
    • Mauro Perego (Sandia National Laboratories)
    • Sivasankaran Rajamanickam (Sandia National Laboratories)
    • Lea Saßmannshausen (University of Cologne)
    • Ichitaro Yamazaki (Sandia National Laboratories)
  • Abstract : FROSch (Fast and Robust Overlapping Schwarz) is a framework for parallel Schwarz domain decomposition preconditioners in Trilinos. Due an algebraic approach, meaning that the preconditioners can be constructed from a fully assembled matrix, FROSch is applicable to a wide range of problems. This talk is focused on the application to nonlinear problems, including computational fluid dynamics and land ice simulations. Techniques for improving the efficiency and the use of GPU architectures are discussed.
• [01916] BDDC Algorithms for Oseen problems with HDG Discretizations
  • Format : Talk at Waseda University
  • Author(s) :
    • Xuemin Tu (University of Kansas)
  • Abstract : In this talk, the balancing domain decomposition by constraints methods (BDDC) are applied to the linear system arising from the Oseen equation with the hybridizable discontinuous Galerkin (HDG) discretization. The original system is reduced to a subdomain interface problem which is asymmetric indefinite but can be positive definite in a special subspace. Edge/face average constraints can ensure all BDDC preconditioned GMRES iterates stay in this special subspace. Some additional edge/face constraints are used to improve the convergence. When the viscosity is large and the subdomain size is small enough, the number of iterations is independent of the number of subdomains and depends only slightly on the subdomain problem size. When the viscosity is small, the convergence can deteriorate.
• [02272] Fully implicit multi-physics solver for advanced fission nuclear power plant
  • Format : Talk at Waseda University
  • Author(s) :
    • Han Zhang (Tsinghua University)
  • Abstract : The fission nuclear reactor power plant is a multi-physics, multi-scale and multi-component coupling system, resulting in a nonlinear partial differential equation system. Fully-implicit methods, such as the Jacobian-free Newton-Krylov method and the Newton-Krylov method, are promising choices for effectively solving such complex nonlinear systems due to their super-linear convergence rate. This talk focuses on the development of fully-implicit solution method for the advanced nuclear reactor power plant, as well as its engineering application.
• [01417] Recent advances on high-performance computing algorithms for patient-specific blood flow simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Rongliang Chen (Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences)
  • Abstract : Patient-specific blood flow simulations have the potential to provide quantitative predictive tools for virtual surgery, treatment planning, and risk stratification. To accurately resolve the blood flows based on the patient-specific geometry and parameters is still a big challenge because of the complex geometry and the turbulence, and it is also important to obtain the results in a short amount of computing time so that the simulation can be used in surgery planning. In this talk, we will precent some recent results of the multi-organ blood flow simulations with patient-specific geometry and parameters on a large-scale supercomputer. Several mathematical, biomechanical, and supercomputing issues will be discussed in detail. We will also report the parallel performance of the methods on a supercomputer with a large number of processors.

MS [02402] Numerical methods for a class of time-dependent PDEs

room : E704

• [02622] IMPROVED UNIFORM ERROR BOUNDS OF THE TIME-SPLITTING HERMITE SPECTRAL METHODS FOR THE LONG-TIME GROSS PITAEVSKII EQUATION WITH WEAK NONLINEARITY
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhongyang Liu (Beijing Normal University)
  • Abstract : The aim of this research is to carry out a improved uniform error bounds for the Strang splitting Hermite pseudospectral methods for the long-time dynamics of the time-dependent Gross–Pitaevskii equation (GPE) with weak nonlinearity, while the nonlinearity strength is characterized by $\epsilon^2$ with a dimensionless parameter $\epsilon\in (0,1]$, for the long time dynamics up to the time at $O(\epsilon^{-2})$. We derive a improved uniform $H_A^1$ error bounds for full discretizations of the one-dimensional GPE by the Strang splitting Hermite pseudospectral method as $O(N^{\frac{2}{3}-\frac{m}{2}}+\epsilon^2\tau^2)$ up to the time at $O(1/\epsilon^2)$. The error bounds are uniformly accurate up to the time at $O(\epsilon^{-2})$ and uniformly valid for $\epsilon.$

MS [00052] Efficient numerical methods for high-dimensional PDEs

room : E705

• [04128] Designing High-Dimensional Closed-Loop Optimal Control Using Deep Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiequn Han (Flatiron Institute, Simons Foundation)
  • Abstract : Designing closed-loop optimal control for high-dimensional nonlinear systems remains a long-standing challenge. Traditional methods, such as solving the Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality. Recent studies introduced a promising supervised learning approach, utilizing deep neural networks to learn from open-loop optimal control solutions. From a PDE standpoint, this method learns solutions along characteristic lines. This talk will first overview this method and identify a limitation in its basic form, the distribution mismatch phenomenon, caused by controlled dynamics. We then propose the initial value problem enhanced sampling method to address this issue. The proposed method presents theoretical guarantees of improvement over the basic version in the classical linear-quadratic regulator and demonstrates significant improvement numerically on several high-dimensional nonlinear problems.
• [04563] An Inverse Problem in Mean Field Games from Partial Boundary Measurement
  • Format : Talk at Waseda University
  • Author(s) :
    • Yat Tin Chow (University of California, Riverside)
    • Samy Wu Fung (Colorado School of Mines)
    • Siting Liu (University of California, Los Angeles)
    • Levon Nurbekyan (University of California, Los Angeles)
    • Stanley Osher (University of California, Los Angeles)
  • Abstract : In this talk, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the population dynamics under the limited aperture. Due to its severe ill-posedness, obtaining a good quality reconstruction is very difficult. Nonetheless, it is vital to recovering the model parameters stably and efficiently to uncover the underlying causes of population dynamics for practical needs. Our work focuses on the simultaneous recovery of running cost and interaction energy in the MFG equations from a finite number of boundary measurements of population profile and boundary movement. To achieve this goal, we formalize the inverse problem as a constrained optimization problem of a least squares residual functional under suitable norms. We then develop a fast and robust operator splitting algorithm to solve the optimization using techniques including harmonic extensions, three-operator splitting scheme, and primal-dual hybrid gradient method. Numerical experiments illustrate the effectiveness and robustness of the algorithm.
• [04470] Automatic partitioning for Boolean CME Low-Rank integrator
  • Format : Talk at Waseda University
  • Author(s) :
    • Martina Prugger (University of Innsbruck)
    • Lukas Einkemmer (University of Innsbruck)
  • Abstract : Cell signaling processes are usually modeled by chemical reactions encoded in a system of ordinary differential equations. The resulting model is deterministic and omits the inherent stochasticity of cell reactions. This is mostly due do the fact, that solving the Chemical Master Equation (CME), which resolves the inherent probabilistic states of the chemical system suffers from the curse of dimensionality. This results in high computational and memory requirements, that prohibit the simulation of the CME for system sizes that are usually required for practical applications. We developed a low-rank integrator for the CME for Boolean networks that enables us to simulate systems to a size of up to 41 different chemical species on a workstation. An integral part of this method is to partition the network into multiple sub-partition, on which the CME is solved exactly. Key to an efficient solver is the distribution of species, while keeping the approximation error between the networks to a minimum. While for small networks, this can still be done easily by a person, for a network of the size of e.g., 41 species, this is no longer feasible. We therefore introduce an automatic partitioner by using the Kernighan-Lin algorithm to select multiple networks that minimize the amount of connections between the sub-networks. We then use information enthropy that evaluates each of the chosen networks. This results in an automatic partitioning tool that reduces the rank that is required to faithfully resolve the biological dynamics.

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

room : E708

• [05281] Computational Models of Cardiac Electro-mechanical Function – Closing the Gaps between Virtual and Physical Reality
  • Format : Talk at Waseda University
  • Author(s) :
    • Gernot Plank (Medical University of Graz)
  • Abstract : A fundamental concern hampering a broader adoption of digital twins in cardiology application is the lack of correspondence between the physiology of a virtual heart and the physical reality. We report on our latest advances addressing these issues. Real-time enabled whole heart electrophysiology as well as computationally efficient whole heart multi-physics models of cardiac electro-mechanics will be discussed, along with techniques for automated patient-specific model calibration.
• [04706] Scaling cardiac digital twins for population-based studies
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuang Qian (King's College London)
    • Devran Ugurlu (King's College London)
    • Elliot Fairweather (King's College London)
    • Marina Strocchi (King's College London)
    • Laura dal toso (King's College London)
    • Yu Deng (King's College London)
    • Alistair Young (King's College London)
    • Martin Bishop (King's College London)
    • Pablo Lamata (King's College London)
    • Steven Niederer (King's College London)
  • Abstract : Cardiac digital twins, provide a physics and physiology-constrained framework, enabling personalised diagnosis and tailored therapies for individual patients. However, building patient-specific digital twins at scale remains challenging. This talk presents an open-sourced automatic pipeline of generating finite element biventricular heart models from CMRs in the UK biobank. Using this pipeline, each digital twin can be created in only 8 mins on a standard desktop, compatible with clinical time scales and also enabling large scale virtual population-based studies.
• [04251] A Local Space-Time Adaptive Scheme to Simulate Cardiac Electrophysiology
  • Format : Talk at Waseda University
  • Author(s) :
    • Dennis Ogiermann (Ruhr University Bochum, Chair of Continuum Mechanics)
    • Luigi E. Perotti (University of Central Florida, Mechanical and Aerospace Engineering Department, Computational Biomechanics Lab)
    • Daniel Balzani (Ruhr University Bochum, Chair of Continuum Mechanics)
  • Abstract : Cardiac electrophysiology simulations are often based on the monodomain model, which is characterized by traveling waves with a steep localized wavefront and slow changes in the remaining domain. This aspect renders schemes based on uniform spatial and temporal discretization expensive. We present a numerical scheme that exploits the localized nature of the rapidly changing wavefront by combining discontinuous Galerkin on an adaptive mesh for the spatial discretization with an elementwise explicit local time stepping.
• [03847] Parallel Performance of Robust and Scalable Multilevel Preconditioners in Cardiac Electrophysiology
  • Format : Talk at Waseda University
  • Author(s) :
    • Edoardo Centofanti (Università degli Studi di Pavia)
  • Abstract : The EMI (Extracellular space, cell Membrane and Intracellular space) model is among the first models for describing the electrical activity of the heart at a cellular level. The resulting system of equations allows discontinuities of potentials between boundaries as well as particular distributions of ion charges on the cellular membranes. In this talk, we will study the performances of different multigrid and multilevel solvers for the solution of such systems both on CPU and GPU architectures.

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

room : E709

• [03089] Error estimates to smooth solutions of high order Runge–Kutta discontinuous Galerkin method for scalar nonlinear conservation laws with and without sonic points
  • Format : Talk at Waseda University
  • Author(s) :
    • Qiang Zhang (Nanjing University)
  • Abstract : In this talk we shall take the fourth order in time Runge--Kutta discontinuous Galerkin method, as an example of high order schemes, to establish a sharp a priori L$^2$-norm error estimates for sufficiently smooth solutions of one-dimensional scalar nonlinear conservation laws. The optimal order of accuracy in time is obtained under the standard Courant-Friedrichs-Lewy condition, and the quasi-optimal and/or optimal order of accuracy in space are achieved for many widely-used numerical fluxes, no matter whether the exact solution contains sonic points or not. Note that the convergence order in space strongly depends on the relative upwind effect of the used numerical flux, which is related to the local flowing speed and the strength of the numerical viscosity provided by the used numerical flux. Two main tools are used in this talk. One is the matrix transferring process, based on the temporal differences of stage errors. It gives a useful energy equation and help us to get the theoretical result under the acceptable temporal-spatial condition. The other is the generalized Gauss-Radau projection of the reference functions, which depends on the relative upwind effect and helps us to achieve the optimal order in space in many cases. Finally some numerical experiments are given to support the theoretical results.
• [02994] Energy stable discontinuous Galerkin methods for compressible Navier–Stoles–Allen–Cahn System
  • Format : Talk at Waseda University
  • Author(s) :
    • Qiaolin He (Sichuan University)
    • Xiaoding Shi (Beijing University of Chemical Technology)
  • Abstract : In this work, we present a fully discrete local discontinuous Galerkin (LDG) finite element method combined with scalar auxiliary variable (SAV) approach for the compressible Navier--Stokes--Allen--Cahn (NSAC) system. We start with a linear and first order scheme for time discretization and the minimal dissipation LDG for spatial discretization, which is based on the SAV approach and is proved to be unconditionally energy stable for one dimensional case. The velocity, the density and the mass concentration of fluid mixture can be solved separately. In addition, a semi-implicit spectral deferred correction (SDC) method combined with the first order scheme is employed to improve the temporal accuracy. Due to the local properties of the LDG methods, the resulting algebraic equations at the implicit level are easy to implement. In particular, we use efficient and practical multigrid solvers to solve the resulting algebraic equations. Although there is no proof of stability for the semi-implicit SDC with LDG spatial discretization, numerical experiments of the accuracy and long time simulations are presented to illustrate the high order accuracy in both time and space, the discretized energy stability, the capability and efficiency of the proposed method. Numerical results show that the initial state determines the long time behavior of the diffusive interface for the two--phase flow, which are consistent with theoretical asymptotic stability results.
• [02714] Superconvergence of LDG method for nonlinear convection-diffusion equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiong Meng (Harbin Institute of Technology)
  • Abstract : In this talk, we present superconvergence properties of the local discontinuous Galerkin (LDG) methods for solving nonlinear convection-diffusion equations in one space dimension. The main technicality is an elaborate estimate to terms involving projection errors. By introducing a new projection and constructing some correction functions, we prove the $(2k+1)$th order superconvergence for the cell averages and the numerical flux in the discrete $L^2$ norm with polynomials of degree $k\ge 1$, no matter whether the flow direction $f'(u)$ changes or not. Superconvergence of order $k +2$ $(k +1)$ is obtained for the LDG error (its derivative) at interior right (left) Radau points, and the convergence ord er for the error derivative at Radau points can be improved to $k+2$ when the direction of the flow doesn't change. Finally, a supercloseness result of order $k+2$ towards a special Gauss-Radau projection of the exact solution is shown. The superconvergence analysis can be extended to the generalized numerical fluxes and the mixed boundary conditions. All theoretical findings are confirmed by numerical experiments.
• [03001] An essentially oscillation-free discontinuous Galerkin method for hyperbolic conservation laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Liu (ICMSEC, AMSS, CAS)
    • Jianfang Lu (South China University of Technology)
    • Chi-Wang Shu (Brown University)
  • Abstract : In this talk, we propose a novel discontinuous Galerkin (DG) method to control the spurious oscillations when solving the scalar hyperbolic conservation laws. The spurious oscillations may be harmful to the numerical simulation, as it not only generates some artificial structures not belonging to the problems but also causes many overshoots and undershoots that make the numerical scheme less robust. To overcome this difficulty, we introduce a numerical damping term to control spurious oscillations based on the classic DG formulation. Compared to the classic DG method, the proposed DG method still maintains many good properties, such as the extremely local data structure, conservation, L2-boundedness, optimal error estimates, and superconvergence. We also extend our methods to systems of hyperbolic conservation laws. Entropy inequalities are crucial to the well-posedness of hyperbolic conservation laws, which help to select the physically meaningful one among the infinite many weak solutions. By combining with quadrature-based entropy-stable DG methods, we also developed the entropy-stable OFDG method. For time discretizations, the modified exponential Runge--Kutta method can avoid additional restrictions of time step size due to the numerical damping. Extensive numerical experiments are shown to demonstrate our algorithm is robust and effective.

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

room : E710

• [03195] Finite element analysis for semilinear problems in liquid crystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Neela Nataraj (Professor )
    • Ruma Maity (Postdoc Fellow)
    • Apala Majumdar (Strathclyde University)
  • Abstract : A unified framework for the error control of different lowest-order finite element methods for approximating the regular solutions of systems of partial differential equations is established under a set of hypotheses. The systems involve cubic nonlinearities in lower order terms, non-homogeneous Dirichlet boundary conditions, and the results are established under minimal regularity assumptions on the exact solution. The results for existence and local uniqueness of the discrete solutions using Newton-Kantorovich theorem and error control are presented. The results are applied to conforming, Nitsche, discontinuous Galerkin, and weakly over penalized symmetric interior penalty schemes for variational models of ferronematics liquid crystals.
• [01845] Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Ricardo Ruiz Baier (Monash University)
    • Martin Hornkjøl (University of Oslo)
    • Alberto Martin (Australian National University)
    • Santiago Badia (Monash University)
    • Kent-Andre Mardal (University of Oslo)
    • Arbaz Khan (IIT Roorkee)
  • Abstract : We present a new stress/total-pressure formulation for poroelasticity that incorporates the coupling with steady nonlinear diffusion modified by stress. This nonlinear problem is written in mixed-primal form, which combines a perturbed twofold saddle-point system with an elliptic problem. We analyze the continuous formulation within the framework of abstract fixed-point theory and Fredholm alternative for compact operators. A mixed finite element method is proposed, and its stability and convergence are analyzed. The resulting model can be used to study the steady case of waste removal in the brain, providing insight into the transport of solutes in poroelastic structures under the influence of stress.
• [03220] Finite element analysis for the Navier-Lamé eigenvalue problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Jesus Vellojin (Universidad del Bío-Bío)
    • Felipe Lepe (Universidad del Bío Bío)
    • Gonzalo Rivera (Universidad de Los Lagos)
  • Abstract : In this talk, the author presents the eigenvalue problem for the Navier-Lamé system. The analysis of the spectral problem is based in the compact operators theory. A finite element method based in polynomials of degree $k\geq 1$ is considered. An a posteriori error analysis is performed, where the reliability and efficiency of the proposed estimator is proved. A series of numerical tests are reported in order to assess the performance of the proposed numerical method.
• [04279] Isogeometric solvers for derived cardiac stem cell reaction-diffusion models
  • Format : Talk at Waseda University
  • Author(s) :
    • Sofia Botti (Università della Svizzera Italiana and University of Pavia)
    • Michele Torre (University of Pavia)
  • Abstract : Regenerative cardiology is recently employing human induced pluripotent stem cells derived cardiomyocytes to advance in patient-specific medicine. A multiphysics approach to the problem allows to couple the cardiac Monodomain reaction diffusion model with stem cell ionic models to simulate the action potential propagation in the engineered ventricle. The coupled model is then discretized using Isogeometric Analysis in space and finite differences in time to obtain a virtual representation of a derived cardiomyocytes ventricle.

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

room : E711

• [04905] Staggered DG methods for elliptic problems on general meshes
  • Format : Talk at Waseda University
  • Author(s) :
    • Eun-Jae Park (Yonsei University)
  • Abstract : In this talk, we present our recent framework on staggered DG methods for elliptic equations on general meshes, which can be flexibly applied to rough grids such as highly distorted meshes. Adaptive mesh refinement is an attractive tool for general meshes due to their flexibility and simplicity in handling hanging nodes. We derive a simple residual-type error estimator. Numerical results indicate that optimal convergence can be achieved for both the potential and vector variables, and the singularity can be well-captured by the proposed error estimator. Then, some applications to Darcy-Forchheimer equations, Stokes equations, and linear elasticity equations are considered. This is joint work with Eric Chung, Dohyun Kim, Dong-wook Shin, and Lina Zhao.
• [04160] Accelerated Gradient and Skew-Symmetric Splitting Methods for Monotone Operator Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jingrong Wei (University of California, Irvine)
    • Long Chen (University of California at Irvine)
  • Abstract : A class of monotone operator equations, which can be decomposed into sum of a gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized accelerated gradient flow, accelerated gradient and skew-symmetric splitting (AGSS) methods are developed and shown to achieve linear rates with optimal lower iteration complexity when applied to smooth saddle point systems with bilinear coupling.
• [03693] Solve electromagnetic interface problems on unfitted meshes
  • Format : Talk at Waseda University
  • Author(s) :
    • Ruchi Guo (University of California Irvine)
  • Abstract : Electromagnetic interface problems widely appear in a lot of engineering applications, such as electric actuators, invasive detection techniques and integrated circuit，which are typically described by Maxwell equations with discontinuous coefficients. Conventional finite element methods require a body-fitted mesh to solve interface problems, but generating a high-quality mesh for complex interface geometry is usually very expensive. Instead using unfitted mesh finite element methods can circumvent mesh generation procedure, which greatly improve the computational efficiency. However, the low regularity of Maxwell equations makes its computation very senstive to the conformity of the approximation spaces. This very property poses challenges on unfitted mesh finite element methods, as most of them resort to non-conforming spaces. In this talk, we will present our recent progress including several methods for this topic.
• [03714] Pressure-robust virtual element methods for the Stokes problem on polygonal meshes
  • Format : Talk at Waseda University
  • Author(s) :
    • Gang Wang (Northwestern Polytechnical University)
  • Abstract : In this talk, we shall introduce two pressure-robust virtual element methods for the Stokes problem on polygonal meshes. The standard virtual element scheme involves a pressure contribution in the velocity error. To achieve the pressure-independent velocity approximation, we define an H(div)-conforming velocity reconstruction operator for the velocity test function and propose the modified scheme by employing it in the approximation of right-hand-side source term assembling. In the first method, we apply the H(div)-conforming elements on the polygons and construct a (theoretically) exactly pressure-robust virtual element scheme. Since basis functions of H(div)-conforming elements are not polynomials on general polygons, quadrature errors will affect the exact pressure-robustness in implementation. To solve it, we reconstruct a (theoretically and numerically) exactly pressure-robust virtual element scheme by designing H(div)-conforming element based on the sub-triangulation of polygon and the lowest-order Raviart-Thomas element. We give the error estimates of two methods and also show numerical examples to support our theories.

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

room : E802

• [02988] A multiscale preconditioner for simulating blood flows in artery with aneurysm
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiao-Chuan Cai (University of Macau)
  • Abstract : In this talk, we discuss some recent development of numerical methods for the simulation of blood flows in patient-specific arteries with aneurysm. Depending on the branching geometry and the patient parameters, the flow can be quite complicated with local vortex structures, but the principal component of the flow is always along the centerline of the artery. Based on this observation, we introduce a two-scale domain decomposition method for unsteady incompressible Navier-Stokes equations in three-dimensional complex patient-specific arteries, and the key component of the preconditioner is a parameterized one-dimensional unsteady Navier-Stokes or Stokes coarse problem defined along the centerline of the artery. The one-dimensional preconditioner and some overlapping three-dimensional subdomain preconditioners are combined additively to form the two-scale method via interpolations using radial basis functions. The most important feature of the method is that the cost of solving the coarse problem is nearly neglectable compared with the subdomain solver. Numerical experiments indicate that the proposed method is highly effective and robust for complex arteries with many branches and aneurysm. This is a joint work with Yingzhi Liu and Fenfen Qi.
• [04469] Spectral Element discretizations in cardiac electrophysiology: a matrix-free approach
  • Format : Talk at Waseda University
  • Author(s) :
    • Pasquale Claudio Africa (mathLab, SISSA International School for Advanced Studies, Trieste)
    • Matteo Salvador (Stanford University)
    • Paola Gervasio (Università degli Studi di Brescia)
  • Abstract : We propose a high-order Spectral Element Method (SEM) matrix-free solver for the numerical solution of cardiac electrophysiology. We compare it to SEM with Numerical Integration and demonstrate that increasing the local polynomial degree leads to improved accuracy and faster computations than reducing the mesh size. Our matrix-free approach, enhanced by a suitable implementation of a Geometric Multigrid (GMG) preconditioner, yields up to 45\(\times\) speed-up compared to a conventional matrix-based solver. Several numerical experiments are analyzed.
• [03783] Monolithic solution strategies for large-scale computational problems from physiology and astrophysics
  • Format : Online Talk on Zoom
  • Author(s) :
    • pietro benedusi (Simula Research Laboratory )
    • Rolf Krause (Università della Svizzera italiana)
    • Patrick Zulian (Università della Svizzera italiana)
  • Abstract : Currently, many problems in applied mathematics result in large-scale computational challenges which require the use of massively parallel machines and scalable solution strategies to minimize the time to solution. In this talk, we present monolithic strategies to numerically solve partial differential equations, for various applications. These strategies consist in framing, whenever possible, a computational problem in a large and possibly sparse (non) linear system which can be solved, in parallel, combining efficient preconditioning techniques and Krylov methods. By contrast, many traditional staggered approaches are based on the solution of a sequence of smaller computational problems. An example of such a paradigm can be found when solving evolutionary problems, where a monolithic strategy (also known as all-at-once approach) can be used, resulting in the assembly of large a space-time system with a block Toeplitz structure, in contrast to standard sequential time-stepping techniques. In this context, we consider the space-time discretization of the anisotropic diffusion equation, using isogeometric analysis in space and a discontinuous Galerkin approximation in time. Drawing inspiration from a former spectral analysis of space-time operators, we propose a parallel multigrid preconditioned GMRES method. The application of this multilevel space-time strategy to non-linear reaction-diffusion problems from electrophysiology (i.e. the monodomain equation and the EMI model) will be also discussed, considering comparison with other recently developed methods. Moreover, we present a monolithic approach to simulate radiative transfer in stellar atmospheres; in this scenario, we present a matrix-free implementation of a multi-fidelity preconditioner. Through simulations on massively parallel systems, we show how monolithic strategies can improve software scalability and discuss the trade-offs of this approach.
• [04869] Platform Portable Distributed Solvers and Preconditioners in Cardiac Simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Fritz Goebel (Karlsruhe Institute of Technology)
    • Hartwig Anzt (Karlsruhe Institute of Technology)
    • Terry Cojean (Karlsruhe Institute of technology)
    • Marcel Koch (Karlsruhe Institute of Technology)
  • Abstract : In the European MICROCARD project we work on simulating the electrophysiology of the human heart with a new Cell-by-Cell model. The model's high resolution and the resulting linear systems pose a computational challenge. In this talk we report on recent developments on scaleable Krylov Methods and Preconditioners in the open source library Ginkgo that we aim to leverage in these simulations.

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

room : E803

• [04191] Multiple Integer Divisions with an Invariant Dividend
  • Format : Talk at Waseda University
  • Author(s) :
    • Daisuke Takahashi (University of Tsukuba)
  • Abstract : In this talk, we propose an algorithm for multiple integer divisions with an invariant dividend and monotonically increasing or decreasing divisors. In such multiple integer divisions, we show that if the dividend and divisors satisfy a certain condition, then if only one quotient is calculated by division first, the remaining quotients can be obtained by correcting the previously calculated quotients at most once.
• [04628] Reduced-Precision Data Representation on Sparse Matrix-Vector Multiplications
  • Format : Talk at Waseda University
  • Author(s) :
    • Daichi Mukunoki (RIKEN Center for Computational Science)
    • Masatoshi Kawai (Nagoya University)
    • Toshiyuki Imamura (RIKEN Center for Computational Science)
  • Abstract : In sparse iterative solvers, data and arithmetic precision affect convergence and solution accuracy, and their precision can be optimized. There is a demand for its kernel, sparse matrix vector multiplication (SpMV), with different precision. Due to its memory-intensive nature, SpMV could benefit from low-precision floating-point formats to improve performance. In this talk, we demonstrate the performance of our SpMV implementations on CPU and GPU, allowing precision adjustment in 8-bit increments from 16 to 64 bits.
• [04862] High-performance multidimensional integration
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elise Helene de Doncker (Western Michigan University)
  • Abstract : Techniques for parallel multidimensional integration will be presented, with applications to Feynman loop integrals in high energy physics. Integrand singularities are addressed with adaptive region partitioning, transformations, and convergence acceleration via linear or nonlinear extrapolation. Parallel implementations are commonly layered over a platform that interfaces with the underlying computer architecture, including MPI (Message Passing Interface), OpenMP for iterated multi-threaded integration, and CUDA kernels supporting integrand evaluation for lattice type rules on thousands of GPU CUDA cores.
• [04875] Introducing MPLAPACK 2.0.1: An Extension of BLAS and LAPACK for Multiple Precision Computation
  • Format : Talk at Waseda University
  • Author(s) :
    • Maho Nakata (RIKEN)
  • Abstract : MPLAPACK, a multiple-precision extension of LAPACK, offers enhanced numerical linear algebra capabilities. Translated from Fortran 90 to C++ using FABLE, MPLAPACK 2.0.1 supports MPBLAS, real and complex versions, and all LAPACK features except mixed-precision routines. Porting legacy C/C++ numerical codes is straightforward, and it supports various numerical libraries for diverse precision levels. MPLAPACK offers OpenMP acceleration for some routines and CUDA support for specific double-double versions. Achieving impressive performance, MPLAPACK is available under the 2-clause BSD license on GitHub.

MS [00390] Recent Advances in Machine Learning Theory and Applications

room : E804

• [01397] Learning Ability of Interpolating Convolutional Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Tian-Yi Zhou (Georgia Institute of Technology)
    • Xiaoming Huo (Georgia Institute of Technology)
  • Abstract : It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully connected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under underparameterized and overparameterized settings. We establish the best learning rates of underparameterized DCNNs without parameter restrictions presented in the literature. We also show that, by adding well-defined layers to an underparameterized DCNN, we can obtain some interpolating DCNNs that maintain the good learning rates of the underparameterized DCNN. This result is achieved by a novel network deepening scheme designed for DCNNs. Our work provides theoretical verification of how overfitted DCNNs generalize well.
• [03542] Classification with Deep Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Lei Shi (Fudan University)
    • Zihan Zhang (Fudan University & City University of Hong Kong)
    • Dingxuan Zhou (University of Sydney)
  • Abstract : Classification with deep neural networks (DNNs) has made impressive advancements in various learning tasks. Due to the unboundedness of the target function, generalization analysis for DNN classifiers with logistic loss remains scarce. This talk will report our recent progress in establishing a unified framework of generalization analysis for both bounded and unbounded target functions. Our analysis is based on a novel oracle-type inequality, which enables us to deal with the boundedness restriction of the target function. In particular, for logistic classifiers trained by deep fully connected neural networks, we obtain the optimal convergence rates only by requiring the H\"{o}lder smoothness of the conditional probability. Under certain circumstances, such as when decision boundaries are smooth and the two classes are separable, the derived convergence rates can be independent of the input dimension. This talk is based on joint work with Zihan Zhang and Prof. Ding-Xuan Zhou.
• [03729] Robust Deep Learning with Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Qiang Wu (Middle Tennessee State University)
    • Shu Liu (Middle Tennessee State University)
  • Abstract : Deep neural networks are playing increasing roles in machine learning and artificial intelligence. Their performance highly depends on the network architecture and the loss function. The classical square loss is widely known to be sensitive to outliers. We propose the use of robust loss and two stage algorithms for deep neural networks, which are able to extract robust features and deal with outliers effectively. Applications in regression analysis and adversarial machine learning will be discussed.

MS [00168] Applications of evolutionary algorithms in differential equation models

room : E811

MS [00211] Mathematics of Geometric Deep Learning

room : E812

• [01769] Machine Learning in Banach Spaces: A Black-box or White-box Method?
  • Author(s) :
    • Qi Ye (South China Normal University)
  • Abstract : In this talk, we study the whole theory of regularized learning for generalized data in Banach spaces including representer theorems, approximation theorems, and convergence theorems. Specially, we combine the data-driven and model-driven methods to study the new algorithms and theorems of the regularized learning. Usually the data-driven and model-driven methods are used to analyze the black-box and white-box models, respectively. With the same thought of the Tai Chi diagram, we use the discrete local information of the black-box and white-box models to construct the global approximate solutions by the regularized learning. Our original ideas are inspired by the eastern philosophy such as the golden mean. The work of the regularized learning for generalized data provides another road to study the algorithms of machine learning including: 1. the interpretability in approximation theory, 2. the nonconvexity and nonsmoothness in optimization theory, 3. the generalization and overfitting in regularization theory. Moreover, based on the theory of the regularized learning, we will construct the composite algorithms combining the model‑driven and data‑driven methods for our current research projects of the big data analytics in education and medicine.
• [01857] Stable Hyperbolic Neural Networks for Graph Generation and Classification
  • Author(s) :
    • Eric Qu (Duke Kunshan University)
    • Dongmian Zou (Duke Kunshan University)
  • Abstract : The past few years have witnessed successful development of hyperbolic neural networks. However, they are known to suffer from instability in training. In this talk, we present two recent works that build novel hyperbolic layers for generation and classification tasks on tree-like and hierarchical-structured data. The first defines a stable hybrid AE-GAN model; the second defines a hyperbolic convolutional layer built upon pre-defined kernel points. We illustrate their competitiveness by showing extensive numerical results.
• [02110] Spectral-Inspired Graph Neural Networks
  • Author(s) :
    • Teresa Huang (Johns Hopkins University)
  • Abstract : Message Passing Neural Networks (MPNNs) can suffer from expressivity issues like over-smoothing and over-squashing. To mitigate such issues, we propose PowerEmbed -- a simple layer-wise normalization technique to boost MPNNs. We show PowerEmbed can provably express the top-k leading eigenvectors of the graph operator, which prevents over-smoothing and is agnostic to the graph topology; meanwhile, it produces a list of representations ranging from local features to global signals, which avoids over-squashing.
• [01563] Negative sampling for graph neural networks based on determinantal point processes
  • Author(s) :
    • Junyu Xuan (University of Technology Sydney)
  • Abstract : Graph neural networks (GNNs) have become the de facto standard of a variety of graph-based applications. Most GNNs are built on a message-passing mechanism and only aggregate information from the first-order neighbours (positive samples), which may lead to over-smoothing, limited expressive power and over-squashing. However, beyond these neighbouring nodes, graphs have a large, dark, all-but forgotten world in which we find the non-neighbouring nodes (negative samples) that are helpful for representation learning.

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

room : E817 -> A715 (changed)

• [02843] Insights from Nonlinear Continuous Data Assimilation for Turbulent Flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Elizabeth Carlson (University of Victoria)
    • Adam Larios (University of Nebraska - Lincoln)
    • Edriss S Titi (University of Cambridge)
  • Abstract : One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. An emerging approach to data assimilation known as the Azouani-Olson-Titi (AOT) algorithm introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. The solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this talk, we will focus on the insights of a nonlinear version of the AOT algorithm and distinguish the clear connections to the physics of the existing systems.
• [02852] Linear response for nonlinear dissipative SPDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Giulia Carigi (University of L'Aquila)
    • Jochen Bröcker (University of Reading)
    • Tobias Kuna (University of L'Aquila)
  • Abstract : A framework suitable to establish response theory for a class of nonlinear stochastic partial differential equations is provided, exploiting coupling methods. The results are applied to the 2D stochastic Navier-Stokes equation and the stochastic two-layer quasi-geostrophic model. In particular, studying the response to perturbations in the forcings for models in geophysical fluid dynamics gives a mathematical insight into whether statistical properties derived under current conditions will be valid under different forcing scenarios.
• [05078] Data assimilation of the 2D rotating NSE
  • Format : Talk at Waseda University
  • Author(s) :
    • Aseel Farhat (Florida State University)
  • Abstract : With sufficiently fast rotation, the solution of the 2D rotating NSE on the $\beta$ plane approaches a nearly zonal state. Additionally, the number of degrees of freedom of the system decrease with faster rotation. We validate this analytically and numerically in the context of a continuous data assimilation algorithm based on nudging.
• [02847] Using machine learning in geophysical data assimilation (some of the issues and some ideas)
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alberto Carrassi (Dept of Physics, University of Bologna)
  • Abstract : We show how ML can be included in the prediction and DA workflow in different ways. First, in “non-intrusive” ML, we show how supervised ML estimates the local Lyapunov exponents. ML is then combined with DA in an integrated fashion to learn a surrogate model from noisy and sparse data, and a parametrization of a physical’s model unresolved scales. DA is pivotal to extract information from the sparse, noisy, data that ML cannot handle alone.

MS [00448] Particle based methods

room : E818

• [04587] Alternatives to Monte Carlo based sampling and high dimensional integration
  • Format : Talk at Waseda University
  • Author(s) :
    • Sahani Pathiraja (University of New South Wales)
  • Abstract : Monte Carlo is a fundamental component of popular methods for uncertainty quantification and Bayesian inference. However, Monte Carlo based techniques are often inefficient in high dimensions, representing distributional tails and in complex time-dependent systems. This is in part due to the reliance on points (i.e. delta functions) to approximate distributions. We numerically and analytically investigate the performance of various sampling techniques that make use of alternatives to delta functions and compare to standard Monte Carlo.
• [05018] Mixtures of Gaussian Process Experts with SMC^2
  • Format : Talk at Waseda University
  • Author(s) :
    • Lassi Roininen (LUT University)
  • Abstract : Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate, while still being thoroughly parallelizable.
• [05073] Eulerian calibration for stochastic transport models
  • Format : Talk at Waseda University
  • Author(s) :
    • Oana Andrea Lang (Imperial College London)
  • Abstract : In this talk I will talk about a new probabilistic approach for calibrating a general class of stochastic nonlinear fluid dynamics models. A key step for ensuring the successful application of the combined stochastic parameterisation and data assimilation procedure is the “correct” calibration of stochastic model parameters. Currently, most methodologies are based on Lagrangian particle trajectories which are simulated starting from each point on both the physical grid and its refined version. Then the differences between the particle positions are used to calibrate the noise. This is computationally expensive and not fully justified from a theoretical perspective. We currently explore an Eulerian approach based on calibrating the amplitude of the individual noises to obtain an approximate representation of uncertainty that uses a finite set of individual noises, and in this talk I will report on the current advances. This is joint work with Prof Dan Crisan and Dr Alexander Lobbe (Imperial College London).
• [05209] Can possibility theory help with uncertainty quantification for neural networks?
  • Format : Talk at Waseda University
  • Author(s) :
    • Jeremie Houssineau (University of Warwick)
  • Abstract : We consider an alternative to the Gaussian version of the stochastic weight averaging method (SWAG), an approach to uncertainty quantification in neural networks. It is well accepted that the uncertainty in the parameters of the network is epistemic rather than being induced by randomness, which motivates the use of possibility theory. We will see how possibility theory helps to overcome difficulties with standard Bayesian neural networks and how it leads to an alternative to SWAG.

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

room : E819

• [03973] Distance estimates for action-minimizing solutions of the n-body problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Bo-Yu Pan (National Chung-Hsing University)
  • Abstract : In this talk we estimate mutual distances of action minimizing solutions for the n-body problem. We will present some quantitative estimates for these solutions, including their action values and bounds for their mutual distances. These estimates will facilitate numerical explorations to locate and search new orbits effectively.
• [04970] Some progress on the N-center problem by variational methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Kuo-Chang Chen (National Tsing Hua University)
  • Abstract : Since Chenciner-Montgomery’s construction of the figure-8 orbit for the 3-body problem, in the past 20+ years variational methods have succeeded in discovering new solutions for the N-body and N-center problems, within certain symmetry of topological classes. I will briefly outline recent progress, main ideas and obstacles, and some ongoing research topics for the N-center problem. In particular, I will outline variational construction of satellite orbits for N=2, and recent joint works with Guowei Yu on periodic and chaotic orbits for N>2.
• [04318] Periodic solutions bifurcated from the figure-eight choreography: non-planar eight and non-symmetric eight
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Fukuda (Kitasato University)
    • Toshiaki Fujiwara (Kitasato University)
    • Hiroshi Ozaki (Tokai University)
  • Abstract : The figure-eight choreography of equal mass three bodies under the homogeneous potential $-1/r^\alpha$ and under the Lennard-Jones type potential $1/r^{12}-1/r^6$, bifurcates in power $\alpha$ and in period T, respectively, where $r$ is a distance between bodies. We found two interesting bifurcation solutions: a figure-eight choreography with an orbit having no spatial symmetry, and a non-planar figure-eight solution which is unfortunately not choreographic.
• [04797] Variational structures for infinite transition orbits of monotone twist maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuika Kajihara (Kyoto university)
  • Abstract : There is a lot of study on the dynamics of area-preserving maps, and Poincare and Birkhoff's works are well-known. In this talk, we define a special class of area-preserving maps called monotone twist maps to consider the variational structures of area-preserving maps. Variational structures determined from twist maps can be used for constructing characteristic trajectories of twist maps. Our goal is to define the variational structure such as giving infinite transition orbits through minimizing methods.

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

room : E820

• [04833] On the motion of several small rigid bodies in a viscous incompressible fluid
  • Format : Talk at Waseda University
  • Author(s) :
    • Eduard Feireisl (Czech Academy of Sciences)
  • Abstract : We consider the motion of N rigid bodies immersed in a viscous incompressible fluid contained in a domain in the Euclidean space Rd, d = 2; 3. We show the fluid flow is not influenced by the presence of the bodies in the asymptotic limit as when the radius of the bodies tends to zero sufficiently fast. The result depends solely on the geometry of the bodies and is independent of their mass densities. Collisions are allowed and the initial data are arbitrary with finite energy.
• [05105] On the motion of a fluid-filled elastic solid
  • Format : Talk at Waseda University
  • Author(s) :
    • Giusy Mazzone (Queen's University)
  • Abstract : Consider the physical system constituted by an elastic solid with an interior cavity entirely filled by a viscous incompressible fluid. The motion of the coupled system is governed by the Navier equations of linear elasticity for the solid, and the Navier-Stokes equations for the fluid. Continuity of stresses and velocities are imposed at the fluid-solid interface, while a zero-traction condition is imposed at the other free boundary of the solid. I will present some results on the existence of strong solutions to the governing equations and discuss their stability properties.
• [05124] Gevrey regularity of a certain fluid-structure PDE interaction
  • Format : Talk at Waseda University
  • Author(s) :
    • George Avalos (University of Nebraska-Lincoln)
  • Abstract : In this talk, we present recent results concerning the qualitative behavior of a coupled partial differential equation (PDE) system which describes a certain fluid-structure interaction (FSI), as it occurs in nature. With respect to the associated strongly continuous contraction semigroup for this model, we present our recent results of Gevrey regularity.
• [05184] Numerical benchmarking of FSI - efficient discretization and numerical solution
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jaroslav Hron (Charles University, Prague)
  • Abstract : The lecture will give an overview of the problem of fluid-structure interaction motivated by blood flow in deformable vessels. Possible discretizations by the finite element method and different coupling strategies will be discussed with a focus on the efficient numerical solution of the monolithic problem. We will discuss some simple benchmark type problems of fluid structure interaction based on finding a suitable simple arrangement with self-induced oscillations.

MS [00666] Simulations and Algorithms for Materials Sciences

room : D101

• [04335] Molecular Dynamics Simulation of Concentrated Entangled Polymers in Athermal Solvents
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiayi wang (HKUST)
  • Abstract : We have developed a coarse-grained model to simulate the geometric and dynamical properties of entangled polymer chains dissolved in athermal solvents. Our model successfully verifies the concentration scaling relationships of the geometric characteristics. In terms of the dynamical aspect, we have discovered that the swelling of the entangled polymer chains in athermal solvents leads to enhanced local chain stiffness or effective system elastic modulus.
• [04386] Multiscale modeling and Simulations of Interfacial Defects in based on PN model
  • Author(s) :
    • Shuyang Dai (Wuhan University)
  • Abstract : A multiscale continuum model is developed to describe the defect structures in crystalline material such as FCC metals. The interface structure for twist, tilt and misfit grain boundaries are described by the dislocation network. The model incorporates both the anisotropy elasticity of each grain in crystalline materials and the molecular dynamics calculation informed interaction between two bulks, i.e., the nonlinear generalized stacking-fault energy. The equilibrium structures are obtained from the numerical simulations of the force balance differential equations. We apply this approach to determine the structure and energetics of twist, tilt and general grain boundaries. We also investigated the dislocation structure in heterogeneous crystalline material. Our model agrees well with the atomistic results. An analytical description is developed based on the obtained structural features.
• [04817] Solving integral equations on non-smooth boundaries
  • Format : Talk at Waseda University
  • Author(s) :
    • Shidong Jiang (Center for Computational Mathematics, Flatiron Institute, Simons Foundation)
    • Johan Helsing (Lund University)
  • Abstract : A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations on non-smooth boundaries. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. The performance of the scheme is illustrated via several numerical examples.
• [05284] A fast algorithm for Dirichlet partition problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Dong Wang (The Chinese University of Hong Kong, Shenzhen)
  • Abstract : A Dirichlet k-partition of a domain is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace--Dirichlet eigenvalues is minimal. In this talk, we propose a new relaxation of the problem by introducing auxiliary indicator functions of domains and develop a simple and efficient diffusion generated method to compute Dirichlet k-partitions for arbitrary domains. The method only alternates three steps: 1. convolution, 2. thresholding, and 3. projection. The method is simple, easy to implement, insensitive to initial guesses and can be effectively applied to arbitrary domains without any special discretization. At each iteration, the computational complexity is linear in the discretization of the computational domain. Moreover, we theoretically prove the energy decaying property of the method. Experiments are performed to show the accuracy of approximation, efficiency and unconditional stability of the algorithm. We apply the proposed algorithms on both 2- and 3-dimensional flat tori, triangle, square, pentagon, hexagon, disk, three-fold star, five-fold star, cube, ball, and tetrahedron domains to compute Dirichlet k-partitions for different k to show the effectiveness of the proposed method. Compared to previous work with reported computational time, the proposed method achieves hundreds of times acceleration.

MS [00062] Analysis and computation of vortical flows

room : D102

• [00075] Motion of three geostrophic vortices
  • Format : Talk at Waseda University
  • Author(s) :
    • Sun-Chul Kim (Chung-Ang University, Seoul, Korea (Republic of))
    • Habin Yim (Chung-Ang University, Seoul, Korea (Republic of))
    • Sung-Ik Sohn (Gangneung-Wonju National University)
  • Abstract : We investigate the dynamics of geostrophic Bessel vortices focusing on the three-vortex case, where the possibility of self-similar motion and general dynamics for arbitrary strengths is studied. It is found that self-similar motions are limited to rigid rotations and self-similar triple collapse is impossible. For a general description, trilinear coordinates are adopted. The physical regions in the phase plane cannot be directly identified, but the boundary approaches the vertices of the triangle in trilinear coordinates in geostrophic vortices.
• [00126] Self-similar vortical flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Volker Wilhelm Elling (Academia Sinica, Taipei)
  • Abstract : Vortex spirals and vortex cusps are important features of self-similar vortical flows near stagnation points. Vortex sheets produced at triple points of Mach reflection have distinguished signs that determine whether interaction with walls or symmetry axes can be attached cusps or detached jets. Progress on analysis, modelling and numerics for such phenomena is discussed, along with applications to shock reflection or non-uniqueness of vortical flows.
• [00150] Near-singular integrals in 3D interfacial Stokes and potential flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Monika Nitsche (University of New Mexico)
  • Abstract : Boundary integral formulations yield efficient numerical methods to solve elliptic boundary value problems. They are the method of choice for interfacial fluid flow in either the inviscid vortex sheet limit, or the viscous Stokes limit. The fluid velocity at a target point is given by an integral over all interfaces. However, for target points near, but not on the interface, the integrals are near-singular and standard quadratures lose accuracy. While several accurate methods for near-singular integrals exist in planar geometries, they do not generally apply to the non-analytic case that arises in axisymmetric or 3D geometries. We present a method based on Taylor series expansions of the integrand about basepoints on the interface that accurately resolve a large class of integrals, and apply it to solve the near-interface problem in planar vortex sheet flow, axisymmetric Stokes flow, and Stokes flow in 3D. The application to multi-nested Stokes flow uses a novel representation of the fluid velocity.
• [00147] The FARSIGHT Vlasov-Poisson code
  • Format : Talk at Waseda University
  • Author(s) :
    • Robert Krasny (University of Michigan)
    • Ryan Sandberg (Lawrence Berkeley National Laboratory)
    • Alexander Thomas (University of Michigan)
  • Abstract : We present electrostatic plasma simulations using a new semi-Lagrangian particle method for the Vlasov-Poisson equations called FARSIGHT. The electron density is represented on adaptively refined and remeshed panels in phase space, and the macroparticles are advected using a regularized electric field kernel and a GPU-accelerated barycentric Lagrange treecode. Results are presented for Landau damping, two-stream instability, and ion beam propagation. Work supported by AFOSR grant FA9550-19-1-0072.

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

room : D401

• [00597] Systematic search for singularities in 3D Euler flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Bartosz Protas (McMaster University)
    • Xinyu Zhao (McMaster University)
  • Abstract : We consider the question about formation of singularities in incompressible Euler flows. Based on the local well-posedness result guaranteeing existence of smooth solutions in the Sobolev space $H^m$, $m>5/2$, we search for potentially singular flows systematically by solving a PDE optimization problem where the $H^3$ norm is maximized at time $T$. Solutions of this problem obtained using an adjoint-based gradient descent method indicate the possibility of singularity formation if the time $T$ is sufficiently long.
• [00371] Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching and related topics
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsuyoshi Yoneda (Hitotsubashi University)
    • Susumu Goto (Osaka University)
    • Tomonori Tsuruhashi (University of Tokyo)
  • Abstract : With the aid of direct numerical simulations of forced turbulence in a periodic domain, we mathematically reformulate the Kolmogorov-Richardson energy cascade in terms of vortex stretching. More precisely, under the assumptions of the scale-locally of the vortex stretching/compressing process and the statistical independence between vortices that are not directly stretched or compressed, we can derive the -5/3 power law of the energy spectrum of statistically stationary turbulence without directly using the Kolmogorov hypotheses.
• [03746]  Structure and scaling of extremely large velocity gradients in hydrdynamic turbulence.
  • Format : Talk at Waseda University
  • Author(s) :
    • Alain Pumir (CNRS and Ecole Normale Supérieure de Lyon)
    • Dhawal Buaria (New York University)
  • Abstract : I will discuss extreme events in the velocity gradient tensor of turbulent flows, using data from Direct Numerical Simulations (DNS) of turbulent flows up to a Taylor-scale Reynolds number of 1300. I will review some essential properties of the velocity gradient tensor, and in particular, the dependence of the strain, conditioned on vorticity, and the dependence on the Reynolds number of the probability density functions of the vorticity and strain. These properties lead to the proposition of a simple framework to quantify the extreme events and the smallest scales of turbulence. This work accentuates the importance of the relation between strain and vorticity in developing an accurate understanding of intermittency in turbulence. In exploring further this relation, I will discuss the unexpected role of strain for very intense vortices, and discuss the self-attenuation of intense vortices in DNS of turbulent flows.
• [00303] A model of turbulent flows based on a random Constantin-Lax-Majda-DeGregorio equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Sakajo (Kyoto University)
    • Yuta Tsuji (Kyoto University)
  • Abstract : The generalized Constantin-Lax-Majda-DeGregorio (gCLMG) equation with the viscous dissipation under a large-scale forcing is utilized as a one-dimensional model of turbulent flows generating the cascade of the conserved quantity. In this talk, we show the global existence of a unique solution of the gCLMG equation subject to random forcing functions that are chosen from a given distribution. Moreover, we numerically investigate the solutions' statistical properties by Galerkin approximation of random variables with generalized Polynomial Chaos.

MS [00118] On mathematical modeling and simulation of droplets

room : D402

• [01886] Hybrid Asymptotic-Numerical Methods for Two-Phase Flow With Soluble Surfactant
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Booty (New Jersey Institute of Technology)
  • Abstract : Surfactant molecules diffuse slowly in bulk flows because of their size, so that the Peclet number of surfactant diffusion is large, and transfer between a stretched drop interface and bulk flow occurs in a thin layer adjacent to the interface that is about one thousandth of the drop radius. Analytical and numerical results of asymptotic, boundary integral, and conformal mapping techniques are presented. This is joint work with Michael Siegel, Ryan Atwater and Samantha Evans.
• [01260] A phase field model for a drop suspended in viscous liquids under the influence of electric fields
  • Format : Talk at Waseda University
  • Author(s) :
    • Shixin Xu (Duke Kunshan Univeristy)
    • Yuzhe Qin (Shanxi University)
    • Huangxiong Huang (Beijing Normal University)
  • Abstract : In this talk, we consider modeling the deformation of a droplet under an electric field. Firstly, we derive the Poisson-Nernst-Planck-Navier-Stokes phase field model based on the energy variational method, and then we obtain a general phase-field leaky dielectric model taking into account the capacitance according to the electroneutrality. Then a detailed asymptotic analysis confirms that the sharp interface limit of our proposed diffusive-interface model is consistent with the sharp interface model. We take a series of numerical experiments to validate the correctness and effectiveness of our model. The numerical result shows the validity of the asymptotic analysis by comparing the diffuse interface method and existing immersed boundary method results. Finally, we compare the deformations for the interface with and without the capacitance. It shows that the capacitance will weak the formation of droplets.
• [05478] Phase-field modeling of colloid-polymer mixtures in microgravity
  • Format : Talk at Waseda University
  • Author(s) :
    • Anand Oza (New Jersey Institute of Technology)
  • Abstract : We present a theoretical model for colloid-polymer mixtures in a microgravity environment. The addition of polymer to a colloidal suspension induces weakly attractive forces between the colloids and leads to a three-phase coexistence region, wherein liquid phase "droplets" coexist with a low-density gas phase and a high-density crystal phase. Colloid-polymer mixtures are thus an archetype for modeling phase transition processes, but the details of the observed colloidal structures remain poorly understood. We construct, analyze and numerically simulate a phase-field model for structure evolution in colloid-polymer mixtures. The model consists of the Cahn-Hilliard equation, which describes phase separation processes in multicomponent mixtures, coupled with the Stokes equation for viscous fluid flow. The results of the model are compared against experiments performed on the International Space Station, using data available on the NASA Physical Sciences Informatics system.

MS [01933] Fluid-structure interactions in Stokes flows

room : D403

• [05143] Accurate close interactions in Stokes flow using coarse grids
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Broms (KTH Royal Institute of Technology)
    • Alex Barnett
    • Anna-Karin Tornberg (KTH Royal Institute of Technology)
  • Abstract : With the aim of controlling the accuracy in near-contacts of rigid particles in viscous flows with a computationally cheap method, we introduce a singularity-free technique that combines the method of fundamental solutions and the method of images. Sources on inner proxi boundaries are complemented as needed by a small set of extra singularities at locations obtained by considering an image system. Results are compared to a well-resolved boundary integral equation method.
• [04881] Bounds on particle configurations in an active suspension
  • Format : Talk at Waseda University
  • Author(s) :
    • Scott Weady (Flatiron Institute)
  • Abstract : We present bounds on orientational order parameters in the Doi-Saintillan-Shelley kinetic theory of active suspensions. Using the energy method, we show isotropic suspensions are nonlinearly stable for sufficiently low activity. A similar approach admits nontrivial bounds on time averages of order parameters for all levels of activity that are consistent with nonlinear simulations. This work highlights the organizing role of activity in particle suspensions and places precise limits on how organized such systems can be.
• [04858] Drag force on spherical particles trapped at a liquid interface
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhi Zhou (Northwestern University)
    • Petia M Vlahovska (Northwestern University)
    • Michael J Miksis (Northwestern University)
  • Abstract : Here we present a combined asymptotic and numerical investigation of the fluid motion past spherical particles attached to a deformable interface undergoing uniform creeping flows in the limit of small Capillary number and small deviation of the contact angle from 90 degrees. The drag and torque coefficients are computed as a function of the contact angle, the viscosity ratio, the Bond number, the slip coefficient along the particle surface, and the distance between two particles.
• [05148] Bacterial collective motion and spread in porous media
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yasser Almoteri (New Jersey Institute of Technology)
    • Enkeleida Lushi (New Jersey Institute of Technology)
  • Abstract : We investigate through modeling, analysis and nonlinear simulations, the motion of micro-swimmers in fluids with resistance, which approximates porous wet media. We use a continuum model to describe the dynamics of bacteria each performing run-and-tumble motions, coupled to the dynamics of the immersing fluid modeled by the Stokes-Brinkman equation with an added active stress. The linear stability of the uniform isotropic state reveals that the Brinkman resistance weakens or fully suppresses the chaotic motion of the bacterial suspension. Simulations of the full nonlinear PDE system confirm the analytical results. We discuss how the fluid resistance inhibits the spread of bacteria, and its interplay with auto-chemotactic interactions and food chasing give rise to non-trivial dynamics. Last, we discuss simulations of the coupled motion of many individually-traced micro-swimmers in Brinkman flows.

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

room : D404

• [00618] L1 maximalr regularity and its application to the Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshihiro Shibata (Department of Mathematics, Waseda University)
  • Abstract : I will talk about the L1 maximal regularity theorem to the Stokes equations and its application to free boundary problem for the Navier-Stokes equations.
• [03780] Fluid flow on surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Gieri Simonett (Vanderbilt University)
    • Mathias Wilke (Martin-Luther-Universität Halle-Wittenberg)
  • Abstract : I will consider the motion of an incompressible viscous fluid on compact surfaces without boundary. Local in time well-posedness is established in the framework of $L_p$-$L_q$ maximal regularity for initial values in critical spaces. It will be shown that the set of equilibria consists exactly of the Killing vector fields. Each equilibrium is stable and any solution starting close to an equilibrium converges at an exponential rate to a (possibly different) equilibrium. In case the surface is two-dimensional, it will be shown that any solution with divergence free initial value in $L_2$ exists globally and converges to an equilibrium.
• [04880] The Curve Shortening Flow for Immersed Curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Guidotti (UC Irvine)
  • Abstract : We will revisit and study the curve shortening flow for immersed curves and its numerical computation.
• [03690] On a thermodynamically consistent model for magnetoviscoelastic fluids in 3D
  • Format : Talk at Waseda University
  • Author(s) :
    • Hengrong Du (Vanderbilt University)
    • Yuanzhen Shao (University of Alabama)
    • Gieri Simonett (Vanderbilt University)
  • Abstract : In this talk, we consider a system of equations that model a non-isothermal magnetoviscoelastic fluid, which is thermodynamically consistent. The system is analyzed by means of the Lp-maximal regularity theory. First, we will discuss the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Finally, we will show that that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria.

MS [00814] Inverse Problems for Moving Targets

room : D405

MS [00915] The mathematics of quantum interaction models

room : D407

• [03826] The spectral problem in Hilbert spaces of analytic functions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Daniel Braak (University of Augsburg)
  • Abstract : In the standard Hilbert space, the spectral problem of Hamilton operators with one degree of freedom takes the form of a lateral connection problem for functions with diverging power series expansions. According to common lore, the solution would require to construct these functions on the whole real line which is usually impossible. It will be demonstrated that this brute-force approach can be avoided by employing Hilbert spaces of analytic functions.
• [03426] The weak limit of renormalized Rabi Hamiltonian
  • Format : Talk at Waseda University
  • Author(s) :
    • Fumio Hiroshima (Kyushu Univerity)
  • Abstract : The weak limit of the renormalized Rabi Hamiltonian with a symmetry breaking term is investigated. It is shown that the spectral zeta function converges to the Riemann zeta function as the coupling constant goes to infinity. Furthermore the asymptotic behavior of the expectation of the number operator is also discussed.
• [03971] PT-Symmetric Quantum Rabi Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Murray Batchelor (Australian National University)
  • Abstract : We explore a PT-symmetric qubit coupled to a quantized light field. The model is solved analytically using the adiabatic approximation (AA) in the parameter regime of interest. We investigate the static and dynamic properties, using both the AA and numerical diagonalization. A series of exceptional points vanish and revive depending on the light-matter coupling strength. This talk is based on arXiv:2212.06586 with X. Lu, H. Li, J.-K. Shi, L.-B. Fan, V. Mangazeev and Z.-M. Li.
• [03421] Spectrum of the noncommutative harmonic oscillator and number theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazufumi Kimoto (University of the Ryukyus)
  • Abstract : The noncommutative harmonic oscillator (NCHO) is a system of differential equations defined by a certain matrix-valued operator, and it is connected to the quantum Rabi model via a confluent process in the Heun differential equation picture. In the talk, I will present number-theoretic aspects of the spectral zeta function of the NCHO, especially those arising from its special values (i.e. values at positive integers).

MS [02557] Collaboration of machine learning and physics-based simulation on earthquake disasters

room : D408

• [03984] Position-dependent inpainting for ground motion interpolation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hirotaka Hachiya (Wakayama University)
  • Abstract : Acquiring continuous spatial data is essential to assess the damaged area just after the earthquake. To this purpose, we propose a framework of supervised spatial interpolation and apply highly advanced deep inpainting methods with the introduction of position-dependent partial convolution, where convolution kernel weights are adjusted depending on their position on an image based on the trainable position-feature map. We show the effectiveness of our proposed method, through experiments using ground-motion data.
• [05004] Construction of strong motion database for data-driven ground-motion prediction models
  • Format : Talk at Waseda University
  • Author(s) :
    • Asako Iwaki (National Resesarch Institute for Earth Science and Disaster Resilience)
    • Nobuyuki Morikawa (National Resesarch Institute for Earth Science and Disaster Resilience)
    • Takahiro Maeda (National Research Institute for Earth Science and Disaster Resilience)
    • Hiroyuki Fujiwara (National Resesarch Institute for Earth Science and Disaster Resilience)
  • Abstract : We have been developing a strong-motion observation database as an infrastructural database utilized for seismic hazard assessment, from which data-driven regression models for ground-motion prediction (ground-motion models; GMMs) are to be constructed. The database is “biased” because there are insufficient number of records with large magnitudes and short distances. Consequently, GMMs are incapable of predicting such ground motion. To overcome this issue, we attempt to utilize simulated ground motion data to supplement the observation database.
• [04967] Linkage of physics simulation and machine learning towards seismic risk assessment
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuzo Yamashita (NIED)
    • Jun Fujiwara (NIED)
    • Asako Iwaki (NIED)
    • Hiroyuki Fujiwara (NIED)
  • Abstract : The authors are developing a seismic risk assessment method with physical simulation and machine learning. Response surfaces of seismic demand are modeled by Gaussian process regression. Low-dimensional features of seismic motions with auto-encoder were used as input data. An active learning method using Bayesian optimization was developed to construct the model with a small number of samplings. As a result, proposed model using samples less than 1/10th of the total data successfully predicted correct values.
• [03740] Automated Building Damage Assessment using Multi-scale Siamese Deep Learning Network
  • Format : Talk at Waseda University
  • Author(s) :
    • Bahareh Kalantar (RIKEN AIP)
    • Naonori Ueda (RIKEN AIP)
  • Abstract : Timely information on building damage location is vital for emergency responders after natural disasters. Our proposed Multi-scale Siamese Building Damage Assessment model assesses damage by localizing buildings and classifying damage level into four categories. The model employs a multi-scale block to handle buildings of varying sizes. The results indicate the model's effectiveness, although it struggles with classifying minor and major damage.

MS [00289] Nonconvex nonlinear programming: Theory and algorithms

room : D501

• [01520] Sensitivity analysis for value functions with application to bilevel programs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kuang Bai (The Hong Kong Polytechnic University)
  • Abstract : In this talk, we will study sensitivity analysis of value functions and optimality conditions of bilevel programs. First, for the sensitivity analysis, based on a recent work of the speaker on parametric nonlinear programs, we will further study the directional sensitivity analysis of value functions for parametric set-constrained problems, which include many classical problems as special cases and can be nonsmooth and nonconvex. In particular, we will derive sufficient conditions for the directional Lipschitz continuity, formulae of the directional derivative and upper estimates for the directional limiting\Clarke subdifferential of value functions. Finally, based on the recent development on directional constraint qualifications and directional optimality conditions, using the directional differential properties of value functions, we will derive sharp optimality conditions for general bilevel programs.
• [03119] Extrapolated Bregman proximal difference-of-convex(DC) algorithm for structured DC optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Bo Wen (Hebei University of Technology)
  • Abstract : In this talk, we mainly consider a Bregman proximal DC method with extrapolation for solving structured DC optimization problems. We first show different extrapolation strategies to possibly accelerate Bregman proximal DC algorithm, and then we discuss the convergence behavior and convergence rates of the Bregman extrapolated proximal DC algorithms. Finally, some numerical experiments have been conducted to illustrate the theoretical results.
• [03077] Relaxed constant positive linear dependence constraint qualification for disjunctive programs
  • Format : Talk at Waseda University
  • Author(s) :
    • Mengwei Xu (Hebei University of Technology)
    • Jane Ye (University of Victoria)
  • Abstract : The disjunctive program is a class of optimization problems in which the constraint involves a disjunctive set which is the union of finitely many polyhedral convex sets. In this paper, we introduce a notion of the relaxed constant positive linear dependence constraint qualification (RCPLD) for the disjunctive program. Our notion is weaker than the one we introduced for a nonsmooth system which includes an abstract set constraint recently (J. Glob. Optim. 2020) and is still a constraint qualification for a Mordukhovich stationarity condition for the disjunctive program. To obtain the error bound property for the disjunctive program, we introduce the piecewise RCPLD under which the error bound property holds if all inequality constraint functions are subdifferentially regular and the rest of the constraint functions are smooth. We then specialize our results to the ortho-disjunctive program, which includes the mathematical program with equilibrium constraints (MPEC), the mathematical program with vanishing constraints (MPVC) and the mathematical program with switching constraints (MPSC) as special cases. For MPEC, we recover MPEC-RCPLD, a MPEC variant of RCPLD and propose the MPEC piecewise RCPLD to obtain the error bound property. For MPVC, we introduce MPVC-RCPLD as a constraint qualification and the piecewise RCPLD as a sufficient condition for the error bound property. For MPSC, we show that both RCPLD and the piecewise RCPLD coincide and hence it is not only a constraint qualification, but also a sufficient condition for the error bound property.
• [03103] An Oracle Gradient Regularized Newton Method for Quadratic Measurements Regression
  • Author(s) :
    • Jun Fan (Hebei University of Technology)
  • Abstract : Recently, recovering an unknown signal from quadratic measurements has gained popularity because it includes as special cases many interesting applications such as phase retrieval, fusion frame phase retrieval and positive operator-valued measure. In this paper, by employing the least squares approach to reconstruct the signal, we establish the non-asymptotic statistical property showing that the gap between the estimator and the true signal is vanished in the noiseless case and is bounded in the noisy case by an error rate of $O(\sqrt{p\log(1+2n)/n})$, where $n$ and $p$ are the number of measurements and the dimension of the signal, respectively. We develop a gradient regularized Newton method (GRNM) to solve the least squares problem and prove that it converges to a unique local minimum at a superlinear rate under certain mild conditions. In addition to the deterministic results, GRNM can reconstruct the true signal exactly for the noiseless case and achieve the above error rate with a high probability for the noisy case. Numerical experiments demonstrate the GRNM performs nicely in terms of high order of recovery accuracy, faster computational speed, and strong recovery capability.

MS [00670] Financial Risk Management and Related Topics

room : D502

• [03952] Gross-revenue-based structural credit risk model
  • Format : Talk at Waseda University
  • Author(s) :
    • Suguru Yamanaka (Aoyama Gakuin University)
    • Hidetoshi Nakagawa (Hitotsubashi University)
  • Abstract : For calculation of firms' default probability, structural models are often used to formulate the stochastic variation of stock variables such as total assets and firm value. In contrast, we propose a new type of structural model based on gross revenue, a flow variable that reflects the income and expenditure of firms. We test the validity of the default probabilities calculated from our proposed model using data on Japanese firms.
• [03406] Insider vs. Outsider: Information and Enlargement of Filtrations
  • Format : Talk at Waseda University
  • Author(s) :
    • Kiichi Kitajima (Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. & Graduate School of Economics, Hitotsubashi University)
  • Abstract : In this presentation, we introduce a stock price process where a large insider can control the price movement through trading. Under the condition that additional insider information is binary, the study establishes that the information drift is a martingale and that the model has a unique equivalent martingale measure when the insider optimizes their trading. We also characterize the stock's expected return by the insider and an outsider with limited information.
• [02711] Sparse factor model of high dimension
  • Format : Talk at Waseda University
  • Author(s) :
    • Benjamin POIGNARD (Osaka University)
    • Yoshikazu TERADA (Osaka University)
  • Abstract : We consider the estimation of factor model-based covariance matrix when the factor loading matrix is sparse. We develop a penalized estimating function framework to account for the identifiability of the factor loading matrix while fostering sparsity. We prove the oracle property of the penalized estimator for factor model, that is the penalization can recover the true sparse support and the estimator is asymptotically normal. These theoretical results are supported by simulations and real data experiments.
• [03676] On a measure of tail asymmetry for the bivariate skew-normal copula
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshinao Yoshiba (Tokyo Metropolitan University)
    • Takaaki Koike (Hitotsubashi University)
    • Shogo Kato (Institute of Statistical Mathematics )
  • Abstract : Asymmetry in the upper and lower tails is an important feature in modeling financial risk factors. We analyze asymptotic behavior of a measure of tail asymmetry at extremely large and small thresholds of the bivariate skew-normal copula. We numerically show, when the correlation or skewness parameters are around at the boundary values, some proposed asymptotic approximations are not suitable to compute the measure of tail asymmetry.

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

room : D505

• [02307] Energy-aware flow shop scheduling with uncertain renewable energy
  • Format : Talk at Waseda University
  • Author(s) :
    • Morteza DAVARI (SKEMA Business School)
    • Masoumeh Ghorbanzadeh (Ferdowsi University)
    • Mohammad Ranjbar (Ferdowsi University)
  • Abstract : This paper investigates an energy-aware flow shop scheduling problem with on-site renewable and grid energy resources. To deal with the uncertainty of renewable energy resources, we first develop two two-stage stochastic programming formulations to minimize the total energy cost purchased from the grid and then, we develop two robust models. Computational results reveal that Benders decomposition algorithms outperform compact models for robust problems and not for stochastic problem.
• [02657] An effective model-driven heuristic algorithm for the collaborative operating room scheduling problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Yang Wang (School of Management, Northwestern Polytechnical University)
    • Haichao Liu (School of Management, Northwestern Polytechnical University)
    • Abraham Punnen (Simon Fraser University)
  • Abstract : In this work, we study a collaborative operating room scheduling problem subject to shared surgeons and downstream wards. We propose an effective model-driven heuristic algorithm to make both weekly surgery assignment and daily sequencing decisions for multiple heterogeneous hospitals. Extensive experimental results disclose the merit of the integrated optimization modelling and the usefulness of coordinating the allocation of key resources within collaborative hospitals.
• [01493] Valid inequalities for the parallel stack loading problem of minimizing the number of badly-placed items
  • Format : Talk at Waseda University
  • Author(s) :
    • Shunji Tanaka (Kyoto University)
    • Sven Boge (Osnabrück University)
  • Abstract : This study addresses the parallel stack loading problem to find an optimal loading plan of incoming items into parallel stacks so that the workload for retrieving them later is minimized. We propose valid inequalities for an integer programming formulation of the problem to minimize the number of badly-placed items as an index of the workload. We examine their effectiveness by computational experiment.
• [01466] Branch-and-Price-and-Cut for the Team Orientation Problem with Interval-Time-Varying Profit
  • Format : Online Talk on Zoom
  • Author(s) :
    • jiaojiao li (National University of Defense Technology)
  • Abstract : This paper studies the team orienteering problem, where the profit depends on whether two visits are completed and the interval time of the two visits. The result of this interaction can be expressed as a discrete profit function. In the practical application of Earth observation satellites, it is often necessary to make two consecutive observations of some important targets at reasonable intervals to improve the observation effect. To solve the problem, we effectively describe the time interval requirement by the number of days between two visits and the combination of time windows, then formulate mixed-integer programming (MIP) models and propose a branch-and-price-cut algorithm, along with valid inequalities for tightening the upper bound. Computational results show the effectiveness of our algorithm. Furthermore, we analyze the impact of the following four aspects on computing time, including basic and modified graph, unidirectional and bidirectional label-setting, ng-path relaxation and dynamic ng-path relaxation, algorithms with and without the valid inequality. Then we present the impact of the third level of branching and non-branching on computing time and profit.

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

room : D514

• [03197] Continuous-Review Inventory Systems with Discontinuous Setup Costs
  • Format : Talk at Waseda University
  • Author(s) :
    • Dacheng Yao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk, we will discuss continuous-review inventory systems, in which the setup cost of each order is a discontinuous function of order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and shortage cost to be a convex function of inventory level, we prove that an (s, S) policy is optimal among all admissible policies under the long-run average cost criterion. However, under the discounted cost criterion, we find that although some (s, S)-type policies are indeed optimal in some cases, any (s, S) policy cannot always be optimal for all initial inventory level x∊R in the other cases.
• [04097] Deep learning methods in insurance and risk management
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhuo Jin (Macquarie University)
  • Abstract : Recently, deep learning approaches has drawn increasing attention in decision making processes. A type of Markov chain approximation-based iterative deep learning algorithm is developed to study the optimal control problems arising from the insurance industry. The optimal controls are approximated as deep neural networks. The framework of Markov chain approximation plays a key role in building the iterative equations and initialization of the algorithm. Optimal parameters of neural networks are then obtained iteratively.
• [04139] Exponential stability of stochastic functional differential equations with impulsive perturbations
  • Format : Talk at Waseda University
  • Author(s) :
    • KY QUAN TRAN (SUNY Korea)
    • George Yin (University of Connecticut)
  • Abstract : This work aims to investigate the moment exponential stability of stochastic functional differential equations subject to impulsive perturbations and Markovian switching. In contrast to existing literature, we propose new criteria for moment exponential stability and a new method for computing moment Lyapunov exponents. Our analysis also shows that the Euler-Maruyama approximation method can effectively reproduce exponential stability in the mean square, provided that the step sizes are sufficiently small.
• [03618] Fully-coupled two-time-scale stochastic functional differential equations with infinite delay
  • Format : Talk at Waseda University
  • Author(s) :
    • Fuke Wu (Huazhong University of Science and Technology)
  • Abstract : This paper examines the fully-coupled two-time-scale stochastic functional differential equations (SFDEs) with infinite delay. The system under consideration involves a slow component and a fast component. This paper aims to establish the averaging principle. To overcome the difficulty due to the infinite delay and the coupling of the segment process, some properties as the Hölder continuity and tightness on a space of continuous functions have to be investigated for the segment process.

MS [00994] Mathematical modeling approach in pharmacokinetics/pharmacodynamics

room : D515

• [05562] Principles and applications of clinical pharmacology and pharmacometrics in the drug development
  • Format : Talk at Waseda University
  • Author(s) :
    • Sungpil Han (The Catholic University of Korea)
  • Abstract : In the rapidly evolving landscape of pharmaceutical research, clinical pharmacology and pharmacometrics have emerged as pivotal disciplines in the drug development process. This presentation will delve into the principles and applications of these disciplines, particularly focusing on the integration of mathematical modeling in pharmacokinetics/pharmacodynamics (PK/PD) to accelerate and optimize drug development. Clinical pharmacology plays a crucial role in understanding the effects of a drug and the mechanisms of its actions in humans, while pharmacometrics aids in quantifying drug, disease, and trial information to aid efficient drug development and regulatory decisions. This presentation will discuss the synergy between these two disciplines, highlighting how they can form the bedrock for creating more effective, safer drugs. A key element in this context is the employment of mathematical models in PK/PD studies. The presentation will demonstrate the use of such models to predict the time course of drug concentration and its consequent effects, thereby guiding optimal dosage and timing strategies. Special emphasis will be placed on the role of mathematical modeling in minimizing adverse drug reactions and predicting drug-drug interactions.
• [05550] Pharmacokinetic Model of Tacrolimus based on Stochastic Simulation and Estimation in Korean Adult Transplant Recipients
  • Format : Talk at Waseda University
  • Author(s) :
    • Suein Choi (Catholic university of Korea)
    • Seunghoon Han (Catholic university of Korea)
  • Abstract : Therapeutic drug monitoring (TDM) is a crucial clinical procedure that involves measuring drug concentrations in a patient's blood or other biological fluids to ensure optimal dosing. To achieve targeted exposure and improve dosing precision, the Bayesian estimation method is utilized, which optimizes individual pharmacokinetic (PK) parameters based on previous TDM data and a population PK model. The development of an accurate PK model is essential, as it integrates clinically relevant covariates and appropriate random effect parameters. However, the nature of TDM data poses certain limitations for PK model development. Although it provides a wealth of real-world data reflecting a wide range of covariates, it primarily consists of trough concentrations, which restricts the information available for model building. To overcome these limitations, we employed the stochastic simulation and estimation (SSE) method, enabling the integration of published PK models with acquired real-world TDM data, even in the absence of raw data from the published models. This approach also allowed us to evaluate clinically meaningful covariates. Using the SSE method, we successfully developed a population PK model for tacrolimus that encompasses both published PK models and newly collected TDM data from the Korean population. This model serves as a robust framework for practical TDM procedures, as it incorporates clinically relevant covariates and reflects real-world settings. Despite the inherent limitations associated with TDM data, the SSE method proved invaluable in leveraging the information contained within TDM data by integrating published PK models while accounting for model variability. Overall, the developed population PK model for tacrolimus, utilizing the SSE method, represents a significant advancement in TDM practices. It enhances dosing precision, incorporates relevant covariates, and provides a solid foundation for guiding therapeutic strategies in clinical settings. By addressing the challenges posed by TDM data limitations, this research contributes to the refinement and optimization of pharmacokinetic modeling for improved patient outcomes.
• [01369] Distributional approaches expressing tumor delay of the transit compartment model
  • Format : Talk at Waseda University
  • Author(s) :
    • Jong Hyuk Byun (Pusan National University)
    • Il Hyo Jung (Pusan National University)
  • Abstract : Transit compartment model describes the way in which drugs inhibit the growth of tumors, based on a system of ODEs describing damaged cells’ transition under the influence of the drug, using Erlang distribution. In our approach, Coxian distribution is used to model the various delays when the number of delay compartments is fixed. In the other approach, the delay compartments are combined into a single form using Mittag-Leffler distribution, without pre-specifying the number of compartments.
• [01975] Accurate Prediction of Drug Interactions Through Cytochrome P450 Induction
  • Format : Talk at Waseda University
  • Author(s) :
    • Yun Min Song (KAIST)
    • Ngoc-Anh Thi Vu (Chungnam National University)
    • Quyen Thi Tran (Chungnam National University)
    • Hwi-yeol Yun (Chungnam National University)
    • Jung-woo Chae (Chungnam National University)
    • Sang Kyum Kim (Chungnam National University)
    • Jae Kyoung Kim (KAIST)
  • Abstract : FDA guidance has recommended several model-based predictions to determine potential drug-drug interactions (DDIs). In particular, the ratio of substrate AUCs under and not under the effect of enzyme inducers is predicted by the Michaelis-Menten model, which is valid only in low-enzyme-concentration conditions. We found that such DDI predictions lead to severe errors. To resolve this, we derived a new equation that significantly improves clinical DDI prediction, which is critical to preventing drug toxicity and failure.

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

room : A201

• [03457] Closed-form solutions and conservation laws of the fifth-order strain wave equation in microstructured solids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mduduzi Thabo Lephoko (North-West University, Mafikeng Campus)
    • Chaudry Masood Khalique (North-West University, South Africa)
  • Abstract : In this presentation, we examine the dynamics of soliton waves associated with higher-order nonlinear partial differential equations, which have applications in various fields of science and engineering. Our focus is on the fifth-order strain wave equation, for which we employ the Lie group theory of differential equations to obtain analytic solutions. Specifically, we use this technique to systematically generate the Lie point symmetries spanned by the equation, which we then use to reduce it to ordinary differential equations that can be solved to obtain closed-form solutions. The ordinary differential equations are solved by direct integration and the engagement of two methods, the simplest method and generalized tanh-function method. We successfully identify soliton solutions, including dark and singular period solitons, and depict them graphically to better understand their physical meaning. We then use the multiplier method to obtain conserved vectors. Our analysis sheds light on the wave structures associated with the strain wave equation and provides insight into the physical implications of the soliton solutions.
• [02308] Symmetry solutions and conservation laws of the derivative nonlinear Schrodinger equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Karabo Plaatjie (North-West University, Mafikeng Campus)
    • Chaudry Masood Khalique (North-West University, South Africa)
  • Abstract : In this talk we study the derivative nonlinear Schrodinger equation.This equation has many applications, for example in the propagation of circular polarized nonlinear Alfven waves in plasmas. We present general and special solutions of this equation using Lie group theory. We also derive conservation laws for the underlying equation.
• [03449] Lie symmetry analysis of new 3-D fifth-order nonlinear Wazwaz equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Oke Davies Adeyemo (North-West University, Mafikeng Campus)
  • Abstract : In this talk, we present the analytical examination of a new (3+1)-dimensional fifth-order nonlinear Wazwaz equation with third-order dispersion terms in ocean physics and other nonlinear sciences. We apply Lie group analysis to obtain various infinitesimal generators admitted by the equation. The generators are used to reduce the understudy equation to achieve copious group-invariant solutions. Thus, various closed-form solutions are obtained for the equation. We further construct its conservation laws.

MS [01063] Challenges in biomathematical modeling and control

room : A206

MS [00592] Optimization and Inverse Problems

room : A207

• [05012] Multiscale hierarchical decomposition methods for ill-posed problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Tobias Wolf (Klagenfurt University)
    • Elena Resmerita (University of Klagenfurt)
    • Stefan Kindermann (Johannes Kepler University Linz)
  • Abstract : The Multiscale Hierarchical Decomposition Method (MHDM) is a popular iterative method based on total variation minimization for mathematical imaging. We consider the method in a more general framework and expand existing results to the case when some classes of convex and nonconvex penalties are employed. Moreover, we discuss conditions under which the iterates of the MHDM agree with solutions of Tikhonov regularization corresponding to suitable regularization parameters. We illustrate our results with numerical examples.
• [05199] Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Elena Resmerita (University of Klagenfurt)
    • Joel Barnett (UCLA)
    • Wen Li (Fordham University)
    • Luminita Vese (UCLA)
  • Abstract : Recovering images corrupted by multiplicative noise is a well known challenging task. Mo- tivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new multiplicative noise removing models to the MHDM form. Theoretical and numerical results show that the MHDM techniques are effective in several situations.
• [03502] A Lifted Bregman Formulation for the Inversion of Deep Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoyu Wang (University of Cambridge)
    • Martin Benning (Queen Mary University of London, London)
  • Abstract : We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors’ recent work on the lifted Bregman formulation on training feed-forward neural networks without the differentiation of activation functions. We propose a family of variational regularisations based on Bregman distances, present theoretical results and support their practical application with numerical examples. In particular, we present the first convergence result (to the best of our knowledge) for the regularised inversion of a single-layer perceptron that only assumes that the solution of the inverse problem is in the range of the regularisation operator, and that shows that the regularised inverse provably converges to the true inverse if measurement errors converge to zero.
• [03398] Stable Phase retrieval with mirror descent
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jean-Jacques Godeme (Normandie Univ, ENSICAEN, CNRS, GREYC, France)
    • Jalal Fadili (Normandie Univ, ENSICAEN, CNRS, GREYC)
    • Myriam Zerrad (Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille)
    • Claude Amra (Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille)
  • Abstract : We aim to reconstruct an $n$-dimensional real vector from $m$ phaseless measurements corrupted by additive noise. We use the mirror descent (or Bregman gradient descent) algorithm to deal with noisy measurements and prove that the procedure is robust to (small enough) noise.

contributed talk: CT194

room : A208

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @A208
• Type : Contributed Talk
• Abstract : In this talk, we will discuss an algorithm for reconstructing multipolar acoustic sources using sparse far-field multifrequency measurements of the scattered field. A hybrid Fourier algorithm exploiting the low rank of the structured Hankel matrix associated with the scattered field is designed. The sparse data is first linked to the Fourier coefficients of the source, then enriched using an annihilation-filter-based Hankel matrix completion approach (ALOHA), and finally inverted for sources using the inverse Fourier transform.
• Classification : 45Qxx, 65Txx, Machine Learning
• Format : Talk at Waseda University
• Author(s) :
  • Abdul Wahab (Nazarbayev University)
  • Abdul Wahab (Nazarbayev University)

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @A208
• Type : Contributed Talk
• Abstract : In this talk, we prove an existence and locally attractivity result for Volterra type nonlinear perturbed random integral equations in separable Banach space under mixed generalised compactness, contraction and caratheodory conditions and also we will prove the existence of maximal and minimal solution Volterra type nonlinear random integral equations with some applications. These types of Volterra type nonlinear perturbed random integral equations are used in various natural phenomena in which randomness occurs.
• Classification : Existence of Solutions and their properties, Random Integral Equations, Applications in Abstract Spaces
• Format : Online Talk on Zoom
• Author(s) :
  • SIDDHARTH GANESH SHETE (Swami Ramanand Teerth Marathwada University Nanded Maharashtra )

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @A208
• Type : Contributed Talk
• Abstract : We analyse a Poisson-Nernst-Planck-Fermi model to describe the evolution of a mixture of finite size ions in liquid electrolytes, which move through biological membranes or nanopores. The global-in-time existence of bounded weak solutions and the weak-strong uniqueness result are proved, via entropy and relative entropy, respectively. Furthermore, an implicit Euler finite-volume scheme for the model is analysed and some simulations are shown.
• Classification : 35-XX, Mathematical and numerical analysis of cross-diffusion system via entropy and relative entropy
• Format : Online Talk on Zoom
• Author(s) :
  • Annamaria Massimini (TU Wien)
  • Ansgar Jüngel (TU Wien)

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @A208
• Type : Contributed Talk
• Abstract : The prime intent of this study is to resolve the multiple faults reconstruction and state tracking issues for the interval type-2 fuzzy systems subject to actuator and sensor faults by using an active fault-tolerant tracking control law based on an unknown input observer approach. Moreover, a set of sufficient conditions namely linear matrix inequality is derived to ensure the tracking performance of the addressed system. Eventually, the derived theoretical results are verified through numerical examples.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Author(s) :
  • Anusuya Sundaram (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

• Session Time & Room : 1D (Aug.21, 15:30-17:10) @A208
• Type : Contributed Talk
• Abstract : A robust reliable boundary control problem for a class of parabolic PDE systems with semi-Markov switching subject to actuator faults, randomly occurring uncertainties and nonlinearities is investigated. Particularly, randomness phenomena are characterized by stochastic variables obeying Bernoulli distribution properties. A boundary controller is developed to ensure the robust performance of the considered system. Sufficient conditions for guaranteeing the input-output finite-time stabilization of the closed-loop system are derived. Proposed method is validated through simulation outcomes.
• Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
• Author(s) :
  • Abinandhitha Radhakrishnan (Bharathiar University)
  • Sakthivel Rathinasamy (Bharathiar University)

MS [00815] Recent trends in continuous optimization

room : A502

• [03316] Derivative-free Low Order-Value Optimization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anderson Ervino Schwertner (State University of Maringá)
    • Francisco Nogueira Calmon Sobral (State University of Maringá)
  • Abstract : The Low Order-Value Optimization (LOVO) problem seeks to minimize the minimum among a finite number of function values within a feasible set and has several applications, such as protein alignment and portfolio optimization, among others. In this work, we are interested in the constrained black-box LOVO problem, whose feasible set is convex, closed, and nonempty. We developed and implemented a derivative-free trust-region algorithm, and established global convergence and worst-case complexity results.
• [04101] A Stochastic Variance Reduced Gradient using Second Order Information
  • Format : Talk at Waseda University
  • Author(s) :
    • Hardik Tankaria (Kyoto University)
    • Nobuo Yamashita (Kyoto University)
  • Abstract : In this talk, we consider to improve the stochastic variance reduced gradient (SVRG) method via incorporating the curvature information of the objective function. We propose to reduce the variance of stochastic gradients using the computationally efficient method of second order approximation by incorporating it into the SVRG. We also incorporate a (Barzilai-Borwein) BB-step size as its variant. We show linear convergence for not only the proposed method but also for the other existing SVRG variants that use second-order information as a variance reduction. We show the numerical experiments on the benchmark datasets and demonstrate the comparison of proposed methods with existing variance reduced methods.
• [03875] Post-Processing with Projection and Rescaling Algorithm for Symmetric Cone Programs
  • Format : Talk at Waseda University
  • Author(s) :
    • Shinichi Kanoh (University of Tsukuba)
    • Akiko Yoshise (University of Tsukuba)
  • Abstract : We propose a post-processing algorithm for symmetric cone programs based on the Projection and Rescaling Algorithm (PRA). Our algorithm is devised to return a more accurate solution using the output solution from MOSEK solver and the PRA proposed by Kanoh & Yoshise (2021). Numerical experiments with SDPLIB instances show that our algorithm outputs a solution with a very small value of DIMACS error compared to the solution that MOSEK solver returned.
• [04338] Random Subsapce Newton method for unconstrained non-convex optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre-Louis Poirion (RIKEN -AIP)
  • Abstract : In this talk, we present a randomized subspace regularized Newton method for a non-convex function. We will be interested in particular to the local convergence rate of the method.

MS [02545] Challenges and Recent Advances in Phylogenetics

room : A508

• [04132] Navigating the Frontiers of Phylogenetic Research: Challenges and Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Momoko Hayamizu (Department of Applied Mathematics, Waseda University)
  • Abstract : This talk serves as an introduction to our mini-symposium on phylogenetic research. It emphasizes key challenges and applications in this rapidly evolving field from both theoretical and biological perspectives. After providing a brief overview of the symposium topics and presentations, I will discuss some of the recent results and open problems related to phylogenetic trees and networks, with a focus on combinatorial and algorithmic approaches.
• [05050] Advances and challenges in statistical inference of phylogenetic networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Luay Nakhleh (Rice University)
  • Abstract : Evolutionary analyses of various groups of eukaryotic species have revealed evidence for reticulation. Reticulate evolutionary histories are best represented as phylogenetic networks. I will describe the multispecies network coalescent (MSNC) model, which allows for modeling vertical and horizontal evolutionary processes acting within and across species boundaries. I will then discuss progress we have made on developing statistical inference methods under the MSNC as well as challenges facing the inference in practice.
• [03613] The Tree of Blobs of a Species Network: Identifiability
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hector D Banos (California State University San Bernardino)
    • Elizabeth S Allman (University of Alaska Fairbanks)
    • John A Rhodes (University of Alaska Fairbanks)
    • Jonathan D Mitchell (Univeristy of Tasmania)
  • Abstract : As genealogical analyses of DNA data have progressed, more evidence has appeared showing that hybridization is often an important factor in evolution. Hybridization has played a crucial role in the evolutionary history of plants, some groups of fish, and frogs, among other species. In such cases, networks are the objects used to represent the relationships between species. The network multispecies coalescent model is a standard probabilistic model describing the formation of gene trees in the presence of hybridization and incomplete lineage sorting. We present a step toward inferring a general species network by showing the identifiability of its tree of blobs, in which all 'hybrid species relationships' are contracted to nodes, so only tree-like relationships between the taxa are shown.
• [03991] Identifiability of phylogenetic networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Leo van Iersel (TU Delft)
  • Abstract : Will we ever be able to reconstruct our own history and the history of other species? What can we reconstruct when we have enough data? And what cannot be reconstructed no matter how much data we collect? Evolutionary histories can be described using directed graphs called phylogenetic networks. Which phylogenetic networks can in principle be reconstructed from data of currently living species, like DNA data, under certain models of evolution? This is an important question to answer in order to be able to develop statistically-consistent methods. I will discuss algorithmic, graph theoretic and algebraic results that are important for answering this question.

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

room : A510

• [03612] Euler-Maclaurin formulas for near-singular integrals
  • Format : Talk at Waseda University
  • Author(s) :
    • Bowei Wu (University of Massachusetts Lowell)
  • Abstract : Near-singular integrals frequently arise in fluid dynamics, material science, and many other scientific applications, where close fluid-structure interactions are common. Numerical approximation of near-singular integrals thus has practical importance. Approximating near-singular integrals using regular quadrature methods is in general inefficient and expensive. But more efficient quadrature rules can be developed by modifying regular quadrature rules using an error correction approach. We introduce new generalized Euler-Maclaurin formulas that are tailored to a family of near-singular functions. High-order accurate modified Trapezoidal quadrature rules are then derived based on these formulas.
• [03009] Near singularity errors in boundary integrals: identification, estimation and swapping
  • Format : Talk at Waseda University
  • Author(s) :
    • Ludvig af Klinteberg (Mälardalen University)
  • Abstract : Evaluating a layer potential close to its source geometry poses numerical difficulties due to the presence of a near singularity. In this presentation I will discuss how the singularity can be understood in terms of its complexified preimage in the parametrization of the source geometry. Finding the preimage numerically allows us to both estimate quadrature errors to high precision, and derive new and more capable quadrature methods.
• [05159] A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Fortunato (Flatiron Institute)
    • David B Stein (Flatiron Institute)
    • Alex H Barnett (Flatiron Institute)
  • Abstract : We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the volumetric inhomogeneity, but require care to be taken near the boundary to ensure that the volume data is globally smooth. We avoid function extension or cut-cell quadratures near the boundary by dividing the domain into two regions: a bulk region away from the boundary that is efficiently treated with a truncated free-space box code, and a variable-width boundary-conforming strip region that is treated with a spectral collocation method and accompanying fast direct solver. Particular solutions in each region are then combined with layer potentials to yield the global solution. The resulting solver has an optimal computational complexity of $O(N)$ for an adaptive discretization with $N$ degrees of freedom. We demonstrate adaptive resolution of volumetric data, boundary data, and geometric features across a wide range of length scales, to typically 10-digit accuracy.
• [04640] An adaptive discretization technique for boundary integral equations in the plane
  • Format : Online Talk on Zoom
  • Author(s) :
    • Adrianna Gillman (University of Colorado, Boulder)
    • Yabin Zhang (Westlake University)
  • Abstract : Typically the discretization of integral equations on two dimensional complex geometries involves the use of a panel based quadrature (such as variants of Gaussian quadrature). The placement of the panels is often ad hoc and based on being able to integrate quantities such as arc-length and/or curvature to a desired accuracy. These quantities do not necessarily correspond to what is needed to achieve accuracy in the solution to a partial differential equation. Alternatively, a refinement strategy based on looking at relative error and wisely choosing which part of the geometry to refine can be done but this involves global solves which can be prohibitively expensive. In this talk, we will present an adaptive discretization technique which is guaranteed to achieve the desired accuracy and does not require the inversion of a full discretized integral equation at each step in the refinement process. Numerical results will illustrate the performance of the method.

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

room : A511

• [05310] Carbuncle-free, well-balanced, positivity preserving methods for the shallow water equations, with application to the circular hydraulic jump
  • Format : Talk at Waseda University
  • Author(s) :
    • David I Ketcheson (King Abdullah University of Science and Technology)
  • Abstract : When a jet of fluid hits a flat plate, the resulting flow consists of two regimes separated by a hydraulic jump. We investigate the behavior of the jump for the shallow water equations. Numerical solvers tend to either exhibit artificial numerical instabilities or suppress the chaotic behavior at high Froude numbers. We propose a new entropy-based Riemann solver that is capable of avoiding carbuncles while allowing the fluid instability to manifest itself.
• [04458] New highly stiff-stable schemes for linear and nonlinear parabolic equations
  • Format : Talk at Waseda University
  • Author(s) :
    • JIE SHEN (Purdue University)
  • Abstract : We construct a class of new highly stiff-stable schemes for linear and nonlinear parabolic equations based on Taylor expansions at time $t_{n+k}$ where $k\ge 1$ is a tunable parameter. We show that their numerical solutions are bounded unconditionally (resp. for sufficiently small time steps) for linear (resp. nonlinear ) parabolic equations, and derive their optimal error estimates for a large class of nonlinear parabolic equations. We also present numerical results to show the advantages of the new schemes compared with the classic IMEX schemes based on Taylor expansions at time $t_{n+1}$.
• [05011] Finite-differences scheme for a tensor PDE model of bionetwork formation and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Clarissa Astuto
    • Giovanni Russo (University of Catania)
    • Peter Markowich (King Abdullah University of Science and Technology)
    • Daniele Boffi (KAUST)
    • Jan Haskovec (KAUST)
  • Abstract : We propose a numerical method for the resolution of a complex biological network. We refer to the Cai-Hu model, where they hypothesized that the topology of the leaf pattern is governed by an optimization of the global energy consumption. The evolution in time of the fluid is governed by an elliptic-parabolic system of partial differential equations and we explore the resulting graph, showing important structural differences when changing the parameters.
• [04882] Asymptotic preserving scheme for ExB drift
  • Format : Talk at Waseda University
  • Author(s) :
    • Umberto Zerbinati (University of Oxford)
    • Giovanni Russo (University of Catania)
  • Abstract : In this talk, we explore an asymptotic preserving scheme for ExB drift. The key idea behind the scheme here presented is to treat the highly oscillatory component of the velocity using an exponential integrator. We will apply this numerical scheme to particles in cell plasma simulation under the effect of a strong constant magnetic field.

MS [00641] Emerging Collaborations: Mathematical Views of Modelling Biological Scales

room : A512

• [02145] Ecological consequences of heterogeneity in host-pathogen population dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Arietta Fleming-Davies (University of San Diego)
  • Abstract : Variation within-species is key in evolutionary processes. We asked how quantitative variation changes along with mean differences in pathogen performance across populations of the hosts they infect. We fit statistical models incorporating a Gamma distribution of host disease susceptibility to experimental dose response data from an insect baculovirus system, to ask how variation in infectivity might change with genotype by genotype (G x G) combinations of pathogen and host populations.
• [02146] Modeling microscale biofluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Amy Lyn Buchmann (University of San Diego)
  • Abstract : Mathematical models can be used to study the role of hydrodynamic interactions in the coordination and self-organization of microorganisms. For example, cilia self-organize to form a metachronal wave that propels the surrounding fluid, yet how this organization occurs is not well understood. Additionally, the coordination of bacterial flagella may be studied to inspire the development of motors in microfluidic devices that can effectively mix and pump a viscous fluid. Here we present a mathematical model to study the interactions between elastic structures in a viscous fluid and investigate their coordination.
• [02152] We are what we eat: a mathematical model of the gut-brain axis.
  • Format : Talk at Waseda University
  • Author(s) :
    • Ami Radunskaya (Pomona College)
  • Abstract : The ``gut-brain axis” is the communication between the enteric nervous system (in the gut) and the central nervous system (in the brain).  Over the past few decades, scientists have collected data that confirms a bidirectional communication channel between these two nervous systems that is closely tied to the bacterial ecology of the gut, the production of serotonin in both the gut and the brain, and the interaction of serotonin with other hormones.  We propose a mathematical model that illuminates both the dynamics of this communication channel and the effect of perturbations due to treatment strategies.
• [02213] Modeling the long term effects of thermoregulation on human sleep
  • Format : Talk at Waseda University
  • Author(s) :
    • Alicia Prieto Langarica (Youngstown State University)
  • Abstract : The connection between human sleep and energy exertion has long been regarded as part of the reasoning for the need to sleep. We used to think that we sleep in order to rest. However, a recent theory proposes a different explanation, one that unifies sleep among all species. This talk presents a mathematical model of human sleep/wake regulation with thermoregulatory functions. The model is used to gain quantitative insight into the effects of ambient temperature on sleep quality and how this relates to the unifying theory for sleep.

MS [00309] Population Dynamics in Biology and Medicine

room : A601

• [01440] Mathematical insights of chemical and Wolbachia-based mosquito control
  • Format : Talk at Waseda University
  • Author(s) :
    • OLGA VASILIEVA (Universidad del Valle)
    • Daiver Cardona-Salgado (Universidad Autonoma de Occidente)
    • Lilian Sofia Sepulveda-Salcedo (niversidad Autonoma de Occidente)
  • Abstract : Wolbachia is a symbiotic bacterium that can block virus replication in Aedes aegypti mosquitoes, the primary transmitters of different vector-borne diseases. This thwarts the virus transmission from mosquitoes to humans. In recent years, Wolbachia-based biocontrol of Ae. aegypti mosquitoes have been gradually replacing the traditional control interventions based on insecticide spraying. In this presentation, we assess the pros and cons of Wolbachia-based biocontrol through the mathematical modeling of the mosquito population dynamics.
• [02743] ON THE ORIGIN OF COMPLEX DYNAMICS IN MULTI-STRAIN DENGUE MODELS
  • Format : Talk at Waseda University
  • Author(s) :
    • Maira Aguiar (Basque Center for Applied Mathematics)
  • Abstract : Dengue fever epidemiological dynamics shows large fluctuations in disease incidence. Multi-strain models show complex dynamics and qualitatively a very good result when comparing empirical data and model simulations, however, the extent of biological mechanisms generating complex behavior in simple epidemiological models is still unexplored. In this talk, I will present a set of models motivated by dengue fever epidemiology and compare different dynamical behaviors originated when increasing complexity into the model framework.
• [04155] Covid-19: Vaccination impact after lockdown lifting and its large fluctuations
  • Format : Talk at Waseda University
  • Author(s) :
    • Nico Stollenwerk (BCAM, Bilbao, Pais Vasco)
  • Abstract : The initial phase of the COVID-19 pandemic in beginning 2020 with exponential growth of infected and hospitalizations led to severe lockdown measures in many countries. The subsequent lifting of the lockdowns prohibited new exponential growth, but lead to large subcritical fluctuations, with power law characteristics close to endemic thresholds, analysed for Basque Country data on a daily base for actual management purposed. We extended the modelling framework sucessfully into the vaccine introduction period.
• [03501] Optimization of Vaccination strategies on a metropolitan area
  • Format : Talk at Waseda University
  • Author(s) :
    • Lucas Machado Moschen (School of Applied Mathematics - FGV EMAp)
    • Maria Soledad Aronna (School of Applied Mathematics - FGV EMAp)
  • Abstract : We propose a model for vaccination in a network that models a typical metropolitan area. By employing tools of mathematical epidemiology and optimal control, we analyze the effectiveness of different allocation policies for distribution of vaccines and we search for optimal strategies.