MS and CT list / Aug. 22, 17:40-19:20.

MS [01107] Efficient methods for Isogeometric Analysis

room : G301

• [04643] Fast computation of electromagnetic wave propagation with spline differential forms
  • Format : Talk at Waseda University
  • Author(s) :
    • Bernard Kapidani (Ecole Polytechnique Fédérale Lausanne)
    • Rafael Vazquez (Ecole Polytechnique Fédérale Lausanne)
  • Abstract : We present a new structure-preserving numerical method for hyperbolic problems which does not rely on the geometric realisation of any dual mesh. We use B-spline based de Rham complexes to construct two exact sequences of discrete differential forms and apply them to solving Maxwell's equations. The method exhibits high order convergence and energy conservation, with computational effort much lower than standard Galerkin. We will also present preliminary results towards extension to multi-patch geometries.
• [05111] Efficient reduced order models for unfitted spline discretizations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Margarita Chasapi (EPFL)
    • Pablo Antolin (EPFL)
    • Annalisa Buffa (EPFL)
  • Abstract : This talk presents a methodology for efficient reduced order modelling of PDEs on unfitted spline discretizations. We are interested in problems formulated on parameterized unfitted geometries and aim to construct efficient reduced basisapproximations. The presented methodology is based on extension of solution snapshots on the background mesh and localization strategies to confine the number of reduced basis functions. Numerical experiments on trimmed spline discretizations show the accuracy and efficiency of the method.
• [04698] Isogeometric Coupling Methods for H(curl) Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Melina Merkel (Technische Universität Darmstadt)
    • Sebastian Schöps (Technische Universität Darmstadt)
  • Abstract : In this work, we present a method for the efficient simulation of electric motors using isogeometric analysis. As these machines include moving parts, conformity of the patches cannot be guaranteed for all rotation angles without modification of the geometry. We therefore use domain decomposition methods, e.g., mortaring or Nitsche-type coupling, for the coupling of stator and rotor. These methods can also be applied to all patches to facilitate patch-parallel computations.
• [05212] Low-rank Tensor Train Methods for IGA with Multiple Patches
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexandra Bünger (University of British Columbia)
    • Martin Stoll (Technical University of Chemnitz)
    • Tom Christian Riemer (Technical University of Chemnitz)
  • Abstract : In IGA, the equation systems for, e.g., optimization problems may quickly become very costly to assemble and solve. We developed a method exploit the underlying tensor structure with low-rank tensor train approximations. This low-rank formulation can be efficiently used in a block-structured iterative solver to solve challenging PDE problems in a compact format. We recently extended this for multi-patch domains and show how the resulting systems can be treated effectively in the tensor train framework.

MS [00324] Minisymposium on Combinatorial Reconfiguration

room : G302

• [04748] Invitation to Combinatorial Reconfiguration
  • Format : Talk at Waseda University
  • Author(s) :
    • Takehiro Ito (Tohoku University)
  • Abstract : Combinatorial Reconfiguration studies reachability and related questions over combinatorial structures. A typical example asks if the solution space of a Boolean formula is connected with respect to the Boolean cube topology, formed by flipping one bit at the time. Reconfiguration problems have been studied intensively in this decade from the algorithmic viewpoints. In this talk, we will give a broad introduction of combinatorial reconfiguration, and show some recent progress on the topic.
• [04759] Geometric algorithms for reconfiguring modular robots
  • Format : Online Talk on Zoom
  • Author(s) :
    • Irene Parada (BarcelonaTech (UPC))
  • Abstract : Modular self-reconfigurable robots consist of units that can move and connect to form larger shapes. A central problem is how to efficiently reconfigure between shapes while maintaining connectivity. We explore the computational complexity of this reconfiguration problem for the most fundamental lattice-based models of modular robots. Some lattices and moves allow for efficient reconfiguration algorithms, while in other models the problem is PSPACE-complete. For those cases, we identify simple conditions that guarantee universal reconfigurability.
• [05218] Toric Promotion and Permutoric Promotion
  • Format : Online Talk on Zoom
  • Author(s) :
    • Colin Defant (Massachusetts Institute of Technology)
  • Abstract : We introduce toric promotion and, more generally, permutoric promotion operators. These operators, which are variants of Schutzenberger's famous promotion operator, act on labelings of a graph. We highlight cases where these operators have surprisingly nice orbit structures. Our investigation of permutoric promotion is surprisingly involved and relies on the analysis of gliding globs, sliding stones, and colliding coins. This work on permutoric promotion is joint with Rachana Madhukara and Hugh Thomas.
• [04747] Triangulations of cyclic polytopes through the lens of reconfiguration
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicholas James Williams (Lancaster University)
  • Abstract : We discuss the reconfiguration problem given by taking the set of triangulations of a cyclic polytope as the state space, with the reconfiguration moves given by bistellar flips (the higher-dimensional analogue of flipping a diagonal within a quadrilateral). The state space is connected, and we will outline how this is proven using a certain partial order on the states called the higher Stasheff-Tamari order. We will further consider as many different other aspects of the reconfiguration as time permits, including the significance of triangulations of higher-dimensional cyclic polytopes for reconfigurations of lower-dimensional cyclic polytopes, efficient combinatorial descriptions of triangulations of cyclic polytopes, and the diameter of the state space.

contributed talk: CT006

room : G304

[00682] Cover Temporal Networks with Densest Subgraphs

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : Temporal networks have been introduced to represent the dynamics of a complex system. In this contribution we consider a problem that asks for a collection of dense temporal subgraphs that covers a given temporal graph. The problem has application in the identification of communities of a complex system, for example of a social network. We present a result on the computational complexity of the problem and a polynomial-time approximation algorithm.
• Classification : 05C85, 05C90, 68R10, 68R05, 68Q25
• Format : Talk at Waseda University
• Author(s) :
  • Riccardo Dondi (Università degli Studi di Bergamo)

[00540] Random product homotopies for decomposing tensors

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : The rank one decomposition of the tensor is considered. The upper bound of rank is derived under which computing the decomposition is equivalent to solving a structured polynomial system that is determined by the full rank factorization of the matricization of the tensor. Under the generic uniqueness conditions, the solutions of the system are isolated and can be efficiently achieved by random product homotopies.
• Classification : 13P15, 15A69, 15A72
• Format : Talk at Waseda University
• Author(s) :
  • Tsung-Lin Lee (National Sun Yat-sen University)

[00459] Tropical linear regression and mean payoff games: or, how to measure the distance to equilibria

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : We study a tropical linear regression problem consisting in finding a best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showing that the value of this problem coincides with the maximal radius of a Hilbert's ball included in a tropical polyhedron. We show that this problem is polynomial-time equivalent to mean payoff games. We illustrate our results by solving an inverse problem from auction theory.
• Classification : 14T90, 91A25, 91B26
• Format : Talk at Waseda University
• Author(s) :
  • Omar Saadi (College of Computing, Mohammed VI Polytechnic University)
  • Marianne Akian (INRIA and CMAP, École polytechnique)
  • Stéphane Gaubert (INRIA and CMAP, École polytechnique)
  • Yang Qi (INRIA and CMAP, École polytechnique)

[02500] Constructing crypto-algorithms using vector-valued functions

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G304
• Type : Contributed Talk
• Abstract : Binary compositions of vector-valued functions defined on an arbitrary set, including finite sets, are introduced. Some properties of the compositions are investigated. In particular, it is proved that each of them is associative. Using the obtained results, crypto-algorithms with a public key have been obtained.
• Classification : 11T71, 94A60, 05B15, 20N05, 20N15
• Author(s) :
  • Fedir Sokhatsky (Vasyl' Stus Donetsk National University)

contributed talk: CT010

room : G305

[01082] Analysis of traffic flow models by triangulation of min-plus matrices

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : Cellular automata model for traffic flow can be described in terms of min-plus linear systems. In this talk, we focus on the triangulation of a min-plus matrix, which is defined based on the roots of characteristic polynomial and the algebraic eigenvectors associated with the roots. It plays an important role in the analysis of the asymptotic behavior of the model. Further the algebraic eigenvectors are shown to give us preferable initial states.
• Classification : 15A80, 37B15, 76A30
• Format : Talk at Waseda University
• Author(s) :
  • Yuki Nishida (Tokyo University of Science)
  • Sennosuke Watanabe (The University of Fukuchiyama)
  • Yoshihide Watanabe (Doshisha University)

[00374] Recent numerical and theoretical advances in the study of matrix sequences

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : We present recent developments in the study of the spectral behaviour of structured matrix sequences. For example, all PDE discretizations, such as FEM, FDM, and DGM, generate these types of sequences. We will mainly discuss matrix-less methods for non-Hermitian sequences, where the generating symbol does not describe the eigenvalue distribution; we can now numerically approximate, with high accuracy, the spectral symbol describing the eigenvalue distribution. Standard double precision eigenvalue solvers typically fail for these matrices.
• Classification : 15Axx, 35Pxx, 65Fxx
• Format : Talk at Waseda University
• Author(s) :
  • Sven-Erik Ekström (Uppsala University)

[00767] Fractal and Fractional

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : Several physical and natural phenomena are characterized on one hand by the presence of different temporal and spatial scales, on the other by the presence of contacts among different components through rough interfaces like domains with non-smooth boundaries and fractal layers. The principal aim of the talk is to propose mathematical models to investigate these phenomena as well as their numerical approximation. Our attention will be focused on fractional Cauchy problems on the random Koch domains with different boundary conditions. Random Koch domains are domains whose boundary are constructed by mixtures of Koch curves with random scales. These domains are obtained as limit of domains with Lipschitz boundary whereas for the limit object, the fractal given by the random Koch domain, the boundary has Hausdorff dimension between 1 and 2. We point out that Random Koch domains provide a suitable setting to model phenomena - taking place across irregular and wild structures in which boundaries are "large" while bulk is "small"- in which the surface effects are enhanced like, for example, pulmonary system, root infiltration, tree foliage, etc..
• Classification : 28A80, 35R11, 26A33, 35J25, 65K15
• Format : Talk at Waseda University
• Author(s) :
  • Raffaela Capitanelli (Sapienza University of Roma)

[01662] Shape Preserving aspects of multivariate zipper fractal functions

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : In this article, a novel class of multivariate zipper fractal functions is introduced by perturbing a classical multivariate function through free choices of base functions, scaling functions, and a binary matrix called signature. In particular, the approximation properties of multivariate Bernstein zipper fractal function are investigated along with non-negativity, and coordinate-wise monotonicity features of the germ function.
• Classification : 28A80, 41A63, 41A29, 41A05, 41A30
• Format : Talk at Waseda University
• Author(s) :
  • Deependra Kumar (Indian Institute of Technology Madras)
  • ARYA KUMAR BEDABRATA CHAND (Indian Institute of Technology Madras)
  • Peter Robert Massopust (Technical University of Munich(TUM) Germany)

MS [02392] Low-Rank Models in Data Science

room : G306

• [04701] Multi-window Gabor phase retrieval
  • Format : Online Talk on Zoom
  • Author(s) :
    • Palina Salanevich (Utrecht University)
  • Abstract : Phase retrieval is the non-convex inverse problem of signal reconstruction from its intensity measurements that is motivated by practical applications. In the talk, we are going to focus on phase retrieval with multi-window Gabor frames, where the measurement vectors follow time-frequency structure natural for imaging and acoustics. We will propose an explicit construction of such frames and show that for them phase retrievability can be achieved with a close to optimal number of phaseless measurements.

MS [00170] Integrable systems, orthogonal polynomials and asymptotics

room : G401

• [03983] Stokes' phenomenon, discretization, and discrete integrability
  • Format : Talk at Waseda University
  • Author(s) :
    • Christopher Lustri (Macquarie University)
  • Abstract : This talk is concerned with integrability in discrete systems, and its relationship with Stokes' phenomenon. Discrete equations such as the discrete Painleve I equation can be written in terms of an infinite-order differential equation. We will consider a family of equations obtained by truncating this infinite-order differential equation at different orders. In this talk we will answer two questions: (1) How does discretization connect the Stokes' phenomenon in continuous and discrete Painleve I? (2) How does integrability emerge in this family of equations in the discrete limit?
• [05269] Borel analysis for the first difference q-Painlevé equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Adri Olde Daalhuis (The University of Edinburgh)
  • Abstract : We discuss the asymptotics of solutions of the first -difference $q$-Painlevé equation $w(qt)w^2(t)w(t/q)=w(t)-t$. Via the $q$-Borel transform we obtain an interesting singularity distribution in the Borel plane.
• [05326] Non-linear Stokes phenomenon for Painleve transcendents and topological recursion
  • Format : Talk at Waseda University
  • Author(s) :
    • Kohei Iwaki (The University of Tokyo)
  • Abstract : I will propose a conjectural statement on the Stokes phenomenon for the topological recursion partition function. Our claim is based on a relation between the topological recursion and the Painleve tau-function through the exact WKB analysis.
• [05496] Asymptotic prediction of tau-function zeros of Painlevé equations
  • Author(s) :
    • Ines Varela Aniceto (University of Southampton)
  • Abstract : Transseries solutions of Painlevé I and II equations include both algebraic asymptotic expansions and exponentially small corrections, valid in pole-free regions. In this talk I will show how summing all exponential terms at each algebraic order provides an analytic continuation into the pole-filled regions of the solutions, where exponentials are no longer suppressed. The same can done for the respective tau-functions to obtain asymptotic predictions for all the arrays of the tau-function zeros.

contributed talk: CT024

room : G402

[02961] An analysis of boundary variations in Laplace-Steklov eigenvalue problems

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : We analyze the influence of boundary perturbations on the spectrum of Laplace-Steklov eigenvalue problems. Both the differential equation and a boundary condition involve the spectral parameter. We derive Hadamard type expressions for the variation of the eigenvalues as the problem domain deforms. Consequently, we provide the convergence characteristics of the eigenvalues on the perturbed domain as its boundary approaches to that of the unperturbed one. Numerical results are obtained using a finite element formulation.
• Classification : 35-XX, 65-XX, FEM analysis of eigenvalues in PDEs
• Format : Talk at Waseda University
• Author(s) :
  • Önder Türk (Middle East Technical University)
  • Eylem Bahadır (Gebze Technical University)

[00698] Rigidity for Sobolev inequalities and radial PDEs on Cartan-Hadamard manifolds

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : We aim at classifying all the Cartan-Hadamard manifolds supporting an optimal function for the $p$-Sobolev inequality. We prove that, under the validity of the Cartan-Hadamard conjecture, which is known to be true in dimension $n\le 4$, the only such manifold is $\mathbb{R}^n$, up to isometries. We also investigate radial solutions to the related $p$-Laplace Lane-Emden equation, obtaining rigidity of finite-energy solutions regardless of optimality. Furthermore, we study the asymptotic behavior of infinite-energy solutions.
• Classification : 35B53, 35J92, 58J05, 58J70, 46E35
• Format : Talk at Waseda University
• Author(s) :
  • Matteo Muratori (Politecnico di Milano)
  • Nicola Soave (Politecnico di Milano)

[02197] Mean-field diffusive coupling to promote dispersal, synchronisation and stability of infectious diseases

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : The scope of mediated infectious diseases is strongly impacted by mobility of humans and mediating agents. The movement of hosts and mediators determines how spatially contagious infectious diseases are spread. Therefore, the metapopulation dynamics of mediated infectious disease model is examined in a patchy scenario where the hosts' and mediators' populations are divided into subpopulations. The network of humans and mediators are utilized to depict the patchy environment. The network patches are connected by mean field diffusive coupling. The patches of related networks synchronize and achieve bistable states as a result of dispersal.
• Classification : 34N05
• Format : Online Talk on Zoom
• Author(s) :
  • Tina Verma (Thapar Instiute of Engineering & Technology)

[01139] Adaptive sampling and transfer learning techniques for solution of PDEs

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : An adaptive sampling technique applied to the deep Galerkin method (DGM), and separately a transfer learning algorithm also applied to DGM is examined, aimed to improve, and speed up the training of the deep neural network when learning the solution of partial differential equations (PDEs). The proposed algorithms improve the DGM method. The adaptive sampling scheme implementation is natural and efficient. Tests applied to selected PDEs discussing the robustness of our methods are presented.
• Classification : 35-04, 65-04, Deep learning for the solution of PDEs
• Format : Online Talk on Zoom
• Author(s) :
  • Andreas Aristotelous (The University of Akron)

[00009] Numerical Solution of Kuramoto–Sivashinsky Equation Using Orthogonal Collocation with Bessel Polynomials as Basis

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
• Type : Contributed Talk
• Abstract : Bessel polynomials has been proposed as a base function in orthogonal collocation to discretize fourth order Kuramoto-Sivashinsky equation. Convergence of numerical results have been analysed through L2 and L∞ norms to discuss the effectiveness of technique. Number of test problems have been solved and comparison of results in space as well as in time direction at different number of collocation points has been presented. The numerical values are presented graphically to confirm applicability of technique.
• Classification : 35E15, 35G20, 65M70, 33C10
• Format : Online Talk on Zoom
• Author(s) :
  • Shelly Arora (Punjabi University, Patiala)
  • Indu Bala (Punjabi University, Patiala)

MS [00234] Differential Galois Theory and Integrability of Dynamical Systems

room : G404

• [03566] Local integrability and regularity of autonomous differential systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiang Zhang (Shanghai Jiao Tong University)
  • Abstract : For finite dimensional smooth autonomous differential systems, which have a singularity with one zero eigenvalue and the others nonresonant, we present our results on existence of local first integrals at the singularity, with emphasis on the regularity of the local first integrals. We first explore the existence of $C^\infty$ local first integrals for analytic differential systems under the Poincar\'e's non-resonant condition. We then show that for the Gevrey class of vector fields, their local first integrals have the same regularity as that of the vector fields provided that the real parts of the nonresonant eigenvalues are all positive or all negative. Lastly, a sharper expression of the loss of the regularity is presented by the lowest order of the resonant terms together with the indices of Gevrey smoothness and the diophantine condition for the case that the Jacobian matrix of the vector field at the singularity is in the diagonal form. The main tools are the homological method, the KAM theory, and the Gevrey normalization theory.
• [04369] Singular solitary waves in the KdV equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuyuki Yagasaki (Kyoto University)
  • Abstract : In this talk we consider the KdV equation and discuss its singular solitons which are called rational solitons, positons or negatons. We are especially interested in the solvability by quadrature for Schrodinger equations appearing as one of the related Lax pair. Some formulas for scattering coefficients of positons or negatons are also given. This is joint work with Katsuki Kobayashi.
• [04649] Korteweg-de Vries traveling waves and Differential Galois Theory
  • Format : Online Talk on Zoom
  • Author(s) :
    • Maria-Angeles Zurro (Autonomous University of Madrid)
  • Abstract : It was conjectured that the abelianity of the identity component of the Galois group of the variational equation is a necessary condition for the integrability of the non-linear PDE itself. In my lecture I will present an algebraic and spectral study of the variational equation around a KdV solitonic potential from the point of view of Galois differential theory. This is part of an ongoing joint work with J. J. Morales-Ruiz and J.-P. Ramis.
• [03529] Real Liouvillian extensions of partial differential fields
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zbigniew Hajto (Faculty of Mathematics and Computer Science UJ)
  • Abstract : I will present Galois theory for partial differential systems defined over formally real differential fields with a real closed field of constants and over formally $p$-adic differential fields with a $p$-adically closed field of constants. For an integrable partial differential system, there exists a formally real (resp. formally $p$-adic) Picard-Vessiot extension. I will explain the applications of this theorem.

MS [01188] Recent Developments in Fluid Dynamics

room : G405

• [04870] Stability of a point charge for the Vlasov-Poisson system
  • Format : Online Talk on Zoom
  • Author(s) :
    • Benoit Pausader (Brown University)
  • Abstract : We consider solutions of the Vlasov-Poisson system starting from initial data (i) a dirac mass (the point charge) and (ii) some small density with respect to Liouville measure (the cloud). We show global existence of the solution and describe the asymptotic behavior in terms of modified scattering. This is joint work with K. Widmayer and J. Jiang.
• [05033] Global axisymmetric Euler flows with rotation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Klaus Widmayer (University of Vienna & University of Zurich)
    • Benoit Pausader (Brown University)
    • Yan Guo (Brown University)
  • Abstract : We discuss the construction of a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity and have non-vanishing swirl.
• [02875] On the analyticity of the Muskat equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jia Shi (MIT)
  • Abstract : The Muskat equation describes the interface of two liquids in a porous medium. We will show that if a solution to the Muskat problem in the case of same viscosity and different densities is sufficiently smooth, then it must be analytic except at the points where a turnover of the fluids happens. We will also show analyticity in a region that degenerates at the turnover points provided some additional conditions are satisfied.

MS [00278] Nonlocal Modeling, Analysis, and Computation

room : G406

• [03632] Nonlocal Boundary Value Problems with Local Boundary Conditions
  • Author(s) :
    • James Scott (Columbia University)
  • Abstract : We state and analyze classical boundary value problems for nonlocal operators. The model takes its horizon parameter to be spatially dependent, vanishing near the boundary of the domain. We show the variational convergence of solutions to the nonlocal problem with mollified Poisson data to the solution of the localized classical Poisson problem with $H^{-1}$ data as the horizon uniformly converges to zero. Several classes of boundary conditions are considered.
• [03718] On the optimal control of a linear peridynamic model
  • Format : Talk at Waseda University
  • Author(s) :
    • Tadele Mengesha (University of Tennessee Knoxville )
    • Abner Salgado (University of Tennessee Knoxville )
    • Joshua Siktar (University of Tennessee Knoxville )
  • Abstract : We present a result on a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to proving existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter, which controls the degree of nonlocality, approaches zero. We then study a finite element-based discretization of this problem, its convergence, and the so-called asymptotic compatibility as the discretization parameter and the horizon parameter vanish simultaneously.
• [03800] Nonlocal half-ball vector operators and their applications to nonlocal variational problems
  • Author(s) :
    • Xiaochuan Tian (UC San Diego)
    • Zhaolong Han (UC San Diego)
  • Abstract : Motivated by the growing interests in nonlocal models, and particularly peridynamics, we present a nonlocal vector calculus framework defined using the half-ball gradient, divergence, and curl operators. Theoretical developments of the nonlocal half-ball vector operators include nonlocal vector identities, nonlocal Poincare inequality on bounded domains, and Bourgain-Brezis-Mironescu type compactness results. As a result, well-posedness of nonlocal variational problems can be obtained, and the applications include nonlocal convection-diffusion problems and the peridynamics correspondence model. In particular, we illustrate that the new peridynamics correspondence model defined by the half-ball vector operator is energy stable which removes the known zero-energy mode instability issue of peridynamics correspondence models.
• [05210] CabanaPD: A meshfree GPU-enabled peridynamics code for exascale fracture simulations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Pablo Seleson (Oak Ridge National Laboratory)
    • Sam Reeve (Oak Ridge National Laboratory)
  • Abstract : Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage simulation, which has been successfully demonstrated as an effective tool for the simulation of complex fracture phenomena in many applications. However, the nonlocal nature of peridynamics makes it highly computationally expensive, compared to classical continuum mechanics, which often hinders large-scale fracture simulations. In this talk, we will present ongoing efforts to develop CabanaPD, a meshfree GPU-enabled peridynamics code for large-scale fracture simulations. CabanaPD is built on top of two main libraries: Kokkos and Cabana, both developed throughout the Exascale Computing Project (ECP). CabanaPD is performance-portable and exascale-capable, and it is designed to run on U.S. Department of Energy’s supercomputers, including the newly deployed Frontier, which is the first exascale machine and today's top supercomputer worldwide.

MS [00068] Models for collective behavior and emergent phenomena

room : G501

• [04504] Model Reduction and Coarse-Graining of Complex Systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hong Duong (University of Birmingham)
  • Abstract : Complex systems in nature and in applications (such as molecular systems, crowd dynamics, swarming, opinion formation, just to name a few) are often described by systems of stochastic differential equations (SDEs) and partial differential equations (PDEs). It is often analytically impossible or computationally prohibitively expensive to deal with the full models due to their high dimensionality (degrees of freedom, number of involved parameters, etc.). It is thus of great importance to approximate such large and complex systems by simpler and lower dimensional ones, while still preserving the essential information from the original model. This procedure is referred to as model reduction or coarse-graining in the literature. In this talk, I will present methods for qualitative and quantitative coarse-graining of several SDEs and PDEs, in the presence or absence of a scale-separation.
• [05047] Splitting methods for optimal control
  • Format : Online Talk on Zoom
  • Author(s) :
    • David Goodwin (Aarhaus University)
    • Mohammadali Foroozandeh (Zurich Instruments)
    • Pranav Singh (University of Bath)
  • Abstract : The optimal control of a physical system requires efficient numerical solvers for computing dynamics, accurate gradients, and efficient optimization routines. Of particular interest in this talk are quantum systems such as spins and electrons under the influence of external time-dependent controls such as lasers and magnetic fields. In this talk I will present a highly efficient optimal control procedure called QOALA which adaptively switches splitting based solvers and utilizes exact gradients.
• [05107] Nonlocal Cross-interaction Systems on Graphs: Energy Landscape and Dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jan-Frederik Pietschmann (University of Augsburg)
    • Markus Schmidtchen (Technische Universität Dresden)
    • Georg Heinze (University of Augsburg)
  • Abstract : We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. We introduce the setting of nonquadratic Finslerian gradient flows on generalized graphs featuring nonlinear mobilities. In a continuous and local setting, this class of systems exhibits a wide variety of patterns, including mixing of the two species, partial engulfment, or phase separation. We showcase how this rich behavior carries over to the graph structure. We present analytical and numerical evidence thereof.

contributed talk: CT030

room : G502

[02107] Nonlinear stochastic heat equation with variable thermal conductivity

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
• Type : Contributed Talk
• Abstract : We consider a stochastic heat equation with variable thermal conductivity, on infinite domain, with both deterministic and stochastic source and with stochastic initial data. The stochastic source appears in the form of multiplicative generalized stochastic process. In our solving procedure we use regularized derivatives and the theory of generalized uniformly continuous semigroups of operators. We establish and prove the result concerning the existence and uniqueness of solution within certain generalized function space.
• Classification : 35D30, 35K05, 47D99
• Format : Talk at Waseda University
• Author(s) :
  • Danijela Rajter-Ciric (Faculty of Sciences, University of Novi Sad)
  • Milos Japundzic (Novi Sad School of Business - Higher Education Institution for Applied Studies)

[00144] The flux perturbed Riemann solution for isentropic Cargo-LeRoux model

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
• Type : Contributed Talk
• Abstract : In this research, we study the pressureless Cargo-LeRoux model of conservation laws, which is modeled from the one-dimensional constant gravity Euler equations. Introducing flux perturbation of a van der Waals isentropic gas equation of state, the exact solution of Riemann problem is derived and establish the existence and uniqueness of the Riemann solution globally. Finally, the influence of van der Waals excluded volume on the physical quantities is illustrated graphically using MATLAB software.
• Classification : 35D30, 35L65, 76L05, 76N10, 76N15
• Format : Talk at Waseda University
• Author(s) :
  • Sahadeb Kuila (DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203)
  • Sumita Jana (DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203)

[00487] A strongly nonlinear anisotropic parabolic-elliptic system: analysis and numerical simulation

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
• Type : Contributed Talk
• Abstract : We study the existence of a capacity solution to a nonlinear coupled parabolic-elliptic system. This system is a generalization of the so-called thermistor problem which models a temperature dependent electrical resistor. In this analysis we have considered the case where $Au$ is an operator of the Leray-Lions class defined in an anisotropic Sobolev space. We also show some numerical simulations of this problem and we discuss the obtained results.
• Classification : 35K55, 35J70, 46E35
• Format : Talk at Waseda University
• Author(s) :
  • Francisco Ortegón Gallego (Universidad de Cádiz)
  • Manar Lahrache (Moulay Ismail University)
  • Mohamed Rhoudaf (Moulay Ismail University)
  • Hajar Talbi (Moulay Ismail University)

[01755] A Study of Imaging in the Existence of Resonance with Multiple Scattering

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
• Type : Contributed Talk
• Abstract : A random medium consisting of many small bodies that can reflect or scatter the incoming waves is called multiple scattering. Imaging becomes difficult to perform in such random media because of sharp responses arising from the underlying interactions of multiply scattered waves at resonance frequencies. In this talk, we present a study by simulating this problem with the Foldy-Lax-Lippmann-Schwinger formalism, which was employed for the multiply scattered waves, in randomly distributed isotropic point-like scatterers.
• Classification : 35P05, 47B06, 78A46
• Author(s) :
  • Ray-Hon Sun (Stanford University)
  • Ray-Hon Sun (Stanford University)

MS [01195] Hyperbolic one-dimensional systems in networks: mathematical modeling and numerical approximations

room : G601

• [02299] The Junction Riemann Problems under transonic scenarios: application to veins.
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Mairal (I3A - Universidad de Zaragoza)
    • Javier Murillo (I3A, University of Zaragoza,)
    • Pilar García-Navarro (I3A - Universidad de Zaragoza)
  • Abstract : Current 1D numerical methods for flow in junctions provide good results in most cases. In the 1D framework, the junction is a singular point. One of the shortcomings of existing methods is their inability to deal with transonic and supersonic flow at junctions in physiological flows. Existing methods that rely on coupling approaches for conservation of mass, energy or momentum and the characteristic equations for subsonic flow conditions are revisited here.
• [02244] Numerical and physical impact of coupling conditions for one dimensional blood flow models
  • Format : Talk at Waseda University
  • Author(s) :
    • Lucas Omar Müller (University of Trento)
  • Abstract : One dimensional blood flow models consist of hyperbolic or hyperbolic-dominant systems of balance laws. This specific mathematical property plays a key role in the derivation of coupling and boundary conditions necessary to model blood flow in networks of vessels. In this talk we will derive coupling and boundary conditions for a general velocity profile and study their physical and numerical impact in simulations of the arterial and venous system across several spatial scales.
• [02355] High-order fully well-balanced numerical methods for one-dimensional blood flow in networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Ernesto Pimentel-García (University of Málaga)
  • Abstract : We are interested in the numerical study of one-dimensional blood flow model in networks with discontinuous mechanical and geometrical properties. We do an exhaustive investigation of all its stationary solutions and we propose high-order fully well-balanced numerical methods that are able to preserve all of them. These methods are able to deal with more than one discontinuous parameter and friction. Some numerical tests are shown to prove its well-balanced and high-order properties.

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

room : G602

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

room : G605

• [03018] Stabilization of 1D evolution systems: new approaches
  • Format : Talk at Waseda University
  • Author(s) :
    • Amaury Hayat (Ecole des Ponts Paristech)
  • Abstract : We discuss recent advances in the F-equivalence (or Fredholm backstepping) method. This consists in reformulating the stabilization problem and to find a control operator such that the PDE system can be inversely mapped to a simpler PDE system. Surprisingly powerful, this approach offers the possibility to treat very general classes of systems. We will also examine traffic flow stabilization. Finally, we will briefly discuss some results on AI for mathematics.
• [02943] Feedback stabilization and inverse problem for a nonlocal transport equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhiqiang Wang (Fudan University)
  • Abstract : In this talk, we will show some results on feedback stabilization and inverse problems for a transport equation with nonlocal velocity. This model arises in the control of semiconductor manufacturing systems which have a highly re-entrant character. Firstly we obtain a semi-global stabilization result by using a time-varying feedback control. Secondly with the help of certain feedback control, we recover the velocity function from the measurements.
• [04252] The controllability of a special class of coupled wave systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jingrui Niu (Sorbonne Université)
    • Pierre Lissy (Université Paris-Dauphine)
  • Abstract : I will present an exact controllability result for coupled wave systems with two distinct speeds. A distributed scalar control function is effective in a subdomain satisfying the geometric control conditions and acts on only one speed. We establish compatibility conditions, which are associated with the particular coupling structure. Furthermore, the exact controllability holds in these compatible spaces if and only if the coupling structure satisfies an operator Kalman rank condition.
• [02522] Geometry of observable sets
  • Format : Talk at Waseda University
  • Author(s) :
    • gengsheng wang (Tianjin University)
  • Abstract : We introduce several observability inequalities in some abstract setting. Then for some concrete evolution equations, such as the heat equation and the Schrodinger equations on the whole space, we give the characterizations of the observable sets such that the aforementioned inequalities hold. We further give some comments.

MS [00874] Recent advances in the analysis and numerics for phase-field models

room : G606

• [02784] Existence of weak solutions to an anisotropic electrokinetic flow model
  • Format : Talk at Waseda University
  • Author(s) :
    • Luisa Plato (WIAS)
    • Robert Lasarzik (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
    • Dietmar Hömberg (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
  • Abstract : In this talk the existence proof of weak solutions in three space dimensions to an anisotropic Navier—Stokes—Nernst—Planck—Poisson system is presented. This models the electrokinetic flow induced by charged particles dissolved in a liquid crystals with constant director field. The existence proof relies on an approximating scheme and weak sequential compactness of the approximating sequence, which follows from the energy law. Weak—strong uniqueness is proven via the relative energy inequality.
• [02502] Global existence for a singular nonlocal phase field system with inertial term
  • Format : Talk at Waseda University
  • Author(s) :
    • Shunsuke Kurima (Tokyo University of Science)
  • Abstract : This talk deals with a nonlocal phase field system with inertial term. Colli-Colturato (2018) have established existence of solutions to a phase field system related to the entropy balance. Also, Colli-Grasselli-Ito (2002) have proved existence for a parabolic-hyperbolic Penrose-Fife phase field system. However, singular nonlocal phase field systems with inertial term seem to be not studied yet. The present work asserts that we can derive existence for a singular nonlocal phase field system with inertial term.
• [02824] A structure-preserving scheme for the Liu-Wu model
  • Format : Talk at Waseda University
  • Author(s) :
    • Makoto Okumura (Konan University)
  • Abstract : Recently, the Cahn-Hilliard equation with new dynamical boundary conditions has been proposed by Liu and Wu. This model has characteristic conservation laws in that each mass of the interior of the domain and the boundary are conserved. In addition, the total energy dissipation law holds. In this talk, we propose a structure-preserving scheme for the Liu-Wu model that retains the conservation and dissipation laws in a discrete sense and show the mathematical and numerical results.
• [02783] Analysis of an Allen--Cahn system in two scale topology optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Robert Lasarzik (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
    • Dietmar Hoemberg (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
    • Moritz Ebeling-RumpIn this talk, we consider an Allen—Cahn system with the obstacle potential that guarantees mass conservation. This equation is coupled to two linear elasticity equations and a nonlocal operator. This system emerged from an algorithm for a (Weierstrass Institut of Applied Analysis and Stochastics Berlin )
  • Abstract : In this talk, we consider an Allen—Cahn system with the obstacle potential that guarantees mass conservation. This equation is coupled to two linear elasticity equations and a nonlocal operator. This system emerged from an algorithm for a problem in two-scale topology optimization using the phase-field approach. We prove the existence of weak solutions for the associated inclusion and comment on different connections of the solvability concept and the numerical algorithm.

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

room : G701

• [00354] Spectral properties of the Neumann–Poincaré operator on rotationally symmetric domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong-Gwan Ji (Korea Institute for Advanced Study)
    • Hyeonbae Kang (Inha University)
  • Abstract : In this talk, we will discuss the spectral properties of the Neumann-Poincaré operator when domains have rotational symmetry. We prove that if a domain $\Omega$, in two dimensions, has rotational symmetry then NP spectrum on $\Omega$ contains NP spectrum on $D$ which generates rotationally symmetric domain $\Omega$ by $m$-th root transformation.
• [01245] Vector field decomposition and eigenvalues of elastic Neumann-Poincaré operators
  • Format : Talk at Waseda University
  • Author(s) :
    • Shota Fukushima (Inha University)
    • Yong-Gwan Ji (Korea Institute for Advanced Study)
    • Hyeonbae Kang (Inha University)
  • Abstract : We show that all vector fields restricted to a surface is decomposed into three components and each component is characterized by the divergence-free or rotation-free harmonic extension to inside or outside of the domain. These three components correspond to three accumulation points of the eigenvalues of the elastic Neumann-Poincaré operator, which is a singular integral operator on the boundary.
• [01265] Essential spectrum of elastic Neumann-Poincar\'e operators with a corner
  • Format : Talk at Waseda University
  • Author(s) :
    • Daisuke Kawagoe (Kyoto University)
  • Abstract : The elastic Neumann--Poincar\'e operator is a boundary integral operator naturally appearing when we solve the Lam\’e system in a bounded domain. For the two-dimensional case, if the boundary is smooth, then its spectrum consists of two sequences of eigenvalues with two accumulation points. In this talk, we consider the situation where the planar domain is smooth except at a corner and show that the essential spectrum appears around the above accumulation points.
• [00662] Fundamental solutions in Colombeau algebra
  • Format : Talk at Waseda University
  • Author(s) :
    • Nobuto Yoneyama (Shinshu university)
    • Yoshihisa Miyanishi (Shinshu University)
  • Abstract : The notion of fundamental solutions {abbreviated by FS} is introduced in Colombeau algebra. Then we can construct a little more generalized FS even for Lewy-type equation whereas there are no FS in the sense of distributions.

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

room : G702

• [05559] The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau System
  • Format : Talk at Waseda University
  • Author(s) :
    • Rafael Bailo (University of Oxford, Mathematical Institute)
    • José Antonio Carrillo (University of Oxford, Mathematical Institute)
    • Jingwei Hu (University of Washington)
  • Abstract : In this talk we will present an extension of the classical Particle-In-Cell (PIC) method for plasmas which can account for the collisional effects modelled by the Landau operator. The method is derived form the gradient-flow formulation of the Landau equation, thereby preserving the collision invariants and the entropy structure. We will discuss the derivation and implementation of the method, as well as several numerical examples to showcase the effects of collisions in plasma simulations.

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

room : G704

• [04546] Interface dynamics in ideal and realistic fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Dan V. Ilyin (California Institute of Technology)
    • Snezhana Abarzhi (University of Western Australia)
  • Abstract : Interfaces and mixing and their non-equilibrium dynamics are ubiquitous to occur in nature and technology. We develop theory of interface dynamics, directly linking flow fields and interfacial transport and discovering fluid instabilities never previously discussed. In ideal and realistic fluids, the interface stability is set by the interplay of the macroscopic inertial mechanism balancing the destabilizing acceleration, whereas microscopic thermodynamics create vortical fields in the bulk. The interface is the place where balances are achieved.
• [03416] Determining control parameters for unsteady pulling of mass-spectrometry emitters
  • Format : Talk at Waseda University
  • Author(s) :
    • Yvonne Stokes (The University of Adelaide)
    • Gagani Pathumika Ranathunga (Oktal Sydac)
    • Michael Chen (The University of Adelaide)
  • Abstract : Asymptotic modelling is used to examine the heating and pulling of an axisymmetric glass tube with an internal overpressure to form a taper with near-uniform bore and small wall thickness at the tip, as desired for mass-spectrometry emitters. There is no unique choice of pulling force and pressure to achieve the desired geometry, which is sensitive to the parameters. Phase plane plots are used to understand the dependence of the geometry on the control parameters.
• [04478] Compressible Vortex Sheets and Free Boudary Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gui-Qiang George Chen (University of Oxford)
  • Abstract : We are concerned with the nonlinear stability/instability of compressible vortex sheets and related interfaces in compressible fluid flows governed by the Euler equations and related nonlinear PDEs. Such problems can be formulated as characteristic free boundary problems for nonlinear hyperbolic conservation laws and related equations. In this talk, we will discuss some recent developments in the analysis of their stability/instability and explore stabilizing mechanisms such as magnetic, relativistic, and compressibility effects.

contributed talk: CT053

room : G709

[00442] On the dynamical properties of a max-plus model identified with the Lozi map

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G709
• Type : Contributed Talk
• Abstract : We focus on a max-plus discretized model that is identified with the Lozi map in this talk. The max-plus model can be derived from the generalized Sel’kov model composed of non-linear differential equations via tropical discretization and ultradiscretization. Based on the Poincare mapping method and the estimation of Lyapunov exponents, the dynamical properties of the max-plus model and its transformation from the generalized Sel’kov model are discussed.
• Classification : 37M20, 37M15, 65P40, 68Q80, 37J70
• Format : Talk at Waseda University
• Author(s) :
  • Shousuke Ohmori (Waseda University)
  • Yoshihiro Yamazaki (Waseda University)

[00457] On limit cycles of discrete dynamical systems with positivity

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G709
• Type : Contributed Talk
• Abstract : We focus on limit cycles of discretized Sel'kov model derived from continuous Sel'kov model via tropical discretization. The discretized model possesses a parameter for time step. We numerically found, by varying the parameter, that density profile of phase in the limit cycles transits between continuous and ultradiscrete, and that the ultradiscrete state corresponds to a max-plus dynamical system. In this talk, we discuss these findings from the viewpoint of nonlinear dynamical systems.
• Classification : 37M20, 37M15, 65P40, 68Q80, 37J70, ultradiscretization, max-plus dynamical system, bifurcation
• Format : Talk at Waseda University
• Author(s) :
  • Yoshihiro Yamazaki (Waseda University)
  • Shousuke Ohmori (Waseda University)

[01239] Convergence analysis of the discrete consensus-based optimization algorithm

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G709
• Type : Contributed Talk
• Abstract : We study stochastic convergence of the discrete Consensus-Based Optimization, called CBO algorithm, in almost-sure sense and in expectation. CBO is a mathematical toy example for non-gradient multi-point optimizer which tries to find the global minimum point of a given cost function. The convergence analysis guarantees the termination of the optimization process. The main result is a joint work with Seung-Yeal Ha, Shi Jin, and Doheon Kim.
• Classification : 37M99, 65p99
• Format : Talk at Waseda University
• Author(s) :
  • Dongnam Ko (The Catholic University of Korea)

[00456] Network representations of attractors for surrogates generation and change detection

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @G709
• Type : Contributed Talk
• Abstract : Attractors arising from delay embedded time-series can characterise system dynamics. However, extracting useful representations is challenging for systems with high-dimensional or complex structure. We propose a data-driven method to represent attractors as networks, where dynamics are encoded as node transition probabilities. The usefulness of this representation is demonstrated in two tasks: (1) surrogate data generation; and (2) change point detection. These methods are applied to chaotic time-series, and experimental ECG data for heart attack detection.
• Classification : 37M10, 37M22, 94C12
• Format : Talk at Waseda University
• Author(s) :
  • Eugene Tan (The University of Western Australia)
  • Shannon Dee Algar (The University of Western Australia)
  • Debora Correa (The University of Western Australia)
  • Thomas Stemler (The University of Western Australia)
  • Michael Small (The University of Western Australia)

MS [00913] Geometric Mechanics and Related Topics

room : G710

• [03436] Noether’s conservation laws via the modified formal Lagrangians
  • Format : Talk at Waseda University
  • Author(s) :
    • Linyu Peng (Keio University)
  • Abstract : Noether’s theorem establishes a one-to-one correspondence between variational symmetries and conservation laws of variational differential equations. In this talk, we extend Noether’s theorem to general differential equations by defining the modified formal Lagrangians. This allows us to construct conservation laws of non-variational differential equations using their symmetries. Worked examples will be provided.
• [05483] Harmonic exponential families on homogeneous spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Koichi Tojo (RIKEN AIP)
    • Taro Yoshino (The University of Tokyo)
  • Abstract : Exponential families play an significant role in the field of information geometry and are useful in Bayesian inference. Widely used families of probability measures, such as normal and gamma distributions can be considered as exponential families on homogeneous spaces with symmetry. Based on this observation, we presented a method to construct exponential families with symmetry using representation theory. In this talk, we will explain the method and its properties, illustrating them with examples.
• [04618] Symmetries and bifurcations of resonant periodic orbits in perturbed Rayleigh-Bénard convection
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahito Watanabe (Waseda University)
    • Hiroaki Yoshimura (Waseda University)
  • Abstract : Rayleigh-Bénard convection is natural convection that appears in a fluid layer with heated bottom and cooled top planes. When Rayleigh number is set just above a critical number, velocity fields of Rayleigh-Bénard convection may oscillate slightly. In such oscillatory convection both stable and chaotic fluid transport may occur. In this talk we explore the global structures of periodic fluid transport in two-dimensional perturbed Rayleigh-Bénard convection in the perspectives of resonance, symmetry, and bifurcation.
• [05475] Geometric models in hydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Tudor Stefan Ratiu (Shanghai Jiao Tong UniversityShanghai Jiao Tong University )
  • Abstract : In this talk the classical geometric formulation of hydrodynamics will be extended by the use of a momentum map with values in Cheeger-Simons differential characters. It will be shown that this extended momentum map admits topological conservation laws. Clebsch variables will be introduced for which the helicity takes integer values.

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

room : G801

• [00647] Uncertainty quantification for stochastic models of damage mechanics
  • Author(s) :
    • Petr Plechac (University of Delaware)
    • Gideon Simpson (l University)
    • Jerome R Troy (University of Delaware)
  • Abstract : We study models used for describing brittle materials which exhibit linear elastic behavior until an applied load reaches a critical yield stress at which point a damage/fracture occurs . The underlying visco-elasto dynamics PDEs are characterized by a non-monotone stress-strain relation with a non-linearity linked to the critical yield stress. We study these equations in the presence of random yield stress field. The developed computational techniques will be demonstrated in numerical examples.
• [00649] On the governing equations of poro-piezoelectric composite materials
  • Author(s) :
    • Miao-Jung Yvonne Ou (University of Delaware)
  • Abstract : Materials such as quartz, cortical bones and cancellous bones exhibit piezo-electric behaviors, for which a mechanical wave such as ultrasound can trigger electro-magnetic waves. In this talk, we consider a porous material made of piezo-electric solid with pores saturated with conducting fluid, a model mimicking in vivo bones. The focus is to understand how the microstructure is encoded in the effective piezoelectric properties of these porous composites by using the two-scale convergence homogenization approach.
• [01237] Homogenization of a suspension of viscous fluid with magnetic particles
  • Author(s) :
    • Yuliya Gorb (NSF)
    • Thuyen Dang (University of Chicago)
    • Silvia Jimenez Bolanos (Colgate University)
  • Abstract : In this talk, the rigorous periodic homogenization for a coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid is discussed. Both one-way and two-way coupling between the fluid and particles are considered. As the size of the particles approaches zero, it is shown that the suspension’s behavior is governed by a generalized homogenized magnetohydrodynamic system, whose parameters are explicitly derived. The two-scale convergence is utilized to justify obtained homogenized behavior of the original heterogeneous system.
• [05177] Energy-efficient flocking of particle systems
  • Author(s) :
    • Alexander Panchenko (Washington State University)
  • Abstract : The talk explores the problem of achieving flocking in multi-agent systems using minimal amount of on-board energy. We also assume that censor capacity is limited. Starting from a model reminiscent of Dissipative Particle Dynamics augmented with self-propulsion forces, we prove existence of an attractor for certain non-dissipative systems. Computer simulations show that velocity alignment is more energy efficient than formation control.

MS [02221] Recent progress on mathematical theory of boundary layer

room : G802

• [03046] Eckhaus instability of the compressible Taylor vortex
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshiyuki Kagei (Tokyo Institute of Technology)
  • Abstract : This talk is concerned with the bifurcation and stability of the compressible Taylor vortex. It is shown that Taylor vortices bifurcate near the criticality for the incompressible problem when the Mach number is sufficiently small. The localized stability of the compressible Taylor vortices is considered and it is shown that the Eckhaus instability of compressible Taylor vortices occurs as in the case of the incompressible ones.
• [03064] Stability of shear flows in inviscid and viscous fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Weiren Zhao (New York University Abu Dhabi)
  • Abstract : In this talk, I will present some recent progress in the asymptotic stability of shear flows in both inviscid and viscous fluids. The inviscid damping and enhanced dissipation phenomenon will be discussed in both linear and nonlinear models.
• [03247] Tollmien-Schlichting waves in the subsonic regime
  • Format : Talk at Waseda University
  • Author(s) :
    • Di Wu (South China University of Technology)
    • Nader Masmoudi (New York University Abu Dhabi)
    • Yuxi Wang (Sichuan University)
    • Zhifei Zhang (Peking University)
  • Abstract : The Tollmien-Schlichting (T-S) waves play a key role during the early stage of the boundary layer transition. In a breakthrough work, Grenier, Guo and Nguyen gave a first rigorous construction of the T-S waves of temporal mode for the incompressible fluid. In this paper, we construct the T-S waves of both temporal mode and spatial mode to the linearized compressible Navier-Stokes system around the boundary layer flow in the whole subsonic regime. The proof is based on a new iteration scheme via solving two quasi-compressible systems related to the incompressible part and compressible part respectively. For the incompressible part, the key ingredient is to solve an Orr-Sommerfeld type equation, which is based on a new Airy-Airy-Rayleigh iteration instead of Rayleigh-Airy iteration introduced by Grenier, Guo and Nguyen.
• [04253] Global Existence of Weak Solutions for Compressible Navier--Stokes--Fourier Equations with the Truncated Virial Pressure Law
  • Format : Talk at Waseda University
  • Author(s) :
    • Fei Wang (Shanghai Jiao Tong University)
    • Didier Bresch (Univ. Savoie Mont Blanc)
    • Pierre-Emmanuel Jabin (Pennsylvania State University)
  • Abstract : This paper concerns the existence of global weak solutions {\it \`a la Leray} for compressible Navier--Stokes--Fourier system with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

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

room : G808

• [00359] A NOVEL QUANTITATIVE INVERSE SCATTERING SCHEME USING INTERIOR RESONANT MODES
  • Format : Talk at Waseda University
  • Author(s) :
    • Xianchao Wang (Harbin Institute of Technology)
  • Abstract : In this talk, we introduce a novel quantitative imaging scheme to identify impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown obstacle from the far-field data via the indicating behaviour of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme of Newton’s type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton’s iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the Newton’s formula involves the geometric quantities of the unknown boundary surface in a natural way.
• [00333] Simultaneous recovery of a scattering cavity and its internal sources
  • Format : Talk at Waseda University
  • Author(s) :
    • Deyue Zhang (Jilin University)
    • Yukun Guo (Harbin Institute of Technology)
    • Yinglin Wang (Jilin University)
    • Yan Chang (Harbin Institute of Technology)
  • Abstract : We consider the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this problem can be decoupled into an inverse cavity scattering problem and an inverse source problem. Then the uncoupled subproblems are respectively solved by the modified optimization and sampling method. Numerical examples will be presented to demonstrate the effectiveness of the method.
• [00259] The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform
  • Format : Talk at Waseda University
  • Author(s) :
    • Shiqi Ma (Jilin University)
  • Abstract : We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [ G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case of simple manifolds, and more generally to manifolds where the geodesic ray transform is stably invertible.
• [00245] Minnaert resonances for bubbles in soft elastic materials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hongjie LI (The Chinese University of Hong Kong)
  • Abstract : In this talk, the low-frequency resonance for acoustic bubbles embedded in soft elastic materials is discussed. This is a hybrid physical process that couples the acoustic and elastic wave propagations. By delicately and subtly balancing the acoustic and elastic parameters as well as the geometry of the bubble, we show that Minnaert resonance can occur for rather general constructions. This study poses a great potential for the effective realisation of negative elastic materials by using bubbly elastic media.

MS [01996] Control and inverse problems on waves, oscillations and flows

room : G809

• [03795] Recovery in vivo viscoelasticity from elastography measured data
  • Format : Talk at Waseda University
  • Author(s) :
    • Yu Jiang (Shanghai University of Finance and Economics)
  • Abstract : This talk will briefly describe how to solve the inverse problem of recovering in vivo viscoelasticity from elastography (magnetic resonance elastography, ultrasound elastography) measurements. To solve it robustly, one need to have a proper partial differential equation model to describe the wave motion inside living body. And based on this PDE model and given interior measurements, theoretical and numerical inverse analyzes need to be performed. As the PDE model, we start with a dynamic viscoelastic model and several simplified models are given. For inversion analysis, we give several practical numerical inversion methods to identify viscoelasticity, such as regularized numerical differentiation method etc.
• [03880] Acousto-electric tomography imaging model and algorithm based on two-point gradient method
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Zhong (School of Mathematics, Southeast University )
  • Abstract : We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by utilizing the two point gradient method, the piecewise constant conductivity can be efficiently reconstructed. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.
• [04269] Numerical method for unique continuation of elliptic equations and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Yu Chen (Shanghai University of Finance and Economics)
    • Jin Cheng (Fudan University)
  • Abstract : Numerical method for unique continuation of elliptic equations is related to information reconstruction from interior local measurements. The conditional stability of unique continuation along analytic sub-manifolds in three dimensions will be provided. A stable numerical algorithm is constructed based on Tikhonov regularization according to the conditional stability, in order to deal with the ill-posedness. The evaluation of reliable region of a reconstruction and potential applications of the present method in atmospheric flows will be discussed.
• [04089] Reconstruction of piecewise smooth diffusion coefficient and initial value with adaptive regularization
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuli CHEN (Hokkaido University)
    • Haibing Wang (Southeast University)
  • Abstract : This talk will present an inverse problem of simultaneously reconstructing the piecewise smooth diffusion coefficient and initial value in a diffusion equation from extra measurements. The inverse problem is transformed into solving an optimization problem with a switchable regularization to simultaneously preserve multiple properties of unknown functions. The existence, stability and consistency result are rigorously analyzed by introducing a domain index. Then, we decompose the optimization problem into a SOLVE-MARK-REFINE-looping scheme and develop an adaptive iterative algorithm. Finally, we present several numerical examples to show the validity of the proposed algorithm.

MS [02474] Applied and Computational Dynamics

room : F308

• [04209] A method of computing Morse decomposition via approximate ODE solvers and its application
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoyuki Miyaji (Kyoto University)
  • Abstract : Computing Conley--Morse graphs for dynamical systems defined by ordinary differential equations using rigorous ODE solvers such as Lohner’s method is suffered from wrapping effects and is computationally expensive. It is especially remarkable when applied to Poincaré maps. In this talk, we apply approximate solvers, such as the Runge--Kutta methods, to computing Morse decomposition. We will discuss its application to Poincaré maps for 4D ODEs arising in modeling the motion of a self-propelled particle.
• [03407] Finite-resolution recurrence in dynamical models
  • Format : Talk at Waseda University
  • Author(s) :
    • Pawel Pilarczyk (Gdansk University of Technology, Faculty of Applied Physics and Mathematics)
    • Justyna Signerska-Rynkowska (Dioscuri Centre in Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences)
    • Grzegorz Graff (Gdansk University of Technology, Faculty of Applied Physics and Mathematics)
  • Abstract : In order to improve the method for rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 (SIAM J. Appl. Dyn. Syst. 8, 757-789), we introduce the notion of finite-resolution recurrence, develop an effective algorithm for its computation, and apply it to a two-dimensional model of a neuron. We additionally use machine learning to distinguish between different types of dynamics observed.
• [04891] Reconstruction of stationary measures from `cycles’ in random dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroki Takahasi (Keio Institute of Pure and Applied Sciences)
  • Abstract : One leading idea in the qualitative understanding of deterministic dynamical systems is to use collections of periodic orbits to structure the dynamics. This idea traces back to Poincar\'e, and has been supported by Bowen who proved that periodic orbits of topologically mixing Axiom A diffeomorphisms equidistribute with respect to the measure of maximal entropy. We consider an analogue of Bowen's equidistribution theorem of periodic orbits in the context of simple random dynamical systems.
• [03823] Computer verifiable criteria for chaos in piecewise smooth dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Paul Glendinning (University of Manchester)
  • Abstract : Many theoretical results on chaotic behaviour in piecewise smooth maps rely on relatively simple criteria that could in principle be checked by hand. I will describe some of these results and how they can be implemented numerically. This makes it possible to demonstrate the existence of phenomena such as robust chaos and unstable manifold variability in examples. Many of the results presented are from joint work with D.J.W. Simpson (Massey University, New Zealand).

MS [01000] Advances in random dynamical systems and ergodic theory

room : F309

• [01767] Lyapunov exponents for random perturbations of coupled standard maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Blumenthal (Georgia Tech)
    • Jinxin Xue (Tsinghua University)
    • Yun Yang (Virginia Tech)
  • Abstract : In this talk, we show how to give a quantitative estimate for the sum of the first N Lyapunov exponents for random perturbations of a natural class 2N-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but non invariant subset of phase space. Concrete models covered by our setting include systems of coupled standard maps, in both `weak' and `strong' coupling regimes. This is a joint work with Alex Blumenthal and Yun Yang.
• [05620] Shear-induced effects Random Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Dennis Chemnitz (Freie Universität Berlin)
    • Maximilian Engel (Freie Universität Berlin)
  • Abstract : The mechanism of shear-induced chaos was first demonstrated by Wang and Young for periodic orbits perturbed by deterministic periodic kicking. In this talk I will present recent results on shear-induced chaos, as well as shear-induced blow-up, in random dynamical systems generated by stochastic differential equations with additive noise.
• [02045] Horseshoes for a class of non-uniformly expanding random circle maps
  • Format : Online Talk on Zoom
  • Author(s) :
    • Giuseppe Tenaglia (Imperial College London)
  • Abstract : We prove the abundance of horseshoe-like behavior in random circle endomorphisms with a positive Lyapunov exponent under large IID noise conditions. By satisfying a transitivity requirement towards an expanding full branch and effectively controlling the tails of hyperbolic times, our results prove that any two disjoint intervals almost surely exhibit horseshoe-like behavior with full probability.

contributed talk: CT039

room : F310

[02609] Reliable and efficient a posteriori error estimates for time-dependent wave equations

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F310
• Type : Contributed Talk
• Abstract : I will discuss a novel equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. Specifically, I will show that the estimator provides fully-guaranteed upper bounds that are asymptotically constant-free and that it is efficient and polynomial-degree-robust, meaning that the efficiency constant does not deteriorate as the approximation order is increased. To the best of my knowledge, this work is the first to propose an estimator for the wave equation that is provably reliable and efficient in the same norm. I will present numerical examples illustrate the theory and suggest that it is sharp.
• Classification : 35L05, 65M15, 65M20, 65M60
• Format : Online Talk on Zoom
• Author(s) :
  • Théophile Chaumont-Frelet (Inria)

[00079] Multi-dimensional Optimal Systems for Chaplygin Gas Cargo-LeRoux model

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F310
• Type : Contributed Talk
• Abstract : The famous Cargo-LeRoux model for the isentropic Chaplygin gas is studied using classical Lie symmetry method. Optimal systems up to six-dimensions are constructed using the adjoint transformation and the invariants of the admitted Lie algebras. We obtain exact solutions to the Cargo-LeRoux model by using the one-dimensional optimal system and discussed the physical behavior of the solutions graphically. Finally, We discussed the evolutionary behavior of a discontinuity wave.
• Classification : 35L40, 70G65, 76N15
• Format : Talk at Waseda University
• Author(s) :
  • Manoj Kumar Pandey (BITS Pilani K K Birla Goa Campus)
  • Pabitra Kumar Pradhan (BITS Pilani K K Birla Goa Campus)

[00159] Wave interactions in drift- flux equations of two-phase flows

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F310
• Type : Contributed Talk
• Abstract : In this talk, we consider the interactions of arbitrary shocks for a $3\times 3$ system of conservation laws governing drift-flux equations of two-phase flows with isothermal and isentropic equation of states. Here, we use the properties of Riemann solution and interaction of weak shocks for this study. Consequently, we reduce the system of equations by taking the projection of shocks in the phase plane to investigate the interactions of arbitrary shocks.
• Classification : 35L40, 35L45, 35L65, 35L67, Hyperbolic system of conservation laws
• Format : Talk at Waseda University
• Author(s) :
  • Minhajul Minhajul (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India)
  • Rakib Mondal (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India)

[00073] Scattering behavior for one dimensional wave maps into Riemannian manifolds

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F310
• Type : Contributed Talk
• Abstract : In this talk, we explore the scattering behavior for wave maps from Minkowski space $\mathbb{R}^{1+1}$ into general Riemannian manifolds, provided the initial data are small. In particular, we show that the nonlinear scattering operator can be linearized as the corresponding linear scattering operator. The underlying physical intuition of this conclusion is that one-dimensional wave maps behave exactly in the same manner as their scattering fields detected by the far-away observers.
• Classification : 35L05, 35A01, 35B40, 35P25, 35R30
• Format : Online Talk on Zoom
• Author(s) :
  • Mengni Li (Southeast University)

[00275] A fast data-driven method for designing compressible shock dominant flows

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F310
• Type : Contributed Talk
• Abstract : We will present a new class of high-order numerical algorithms for computational fluid dynamics. Called "GP-MOOD," the new finite volume method is based on the Gaussian Processes modeling that generalizes the Gaussian probability distribution. Solutions at shocks and discontinuities are handled by the improved Multidimensional Optimal Order Detection (MOOD) strategy, which controls numerical stability and accuracy in an "a posteriori" shock-capturing formalism. We also introduce a new data-driven "a priori" MOOD method.
• Classification : 35L25, 76N15, 85-08, 65M08
• Format : Online Talk on Zoom
• Author(s) :
  • Dongwook Lee (University of California Santa Cruz)

MS [00063] Recent Advances on Nonlocal Interaction Models

room : F311

• [00157] Pattern formation in particle systems: spherical shells to regular simplices
  • Format : Talk at Waseda University
  • Author(s) :
    • Robert John McCann (University of Toronto, Department of Mathematics)
  • Abstract : Flocking and swarming models address mathematical biological pattern formation. When organisms interact through a difference of power laws attractive over large distances yet repulsive at short distances, we detail a phase transition which separates a region where the minimum energy configuration is uniquely attained by a uniform distribution of organisms over a spherical shell, from a region in which it is uniquely attained by equidistributing the organisms over the vertices of a regular top-dimensional simplex.
• [05071] Some remarks on minimization of nonlocal attracting repulsing energies
  • Format : Online Talk on Zoom
  • Author(s) :
    • Aldo Pratelli (University of Pisa)
    • Ihsan Topaloglu (Virginia Commonwealth University)
    • Davide Carazzato (SNS, Pisa)
    • Nicola Fusco (University of Naples)
  • Abstract : We will discuss some results on the minimization of nonlocal energies of attraction-repulsion type. In particular, we will be interested in existence and regularity of minimizing sets, and of generalised solutions, i.e., functions or measures. Some of the presented results are well-known, some others are recent or very recent developments. Some of the results have been obtained in various collaborations with D. Carazzato, N. Fusco, I. Topaloglu.
• [00145] On a Becker-Döring model for prions and an associated nonlocal problem.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Klemens Fellner (University of Graz)
  • Abstract : Prions are able to self-propagate biological information through the transfer of structural information from a misfolded/infectious protein in a prion state to a protein in a non-prion state. Prions cause diseases like Creuzfeldt-Jakob. Prion-like mechanisms are associated to Alzheimer, Parkinson ans Huntington diseases. We present a fundamental bi-monomeric, nonlinear Becker-Döring type model, which aims to explain experiments in the lab of Human Rezaei showing sustained oscillatory behaviour over multiple hours. We exemplify a mechanism of oscillatory behaviour and show numerical simulations. An interesting non-local problem describes an associated self-similar structure.
• [04453] Shape Optimization for nonlocal anisotropic energies
  • Author(s) :
    • Lucia Scardia (Heriot-Watt University)
  • Abstract : We address the problem of shape optimisation for sets with fixed mass, in the case of attractive-repulsive nonlocal energies. More precisely, we focus on energies whose repulsive part is an anisotropic Newtonian potential, and whose attractive part is radially symmetric, and quadratic. For the fully radially symmetric case, it is known that the existence of minimisers depends on the value of the mass: there is a critical value such that minimisers are balls above it, and do not exist below it. We show that a similar dichotomy occurs also in the anisotropic case. The anisotropy, however, introduces an additional critical value that makes the analysis subtle. This is work in collaboration with Riccardo Cristoferi and Maria Giovanna Mora.

MS [00154] Homogenization of PDEs in domains with oscillating boundaries or interfaces

room : F312

• [00402] Heat conduction in composite media involving imperfect contact conditions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Micol Amar (Sapienza Università di Roma)
    • Daniele Andreucci (Sapienza Università di Roma)
    • Claudia Timofte (University of Bucharest)
  • Abstract : We present a model which exhibit simultaneously jumps in the solution and in the flux, involving also the mean average of the physical fields representing the different phases. The starting model is a composite made by a hosting medium containing a periodic array of inclusions of small size, coated by a thin layer made by two different materials, one encapsulated in the other. The smallness of the thin layer leads us to perform first a two-step concentration procedure. The periodic structure leads to a homogenization limit, in order to achieve a macroscopic description.
• [00399] Homogenization by unfolding of a Bingham fluid in a thin domain with rough boundary
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carmen Perugia (Department of Science and Technology, University of Sannio)
    • Manuel Villanueva-Pesqueira (Universidad Pontificia Comillas)
    • Giuseppe Cardone (University of Naples "Federico II")
  • Abstract : We consider a Bingham flow in a thin domain with rough boundary and with no-slip boundary condition on the whole boundary of the domain. By using an adapted linear unfolding operator we perform a detailed analysis of the asymptotic behavior of the Bingham flow when thickness of the domain and roughness periodicity tends to zero. We obtain the homogenized problem for the velocity and the pressure, which preserves the nonlinear character of the flow.
• [00401] Homogenization of Stokes system with Neumann condition on highly oscillating boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Bidhan Chandra Sardar (Indian Institute of Technology Ropar)
  • Abstract : We consider the steady Stokes system in a $n$-dimensional domain $\Omega_{\varepsilon}$ with a rapidly oscillating $(n - 1)$ dimensional boundary prescribed with Neumann boundary condition and periodicity along the lateral sides is considered. We aim to study the limiting analysis $(as\; \varepsilon\to 0)$ of the steady Stokes problem and identify the limit problem in a fixed domain. Finally, show the weak convergences of velocities are improved to strong convergence by introducing corrector terms.
• [00407] Fluids with a non-slip condition on a non-periodic oscillating boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Casado-Díaz (University of Seville)
    • Manuel Luna-Laynez (University of Seville)
  • Abstract : It is known that a viscous fluid with a non-slip condition on a rough boundary behaves as if an adherence condition is imposed. This is the case for a boundary given by $x_3=\delta_\varepsilon\psi(x_1/\varepsilon,x_2/\varepsilon)$, $\psi$ periodic, and $\delta_\varepsilon/\varepsilon^{3\over 2}$ tending to infinity. The rugosity has not effect if it tends to zero. In the critical case a new zero order term appears in the boundary condition. Here, we extend these results to non-periodic boundaries.

contributed talk: CT066

room : F401

[00629] Stability Analysis of Split Equality and Split Feasibility Problems

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : In this talk, the stability of solutions to parametric split equality and split feasibility problems is addressed for the first time. Characterizations for the Lipschitz-likeness of solution maps are obtained by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich on parametric generalized equations. Examples are presented to illustrate how the obtained results work in practice and to show that extra mild assumptions made cannot be omitted.
• Classification : 49J53, 49K40, 65K10, 90C25, 90C31
• Format : Talk at Waseda University
• Author(s) :
  • Huong Thi Vu (Institute of Mathematics, Vietnam Academy of Science and Technology)
  • Yen Dong Nguyen (Institute of Mathematics, Vietnam Academy of Science and Technology)

[02374] Embarrassingly-parallel optimization algorithms for high-dimensional optimal control

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : Developing efficient algorithms for Hamilton--Jacobi partial differential equations $(\text{HJ PDEs})$ is crucial for solving high-dimensional optimal control problems in real time but notoriously tricky due to the so-called curse of dimensionality. In this talk, we present novel grid-free and embarrassingly-parallel optimization algorithms for solving a broad class of HJ PDEs relevant to high-dimensional state-dependent optimal control problems. We illustrate their performance and efficiency on large-scale multi-agent path planning problems.
• Classification : 49L12, 65K10, 90C30, 49M29, 49M37
• Format : Talk at Waseda University
• Author(s) :
  • Gabriel Provencher Langlois (New York University)
  • Jerome Darbon (Brown University)

[00567] Topology-aware algorithm for constructing cartograms from density-equalising map projections

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : Cartograms are maps in which the areas of enumeration units $\text{(}$e.g. administrative divisions$\text{)}$ are proportional to quantitative data $\text{(}$e.g. population$\text{)}$. Generating cartograms with density-equalising map projections guarantees that geographic neighbours remain neighbours in the cartograms if all boundaries are infinitely dense sequences of points. However, computers represent boundaries with only finitely many points, often causing invalid topologies in the cartogram. This talk shows how line densification and topology-aware simplification solve this problem.
• Classification : 51M30, 53-08, 68-04
• Format : Talk at Waseda University
• Author(s) :
  • Michael T Gastner (Yale-NUS College)
  • Nguyen Phong Le (Yale-NUS College)
  • Nihal Z Miaji (Yale-NUS College)
  • Adi Singhania (Yale-NUS College)

[00238] Numerical Schemes for Generalized Isoperimetric Constraint Fractional Variational Problem

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
• Type : Contributed Talk
• Abstract : This paper discusses three numerical schemes for Generalized Isoperimetric Constraint Fractional Variational Problems (GICFVPs) defined using generalized fractional derivatives. Three Numerical schemes, i.e. linear, quadratic, and quadratic-linear schemes, are used to get numerical solutions of a GICFVP. The convergence rate of the linear and quadratic schemes for $\alpha\in(0,1)$ are $2-\alpha$ and $3-\alpha$. It is observed that the presented schemes perform well, and when the step size $\mathrm{h}$ is decreased, the desired solution is attained.
• Classification : 49R99, 65K10, 65L60, 65L70
• Format : Online Talk on Zoom
• Author(s) :
  • DIVYANSH PANDEY (IIT (BHU), Varanasi)
  • Rajesh Kumar Pandey (IIT (BHU), Varanasi)

MS [00802] Numerical Algorithms for the Eikonal Equation and Its Applications

room : F402

• [03777] Approximate viscosity solutions of hamilton-Jacobi equations: a review
  • Format : Online Talk on Zoom
  • Author(s) :
    • Italo Capuzzo Dolcetta Italo (Sapienza Università di Roma)
  • Abstract : Semi-discretization methods to approximate viscosity solutions of Hamilton-Jacobi equations arising in different applied contexts such as optimal control, shape from shading, homogenization, and mean field games
• [04731] Eikonal equation in 3D shape reconstruction and 3D printing
  • Format : Online Talk on Zoom
  • Author(s) :
    • Silvia Tozza (Dept. of Mathematics, University of Bologna)
  • Abstract : The topic of this talk is related to Hamilton-Jacobi equations and their numerical resolution in the context of Image Processing. More in details, we will deal with the 3D reconstruction of the shape of an object (the resolution of the so-called Shape-from-Shading problem via a differential approach) and some problems related to 3D printing of the reconstructed object. In particular cases, the Hamilton-Jacobi equation describing these problems reduces to the eikonal equation.
• [04972] The redistancing problem using Hopf-Lax formula and its applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Byungjoon Lee (The Catholic University of Korea)
  • Abstract : The redistancing, or reinitialization, problem is an important subject when one considers the signed distance function to the interface. There have been many researches on redistancing a given function to a signed distance function, based on numerical methods to solve the following eikonal equation: $$\frac{\partial\phi}{\partial t}\left(x,t\right)+\lVert\nabla_x\phi(x,t)\rVert_2=0,\ \left(x,t\right)\in \mathbb{R}^n\times\left(0,\infty\right)$$ In this talk, we review the novel redistancing technique based on Hopf-Lax formula equipped with the split Bregman approach and discuss on its applications.
• [04630] Comparison study of image-segmentation techniques by a curvature-driven flow of planes curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Shigetoshi Yazaki (Meiji University)
  • Abstract : In this talk, we deal with image segmentation by a curvature-driven flow of curves in the plane. We focus on images in the plane. Several methods to image segmentation are discussed. For instance, the minimum radius method, L2-gradient flow method, stepwise method, etc. Then, all methods are compared in the qualitative computational study.

MS [00690] Computational methods for interfaces in physics an mechanics

room : F403

• [05615] Advanced discretization schemes for phase-field fracture
  • Format : Talk at Waseda University
  • Author(s) :
    • Blaise Bourdin (McMaster UniversityMcMaster University)
    • Frédéric Marazzato (Louisiana State University)
  • Abstract : Variational phase-field models of fracture have established themselves as a powerful and efficient computational approach in fracture mechanics. They are based on a regularization of Francfort and Marigo variational energy, where the crack geometry and discontinuous displacements are represented by smooth functions The most common implementations are based on finite element discretization via continuous finite elements, and a staggered minimization scheme. In this talk, we present a new discretization scheme where displacements are discretized using discontinuous Lagrange elements and the phase field variable by Crouzeix-Raviart elements. We compare this scheme to the classical continuous Galerkin scheme and highlight how it leads to a better approximation of the fracture energy.
• [01899] Numerical approximation of a viscoelastic Cahn--Hilliard model for tumour growth
  • Format : Talk at Waseda University
  • Author(s) :
    • Dennis Trautwein (University of Regensburg)
    • Harald Garcke (University of Regensburg)
  • Abstract : In this talk, we present a phase-field model for tumour growth, where a diffuse interface is separating a tumour from the surrounding host tissue. In our model, we include biological effects like chemotaxis and transport processes by an internal velocity field. We include viscoelastic effects with a general Oldroyd-B type description with stress relaxation and stress generation by growth. We analyze a numerical approximation of the model with a fully-practical, stable and converging discrete scheme, which preserves the physical properties of the model. Finally, we illustrate properties of solutions with the help of numerical simulations.
• [02809] A second order Cahn Hilliard model for wetting simulation
  • Format : Talk at Waseda University
  • Author(s) :
    • elie bretin (ICJ & INSA Lyon )
  • Abstract : We focus in this talk to the approximation of surface diffusion flow using a Cahn–Hilliard-type model. We introduce a new second order variational phase field model that associates the classical Cahn-Hilliard energy with two degenerate mobilities. We also propose some simple and efficient numerical schemes to approximate the solutions and provide 3D numerical simulations of the wetting of a thin tube on various solid supports. This work was done in collaboration with R. Denis, S. Masnou, G. Terii and A. Sengers
• [04707] Finite element minimization of line and surface energies arising in liquid crystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Dominik Stantejsky (McMaster University)
  • Abstract : Originating in the study of defect structures in nematic liquid crystals, we consider the numerical minimization of an energy posed for two-dimensional surfaces $T$ involving the surface area of $T$ outside an obstacle $E$, as well as the length of the boundary $\partial T$ and a surface integral over the obstacle surface, generalizing both the obstacle- and Plateau problem. We propose a finite element representation of the energy and minimize using an ADMM algorithm.

MS [00384] Origami Engineering (1/2)

room : F411

• [01571] Laboratory-scale Workshop for Enhancing Designability of Origami Cores
  • Format : Talk at Waseda University
  • Author(s) :
    • Sachiko Ishida (Meiji University)
  • Abstract : The objective of this study is to develop a laboratory-scale fabrication method to prototype origami-like foldable cores with our own designs. As the first attempt, we formed honeycomb cores in such a way that thermoplastic sheets were pressed between heated molds with corrugated configuration and glued together. This method worked well to enhance designability of honeycomb cores, because the press forming was applicable even for complex designs and could improve shape accuracy.
• [01618] Strip folding as Boolean matrix algebra and its Categorical Meanings
  • Format : Talk at Waseda University
  • Author(s) :
    • Yiyang Jia (Seikei University)
    • Jun Mitani (University of Tsukuba)
  • Abstract : Strip folding, known as map folding in the one-dimensional case, derives from a classical flat-foldability decision problem in the field of computational origami. In this manuscript, different from the existing computational and algorithmic methodology, we investigate strip folding using abstract algebraic language and then characterize it from a categorical viewpoint. We first present a boolean matrix description of strip folding, based on which we then build the category of strip folding. This category gives rise to a natural meet semi-lattice structure. Furthermore, in this category, every product exists. We use the right adjoint functor of the diagonal functor to define these products. Furthermore, the definition of products can be used to build a Grothendieck topology in the space of flatly folded states. Our result shows that the analysis of strip folding can be associated with contemporary mathematical methodologies such as category theory and algebraic geometry.
• [02328] Application of the proposed method to a transport origami box
  • Format : Online Talk on Zoom
  • Author(s) :
    • Toshie Sasaki (Meiji University)
    • Yang Yang (Meiji University)
    • Ichiro Hagiwara (Meiji University)
  • Abstract : Fruits and vegetables are damaged during transportation because there is a mortal frequency band for each transport. We propose a new method named “Energy Density Topology Changing Method” based on the fact that the eigen frequency is determined by equivalent stiffness and equivalent mass. We demonstrate the effectiveness of this method by showing that it can be successfully applied to a transport origami box which cannot be applied by conventional topology optimization method.

contributed talk: CT075

room : F412

[02436] Subordinated Stochastic Processes and Applications

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F412
• Type : Contributed Talk
• Abstract : A Subordinated stochastic process is obtained by time changing a parent process X_t with a positive non-deceasing stochastic process T_t. The process T_t is called the directing process or the random clock. Subordinated processes demonstrate interesting probabilistic properties and have applications in finance, economics, statistical physics, anomalous diffusion and fractional calculus. Also scaling limits of continuous time random walk depending on the conditions on mean waiting times and second moments conditions on jumps converges weakly to different subordinated stochastic process. The aim of this talk is to discuss the concept of subordinated processes and their connections to different fields.
• Classification : 60G10, 60G18, 60G20, 62M10, 60G51
• Format : Talk at Waseda University
• Author(s) :
  • Arun Kumar (Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India 140001)

[00572] Model uncertainty for statistical arbitrage

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F412
• Type : Contributed Talk
• Abstract : We consider an optimal stopping problem that addresses \textit{model uncertainty}, which affects the model assumptions, e.g., the parameters embedded in the probability distribution. The result presented in this talk shows the explicit form of the boundary indicating the optimal stopping time, assuming the portfolio value as an Ornstein-Uhlenbeck process. Applying our method might make statistical arbitrage more robust because the trading code for statistical arbitrage often depends on incorrect estimation.
• Classification : 60G40, 60G10, 91G80
• Format : Talk at Waseda University
• Author(s) :
  • Daisuke Yoshikawa (Kansai University)

[00583] The empirical measure of invariant fields on sphere-cross-time

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F412
• Type : Contributed Talk
• Abstract : In this talk we investigate geometric properties of random fields on the two-dimensional sphere evolving over time, that are widely used in several scientific areas to model and analyze data (e.g. in Climate Science related to Earth surface temperature). In particular we study the behavior for large time of their excursion area at any threshold, establishing both asymptotic variances and limit theorems. We will show that phase transitions can occur for specific levels and memory.
• Classification : 60G60, 33C55, 60D05, 60F05, 62M15
• Format : Talk at Waseda University
• Author(s) :
  • Domenico Marinucci (University of Roma "Tor Vergata")
  • Maurizia Rossi (University of Milano-Bicocca)
  • Anna Vidotto (University of Napoli "Federico II")

[01271] Localized and degenerate controls for the incompressible Navier--Stokes system

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F412
• Type : Contributed Talk
• Abstract : This talk concerns the global approximate controllability of incompressible Newtonian fluids driven by a physically localized and degenerate interior control. By introducing transported Fourier modes as building blocks, we act on the planar Navier--Stokes system via four scalar controls that depend only on time and appear as coefficients in an effectively constructed driving force supported in a given subdomain. The four unknown parameters can be computed by merely solving a linear transport controllability problem.
• Classification : 35Q30, 35Q49, 76B75, 93B05, 93B18
• Format : Talk at Waseda University
• Author(s) :
  • Manuel Rissel (New York University Shanghai)
  • Vahagn Nersesyan (New York University Shanghai)

[00683] Linearized Saint-Venant Equation with Lateral Inflow in a Finite Channel

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @F412
• Type : Contributed Talk
• Abstract : We present a solution for linearized Saint-Venant equations with uniformly distributed lateral inflow for a finite rectangular channel. The discharge is presented as the convolution of the distributed lateral inflow and lateral channel response function. We study the behavior of lateral channel response function for different parameters. To find discharge at any location of a channel for a given channel width, the choice of reference discharge and slope of the channel play a significant role.
• Classification : 35Q35, 44A10
• Author(s) :
  • Swaroop Nandan Bora (Indian Institute of Technology Guwahati)
  • Shiva Kandpal (Indian Institute of Technology Guwahati)

MS [01494] Queues and Related Stochastic Models

room : E501

• [03351] The rational outcome of queueing games: A fixed-point iteration based approach
  • Format : Talk at Waseda University
  • Author(s) :
    • Hung Q Nguyen (Advanced Artificial Intelligence Innovation Center, Hitachi, Ltd. Research & Development Group)
    • Tuan Phung-Duc (University of Tsukuba)
  • Abstract : In this study, we consider a class of queueing games characterized by the following feature: expected waiting times of enqueued agents are affected by joining strategies of later comers. We survey several queueing models and generalize an iterative algorithm that may universally apply in a class of queueing game problems to computationally solve for the rational outcome of the game.
• [03189] Workload analysis of fluid polling models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stella Kapodistria (Eindhoven University of Technology)
  • Abstract : In this presentation, we analyze a two-queue random time-limited Markov-modulated polling model. In the first part of the talk, we investigate the fluid version: fluid arrives at the two queues as two independent flows with deterministic rate. There is a single server that serves both queues at constant speeds. The server spends an exponentially distributed amount of time in each queue. After the completion of such a visit time to one queue, the server instantly switches to the other queue, i.e., there is no switch-over time. For this model, we derive a functional equation for the LST of the two-dimensional workload distribution that leads to a Riemann–Hilbert boundary value problem (BVP). After taking a heavy-traffic limit, and restricting ourselves to the symmetric case, the BVP simplifies and can be solved explicitly. In the second part of the talk, allowing for more general (Lévy) input processes and server switching policies, we investigate the transient process limit of the joint workload in heavy traffic. Again solving a BVP, we determine the stationary distribution of the limiting process. We show that, in the symmetric case, this distribution coincides with our earlier solution of the BVP, implying that in this case the two limits (stationarity and heavy traffic) commute. This is joint work with M. Saxena, O.J. Boxma and O. Kella.

MS [01058] Recent advances in stochastic nonlinear dynamics: modeling, data analysis

room : E502

• [02193] Response prediction of dynamical systems with the GCM-DL method
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaole Yue (Northwestern Polytechnical University)
    • Yong Xu (Northwestern polytechnical university)
    • Xiaocong Liu (Northwestern Polytechnical University)
    • Yue Zhao (Northwestern Polytechnical University)
  • Abstract : Generalized cell mapping method based on deep learning is proposed which can predict responses of dynamical systems from experimental data with part of information about physical model. This method trains the neural network model from a small amount of experimental data and obtains the potential dynamic model. The global characteristics of system are analyzed by GCM method. By introducing deconvolution layer and image super-resolution, the probability density function of stochastic dynamic system response is estimated.
• [02190] Complex dynamics of a conceptual airfoil structure with consideration of extreme flight conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Qi Liu (Tokyo Institute of Technology)
  • Abstract : An aircraft in practice serves under extreme flight conditions, that will have a substantial impact on its flight safety. Understanding dynamics of airfoil structure of an aircraft subjected to severe load conditions is thus extremely valuable and necessary. In this study, we will explore the complicated dynamical behaviors of a conceptual airfoil excited by an external harmonic force and an extreme random load. Importantly, such an extreme random load is portrayed by a non-Gaussian Lévy noise with a heavy-tailed feature. We theoretically deduce amplitude-frequency equations associated with the deterministic airfoil system. We observe excellent agreements between the analytical solutions and the numerical ones, as well as bistable behaviors. Besides, the effects of the extreme random load on the airfoil system are thoroughly investigated. Interestingly, within the bistable regime, the extreme random load can lead to stochastic transition and stochastic resonance. Due to its heavy-tailed nature, the Lévy noise would increase the possibility of a highly unexpected stochastic transition behavior between desirable low-amplitude and catastrophic high-amplitude oscillations compared with the Gaussian scenario. Such vibration patterns might damage or destroy the airfoil structure, which will put an aircraft in great danger. All the findings would be helpful in ensuring the flight safety and enhancing the strength and reliability of airfoil structure operating at extreme flight conditions.
• [02205] Pattern Dynamics of Higher Order Reaction-Diffusion network
  • Format : Talk at Waseda University
  • Author(s) :
    • Jianwei Shen (North China University of Water Resources and Electric Power)
  • Abstract : In this paper, we will investigate the pattern dynamics of higher order reaction-diffusion network by group interactions and prove the interplay between different orders of interaction can affact the emergence of turing patterns. Our results try to the mechanism of many body interaction on complex network.
• [02243] Three occurrence mechanisms of extreme events in stochastic dynamical systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yongge Li (Northwestern Polytechnical University)
    • Dan Zhao (Northwestern Polytechnical University)
    • Yong Xu (Northwestern polytechnical university)
  • Abstract : In this work, three mechanisms for the occurrence of extreme events in stochastic dynamical systems are given. Firstly, for systems with a bifurcation structure, if the difference of the branches at the bifurcation point is large, then a time-varying amplitude of the external periodic excitation is able to induce an extreme event. This is verified in the rolling motion of a ship system. Secondly, for systems with rare attractors, a random pulse excitation, such as Poisson white noise, is able to drive the system to escape from the basin of general attractor to that of rare attractor. However, the basin of rare attractor is so small that the system will go back to the general state immediately. Such a kind of transition is also extreme event. Finally, an extreme excitation can also generate extreme event, such as the Lévy noise. In such cases, it does not require much about the systems, but the extreme excitations work. These results provide theoretical guidance for further prediction and avoidance of extreme events.

MS [01858] Interplay among Manifold Learning, Stochastic Calculus, and Volatility Estimation

room : E503

• [02841] Convergence of Hessian estimator from random samples on a manifold
  • Format : Talk at Waseda University
  • Author(s) :
    • Chih-Wei Chen (National Sun Yat-sen University)
    • Hau-Tieng Wu (Duke University)
  • Abstract : We provide a systematic convergence analysis of the Hessian operator estimator from random samples supported on a low dimensional manifold. We show that the impact of the nonuniform sampling and the curvature on the widely applied Hessian operator estimator is asymptotically negligible.
• [02848] Limit Theorems for the Positive Semidefinite Modification of Malliavin-Mancino Estimator for the Spot Volatility Process
  • Format : Talk at Waseda University
  • Author(s) :
    • Reika Kambara (Nomura Asset Management Co., Ltd.)
  • Abstract : In this talk, the consistency, and the asymptotic normality of the class of Fourier-type estimators introduced by Akahori et al. will be discussed. The class, parameterized by a sequence of probability measures, is a modification of the Fourier series method introduced by Malliavin and Mancino, modified so that the estimator is positive semidefinite.
• [04489] Convergence of Laplacian and its rate for submanifolds that are not necessarily smooth
  • Format : Talk at Waseda University
  • Author(s) :
    • Masayuki Aino (Proxima Technology)
  • Abstract : The continuous limit of Laplacian Eigenmaps gives the eigenfunctions of the Laplacian on submanifolds in Euclidean space . Such studies have been based on the assumption that a quantity called Reach is bounded from below. Submanifolds with non-differentiable points cannnot be approximated under such an assumption. In this talk, I discuss the convergence of Laplacian Eigenmaps and its rates when the Reach assumption is replaced by a weaker assumption such that non-differentiable points can appear.

MS [01221] FreeFEM software package for finite element modeling of PDEs

room : E504

• [02183] Phase field crack growth simulation using IPOPT package
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Takaishi (Musashino University)
  • Abstract : As the energy gradient flow equation of the Bourdin model, we introduced the time evolution model of irreversible crack growth by the phase field method. Its weak solution can be written in terms of variational inequalities, since it includes the irreversible crack state. Simulation results for this model with the IPOPT package in FreeFEM shows the energy dissipation process of crack growth precisely.
• [02252] Direct factorization of indefinite matrix for constrained problem in finite element modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Atsushi Suzuki (RIKEN Center for Computational Science)
  • Abstract : Finite element computation of some physical problem with constraint uses a variational problem with Lagrange multipliers as dual variables. Physical constraints are supposed as incompressibility of the fluid, boundary conditions on internal interfaces, and so on. A linear system obtained by a discretization becomes indefinite and then the multifrontal method for parallelization of direct methods may suffer pseudo singularity of subproblems. Careful pivoting with keeping pair of primal and dual unknowns makes the factorization stable.
• [02281] An easy-to-use framework for the density-based topology optimization of multiphysics systems written in FreeFEM-PETSc-ParMmg
  • Format : Talk at Waseda University
  • Author(s) :
    • Hao Li (Kyoto University)
    • Minghao Yu (China Academy of Engineering Physics)
    • Pierre Jolivet (LIP6, Sorbonne Universite)
    • Joe Alexandersen (University of Southern Denmark)
    • Atsushi Suzuki (Osaka University)
    • Shinji Nishiwaki (Kyoto University)
  • Abstract : Large-scale 3D topology optimization has been a big trend in the previous decade. However, it features a high computational cost, which may not always be available to general users. We constructed an easy-to-use and fully distributed framework written in FreeFEM-PETSc-ParMmg. We present various 2D and 3D benchmarks including a structural problem, a transient thermal cloaking design, and a thermal-fluidic problem.
• [02204] Recent advances with FreeFEM in parallel and its interface to PETSc
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre Jolivet (CNRS)
  • Abstract : In this talk, I will present some new features of FreeFEM and its interface to PETSc and SLEPc. Coupled together, these libraries offer a flexible infrastructure to deal with coupled and/or high-dimensional systems, using MPI for distributed-memory parallelism. I will showcase some examples from fluid dynamics, radiative transfer, and boundary integral equations.

contributed talk: CT099

room : E505

[00903] Port-Hamiltonian form and stochastic Galerkin method for ordinary differential equations

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
• Type : Contributed Talk
• Abstract : We consider systems of ordinary differential equations (ODEs) including random variables. Based on a polynomial chaos expansion, a stochastic Galerkin approach yields a larger deterministic system of ODEs. We investigate port-Hamiltonian formulations of the original systems and the Galerkin systems. A structure-preserving stochastic Galerkin projection is constructed, which produces a larger port-Hamiltonian system. Furthermore, the associated Hamiltonian functions are compared. We present results of numerical computations using a test example.
• Classification : 65L05, 34F05, uncertainty quantification
• Format : Talk at Waseda University
• Author(s) :
  • Roland Pulch (University of Greifswald)

[02106] Numerical solver of ordinary differential equations based on IMT-DE variable transformation

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
• Type : Contributed Talk
• Abstract : We propose a numerical solver of initial value problems of ordinary differential equations based on the IMT-DE variable transformation, a variant of the transformation of the IMT quadrature formula. We solve the Volterra integral equation equivalent to the initial value problem by the Picard iteration, which is numerically executed by the numerical indefinite integration based on the IMT-DE transformation. This study is an example of the applications of the IMT type transformations to various computations.
• Classification : 65L05, 65R20, 65D30
• Format : Talk at Waseda University
• Author(s) :
  • Hidenori Ogata (The University of Electro-Communications)

[00889] Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
• Type : Contributed Talk
• Abstract : Relaxation Runge-Kutta methods, which are a slight modification of the RK methods, have been introduced to preserve invariants of initial-value problems. So far, this approach has been applied to preserve only one nonlinear functional in the numerical solution of a problem. In this talk, I will present the generalization of the relaxation approach for RK methods to preserve multiple nonlinear invariants of a dynamical system. The significance of preserving multiple invariants and its impact on long-term error growth will be illustrated via several numerical examples.
• Classification : 65L04, 65L20, 65M06, 65M12, 65M22
• Format : Talk at Waseda University
• Author(s) :
  • Abhijit Biswas (King Abdullah University of Science and Technology (KAUST))
  • David Isaac Ketcheson (King Abdullah University of Science and Technology (KAUST))

[01007] Stability & Accuracy of Free-Parameter Multistep Methods for 1st & 2nd-order IVPs

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
• Type : Contributed Talk
• Abstract : Dahlquist's First Stability Barrier limits the order of stable $k$-step multistep methods, allowing us to add free parameters. Within the parameter domain where a $k$-step family of methods is stable, we explore the parameters' effect on error and stability domains. For first-order IVP's, we investigate explicit methods for $k=2,3$ and implicit methods for $k=3,4$, generalizing Adams & BDF methods. For second-order IVP's, we analyze explicit and implicit methods for $k=3,4$, generalizing Störmer & Cowell methods.
• Classification : 65L06, 65L07, 65L20
• Author(s) :
  • Michelle Ghrist (Gonzaga University)
  • Ben Lombardi (Gonzaga University)
  • Alana Marie Dillinger (Twin Cities in Motion)

[02138] Convergence Analysis of Leapfrog for Geodesics

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
• Type : Contributed Talk
• Abstract : The leapfrog algorithm was proposed in Noakes’98 to find geodesics joining two given points $x_0$ and $x_1$ on a path-connected complete Riemannian manifold. The basic idea is to choose some junctions between $x_0$ and $x_1$ that can be joined by geodesics locally and then adjust these junctions. In this talk, we find the relationship between the leapfrog's convergence rate $\tau_{i,n}$ of $i$-th junction with the maximal root $\lambda_n$ of a polynomial.
• Classification : 65L10, 65D15, 49J45, 53C22
• Format : Online Talk on Zoom
• Author(s) :
  • Erchuan Zhang (University of Western Australia)
  • Lyle Noakes (University of Western Australia)

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

room : E507

• [04861] Next-Generation Reservoir Computing, and On Explaining the Surprising Success of a Random Neural Network for Forecasting Chaos
  • Format : Online Talk on Zoom
  • Author(s) :
    • Erik Matthew Bollt (Clarkson University)
  • Abstract : Machine learning is widely popular and successful, including for data-driven science, especially for forecasting complex dynamical systems. Reservoir computers (RC) have emerged as random neural networks, for simplicity and computational advantage, where only read-out weights are trained. That it is cheap is clear, but that it works at all is perhaps a surprise, which we explain here. Furthermore our discussion leads to a new, equivalent even simpler variant we call, next generation reservoir computing, NG-RC.
• [05356] Minimax optimal inference of inhomogeneous diffusions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Grant Rotskoff (Stanford University)
  • Abstract : Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a $d$-dimensional stochastic differential equation of the form $$ d\boldsymbol{x}_t=\boldsymbol{b}(\boldsymbol{x}_t)dt+\Sigma(\boldsymbol{x}_t)d\boldsymbol{w}_t, $$ we show that no diffusion estimator using $N$ discretely sampled data points converges faster than $N^{-\frac{2s+2}{2s+2+d}}$ when the drift $\boldsymbol{b}$ and diffusion tensor $D = \Sigma\Sigma^{T}$ are $s$ and $s+1$-Hölder continuous, respectively. We further propose neural network estimators for both $D$ and $\boldsymbol{b}$, establish convergence guarantees, and show that the estimators achieve a nearly optimal rate for correlated data.
• [05361] Nonlinear Time Series Analysis and Data Driven Forecasting: Regional Weather Prediction & Earth's Geodynamo
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luke Fairbanks (UCSD)
    • Ashley Thorshov (UCSD)
  • Abstract : Amongst the zoo of complex systems analysis frameworks and methods exist some which leverage tools from mathematics and physics with machine learning to attempt a more interpretable and possibly better results with respect to time series prediction of said systems. Our work in the domains of weather prediction and the geodynamo is a model for the interdisciplinary union between experimentalists, theorists, and computational researchers such as ourselves in the pursuit of complex system algorithmic synchronization.
• [04474] Random Features for Epidemic Prediction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Esha Saha (University of Waterloo)
    • Lam Ho (Dalhousie University )
    • Giang Tran (University of Waterloo)
  • Abstract : Predicting the evolution of diseases is challenging. Compartmental models stratify the population into compartments and model the dynamics using dynamical systems. These predefined systems may not capture the true dynamics of the epidemic due to the complexity variable interactions. We propose Sparsity and Delay Embedding based Forecasting (SPADE4) for predicting epidemics for predicting the future trajectory of a variable without the knowledge of the underlying system using random features and Takens' delay embedding theorem.

MS [01199] Recent advances of scientific computing and applications

room : E508

• [04888] Plant virus propagation models with delay and stochasticity
  • Author(s) :
    • Benito Chen-Charpentier (University of Texas at ArlingtonUniversity of Texas at Arlington)
  • Abstract : Plant diseases caused by a virus are mostly transmitted by a vector that bites an infected plant and bites a susceptible one. There is a delay between the time a plant gets bitten by an infected vector and the time it is infected. In this paper we consider two simple models of plant virus propagation and study different ways in which delays can be incorporated including the addition of an exposed class for the plants. Simulations are done and comparisons with the results for the models without delays are presented.
• [05157] Numerical studies to the Chaplygin gas equation
  • Author(s) :
    • Ying Wang (University of Oklahoma)
  • Abstract : In this talk, we will discuss the numerical solutions to the Riemann problem for Chaplygin gas equation, which is the Euler equations equipped with the state equation p = $-1/\rho$. The spatial discretization is performed using WENO reconstruction and time integration is achieved using TVD RK4. The numerical results confirm high order of accuracy. This is a joint work with Ling Jin.
• [05160] Fully coupled averaging with singularities.
  • Author(s) :
    • Alexander Grigo (University of Oklahoma)
  • Abstract : In this talk I will present an averaging theorem for a fully coupled system with singularities. Specifically, I will discuss a particular fast-slow system that arises in modeling energy transport in an open system of interacting hard-spheres. The technical part of this work addresses how to deal with singularities of the dynamics and the fact that the dynamics is fully coupled.

MS [00584] Advanced Methods for Structured Eigenvalue Problems and Nonlinear Equations

room : E603

• [01293] Newton-Noda iteration for nonlinear eigenvalue problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ching-Sung Liu (National University of Kaohsiung)
  • Abstract : In this talk, we will introduce nonlinear eigenvalue problems, including tensor eigenvalue problems and nonlinear Schrödinger equations. We present a Newton-Noda iteration (NNI) to find positive eigenvectors of nonlinear problems. A great advantage of this method is that it converges quadratically and maintains positivity, i.e., the vector approximating the Perron vector (or ground state vector) is strictly positive in each iteration.
• [01584] Phase Retrieval of Quaternion Signal via Wirtinger Flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Junren Chen (University of Hong Kong)
    • Michael Kwok-Po Ng (University of Hong Kong)
  • Abstract : Quaternion phase retrieval (QPR) is concerned with the recovery of quaternion signal from magnitude of quaternion linear measurements. We develop the scalable algorithm quaternion Wirtinger flow (QWF) for solving QPR, and establish its linear convergence guarantee. We develop a variant of QWF that can effectively utilize a pure quaternion priori by incorporating a quaternion phase factor estimate into QWF iterations.
• [01454] Numerical Methods for the Complete Solution of Multiparameter Eigenvalue Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bo Dong (Dalian University of Technology)
  • Abstract : The linear/nonlinear multiparameter eigenvalue problems appear frequently in the study of multiparameter Sturm-Liouville problems and delay differential equations with some delays. In this talk, I will introduce two classes of numerical methods for solving the multiparameter eigenvalue problems: the method of transforming to silmultaneous eigenvalue problems and the homotopy method. The former is suitable for small-scale and medium-scale problems while the latter tends to be more effective in terms of speed, accuracy and memory storage as the problem size grows. Numerical experiments and applications are presented to show the efficiency of these two classes of methods.
• [02763] Perturbation theory for the symmetry eigenvalue problem and singular value decomposition followed by deflation techniques
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiang Wang (Nanchang University)
    • Hongjia Chen (Nanchang University)
  • Abstract : The calculation of the dominant eigenvalues of a symmetric matrix $A$ together with its eigenvectors, followed by the calculation of the deflation of $A_1 = A - \rho U_kU_k^T$ corresponds to one step of the Wielandt deflation technique, where $\rho$ is a shift and $U_k$ are eigenvectors of $A$. In this paper, we investigate how the eigenspace of $A_1$ changes when $A_1$ is perturbed to $\tilde{A}_1 = A - \rho \tilde{U}_k\tilde{U}_k^T$, $\tilde{U}_k$ are approximate eigenvectors of $U_k$. We establish the bounds for the angle of eigenspaces of $A_1$ and $\tilde{A}_1$ based on the Davis-Kahan theorem. Moreover, in the practical implementation for singular value decomposition, once one or several singular triplets converge to a preset accuracy, they should be deflated by $B_1 = B - \gamma W_kV_k^H$ with $\gamma$ is a shift and $W_k$ and $V_k$ are singular vectors so that they will not be re-computed. We investigate how the singular subspaces of $B_1 = B - \gamma WV^H$ changes when $B_1$ is perturbed to $\tilde{B}_1 = B - \gamma \widetilde{W}\widetilde{V}^H$, $\widetilde{W}$ and $\widetilde{V}^H$ are approximate singular vectors. We also establish the bounds for the angle of singular subspaces of $B_1$ and $\tilde{B}_1$ based on the Wedin theorem. We show, by numerical experiment, the angles of eigenspaces and the angles of singular subspaces are well--predicted by these bounds with an appropriable shift.

MS [02448] Verified Numerical Computations and Applications

room : E604

• [04361] Verified computation for shape derivative of the Laplacian eigenvalues
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryoki Endo (Niigata University)
    • Xuefeng Liu (Niigata University)
  • Abstract : The shape derivative of Laplacian eigenvalues with respect to domain deformations was theoretically investigated by Hadamard in the early 20th century. However, the rigorous computation of these derivatives is not an easy task, since there exists the singularity for repeated eigenvalues. In this study, we propose a verified computation method for the shape derivative of Laplacian eigenvalues using guaranteed computation of both eigenvalues and eigenfunctions.
• [04568] Constructive error estimates for a full-discretized periodic solution of heat equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuma Kimura (Saga University)
    • Teruya Minamoto (Saga University)
    • Mitsuhiro T. Nakao (Waseda University)
  • Abstract : In this talk, we consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation with time-periodic condition; $\frac{\partial u}{\partial t}-\nu\Delta u=f(x,t)$ in $\Omega \times J$, $u(x,t)=0$ on $\partial\Omega \times J$, $u(x,0)=u(x,T)$ on $\Omega$. Our numerical scheme is based on the finite element semi-discretization in space direction combined with the Fourier expansion in time. Several numerical examples will be shown to illustrate the theoretical results.
• [03685] A Numerical verification method for a self-similar solution to the linear elliptic differential equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Kouta Sekine (Chiba Institute of Technology)
    • Taiyou Fuse (Chiba Institute of Technology)
  • Abstract : In this talk, we propose a numerical verification method for self-similar solutions of linear partial differential equations on \({\mathbb R}\) using the Galerkin approximation with extended Hermite polynomials. In particular, we derive a Gaussian quadrature method for extended Hermite polynomials to errors in numerical quadrature over infinite interval. Also, we also introduce the projection error constant for obtaining the discretisation error of the Hermite-Galerkin approximation.
• [04321] A computer-assisted proof for a nonlinear differential equation involved with self-similar blowup in wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshitaka Watanabe (Kyushu University)
    • Kaori Nagatou (Karlsruhe Institute of Technology)
    • Michael Plum (Karlsruhe Institute of Technology)
    • Birgit Schörkhuber (University of Innsbruck)
    • Mitsuhiro T. Nakao (Waseda University)
  • Abstract : An existence proof with its specific shape of a non-trivial solution of a nonlinear ordinary differential equation involved with self-similar blowup in three-dimensional wave equations is presented. The proof is computer-assisted based on a fixed-point and Newton-type formulation, and the result takes into account the effects of rounding errors of floating-point arithmetic in computer.

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

room : E605

• [05448] The Unrolled Dynamics Modeling for Computed Tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Haimiao Zhang (Beijing Information Science and Technology University)
  • Abstract : Deep learning revolutionized the research paradigm of medical imaging in the last decades. In this talk, I will show our works on combining classical mathematical models in computed tomography (CT) imaging with the modern deep neural network. These new computational imaging techniques give us a broader way of dealing with the medical imaging problem. Furthermore, numerical results demonstrated that the proposed deep models could be generalized to different datasets, scanning geometries, and noise levels.
• [04836] Dictionary learning for an inverse problem in quantitative MRI
  • Format : Talk at Waseda University
  • Author(s) :
    • Guozhi Dong (Central South University)
    • Michael Hintermueller (Weierstrass Institute Berlin)
    • Clemens Sirotenko (WIAS Berlin)
  • Abstract : The field of quantitative Magnetic Resonance Imaging aims at extracting physical tissue parameters from a sequence of highly under sampled MR images. Mathematically, this can be achieved by estimating a set of unknown parameters in an ODE model. We employ dictionary learning based approaches to regularize the reconstruction process and investigate iterative schemes to solve the resulting non-convex and non-smooth problems for stationarity. Moreover numerical results and open questions are presented.
• [05295] Deformable volumetric Image registration based on unsupervised learning
  • Author(s) :
    • Ahsan Raza Siyal (University of Innsbruck)
  • Abstract : Deformable image registration has found its way into clinical routine, from image-guided adaptive radiotherapy to brain surgery. The traditional methods optimize an objective function independently for each pair of images, which is highly expensive in terms of time and computation. On the other hand, the deformable registration task can be defined as a parametric function and optimize its parameters on available image pairs and the function can be modeled as neural networks which learn the off-set displacement field through unsupervised loss function which contains data similarity term and a regularization term.

MS [01661] Recent Development on the Methods and Applications of Complex PDE systems

room : E606

• [04493] A Level-Set Framework for Implicit Solvation
  • Format : Talk at Waseda University
  • Author(s) :
    • Li-Tien Cheng (UC San Diego)
  • Abstract : Implicit solvation involves the study of the effects solute atoms have on a surrounding solvent, which can be particularly important in, for example, the process of protein docking. An implicit treatment of the solvent gives rise to an interface between solute and solvent. We introduce a level-set framework applied to a variational free-energy setup for constructing such an interface, and consider efficient and accurate solvers in the presence of curvature, electrostatic, and mechanical effects.
• [04909] Adaptive ANOVA and reduced basis methods to anisotropic stochastic PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Heyrim Cho (University of California Riverside)
    • Bedřich Sousedík (University of Maryland, Baltimore County)
    • Howard Elman (University of Maryland, College Park)
  • Abstract : The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. We study the stochastic collocation methods that can be combined with reduced basis methods to solve high-dimensional parameterized stochastic PDEs. We also propose an adaptive algorithm using a probabilistic collocation method (PCM) and ANOVA decomposition. This procedure involves two stages. First, the method employs an ANOVA decomposition to identify the effective dimensions, i.e., subspaces of the parameter space in which the contributions to the solution are larger, and sort the reduced basis solution in a descending order of error. Then, the adaptive search refines the parametric space by increasing the order of polynomials until the algorithm is terminated by a saturation constraint. We demonstrate the effectiveness of the proposed algorithm for solving a stationary stochastic convection-diffusion equation, a benchmark problem chosen because solutions contain steep boundary layers and anisotropic features. We also solve the Stokes-Brinkman equations that model fluid flow in highly heterogeneous porous media.
• [04915] Theoretical Principles of Enhancer-Promoter Communication in Gene Expression
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiajun Zhang (Sun Yat-sen University)
  • Abstract : Recent experimental evidence strongly supports that long-range enhancer-promoter interactions have important influences on gene-expression dynamics, but it is unclear how the interaction information is translated into gene expression over time. To address this challenge, we develop a general theoretical framework that integrates chromatin dynamics, enhancer-promoter communication, and gene-state switching to study gene expression. Our model and results provide quantitative insight into both spatiotemporal gene-expression determinants and cellular fates during development.

MS [00340] New trends in phase fields: theory & applications

room : E701

• [03070] NONLOCAL CAHN-HILLIARD TYPE MODEL FOR IMAGE INPAINTING
  • Author(s) :
    • Majdi AZAIEZ (Bordeaux INP & I2M UMR 5295)
    • Dandan JIANG (Xiamen University)
    • Chuanju Xu (Xiamen University )
    • Alain Miranville (Poitier University)
  • Abstract : In this talk, we propose a Cahn-Hilliard type nonlocal model for image inpainting which is equipped with a nonlocal diffusion operator for image inpainting. For its approximation we use the modified convex splitting method for the temporal discretization with the non-local diffusion term treated implicitly, and the fidelity term treated explicitly. Spatial discretization is performed by the Fourier collocation method. We will provide several numerical experiments to assess the efficiency of our method.
• [03100] A Variety of Gradient Flows: Modeling and Numerical Methods
  • Author(s) :
    • Chuanju Xu (Xiamen University)
  • Abstract : In this talk I will discuss a variety of gradient flow models for multi-phase problems, derived from an energy variational formulation. The models includes fractional differential equations, equations describing the interfacial dynamics of immiscible and incompressible two-phase fluids, dendritic crystal growth model, thermal phase change problems etc. The talk starts with a review of the models and numerical methods for these models. Then a new class of time-stepping schemes will be discussed.

contributed talk: CT102

room : E702

[01142] Thermodynamically Consistent Finite Volume Schemes for Electrolyte Simulations

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : In order to account for finite ion sizes and solvation effects, the classical Nernst-Planck-Poisson system describing ion transport in electrolytes needs to be enhanced by cross-diffusion - like terms. For this situation, we present a space discretization scheme which adapts the classical Scharfetter-Gummel exponential fitting upwind flux for the Voronoi box finite volume method. Numerical examples use the Julia package VoronoiFVM.jl which takes advantage of automatic differentiation to handle the strong nonlinearities of the system.
• Classification : 65M08, 65M12, 78A57, 65N08, 35Q81
• Format : Talk at Waseda University
• Author(s) :
  • Jürgen Fuhrmann (Weierstrass Institute for Applied Analysis and Stochastics)
  • Benoit Gaudeul (Univ. Paris Saclay)

[01004] An Error Estimate for an Implicit-Upwind Finite Volume Scheme for Boussinesq Model

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : This study contains an error estimate for a Finite Volume Method-based Implicit-Upwind scheme for the d-dimensional(d=2 or 3) Boussinesq Model, which describes several buoyancy-driven Hydrodynamic phenomena such as natural-convection in a cavity and Marsigli Flow. For each time level, the L2- norms of the error for the temperature and velocity components are found to be of order (h + k), where h is the spatial grid size and k is the time step size.
• Classification : 65M08, 65M15, 65N08, 65N15
• Format : Talk at Waseda University
• Author(s) :
  • Chitranjan Pandey (Indian Institute of Technology Kanpur, India)
  • B.V. Rathish Kumar (Indian Institute of Technology Kanpur, India)

[02560] A Composite Adaptive Finite Point Method for 2D Burgers' Equation

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : This paper focuses on solving the unsteady 2D Burgers equation. We present a minimal machinery algorithm based on an operator splitting technique into different temporal levels in conjunction with an adaptive finite point method (AFPM). The advisability of the AFPM is that it efficiently adjusts itself to fit into the local properties of the exact solution, and its user-friendliness makes it easy to implement and cost-effective. Mathematical estimates like stability, consistency, and convergence analysis support the presented method.
• Classification : 65M06, 65M12
• Author(s) :
  • Ashish Awasthi (National Institute of Technology Calicut)
  • Sreelakshmi A (National Institute of Technology Calicut)
  • Shyaman V P (National Institute of Technology Calicut)

[02452] Fifth-order WENO Schemes with Z-type Nonlinear Weights for Hyperbolic Conservation Laws

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : In this talk, we propose the variant Z-type nonlinear weights in the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. We take new smoothness indicators and follow the form of Z-type nonlinear weights introduced by Borges et al., leading to fifth order accuracy in smooth regions and sharper approximations around discontinuities. Finally, numerical examples are presented to demonstrate the advantages of the proposed WENO schemes in shock-capturing.
• Classification : 65M06
• Author(s) :
  • Jiaxi Gu (Pohang University of Science and Technology)
  • Xinjuan Chen (Jimei University)
  • Jae-Hun Jung (Pohang University of Science and Technology)

[01015] VMSFE Analysis of Transient MHD-NS Flow

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E702
• Type : Contributed Talk
• Abstract : In this work, a thorough investigation of the transient magnetohydrodynamic Navier-Stokes (MHD-NS) equations is carried out applying variational multiscale stabilized finite element (VMSFE) technique. The convergence characteristics of VMSFE scheme (Apriori Estimate) has been derived in this study. The VMSFE method's credibility is stablished by numerical experiments on multiply driven cavity flow. The flow pattern is traced for various Hartmann, Reynolds, and magnetic force inclination angle values.
• Classification : 65L60, 65K15
• Format : Talk at Waseda University
• Author(s) :
  • Anil Rathi (Indian Institute of Technology, Kanpur (India))
  • B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))
  • Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)

MS [00721] Data-driven and Model Reduction methods for Subsurface Applications

room : E703

• [04298] Deep Learning Methods for PDEs and Reduced Order Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Wang (University of Houston)
  • Abstract : In this talk, we will discuss the use of neural networks to solve high-dimensional partial differential equations (PDEs) without being affected by the curse of dimensionality. We will explore three key questions: (1) How to formulate PDE problems as optimization problems for deep learning techniques, (2) The accuracy of neural network approximations, and (3) Systematic training for global minimum convergence. In specific, We will present various optimization formulations for the high-dimensional quadratic porous medium equation, analyze generalization and approximation errors for Ritz methods, and propose an adaptive optimization strategy for training residual neural networks. Numerical results will be provided to demonstrate the effectiveness of the proposed methods.
• [03429] Nonlocal multicontinua with representative volume elements
  • Format : Talk at Waseda University
  • Author(s) :
    • Wing Tat Leung (City University of Hong Kong)
  • Abstract : In this talk, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing boundary effects. We discuss different choices of constraints for cell problems. We present numerical results that show how oversampling reduces boundary effects. Finally, we discuss the relation of the proposed methods to our previously developed methods, Nonlocal Multicontinuum Approaches.
• [05249] Physics-informed neural networks for learning the homogenized coefficients of multiscale elliptic equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jun Sur Richard Park (KAIST)
    • Xueyu Zhu (Department of Mathematics, University of Iowa)
  • Abstract : Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when the multiscale coefficient is known, if possible. Our approach adopts physics-informed neural networks (PINNs) algorithm to estimate the G-limits from the multiscale solution data by leveraging a priori knowledge of the underlying homogenized equations. Unlike the existing approaches, our approach does not rely on the periodicity assumption or the known multiscale coefficient during the learning stage. We demonstrate that the proposed approach can deliver reasonable and accurate approximations to the G-limits as well as homogenized solutions through several benchmark problems.

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

room : E704

• [02675] Transfer Learning Enhanced Physics-informed DeepONets for Long-time Prediction
  • Format : Talk at Waseda University
  • Author(s) :
    • wuzhe xu (University of Massachusetts Amherst)
  • Abstract : Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution equations in a finite time horizon. Nevertheless, the vanilla DeepONet suffers from the issue of stability degradation in the long-time prediction. This paper proposes a transfer-learning aided DeepONet to enhance the stability. Our idea is to use transfer learning to sequentially update the DeepONets as the surrogates for propagators learned in different time frames. The evolving DeepONets can better track the varying complexities of the evolution equations, while only need to be updated by efficient training of a tiny fraction of the operator networks. Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of DeepONet while maintaining similar computational cost but also substantially reduces the sample size of the training set.
• [03360] Generic bounds on the approximation error for physics-informed (and) operator learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tim De Ryck (ETH Zürich)
    • Siddhartha Mishra (ETH Zürich)
  • Abstract : We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator learning. These bounds guarantee that PINNs and (physics-informed) DeepONets or FNOs will efficiently approximate the underlying solution or solution operator of generic PDEs.
• [03124] Overcoming Fundamental Limitations of Current AI Approaches: From Digital to Analog Hardware
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gitta Kutyniok (LMU Munich)
    • Holger Boche (TU Munich)
    • Adalbert Fono (LMU Munich)
    • Aras Bacho (LMU Munich)
    • Yunseok Lee (LMU Munich)
  • Abstract : Artificial intelligence is currently leading to one breakthrough after the other. However, one current major drawback is the lack of reliability of such methodologies. In this talk, we will discuss fundamental limitations, showing that there do exist severe problems in terms of computability on any type of digital hardware, which seriously affects their reliability. At the same time, we also show that analog hardware such as neuromorphic computing or quantum computing could achieve true reliability.

MS [00201] Data-Driven Methods for Rough PDEs

room : E705

• [04555] Recent Advances in Rigorous Koopmanism
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthew Colbrook (University of Cambridge)
    • Qin Li (UW-Madison)
    • Ryan Raut (University of Washington)
    • Alex Townsend (Cornell University)
  • Abstract : Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. They have received considerable attention over the last decade, yet computing their spectral properties is a major challenge. I will present some recent advances in data-driven computation of Koopman spectral properties, including ResDMD and its analogue for stochastic dynamical systems. These new algorithms verifiably converge to the correct spectral properties (avoiding issues such as spectral pollution).
• [05147] Solving path-dependent PDEs with signature kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Cristopher Salvi (Imperial College London)
  • Abstract : In talk I will introduce a kernel framework for solving path-dependent PDEs (PPDEs) leveraging signature kernels, a recently introduced class of kernels indexed on path space. The proposed method recast the original infinite dimensional optimsation problem to an optimal recovery problem that approximates the solution of a PPDE with an element of minimal norm in the (signature) reproducing kernel Hilbert space constrained to satisfy the PPDE at a finite collection of collocation paths. By the representer theorem, the optimisation has a unique, analytic solution expressed entirely in terms of simple linear algebra operations. I will will discuss some motivating examples from rough volatility and present numerical results on option pricing under a rough Bergomi model.
• [05248] Kernel Methods for Rough PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Edoardo Calvello (California Institute of Technology )
    • Ricardo Baptista (California Institute of Technology)
    • Matthieu Darcy (California Institute of Technology )
    • Houman Owhadi (California Institute of Technology)
    • Andrew Stuart (California Institute of Technology)
    • Xianjin Yang (California Institute of Technology)
  • Abstract : Following the promising success of kernel methods in solving non-linear partial differential equations (PDEs), we investigate the application of Gaussian process methods to solve PDEs with rough right-hand side. We introduce an optimal recovery scheme defined by a Reproducing Kernel Hilbert Space (RKHS) of functions of greater regularity than that of the PDE’s solution. We illustrate the resulting theoretical framework for the recovery of solutions to the PDE and related numerical experiments.

MS [01028] High-order numerical methods for nonlinear PDEs

room : E708

• [05134] Error Analysis of IMEX and Time-Splitting Schemes for the Logarithmic Schrodinger’s Equation
  • Author(s) :
    • Li-Lian Wang (Division of Mathematical Sciences, Nanyang Technological University)
  • Abstract : The Schrodinger’s equation with a logarithmic nonlinear term (LogSE): f(u)=u log(|u|^2) exhibits rich dynamics, but such a nonlinearity presents significant challenges in both numerical solution and error analysis. Compared with usual cubic case, f(u) is non-differentiable at u=0 but possesses certain Holder continuity. In this talk, we shall report our recent attempts in numerical study of LogSE with a focus on time discretization via implicit-explicit scheme and time-splitting scheme and on the introduction of new tools for the error analysis. This talk is based on joint works with Jingye Yan (Jiangsu University, China) and Xiaolong Zhang (Hunan Normal University, China).
• [04415] Optimal $L^2$ error estimates of unconditionally stable FE schemes for the Cahn-Hilliard-Navier-Stokes system
  • Author(s) :
    • Wentao Cai (Beijing Computational Science Research Center)
    • Weiwei Sun (BNU-HKBU United International College)
    • Jilu Wang (Harbin Institute of Technology (Shenzhen))
    • Zongze Yang (The Hong Kong Polytechnic University)
  • Abstract : The paper is concerned with the analysis of a popular convex-splitting finite element method for the Cahn-Hilliard-Navier-Stokes system, which has been widely used in practice. Since the method is based on a combined approximation to multiple variables involved in the system, the approximation to one of the variables may seriously affect the accuracy for others. Optimal-order error analysis for such combined approximations is challenging. The previous works failed to present optimal error analysis in $L^2$-norm due to the weakness of the traditional approach. Here we first present an optimal error estimate in $L^2$-norm for the convex-splitting FEMs. We also show that optimal error estimates in the traditional (interpolation) sense may not always hold for all components in the coupled system due to the nature of the pollution/influence from lower-order approximations. Our analysis is based on two newly introduced elliptic quasi-projections and the superconvergence of negative norm estimates for the corresponding projection errors. Numerical examples are also presented to illustrate our theoretical results. More important is that our approach can be extended to many other FEMs and other strongly coupled phase field models to obtain optimal error estimates.
• [02750] Constructing structure-preserving schemes via Lagrange multiplier approach
  • Author(s) :
    • Qing Cheng (Tongji University)
    • Jie Shen (Purdue University)
  • Abstract : In the talk, I will introduce a new Lagrange multiplier approach to construct efficient and accurate structure-preserving schemes for a class of semi-linear and quasi-linear parabolic equations. To be more specific, I will introduce how to construct positivity/bound-preserving, length-preserving, energy-dissipative schemes for a large class of PDEs. I will establish stability results under a general setting, and carry out an error analysis for second-order structure-preserving schemes. Finally, I will apply our approach to several typical PDEs which preserve structures described above. Some numerical results will be presented to validate our approach.

MS [00827] Stochastic Rounding for Reduced-Precision Arithmetic in Scientific Computing

room : E709

• [03817] Implementation of Stochastic Rounding
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mantas Mikaitis (University of Leeds)
  • Abstract : In this talk we will review the latest developments in implementing stochastic rounding. We will first revisit the current methods of implementing stochastic rounding in hardware and software packages, such as CPFloat and MATLAB chop. We will present the main challenges and open problems, such as the reproducibility and precision of pseudo-random numbers. We will also review the commercial hardware that currently includes stochastic rounding, such as Graphcore IPU, Amazon Trainium, and Tesla Dojo devices. Finally, we will outline the list of features required for stochastic rounding to be standardized.
• [04133] Software Simulation of Stochastic Rounding
  • Format : Online Talk on Zoom
  • Author(s) :
    • Massimiliano Fasi (Durham University)
    • Mantas Mikaitis (University of Leeds)
  • Abstract : Implementing a stochastically rounded mathematical function requires three steps: 1) evaluating the function using a high-precision floating-point arithmetic; 2) drawing a pseudo-random number from some uniform distribution; and 3) rounding the high-precision result to the target precision. We describe how stochastic rounding can be performed using only integer arithmetic and bit-level operations, and we summarize the major challenges and open questions surrounding the implementation of this rounding mode.
• [04508] Bounds on Non-linear Errors for Variance Computation with Stochastic Rounding
  • Format : Talk at Waseda University
  • Author(s) :
    • El-Mehdi El Arar (Paris-Saclay University-UVSQ- LI-PaRAD )
    • Devan Sohier (Paris-Saclay University-UVSQ- LI-PaRAD )
    • Pablo de Oliveira Castro (Paris-Saclay University-UVSQ- LI-PaRAD )
    • Eric Petit (Intel Corp)
  • Abstract : This work's main objective is to investigate non-linear errors and pairwise summation using stochastic rounding (SR) in variance computation algorithms. We estimate the forward error of computations under SR through two methods: 1 a bound of the variance and Bienaymé–Chebyshev inequality, 2 martingales and Azuma–Hoeffding inequality. We examine two algorithms, "textbook" and "two-pass", both with non-linear errors. We show that they have probabilistic bounds under SR in $O(\sqrt{n}u)$ instead of $nu$ for the deterministic bounds.
• [04837] Trace estimation via asynchronous stochastic rounding
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lior Horesh (IBM T. J. Watson Research Center)
    • Vasileios Kalantzis (IBM T. J. Watson Research Center)
    • Georgios Kollias (IBM T. J. Watson Research Center)
    • Shashanka Ubaru (IBM T. J. Watson Research Center)
    • Chai Wah Wu (IBM T. J. Watson Research Center)
  • Abstract : We present a framework of randomized algorithms that include stochastic rounding and asynchronous updates and apply it to randomized linear algebra algorithms. In particular, we analyze an application to trace estimation and show its efficacy on various real-world datasets.

MS [00626] Finite element complexes for structure-preservation in continuum mechanics

room : E710

• [02976] Finite element gradgrad and divdiv complexes in three dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Hu (Peking University)
    • Yizhou Liang (University of Augsburg)
    • Rui Ma (Beijing Institute of Technology)
  • Abstract : We introduce the first family of conforming discrete gradgrad complexes and divdiv complexes in three dimensions. In gradgrad complexes, the first construction of finite element spaces of $H(\operatorname{curl},\mathbb{S})$ and $H(\operatorname{div},\mathbb{T})$ was proposed, and in divdiv complexes , finite element spaces of $H(\operatorname{sym}\operatorname{curl},\mathbb{T})$ are newly constructed. We prove that these finite element complexes are exact. We also present a special family of degrees of freedom of these complexes.
• [05087] Structure-preserving discretization for wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Sanna Mönkölä (University of Jyväskylä)
    • Jonni Lohi (University of Jyväskylä)
    • Markus Kivioja (University of Jyväskylä)
    • Tytti Saksa (University of Jyväskylä)
    • Lauri Kettunen (University of Jyväskylä)
    • Tuomo Rossi (University of Jyväskylä)
  • Abstract : We present a comprehensive framework for linear wave equations to consider hyperbolic problems in both classical and quantum mechanics. The framework is based on differential geometry in $(d+1)$-dimensional spacetime. To discretize the equations, we use a spacetime extension of the discrete exterior calculus including a leapfrog-style evolution in the time direction. To demonstrate the efficacy of this approach, we carry out numerical simulations using a C++ software library developed at the University of Jyväskylä.
• [03866] Regge finite elements and the linearized Einstein tensor
  • Format : Talk at Waseda University
  • Author(s) :
    • Evan Gawlik (University of Hawaii)
    • Michael Neunteufel (TU Wien)
  • Abstract : In general relativity, the linearization of the Einstein tensor plays an important role in studies of gravitational waves. We study the action of this differential operator on elements of the Regge finite element space: piecewise polynomial symmetric (0,2)-tensor fields with tangential-tangential continuity across simplex interfaces. We show that the Regge finite elements and the linearized Einstein operator fit into a commutative diagram of differential complexes that generalizes one studied by Christiansen in the lowest-order setting.
• [03058] Variational structures in cochain projection based discretization of classical field theories
  • Format : Talk at Waseda University
  • Author(s) :
    • Brian Tran (UC San Diego)
    • Melvin Leok (UC San Diego)
  • Abstract : Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite element methods. Multisymplectic variational integrators are a class of geometric numerical integrators for Lagrangian and Hamiltonian field theories, and they yield methods that preserve the multisymplectic structure and momentum-conservation properties of the continuous system. In this talk, we discuss the synthesis of these two approaches, by constructing discretization of the variational principle for Lagrangian field theories utilizing structure-preserving finite element projections. In our investigation, compatible discretization by cochain projections plays a pivotal role in the preservation of the variational structure at the discrete level, allowing the discrete variational structure to essentially be the restriction of the continuum variational structure to a finite-dimensional subspace. The preservation of the variational structure at the discrete level will allow us to construct a discrete Cartan form, which encodes the variational structure of the discrete theory, and subsequently, we utilize the discrete Cartan form to naturally state discrete analogues of Noether's theorem and multisymplecticity. Time permitting, we will relate the covariant spacetime discretization to the tensor product discretization approach using variational integration in space and symplectic integration in time.

MS [02479] Recent advances for modeling, numerical algorithm, and applications in electronic structure calculation

room : E711

• [04686] Numerical method for the Elasticity Transmission Eigenvalues
  • Format : Talk at Waseda University
  • Author(s) :
    • xia ji (Beijing institute of technology )
  • Abstract : We develop a discontinuous Galerkin method computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. For high order problems, DG methods are competitive since they use simple basis functions, the numerical implementation is much easier compared with classical conforming finite element methods. In this talk, we propose an interior penalty discontinuous Galerkin method using C0 Lagrange elements (C0IP) for the transmission eigenvalue problem for elastic waves and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.
• [03287] A multi-mesh adaptive finite element method for Kohn--Sham equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yang Kuang (Guangdong University of Technology)
  • Abstract : We present a multi-mesh adaptive finite element method for solving the Kohn–Sham (KS) equation. Specifically, the KS equation and the Poisson equation corresponding to the Hartree potential is solved in two different adaptive meshes on the same computational domain. With the presented method, we are able to evaluate the Hartree potential and Hartree energy more accurately, so as to reach a better accuracy with less computational cost in the all-electron calculations.
• [03432] Mathematical theory and numerical methods for Bose-Einstein condensation with higher order interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Xinran Ruan (Capital Normal University)
    • Weizhu Bao (National University of Singapore)
    • Yongyong Cai (Beijing Normal University)
  • Abstract : The binary interaction in Gross-Pitaevskii equation, which is a big success in describing Bose-Einstein condensate, is typically chosen as Fermi contact interaction. However, in certain cases, higher order interaction (HOI) needs to be included. In the talk, I will show new phenomenon introduced by HOI, such as the non-Gaussian type approximations in dimension reduction problems，new types of Thomas-Fermi approximations. Besides, two algorithms for computing ground states, which overcome the stability issue, will be presented.
• [03403] Solving Schrodinger equation using tensor neural network
  • Format : Talk at Waseda University
  • Author(s) :
    • Hehu Xie (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk, we introduce a prototype of machine learning method to solve high dimensional partial differential equations by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for the functions constructed by the tensor neural network within tolerable computational complexity. The corresponding machine learning method is built for solving high dimensional Schrodinger equation with high accuracy. Some numerical examples are provided to validate the accuracy and efficiency of the proposed algorithms. This work is collaborated with Yifan Wang and Pengzhan Jin.

MS [02056] Recent Advances in Partitioning Method for the Structures

room : E802

• [03098] Development of partitioning method for thermoelastic Interaction Problems with energy flux constraint
  • Format : Online Talk on Zoom
  • Author(s) :
    • Chang-uk Ahn (Kyung Hee University)
    • Alexandre Cortiella (University of Colorado)
    • Jin-gyun Kim (Kyung Hee University)
    • Kwang-chun park (Korea Advanced Institute of Science and Technology)
  • Abstract : This study presents a partitioned symmetric formulation for transient thermoelastic interaction problems. The thermoelastic interaction problem is a multiphysics problem in which the wave (i.e., hyperbolic type) equation and the diffusion (i.e., parabolic type) equation are coupled. The classical formulation of thermoelastic problems is non-symmetric, and its partitioned form has only been developed in ways that the domains are decoupled in the discrete domain. Based on this motivation, we propose a constraint of energy flux that allows partitioning the thermoelastic problem in a continuum domain. To do this, we construct two separate variational formulations of the uncoupled thermal conduction and uncoupled structural systems. In other words, two separate variational formulations of the uncoupled thermal conduction and uncoupled structural systems are augmented by the constraint of energy exchanges between the elastic body and the thermal conduction body via the method of Lagrange multipliers. Finally, this study introduces a solution algorithm including implicit-implicit time integration strategies, and the present partitioned formula is verified by well-organized numerical examples.
• [04222] A Componenet Mode Synthesis Method Using a Displacement-Based Partitioned Approach
  • Format : Online Talk on Zoom
  • Author(s) :
    • Muhammad Faizan Baqir (Kyung Hee University )
    • K. C. Park (University of Colorado)
    • Jin Gyun Kim (Kyung Hee University)
  • Abstract : A new Partitioned component mode synthesis (P-CMS) is presented, which employs a recently developed Displacement-based Partitioned (DP) formalism. The reduced system matrices are generated via block-by-block substructural matrix computations, directly yielding reduced-order models. The proposed P-CMS method can provide a robust mode selection criterion that remains a challenge in most existing CMS methods. Details of the proposed P-CMS procedure along with numerical examples will be presented in this talk.
• [03460] Iterative Algorithm for Quasistatic Structural Problems Employing Only Partitioned Displacements
  • Format : Talk at Waseda University
  • Author(s) :
    • SANGJOON SHIN (Seoul National University)
    • Seung-Hoon Kang (Seoul National University)
    • Kwang-Chun Park (University of Colorado Boulder)
  • Abstract : We report some initial results from the ongoing research on partitioned parallel solution of quasistatic structural problems that employ only partitioned displacements. A notable feature of the present method is the absence of Lagrange multipliers that inevitably manifest in standard partitioned formalisms. Various preconditioning and regularizations that take advantages of the present Displacement-only Partitioned (DP) formulation will be presented and compared with FETI and its allied solution methods.

contributed talk: CT121

room : E803

[00310] Human Activity Recognition from Inertial Motion Data

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E803
• Type : Contributed Talk
• Abstract : Human activity recognition (HAR) using inertial motion streaming has gained a lot of momentum in recent years. This has been driven by smart environments and the ubiquity of inertial-motion sensors in modern commodity devices. HAR applications span all aspects of human life such as healthcare, sports, manufacturing, etc. In this talk we give a brief description of the state-of-the-art work in HAR including action recognition, biometrics analysis (gender, age,..), sensor’s location determination, gait analysis, etc.
• Classification : 68T01, 68T05, 92C47
• Format : Talk at Waseda University
• Author(s) :
  • Walid Gomaa (Egypt Japan University of Science and Technology)

[01035] Reinforcement learning-based routing strategy in IoT applications using MDC

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E803
• Type : Contributed Talk
• Abstract : WSNs and IoT devices consume more power for data transmission. To reduce energy consumption, most of the traditional learning methodologies need enormous volumes of data and feature engineering, thus raising the learning complexity. A reliable reinforcement learning-based MDC model for effective routing is proposed to lower the learning complexity. Furthermore, the Q-Learning methodology is used to enhance learning along the shortest path. Combining these techniques can improve network stability while also enhancing routing performance significantly.
• Classification : 68T01, 68T07, 68T35, Reinforcement learning, Machine Learning
• Format : Talk at Waseda University
• Author(s) :
  • Muralitharan Krishnan (Sungkyunkwan University)
  • Yongdo Lim (Sungkyunkwan University)

[01078] DNN-based hybrid ensemble learning strategy for XSS detection and defense

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @E803
• Type : Contributed Talk
• Abstract : Due to the high level of intelligence displayed by attackers, existing web-based security applications have failed. When attackers make changes to an organization's data, it is one of the most dangerous attacks (XSS). Combining ML and DL frameworks is proposed as a way to detect and defend against XSS assaults with high accuracy and efficiency. Using this representation, a new method is developed for integrating stacking ensembles into web-based software, which is called "hybrid stacking".
• Classification : 68T01, 68T05, 68T07, Machine Learning, Deep Learning
• Format : Online Talk on Zoom
• Author(s) :
  • Seethalakshmi Perumal (MIT Campus, Anna University - Chennai)

MS [02387] Recent Advances on Distributed Optimization

room : E804

• [03522] Optimal Gradient Tracking for Decentralized Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Ming Yan (The Chinese University of Hong Kong, Shenzhen)
  • Abstract : We focus on solving the decentralized problem over a network. Assuming smoothness and strong convexity, we propose Optimal Gradient Tracking (OGT), which simultaneously achieves the optimal gradient computation complexity and communication complexity. Its development involves two building blocks that are of independent interest. The first is the decentralized gradient tracking method, SSGT, which achieves optimal gradient computation. The second is a loopless method that achieves similar performance as Chebyshev acceleration.
• [03541] Optimal Complexity in Distributed Learning with Communication Compression
  • Format : Talk at Waseda University
  • Author(s) :
    • Yutong He (Peking University)
    • Xinmeng Huang (University of Pennsylvania)
    • Wotao Yin (Alibaba (US) Group)
    • Kun Yuan (Peking University)
  • Abstract : Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication compression, a theoretical lower bound is still missing. Analyses of algorithms with communication compression have attributed convergence to two abstract properties: the unbiased property or the contractive property. In this talk, we consider distributed stochastic algorithms for minimizing smooth convex and non-convex objective functions under communication compression. We establish convergence lower bounds for algorithms whether using unbiased or contractive compressors. To close the gap between the lower bound and the existing upper bounds, we further propose an algorithm, NEOLITHIC, which almost reaches our lower bound (up to logarithm factors) under mild conditions. The experimental results validate our findings.
• [03556] Asymptotic Network Independence in Distributed Stochastic Gradient Methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Shi Pu (The Chinese University of Hong Kong, Shenzhen)
  • Abstract : We discuss the so-called asymptotic network independence property in distributed stochastic optimization, which is achieved whenever a distributed method executed over a network of $n$ nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network; it is as if the network is not even there! We explain this property through examples involving the training of ML models and present a short mathematical analysis. We also discuss the transient times for distributed stochastic gradient methods to achieve network independent convergence rates. Finally, we introduce some recent works on distributed random reshuffling (RR) methods.
• [03570] Unified and Refined Analysis of Decentralized Optimization and Learning Algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Sulaiman A Alghunaim (Kuwait University)
  • Abstract : Decentralized multi-agent optimization is a powerful paradigm with numerous applications in learning and engineering design. In these setups, a network of agents is linked by a graph, and agents are only allowed to share information locally. Through localized interactions, they seek the minimizer of a global optimization problem. In decentralized consensus problems, the agents are linked by a common consensus variable on which they must agree. This talk will present a unified and improved analysis for decentralized consensus optimization methods. We demonstrate how the analysis of several state-of-the-art bias-correction decentralized methods, such as EXTRA, Exact-Diffusion, NIDS, and Gradient-Tracking methods, can be unified by a decentralized algorithmic framework that encompasses these methods. We develop a novel analysis technique that establishes the framework's convergence under nonconvex, convex, and strongly convex objectives. We provide refined and improved convergence rate bounds. The analysis reveals important characteristics for these methods, such as how their performances are influenced by network graph.

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

room : E811

• [03799] Stochastic Gradient Descent with Conjugate Gradient-style Momentum
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bao Wang (University of Utah)
    • Qiang Ye (University of Kentucky)
  • Abstract : Momentum may be crucial in stochastic gradient-based optimization algorithms for convergence acceleration. The classical conjugate gradient algorithm may be considered as gradient descent with momentum. In this talk, we introduce a stochastic gradient descent algorithm with a conjugate gradient-style momentum. We will discuss its convergence properties and present some numerical examples to demonstrate its effectiveness.
• [01342] Robust randomized preconditioning for kernel ridge regression
  • Format : Talk at Waseda University
  • Author(s) :
    • Mateo Diaz Diaz (Johns Hopkins University)
    • Ethan Epperly (Caltech)
    • Zachary Frangella (Stanford)
    • Joel Tropp (Caltech)
    • Robert Webber (California Institute of Technology)
  • Abstract : We advocate two randomized preconditioning approaches for applying kernel ridge regression (KRR) to a moderate or large number of data points ($N \geq 10^4$). RPCholesky preconditioning is guaranteed to solve the exact KRR equations involving the $N \times N$ kernel matrix in just $\mathcal{O}(N^2)$ operations, assuming eigenvalue decay. KRILL preconditioning is guaranteed to solve the restricted KRR equations involving a $N \times k$ kernel submatrix in just $\mathcal{O}((N + k^2) k \log k)$ operations, with no assumptions on the kernel matrix or the regularization parameter. Experiments with dozens of data sets validate the effectiveness of RPCholesky and KRILL. Additionally, our theoretical analysis shows that RPCholesky and KRILL have stronger robustness properties compared to other commonly used preconditioners.
• [01305] Structured matrix recovery using randomized matrix-vector products
  • Format : Talk at Waseda University
  • Author(s) :
    • Diana Halikias (Cornell University)
    • Alex Townsend (Cornell University)
  • Abstract : Can one recover a matrix efficiently from only matrix-vector products? If so, how many are needed? We describe randomized algorithms of this type for various structured matrices. In particular, we recover an $N\times N$ hierarchical matrix with rank-$k$ off-diagonal blocks using $\mathcal O(k\log(N))$ matrix-vector products. While existing algorithms employ a recursive “peeling" procedure of elimination, we use recursive projection, which may be preferable when matrix-vector products are noisy, or for recovering the nearest hierarchical matrix.

MS [00432] Empirically Driven Deep Learning Theory

room : E812

• [04878] Understanding Deep Learning Through Optimization Geometry
  • Format : Talk at Waseda University
  • Author(s) :
    • Nathan Srebro (TTIC)
  • Abstract : I will survey the approach emerging in recent years for understanding deep learning through the optimization geometry in function space induced by the architecture. To appreciate this view, its ability to explain empirical phenomena, and also its limitations, we will see how many phenomena can be understood through a detailed study of optimization geometry in a simple deep linear model.
• [04289] Feature Learning in Two-Layer Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Murat Erdogdu (University of Toronto)
  • Abstract : We study the effect of gradient-based optimization on feature learning in two-layer neural networks. We consider the non-asymptotic setting, and we show that a network trained via SGD exhibits low-dimensional representations, with applications in learning a monotone single-index model.
• [03006] On the Implicit Geometry of Deep-net Classifiers
  • Format : Talk at Waseda University
  • Author(s) :
    • Tina Behnia (University of British Columbia)
    • Ganesh Ramachandra Kini (University of California, Santa Barbara)
    • Vala Vakilian (University of British Columbia)
    • Christos Thrampoulidis (University of British Columbia)
  • Abstract : The talk will address the following questions: What are the unique structural properties of models learned by deep-net classifiers? Is there an implicit bias towards solutions of a certain geometry and how does this vary across architectures and data? Specifically, how does this implicit geometry change under label imbalances, and is it possible to use this information to design better loss functions for learning with imbalances?
• [05316] Does the loss function matter in overparameterized models?
  • Format : Online Talk on Zoom
  • Author(s) :
    • Vidya Muthukumar (Georgia Institute of Technology)
  • Abstract : Recent years have seen substantial interest in a first-principles theoretical understanding of the behavior of overparameterized models that interpolate noisy training data, based on their surprising empirical success. In this talk, I compare classification and regression tasks in the overparameterized linear model. On the one hand, we show that with sufficient overparameterization, solutions obtained by training on the squared loss ( minimum-norm interpolation) typically used for regression, are identical to those produced by training on exponential and polynomially-tailed losses, typically used for classification. On the other hand, we show that there exist regimes where these solutions are consistent when evaluated by the 0-1 test loss function, but inconsistent if evaluated by the mean-squared-error test loss function. Our results demonstrate that: a) different loss functions at the training (optimization) phase can yield similar solutions, and b) a significantly higher level of effective overparameterization admits good generalization in classification tasks as compared to regression tasks.

MS [00908] Machine Learning and Data-Driven Applications using Geometric Integration

room : E817 -> A715 (changed)

• [03459] Geometric integration in machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • James Jackaman (NTNU)
  • Abstract : Here, as a primer, we give an overview of the role geometric integration (of Hamiltonian systems) has played in the design of neural networks in recent years, with an empathsis on the stability guarantees this provides and the structures incorporated into the networks. Time permitting, we will move on to discuss how convolutional networks can be understood through finite differences and the theoretical benefits this comparison yields.
• [03490] Application of the Kernel Method to Learning Hamiltonian Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Taisei Ueda (Kobe University)
    • Takashi Matsubara (Osaka University)
    • Takaharu Yaguchi (Kobe University)
  • Abstract : Recently, methods for learning Hamiltonian systems from data have attracted much attention. While the most methods are based on neural networks, neural networks have some drawbacks, such as the possibility of falling into a local optimum. In this talk, we propose a method based on the kernel method, thereby overcoming the problems.
• [03180] Structured neural networks and some applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Davide Murari (Norwegian University of Science and Technology)
    • Elena Celledoni (Norwegian University of Science and Technology)
    • Brynjulf Owren (Norwegian University of Science and Technology)
    • Ferdia Sherry (University of Cambridge)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : Neural networks have gained much interest because of their effectiveness in many applications related to high-dimensional function approximation problems. This success is often supported by experimental evidence, while the theoretical properties of these models need to be better understood. When one knows that the target function to approximate or the data being processed has some properties, it might be desirable to reproduce them in the neural network design. This talk presents a framework that makes ODEs and numerical methods work together to model neural networks having prescribed properties. Such an approach is supported by offering particular applications for data-driven modelling and image analysis.

MS [00793] SIAM Student Chapter Research Presentations

room : E818

• [03324] Continuum Limit of Nonlocal Diffusion on Inhomogeneous Networks
  • Author(s) :
    • Itsuki Watanabe (Waseda University)
  • Abstract : We present two limit theorems for the zero-range process with nonlocal diffusion on inhomogeneous networks. The deterministic model is governed by the reaction–diffusion equation with an integral term in space instead of a Laplacian. By constructing the reproducing kernel Hilbert space to consider the inhomogeneities of the network structure, we prove that the law of large numbers and the central limit theorem hold for our models.
• [03390] Computing the invariant measure of the N-vortex problem on the sphere by Hamiltonian Monte Carlo
  • Author(s) :
    • Kota Takeda (Kyoto University)
    • Takashi Sakajo (Kyoto University)
  • Abstract : We consider Hamiltonian Monte Carlo(HMC) to approximates a given target distribution on manifolds embedded in Euclidean space. Its efficiency is guaranteed by the exponential convergence property called geometric ergodicity. We have proven that HMC has geometric ergodicity for smooth distributions on compact manifolds. As an application, we compute the invariant measure of the N-vortex problem on the unit sphere by HMC.
• [03516] REGULARIZED ADAPTIVE HUBER MATRIX REGRESSION AND DISTRIBUTED LEARNING
  • Author(s) :
    • YUE WANG (City University of Hong Kong)
  • Abstract : Matrix regression provides a powerful technique for analyzing matrix-type data, as exemplified by many contemporary applications. Despite the rapid advance, distributed learning for robust matrix regression to deal with heavy-tailed noises in the big data regime still remains untouched. In this paper, we first consider adaptive Huber matrix regression with a nuclear norm penalty, which enjoys insensitivity to heavy-tailed noises without losing statistical accuracy. To further enhance the scalability in massive data applications, we employ the communication-efficient surrogate likelihood framework to develop distributed robust matrix regression, which can be efficiently implemented through the ADMM algorithms. Under only bounded $(1+\delta)$-th moment on the nose for some $\delta \in (0, 1]$, we provide upper bounds for the estimation error of the central estimator and the distributed estimator and prove they can achieve the same rate as established with sub-Gaussian tails when only the second moment of noise exists. Numerical studies verify the advantage of the proposed method over existing methods in heavy-tailed noise settings.
• [03650] Optimal Contextual Bandits with Knapsacks under Realizability via Regression Oracles
  • Author(s) :
    • Jialin ZENG (Hong Kong University of Science and Technology)
    • Yuxuan HAN (Hong Kong University of Science and Technology)
    • Yang WANG (Hong Kong University of Science and Technology)
    • Yang XIANG (Hong Kong University of Science and Technology)
    • Jiheng ZHANG (Hong Kong University of Science and Technology)
  • Abstract : We study the stochastic contextual bandit with knapsacks (CBwK) problem, where each action, taken upon a context, not only leads to a random reward but also costs a random resource consumption in a vector form. The challenge is to maximize the total reward without violating the budget for each resource. We study this problem under a general realizability setting where the expected reward and expected cost are functions of contexts and actions in some given general function classes F and G, respectively. Existing works on CBwK are restricted to the linear function class since they use UCB-type algorithms, which heavily rely on the linear form and thus are difficult to extend to general function classes. Motivated by online regression oracles that have been successfully applied to contextual bandits, we propose the first universal and optimal algorithmic framework for CBwK by reducing it to online regression. We also establish the lower regret bound to show the optimality of our algorithm for a variety of function classes.

MS [00065] Recent Advances on Stochastic Hamiltonian Dynamical Systems

room : E819

• [04130] Schrodinger Meets Onsager
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qiao Huang (Nanyang Technological University)
  • Abstract : In this talk, we will use the framework of stochastic geometric mechanics to describe relations between Schrodinger's variational problem and Onsager's approach to nonequilibrium statistical mechanics. Especially, we will rebuild Onsager's reciprocal relations by introducing Riemannian structures on thermodynamic spaces, and propose a definition of entropy for nonequilibrium systems. This is joint work with Jean-Claude Zambrini.
• [00806] Recent progress in spatial isosceles three body problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lei Liu (Peking University)
  • Abstract : Recently, we discovered some new and strong connections between the spatial isosceles three body problem and Symplectic Dynamics. From this perspective, more information can be obtained. Therefore, under the light of Symplectic Dynamics, we obtain plenty of new results. In this talk, we will introduce the isosceles three body problem in symplectic and dynamical point of view, including the dimensional reduction, dynamical analysis, index estimates, open book decomposition and convexity. Finally, I will prove the existence of infinite many oscillate periodic motions in certain parametrical setting.

MS [01800] Numerical methods for fluid-structure interaction and poroelasticity

room : E820

• [04829] Cell-Based Numerical Approach to Evaluate CTC Binding Behavior in Microfluidic Device
  • Format : Talk at Waseda University
  • Author(s) :
    • YIFAN Wang (Texas Tech University)
  • Abstract : Circulating tumor cells (CTCs) are malignant cells that break free from the primary tumor and enter the bloodstream. Early detection of CTCs is crucial for diagnosis, but challenging because they are infrequent in blood samples. Microfluidic devices offer a promising detection technique, either actively enriching CTCs through external fields or passively separating them from other cells based on physical properties. A microfluidic device has been proposed by our collaborator at Texas Tech University to isolate CTCs from blood samples, with different micro-post sizes and layouts tested to optimize capture efficiency. However, the complex transport and adhesion behaviors of CTCs in blood cell suspensions remain incompletely understood. Here, we present a cell-based numerical approach based on the Lattice Boltzmann method to evaluate the binding behavior and trajectories of CTCs under different flow conditions, including cell size and coating density, microfluidic design, and cell collisions. Our validated results are used to improve the device design.
• [02971] A Banach spaces-based fully-mixed formulation for the Navier–Stokes/Darcy coupled problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Segundo Villa Fuentes (Monash University)
    • Ricardo Oyarzúa (Universidad del Bío-Bío)
    • Sergio Caucao (Universidad Católica de la Santísima Concepción)
  • Abstract : In this work we present and analyze a fully-mixed formulation for the coupling Navier–Stokes/Darcy equations. Our approach is based on the introduction of a modified pseudostress tensor in the Navier–Stokes equations for the fluid, whereas the standard dual-mixed formulation for the Darcy model is considered. With this, we obtain a Banach spaces-based mixed variational formulation and a twofold saddle point structure. Fixed-point strategy, together with the Banach–Nečas–Babuška and Banach’s fixed point theorems, are employed to prove the well-posedness of the continuous and discrete formulations.
• [03829] Numerical simulation of the time-fractional Navier-Stokes-Fokker-Planck (tfNSFP) equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jonas Beddrich (Technical University of Munich)
    • Endre Süli (University of Oxford)
    • Barbara Wohlmuth (Technical University of Munich)
  • Abstract : The tfNSFP system describes the flow of dilute polymeric fluids. It is attractive as it enhances standard models for the viscoelasticity of polymer molecules by accounting for memory effects. The problem is challenging since it is non-local in time and defined on the Cartesian product of two d-dimensional spaces. We present a numerical method that combines a rational approximation approach, a space-splitting approach, and the Hermite spectral method to solve the tfNSFP equation.

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

room : D101

• [05260] Exascale challenges and opportunities for fundamental research
  • Format : Online Talk on Zoom
  • Author(s) :
    • Christophe Calvin (CEA)
    • France Boillod-Cerneux (CEA)
    • Valérie Brenner (CEA)
  • Abstract : With the exascale come new challenges: the processing of massive data coupled with digital simulation becomes intrinsic to science. In addition, the constraints brought by the architectures of calculation for the exascale impose to also rethink the scientific applications. We are therefore faced with two major challenges. The 1st one: how the new exascale calculators, inscribed in a digital continuum, will be able to provide solutions for the processing of complex workflows combining data processing and simulation. The 2nd, how to design or redesign the applications in order to be able to exploit the architectures of the exascale supercomputers. We will illustrate these 2 challenges through different use cases at the CEA’s Fundamental Research Division.
• [03605] An algorithm reducing by 2 the number of operations for the PageRank method, and its generalisation for stochastic matrix-vector products
  • Format : Online Talk on Zoom
  • Author(s) :
    • serge georges petiton (University of Lille, CNRS)
    • Maxence Vandromme (RATP Smart Systems)
  • Abstract : We propose an efficient PageRank algorithm that reduces the complexity by a factor two. We implement the method using row-major and column-major sparse matrix formats. The experiments are done on two different Intel processors from recent generations. The column-major storage format version of our method shows good scaling and outperforms the standard PageRank in a majority of cases. We also propose generalisations of this algorithm to the multiplication of stochastic matrices by a vector product.
• [03705] Accelerating Cardiac Electrophysiology Simulations using novel AI Hardware
  • Format : Talk at Waseda University
  • Author(s) :
    • Johannes Langguth (Simula Research Laboratory)
    • Luk Bjarne Burchard (Simula Research Laboratory)
    • Xing Cai (Simula Research Laboratory)
  • Abstract : Recent advances in personalized arrhythmia risk prediction show that computational models can provide not only safer but also more accurate results than invasive procedures. However, biophysically accurate simulations require solving linear systems over fine meshes and time resolutions, which require significant computational resources. However, by leveraging sophisticated parallelization patterns as well as non-traditional hardware architectures, it is possible to meet the computational demands of these simulations. A major recent development in computer hardware was the rise of dedicated accelerator hardware for machine learning applications such as the Graphcore IPUs and Cerebras WSE. These processors have evolved from the experimental state into market-ready products, and they have the potential to constitute the next major architectural shift after GPUs saw widespread adoption a decade ago. In this talk, we present ongoing work on the parallelization of finite volume computations over an unstructured mesh using these new accelerators. We compare them to traditional CPUs and GPUs and point out challenges and opportunities of this new hardware for extreme scale computing.
• [05304] A Medical Data Analytics Framework Transforming Big Data to Better Healthcare
  • Format : Talk at Waseda University
  • Author(s) :
    • Weichung Wang (National Taiwan University)
  • Abstract : Incorporating data science is crucial for the next-generation medical workflows that rely on high-performance computing to analyze large-scale medical data for digital and precision medicine. The "Medical Data Analytics Framework" combines project design, multimodality data, intelligent analytics, medical workflows, regulation, ethics, deployment, and operations to achieve an end-to-end R&D life-cycle in medical AI that positively impacts clinical workflows. This interdisciplinary framework reduces physicians' workload and assists in diagnosing with advanced algorithms and software.

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

room : D102

MS [00587] Recent Advances in Numerical Methods for Nonlinear Hyperbolic PDEs

room : D401

• [02636] Error analysis of finite volume methods for the Euler equations via relative energy
  • Format : Talk at Waseda University
  • Author(s) :
    • Maria Lukacova (University of Mainz)
    • Bangwei She (Capital Normal University)
    • Yuhuan Yuan (University of Mainz)
  • Abstract : We present an overview of our recent results for the error analysis of some finite volume methods for multidimensiona Euler system. To control global error, we apply the relative energy principle and estimate the L2 norm between a numerical solution and the strong solution. If time permits, we will present an extension to the error analysis of the random Euler system approximated by the Monte Carlo finite volume method.
• [04782] Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Kurganov (Southern University of Science and Technology)
  • Abstract : The talk will focus on numerical methods for nonconservative hyperbolic systems of balance laws. I will introduce well-balanced path-conservative central-upwind schemes, which are based on the flux globalization: both source and nonconservative product terms are incorporated into the global flux. The resulting quasi-conservative system is numerically solved using a semi-discrete central-upwind scheme with the numerical fluxes are evaluated using the path-conservative technique. Applications to several shallow water models will be demonstrated.
• [01953] High order well-balanced and asymptotic preserving WENO schemes for the shallow water equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yulong Xing (Ohio State University)
  • Abstract : Shallow water equations (SWEs) with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. In this presentation, we will talk about the applications of high-order semi-implicit well-balanced and asymptotic preserving (AP) WENO methods to this system. We consider the Froude number ranging from O(1) to 0, which in the zero Froude limit becomes the “lake equations” for balanced flow without gravity waves. We apply a well-balanced finite difference WENO reconstruction, coupled with a stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting semi-implicit scheme can be shown to be well-balanced, AP and asymptotically accurate at the same time. Both one- and two-dimensional numerical results are provided to demonstrate the high order accuracy, AP property and good performance of the proposed methods in capturing small perturbations of steady state solutions.

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

room : D402

• [02821] Hydrodynamics of Tunable Janus Particles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rolf Josef Ryham (Fordham University)
    • Yuan Nan Young (New Jersey Institute of Technology)
    • Bryan Quaife (Florida State University)
    • Szu-Pei Fu (Trinity College)
  • Abstract : We use a model recently developed for the many-body hydrodynamics of amphiphilic JPs under a viscous background flow to investigate distinct particle phases that arise when accounting for asymmetric and polar hydrophobes. We quantify the macroscopic properties of novel JP phases under a linear shear and a Taylor-Green mixing background flow and quantify their macroscopic, complex-fluid behavior. These numerical results provide insight into dynamic control of non-equilibrium active biological systems with similar self-organization.
• [02823] Sharp interface problem of Ohta-Kawasaki Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Amlan K Barua (IIT Dharwad)
  • Abstract : The Ohta Kawasaki (OK) model investigates mesoscopic phase separation in block copolymers. In this talk, we discuss a sharp interface version of OK equations using matched asymptotic expansions. The resultant equations resemble a Hele-Shaw type system. We suggest a boundary integral formulation of the problem and propose highly accurate numerical techniques to solve the equations. We conduct long-time simulation using our numerical methods. The simulation results show the emergence of various interesting configurations.
• [02835] Phase-field modeling and simulation of controllable dendritic growth
  • Format : Talk at Waseda University
  • Author(s) :
    • Darae Jeong (Kangwon National University)
  • Abstract : In this study, we consider the controllable dendritic growth model with phase-field method. The governing system consists of three equations that are for capturing the interface between solid and melt phases, diffusion of the temperature, and structure by molecular orientations in solid. We propose the time-dependent adaptive mesh and finite-difference algorithm, which is designed to efficiently solve the governing system. After that, we present several numerical simulation to show the various patterns and its corresponding parameter effect for crystal formation. And we demonstrate the effectiveness of our approach by comparing numerical results with other method.

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

room : D403

• [05155] Geothermal management with an integrated optimization method accelerated by a general thermal decline model and deep learning
  • Author(s) :
    • Bicheng Yan (King Abdullah University of Science and Technology )
    • Manojkumar Gudala (King Abdullah University of Science and Technology )
    • Shuyu Sun (KAUST)
  • Abstract : Geothermal modeling is complex due to the coupled thermo-hydro-mechanical physics, which brings computational challenges for geothermal management. To tackle with this, we developed a parsimonious thermal decline model to capture the early thermal breakthrough and the later decline behavior. Further, a forward neural network maps the reservoir parameters to the decline model parameters, and it is integrated with a multi-objective optimizer, which considers reservoir uncertainties and subjects engineering constraints for robust reservoir optimization.
• [05424] Gym-preCICE: Reinforcement Learning Environments for Active Flow Control
  • Author(s) :
    • Ahmed H. Elsheikh (Heriot-Watt University)
    • Mosayeb Shams (Heriot-Watt University)
  • Abstract : We introduce Gym-preCICE, a Python adapter to facilitate designing and developing Reinforcement Learning (RL) environments for single- and multi-physics Active flow control (AFC) applications. In an actor-environment setting, Gym-preCICE takes advantage of preCICE, an open-source coupling library for partitioned multi-physics simulations, to handle information exchange between a controller (actor) and an AFC simulation environment. The developed framework results in a seamless non-invasive integration of realistic physics-based simulation toolboxes with RL algorithms.
• [05495] Ensemble schemes for the numerical solution of a random transient heat equation with uncertain inputs
  • Author(s) :
    • Xianbing Luo (Guizhou University)
    • Meng Li (Guizhou University)
    • Tingfu Yao (Guizhou University)
    • Changlun Ye (Guizhou University)
  • Abstract : Ensemble-based time stepping schemes are applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. (1) By introducing ensemble mean, we use HDG method to obtain optimal convergence order for random diffusion coefficient problem. (2) By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equation. (3) By introducing two Max ensemble for Robin boundary and diffusion coefficients problem, we propose a unconditional stability ensemble method. Stability analysis and error estimates are derived. Numerical examples verify the theoretical results and the validity of the ensemble method.

contributed talk: CT154

room : D405

[02160] Using quantum mechanics for calculation of different infinite sums

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : Certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem. For simplicity we illustrate the method by exploring the problem of a particle in a box. Twofold calculation of the mean value of energy for the polynomial wave function inside the well yields even argument p of Riemann zeta and related functions. This method can be applied to a wide class of exactly solvable quantum mechanical problems.
• Classification : 81P10, 35J10, 35L05, 37N20
• Format : Talk at Waseda University
• Author(s) :
  • Milica Pavkov Hrvojevic (Facuty of Sciences University of Novi Sad )
  • Petar Mali (Faculty of Sciences University of Novi Sad)
  • Milica Rutonjski (Faculty of Sciences University of Novi Sad)
  • Slobodan Radosevic (Faculty of Sciences University of Novi Sad)

[00684] Aggregation of Anisotropic Inclusions on Elastic Membranes

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : Elastic interactions mediated by biological membranes are an important class of sorting mechanisms used to organise proteins in living systems and with applications for biotechnology. Proteins that bind to the membrane and generate this curvature are often anisotropic and this broken symmetry yields new phenomena in their interactions. In this talk, I will discuss the many-body structures that can emerge from these elastic, quadrupole-like interactions and explore the consequences of these aggregates.
• Classification : 74L15, 92C10, 92C37, 74G10
• Format : Talk at Waseda University
• Author(s) :
  • Matthew William Cotton (University of Oxford)
  • Jon Chapman (University of Oxford)
  • Alain Goriely (University of Oxford)

[02433] Response Surface Methodology-Based Model Updating Using FRF Curvature

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : We propose a Response Surface Methodology (RSM) based model updating approach using Frequency Response Function (FRF) curvature as the response for optimization. The optimization algorithm is based on a multi-objective function that is solved using MATLAB. The updated model is then used for identifying structural damage. The proposed approach is validated through numerical simulations on a simply supported beam and an experimental study on a free-free aluminum beam. The results demonstrate that the RSM-based model updating approach can accurately identify the location and severity of damage in structures.
• Classification : 82M20, 90C29
• Format : Online Talk on Zoom
• Author(s) :
  • Nur Raihana Sukri (Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia)
  • Syarifah Zyurina Nordin (Malaysia Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia)
  • Nurulakmar Abu Husain (Malaysia Japan International Institute of Technology, Universiti Teknologi Malaysia)

[01509] Hydromagnetic Hybrid Nanofluid Flow Over a Rotating Stretching Disk

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : The research aim in the this article is to study the effect of magnetic field on the unsteady flow and heat transfer of an incompressible nanofluid due to a rotating disc. In addition, the flow is taken to be in a Darcy-Forchheimer porous medium. The governing set of highly non-linear PDEs are converted into set of highly non-linear ODEs using suitable similarity transformations. The system consisting of non-linear ODEs is numerically solved by the Spectral Quasi Linearization Method (SQLM). The solutions for the local skin friction along the radial direction, local skin friction along tangential direction, and the local heat transfer rate at the surface of the disc for different values of the suitable parameters are also obtained. The results of dimensionless velocity and temperature profiles are shown graphically where the values of local skin-friction coefficients and the heat transfer coefficients are presented in tabular form. A statistical analysis in the form of regression analysis is also performed to estimate the skin-friction and heat transfer coefficients.
• Classification : 76W05, 76S05
• Format : Talk at Waseda University
• Author(s) :
  • Raj Nandkeolyar (Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur)
  • Premful Kumar (Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur)

[01906] Adjoint-Based Shape Optimization of Periodic Units for Compact Heat Transfer Devices

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D405
• Type : Contributed Talk
• Abstract : We present a DOLFIN/FEniCS framework for shape optimization of compact heat transfer devices consisting of periodic units. The framework relies on highly parallelized, efficient finite-element solvers for the three-dimensional periodically developed flow and heat transfer equations and their eigenvalue problems. The adjoint-based shape calculus is implemented by means of automated differentiation and operator overloading. Design constraints are incorporated through an augmented Lagrangian method. The optimized surfaces are compared with designs obtained through density-based topology optimization.
• Classification : 80M50, 80M10, 49M41, 80M40, 76S05
• Format : Talk at Waseda University
• Author(s) :
  • Geert Buckinx (VITO)
  • Stephan Schmidt (Humboldt University Berlin)

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

room : D407

• [05038] Mean-field convergence in L^2-norm for a diffusion model with aggregation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexandra Holzinger (TU Wien )
  • Abstract : Aggregation effects appear in many applications arising from biology and physics which makes it interesting to study this phenomena also in mean-field settings. It is well-known that a class of local diffusion-aggregation equations can bederived by using classical mean-field limits. In this talk I will explain the benefits we get by showing a result in L^2-norm and how this is connected to fluctuations around the mean-field limit.
• [04613] Macroscopic limits of kinetic equations for the switch in cell migration via binary interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Gissell Estrada-Rodriguez (University of OxfordU)
  • Abstract : Motivated by experimental results on the immune response to cancer, we considered a system of particles, I, in an inactive state, where they follow a nonlocal (Levy) movement. After a collision with particles in population D, they change to an active state, A, resulting in a more localised (Brownian) movement. Activation is described via binary interactions between I and D. Moreover, cell motion is represented as a velocity-jump process, with the running time of I following a long-tailed distribution, which is consistent with a Levy walk, and the running time of A following a Poisson distribution, which corresponds to Brownian motion. We formally show that the macroscopic limit of the model comprises a coupled system of balance equations for the one-particle distribution functions of populations I, D and A. The modelling approach presented here and its possible generalisations are expected to find applications in the study of the immune response to cancer and in other biological contexts in which switch from non-local to localised migration patterns occurs.
• [04647] Towards a new mathematical model of the visual cycle
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Cesare Biagio Alasio (Sorbonne UniversitéSorbonne Université)
  • Abstract : The visual cycle is a fundamental bio-chemical process allowing photoreceptors to convert light into electrical signals and return to the dark state. I will present a new mathematical model involving coupled ODEs and PDEs for the kinetics of retinal photo-sensitive molecules after light exposure. This reaction-diffusion-type model provides a first step in the study of the accumulation of toxic by-products in the eye in connection with retinal diseases such as age-related macular degeneration.
• [04418] Structured Model for the Size-spectrum Evolution in Aquatic Ecosystems
  • Format : Talk at Waseda University
  • Author(s) :
    • Laura Kanzler (CEREMADE - Université Paris-Dauphine)
  • Abstract : Trophic interactions between animals in the ocean were matter of interest since the 60’, where it was quickly discovered that the individuals’ body size acts as ’master trait’ in food webs of animals, giving rise to emergent distributions of biomass, abundance and production of organisms. We propose and investigate a deterministic jump-growth model of Boltzmann type, aiming to capture this emergence phenomenon in aquatic ecosystems. The equation of interest is derived from individual based dynamics governed by a stochastic process. Following the observation of the body mass being the crucial trait in these dynamics it is based on the assumption that binary interactions between individuals in the ecosystem take place: A predator feeding on a prey, which then results in growth of the predator with assimilating a certain (usually very small) amount of its prey’s mass as well as plankton production. Analytical results in various parameter regimes are discussed and numerical simulations underlying these observations are given.

MS [00752] Theory and efficient methods for large-scale structured optimization models

room : D408

• [01213] Augmented Lagrangian method for matrix optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Ding (Chinese Academy of Sciences)
  • Abstract : In this talk, we will introduce some new convergence results on the matrix optimization problems including nonlinear semidefinite programming and nonsmooth optimization on Riemannian manifold.
• [02195] Determinantal point processes for sampling minibatches in SGD
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rémi Bardenet (Université de Lille)
    • Subhroshekhar Ghosh (National University of Singapore)
    • Meixia Lin (Singapore University of Technology and Design)
  • Abstract : In this work, we contribute an orthogonal polynomial-based determinantal point process paradigm for performing minibatch sampling in SGD. Our approach leverages the specific data distribution at hand, which endows it with greater sensitivity and power over existing data-agnostic methods. We substantiate our method via a detailed theoretical analysis of its convergence properties, interweaving between the discrete data set and the underlying continuous domain. In particular, we show how specific DPPs and a string of controlled approximations can lead to gradient estimators with a variance that decays faster with the batchsize than under uniform sampling. Coupled with existing finite-time guarantees for SGD on convex objectives, this entails that, for a large enough batchsize and a fixed budget of item-level gradients to evaluate, DPP minibatches lead to a smaller bound on the mean square approximation error than uniform minibatches. Moreover, our estimators are amenable to a recent algorithm that directly samples linear statistics of DPPs without sampling the underlying DPP, thereby reducing computational overhead.
• [02194] Bregman Proximal Point Algorithm Revisited: A New Inexact Version and its Inertial Variant
  • Format : Talk at Waseda University
  • Author(s) :
    • Lei Yang (Sun Yat-Sen University)
    • Kim-Chuan Toh (National University of Singapore)
  • Abstract : In this talk, we focus on a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related problems arising in recent years. To solve this problem, we revisit the classic Bregman proximal point algorithm (BPPA) and introduce a new inexact stopping condition for solving the subproblems, which can circumvent the underlying feasibility difficulty often appearing in existing inexact conditions when the problem has a complex feasible set. Our inexact condition also covers several existing inexact conditions as special cases and hence makes our inexact BPPA (iBPPA) more flexible to fit different scenarios in practice. As an application to the standard optimal transport (OT) problem, our iBPPA with the entropic proximal term can bypass some numerical instability issues that usually plague the popular Sinkhorn's algorithm in the OT community. The iteration complexity of $O(1/k)$ and the convergence of the sequence are also established for our iBPPA under some mild conditions. Moreover, inspired by Nesterov's acceleration technique, we develop an inertial variant of our iBPPA, denoted by V-iBPPA, and establish the iteration complexity of $O(1/k^{\lambda})$, where $\lambda\geq1$ is a quadrangle scaling exponent of the kernel function. In particular, when the proximal parameter is a constant and the kernel function is strongly convex with Lipschitz continuous gradient (hence $\lambda=2$), our V-iBPPA achieves a faster rate of $O(1/k^2)$ just as existing accelerated inexact proximal point algorithms. Some preliminary numerical experiments for solving the standard OT problem are conducted to show the convergence behaviors of our iBPPA and V-iBPPA under different inexactness settings. The experiments also empirically verify the potential of our V-iBPPA for improving the convergence speed.
• [02388] On efficient and scalable computation of the nonparametric maximum likelihood estimator in mixture models
  • Format : Talk at Waseda University
  • Author(s) :
    • Yangjing ZHANG (Chinese Academy of Sciences)
    • Ying Cui (University of Minnesota)
    • Bodhisattva Sen (Columbia University)
    • Kim-Chuan Toh (National University of Singapore)
  • Abstract : The nonparametric maximum likelihood estimation is a classic and important method to estimate the mixture models from finite observations. In this talk, we propose an efficient semismooth Newton based augmented Lagrangian method (ALM). By carefully exploring the structure of the ALM subproblem, we show that the computational cost of the generalized Hessian is independent of the number of grid points. Extensive experiments are conducted to show the effectiveness of our approach.

MS [00357] Topics at the Interface between Applied mathematics and Microeconomics

room : D501

• [01659] Commitment games with mutual interferences
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryosuke Ishii (Shimonoseki City University)
  • Abstract : As a stabilization device of an efficient outcome that is not an equilibrium as it now stands outcome, commitments have been assembled in game theory literature. Earlier studies suggest that efficient outcomes are subgame perfect if a game is expressed by an extensive form with a perfect information. However, an outcome of a game with simultaneous moves is not always efficient, most often happen when players face a prisoners' dilemma like situation. This research considers a game in which players can determine success or failure of other players' commitment one another. The result is similar to a Folk Theorem. That is, players can achieve efficiency in prisoners' dilemma games. In contrast, the worst mixed equilibrium outcome is subgame perfect in coordination games.
• [01666] Equilibria in a spatial competition with uninformed consumers
  • Format : Talk at Waseda University
  • Author(s) :
    • Kuninori Nakagawa (University of Hyogo)
    • Shinnosuke Kawai (Shizuoka University)
  • Abstract : We extend a model that analyses explicit product differentiation in Varian's model of sales using a one-dimensional spatial competition framework. We study the price equilibrium in the case of a uniform distribution of informed consumers. We give examples of price game equilibria given pairs of locations and discuss the difficulties associated with computing equilibria.
• [01655] Gradient flows in travelers’ visitation network: comparison with centrality indices
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yujiro Kawasaki (Nagoya Institute of Technology)
    • Kenta Kojima (Kansai University)
    • Jun'ichi Miki (Tohoku University of Community Service and Science)
  • Abstract : The Hodge decomposition defined on discrete graphs has been applied to analyzing network structures related to various economic activities. We use the travel data of tourists visiting a regional city in Japan to examine the effectiveness of the Hodge decomposition on the network of tourist movements between sightseeing spots. By employing centrality indices together, we provide robust trends of tourist visits and, thus, the function of each sightseeing spot.
• [01678] Information Design and Pre-trade Investment
  • Format : Online Talk on Zoom
  • Author(s) :
    • Keiichi Kawai (Keio University)
  • Abstract : We analyze a bilateral trade model where, after the buyer makes a take-it-or-leave-it offer, the seller can make a costly investment which stochastically increases the value of the good to both players. The seller partially learns about the investment outcome before deciding whether to trade. The efficiency of the outcome is undermined by both the adverse selection problem in trade, and the seller’s moral hazard in investment. We identify all second-best outcomes.

MS [01671] Financial Modeling

room : D502

MS [00715] Recent Trends in Market Design

room : D505

• [01399] Best of Both Worlds in Fair Division
  • Format : Talk at Waseda University
  • Author(s) :
    • Rohit Vaish (IIT Delhi)
  • Abstract : Traditional approaches for fair allocation of indivisible resources focus either on randomized allocations that are fair in expectation or deterministic allocations that are approximately fair. I will discuss an algorithmic framework that reconciles randomization and approximation. Specifically, I will present an algorithm for finding a randomized allocation of indivisible goods that is ex-ante fair, i.e., envy-free in expectation, and ex-post approximately fair, i.e., envy-free up to one good. https://arxiv.org/abs/2005.14122 https://arxiv.org/abs/2004.02554
• [01408] Strong Revenue (Non-)Monotonicity of Single-parameter Auctions
  • Format : Talk at Waseda University
  • Author(s) :
    • Ziyun Chen (Tsinghua University)
    • Zhiyi Huang (The University of Hong Kong)
    • Dorsa Majdi (Sharif University of Technology)
    • Zipeng Yan (The University of Hong Kong)
  • Abstract : Consider Myerson’s optimal auction with respect to an inaccurate prior, e.g., estimated from data, which is an underestimation of the true value distribution. Can the auctioneer expect getting at least the optimal revenue w.r.t. the inaccurate prior since the true value distribution is larger? This so-called strong revenue monotonicity is known to be true for single-parameter auctions when the feasible allocations form a matroid. We find that strong revenue monotonicity fails to generalize beyond the matroid setting, and further show that auctions in the matroid setting are the only downward-closed auctions that satisfy strong revenue monotonicity. On the flip side, we recover an approximate version of strong revenue monotonicity that holds for all single-parameter auctions, even without downward-closedness. As applications, we get sample complexity upper bounds for single-parameter auctions under matroid constraints, downward-closed constraints, and general constraints. They improve the state-of-the-art upper bounds and are tight up to logarithmic factors.
• [01530] Representation Theorems for Path-Independent Choice Rules
  • Format : Talk at Waseda University
  • Author(s) :
    • Koji Yokote (The University of Tokyo)
    • Isa E. Hafalir (University of Technology Sydney)
    • Fuhito Kojima (The University of Tokyo)
    • M. Bumin Yenmez (Boston College)
  • Abstract : Path independence is arguably the most important property of choice rules in market design. For example, it guarantees the existence of a desirable matching in two-sided markets. We show that a choice rule is path independent if and only if it is rationalized by a valuation function satisfying ordinal concavity. We also provide a representation result for choice functions that satisfy path independence and the law of aggregate demand using valuation functions satisfying ordinal concavity.
• [01261] Fair division algorithms for house chores
  • Format : Talk at Waseda University
  • Author(s) :
    • Ayumi Igarashi (The University of Tokyo)
  • Abstract : Couples often encounter the challenge of sharing house chores. This raises the fundamental question of how to divide chores. In this paper, we present a new application for a fair division of household chores. Our platform, called Kajibuntan, allows couples to specify the set of chores to be shared, their preferences over them, and the current allocation. Our tool visualizes the current allocation and makes proposals according to their preferences based on the theory of fair division. The goal of our tool is to provide a systematic and transparent system to divide household chores and help creating harmony in the home.

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

room : D514

• [02892] Skew Brownian Motion with Two-Valued Drift
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaowen Zhou (Concordia University)
  • Abstract : We consider a skew Brownian motion with two-valued drift as the unique solution to the following SDE dX_t=\big(\mu_- 1_{\{X_ta\}}\big)dt +dB_t+\beta dL^a_t(X), where $\mu_-$ and $\mu_+ $ are constants, $-1<\beta<1$, $B$ is a Brownian motion and $L^a_t(X)$ denotes the symmetric local time for $X$ at level $a$. Such a process can be identified as a regime switching model depending on whether the process $X$ takes values above or below level $a$. In this talk we present some properties for such processes and discuss an optimization problem that is motivated by the optimal dividend problem for risk processes. This talk is based on joint work with Zhongqin Gao.
• [02928] Pathwise uniqueness of SDEs driven by stable processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Tsukada (Kagoshima University)
  • Abstract : We consider one-dimensional stochastic differential equations (SDEs) driven by strictly stable processes. In this talk, we give some non-Lipschitz conditions on diffusion and drift coefficients under which the pathwise uniqueness of solutions to the SDEs is established. Moreover, we provide sufficient conditions for the non-contact property of strong solutions to the SDEs with different initial values.
• [05583] Mean field portfolio games
  • Format : Talk at Waseda University
  • Author(s) :
    • Guanxing Fu (The Hong Kong Polytechnic University)
  • Abstract : We study mean field portfolio games, which is proved to be equivalent to an (F)BSDE, by martingale optimality principle and dynamic programming principle. A key implication is the uniqueness result of the game. Closed form solution is possible under stronger assumptions. If time permits, I will introduce possible extensions.
• [03375] A mean-field version of Bank--El Karoui’s representation of stochastic processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaolu Tan (The Chinese University of Hong Kong)
  • Abstract : We investigate a mean-field version of Bank--El Karoui's representation theorem of stochastic processes. Under different technical conditions, we established some existence and uniqueness results. As motivation and first applications, the results of mean-field representation provide a unified approach for studying various mean-field games (MFGs) in the setting with common noise and multiple populations, including the MFG of timing and the MFG with singular control, etc. As a crucial technical step, a stability result was provided on the classical Bank--El Karoui’s representation theorem. It has its own interests and other applications, such as deriving the stability results of optimizers (in the strong sense) for a class of optimal stopping and singular control problems.

contributed talk: CT192

room : D515

[02459] Functional ODE observers for DAE control systems

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D515
• Type : Contributed Talk
• Abstract : Many control systems have essential features, which can only be expressed if system dynamics is described by simultaneous differential and algebraic equations (DAEs). For example, the classical state space models, governed only by ordinary differential equations (ODEs), cannot adequately treat impulses that occur in electrical circuits. This talk is devoted to the problem of designing functional observers for linear DAEs. A new and milder sufficient condition for functional observers is proved.
• Classification : 93B53, 93B07, 93A10, 93C99, 93D05
• Format : Talk at Waseda University
• Author(s) :
  • Nutan Kumar Tomar (Indian Institute of Technology Patna)
  • Juhi Jaiswal (Indian Institute of Technology Madras)
  • Pabitra Kumar Tunga (Indian Institute of Technology Patna)

[00415] Finite time horizon mixed control of vibrational systems

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D515
• Type : Contributed Talk
• Abstract : We consider a vibrational system control problem over a finite time horizon. The performance measure of the system is taken to be $p$-mixed $H_2$ norm which generalizes the standard $H_2$ norm. Our novel procedure efficiently takes into account the structure of the vibrational system. An objective function is represented in terms of integrals which are solved using adaptive quadrature rules. We illustrate our approach by numerical examples concerning an $n$-mass oscillator with one damper.
• Classification : 93C05, 93C15, 74D99, 70Q05
• Format : Talk at Waseda University
• Author(s) :
  • Zoran Tomljanovic (University of Osijek, Department of Mathematics)
  • Ivica Nakic (epartment of Mathematics, University of Zagreb)
  • Marinela Pilj Vidakovic (University of Osijek, Department of Mathematics)

[00348] Design of control for IT2 fuzzy stochastic systems with multi disturbances

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @D515
• Type : Contributed Talk
• Abstract : Anti disturbance control design problem is proposed for a class of interval type-2 fuzzy stochastic systems subject to uncertainty and multiple disturbances. A fuzzy exogenous system considers a new fuzzy disturbance observer to precisely evoke the properties of interval type 2 fuzzy stochastic models with multiple disturbances. In order to ensure the stochastic stability of the closed-loop fuzzy system, a new sufficient condition is constructed using the method of linear matrix inequalities by integrating the $\textit{Ito}$ operator and choosing the appropriate Lyapunov-Krasovskii functional candidate dissipativity performance index. Finally, the provided theory is demonstrated with the example.
• Classification : 93Bxx, 93Exx, 93Dxx
• Format : Online Talk on Zoom
• Author(s) :
  • Aarthi Subramanian (Research Scholar, Anna University Regional Campus Coimbatore)
  • Marshal Anthoni S (Anna University Regional Campus Coimbatore)

contributed talk: CT187

room : A201

[01964] Competitions between stage-structured species in a patchy environment

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @A201
• Type : Contributed Talk
• Abstract : In this study, an ecological model with two life stages, immature and mature, and incorporating both intra- and inter-competitions between two species is explored to study invasion of species in a two-patch environment. It can be applied to exploring evolution of insects like Drosophila and beetles, which experience larva and adult (immature and mature life stages). The monotone dynamics in such a model provides us a property to explore its local and global dynamics. The model can also admit complex dynamics with multiple positive equilibria and limit point bifurcation when both species persist.
• Classification : 92D25, 92D40, 37N25
• Format : Talk at Waseda University
• Author(s) :
  • Chang-Yuan Cheng (National Pingtung University National Pingtung University)

[01854] Dynamic Roughness in the Term Structure of Oil Markets Volatility

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @A201
• Type : Contributed Talk
• Abstract : This paper analyses the attributes and the significance of the roughness of oil market volatil- ity. We employ unspanned stochastic volatility models driven by rough Brownian motions that yield semi-analytic prices for futures options entailing efficient calibration applications. We calibrate option prices written on oil futures and provide empirical evidence of the dy- namic nature of the roughness in oil volatility. The calibrated option-implied Hurst param- eter varies over time, but rough stochastic volatility models provide a better fit to the term structure of implied oil volatility compared to classical stochastic volatility. Furthermore, including the Hurst parameter into the set of implied parameters benefits the stability of the calibrated parameters and improves pricing performance.
• Classification : 91Gxx, 60Lxx, 60Hxx
• Format : Talk at Waseda University
• Author(s) :
  • Christina Nikitopoulos (UTS)
  • Messias Alfeus (Stellenbosch University)
  • Ludger Overbeck (Justus-Liebig-University Giessen)

[00205] `Period doubling' induced by optimal control in a behavioral SIR epidemic model.

• Session Time & Room : 2E (Aug.22, 17:40-19:20) @A201
• Type : Contributed Talk
• Abstract : We consider a behavioral SIR epidemic model to describe the action of the public health system aimed at enhancing the social distancing during an epidemic outbreak. An optimal control problem is proposed where the control acts in a specific way on the contact rate. We show that the optimal control of social distancing is able to generate a period doubling–like phenomenon. Namely, the ‘period’ of the prevalence is double the ‘period’ of the control, and an alternation of small and large peaks of disease prevalence can be observed.
• Classification : 92D30, 34C60, 93C15
• Format : Online Talk on Zoom
• Author(s) :
  • Sileshi Sintayehu Sharbayta (Addis Ababa University)
  • Bruno Buonomo (University of Naples Federico II)
  • Alberto d'Onofrio (University of Trieste)
  • Tadesse Abdi (Addis Ababa University)

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

room : A206

• [04485] Constrained Optimal Sensing for Nuclear Digital Twins
  • Format : Talk at Waseda University
  • Author(s) :
    • Krithika Manohar (University of Washington)
  • Abstract : We develop a constrained optimization for sensor placement in nuclear digital twins where sensing capability may be severely constrained or limited. These constraints may arise in certain areas of a reactor due to hostile operating conditions, accessibility issues, and physical limitations on sensing capability. Our data-driven method optimizes sensor placement with constraints for full flow field reconstruction, leveraging reduced order models of flow physics. We demonstrate the technique is near optimal using empirical and theoretical validation and provide uncertainty analyses for noisy sensor measurements. The method is demonstrated on a nuclear fuel rod prototype which is heated to mimic the neutronics effect of nuclear fuel within the Transient Reactor Test facility (TREAT) at Idaho National Laboratory.
• [03365] Exploring security challenges in enhancing Digital Twins capabilities with ChatGPT
  • Format : Talk at Waseda University
  • Author(s) :
    • Xingheng Liu (NTNU)
    • Shen Yin (NTNU)
    • Jie Liu (NTNU)
    • Jørn Vatn (NTNU)
    • Asmae Bni (NTNU)
  • Abstract : Digital twins offer valuable insights for monitoring and managing physical systems. With the upsurge of ChatGPT, integrating it with digital twins during the design or operation phase could unlock new capabilities. However, this integration may introduce new security challenges and vulnerabilities. In this talk, we will briefly discuss the potential of enhancing digital twins with ChatGPT and the associated security concerns, emphasizing the importance of addressing these issues to ensure robust, secure DTs.
• [04925] Reduced order modelling for large-scale CFD
  • Format : Talk at Waseda University
  • Author(s) :
    • Zoltán Horváth (Széchenyi István University)
    • Mátyás Yves Constans (Széchenyi István University)
  • Abstract : The RedSim in-house reduced-order modeling (ROM) software for the 3D compressible Euler and Navier-Stokes equations is introduced. RedSim’s core consists of a finite volume code running on GPUs and the proper orthogonal decomposition-based ROM-module. The application of RedSim to digital twinning for urban air pollution (in HiDALGO2 EuroHPC Centre of Excellence) and an acoustics problem in the automotive industry are presented. Numerical experiments raise mathematical challenges, which will be presented and some of them solved.
• [04687] Comparison of physics-based and data-driven surrogate models of a gas-bearings supported rotor
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dimitri Goutaudier (EPFL)
    • Jürg Schiffmann (EPFL)
    • Fabio Nobile (EPFL)
  • Abstract : Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have several advantages over traditional lubricated bearings but they more complex to operate and exhibit nonlinear behaviors. In this contribution, we present physics-based and data-driven frameworks to compute the dynamics of a gas-bearings supported rotor operating at very high rotation speeds. We compare the numerical performances of the two approaches, and we propose research directions to improve the models.

MS [02012] Splitting Optimization: Theory, Methodology and Application

room : A207

• [02878] Decentralized Entropic Optimal Transport for Privacy-preserving Distributed Distribution Comparison
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiangfeng Wang (East China Normal University)
  • Abstract : Privacy-preserving distributed distribution comparison measures the distance between the distributions whose data are scattered across different agents in a distributed system and cannot be shared among the agents. In this study, we propose a novel decentralized entropic optimal transport (EOT) method, which provides a privacy-preserving and communication-efficient solution to this problem with theoretical guarantees. In particular, we design a mini-batch randomized block-coordinate descent (MRBCD) scheme to optimize the decentralized EOT distance in its dual form. The dual variables are scattered across different agents and updated locally and iteratively with limited communications among partial agents. The kernel matrix involved in the gradients of the dual variables is estimated by a distributed kernel approximation method, and each agent only needs to approximate and store a sub-kernel matrix by one-shot communication and without sharing raw data. We analyze our method's communication complexity and provide a theoretical bound for the approximation error caused by the convergence error, the approximated kernel, and the mismatch between the storage and communication protocols. Experiments on synthetic data and real-world distributed domain adaptation tasks demonstrate the effectiveness of our method.
• [02881] An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenxing Zhang (University of Electronic Science and Technology of China)
  • Abstract : Primal-dual hybrid gradient method (PDHG) is a canonical and popular prototype for solving saddle point problem (SPP). However, the nonlinear coupling term in SPP excludes the application of PDHG on far-reaching real-world problems. In this talk, we devise a variant iterative scheme for solving SPP with nonlinear function by exerting an alternative extrapolation procedure. Under the metrically regular assumption on KKT mapping, we simplify the local convergence of the proposed method on contractive perspective. Numerical simulations on a PDE-constrained nonlinear inverse problem and parametric blind deconvolution demonstrate the compelling performance of the proposed method.
• [02882] A balanced Douglas-Rachford splitting algorithm for convex minimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Xingju Cai (Nanjing Normal University)
  • Abstract : The Douglas-Rachford algorithm is a classical and effective splitting method to solve the inclusion problems. Recently, an adaptive Douglas-Rachford splitting algorithm is proposed for the monotone inclusion, which allow one operator be weakly monotone. We apply the idea of adaptive Douglas-Rachford splitting method (ADRSM) to differentiable convex optimization problems with abstract constraints, and more attractive results can be obtained for the convex optimization problem. We propose accurate and inaccurate versions of the algorithm respectively, and prove the global convergence of the algorithms. We extend these results to two separable convex optimization problems with linear constraints. In numerical experiments, we compare our algorithms with other commonly used algorithms and the results verify the effectiveness of our algorithms.
• [02904] A projection-like method for quasimonotone variational inequalities without Lipschitz continuity
  • Format : Talk at Waseda University
  • Author(s) :
    • Lingling Xu (Nanjing Normal University)
    • Xiaoxi Jia (Institute of Mathematics, University of würzburg,)
  • Abstract : For most projection methods, the operator of a variational inequality problem is assumed to bemonotone (or pseudomonotone) and Lipschitz continuous. In this paper, we present a projection-like method to solve quasimonotone variational inequality problems without Lipschitz continuity. Under some mild assumptions, we prove that the sequence generated by the proposed algorithm converges to a solution. Numerical experiments are provided to show the effectiveness of the method.

CSIAM

room : A208 -> D604 (changed)

[EM009] Semantic Information Theory: Where Shannon Meets Gardner

• Session Date & Time : 2E (Aug.22, 17:40-19:20) @A208
• Type : Talk in Embedded Meeting
• Abstract : With the development of information technologies, we need to explore level-2 information theory, which is named semantic level in Weaver and Shannon’s pioneer work. In this talk, we will first survey some results in reliable communication problem and Shannon capacity. Then, the semantic communication problem will be discussed, where the generalized Gardner capacity will be proposed as the core concept. In the last part, we will introduce our work on graphon entropy for computational semantics.
• Format : Talk at Waseda University
• Author(s) :
  • Bo Bai (Huawei Technology, Co., Ltd.)
  • Tianqi Hou (Huawei Technology, Co., Ltd.)
  • Xueyan Niu (Huawei Technology, Co., Ltd.)
  • Lei Deng (Huawei Technology, Co., Ltd.)

[EM010] Data- and Model-Driven Approaches for Computational Imaging

• Session Date & Time : 2E (Aug.22, 17:40-19:20) @A208
• Type : Talk in Embedded Meeting
• Abstract : Computational imaging, crucial for observing and understanding the natural world, traditionally involved three distinct components: image sensing, reconstruction, and analysis. This talk explores the shift towards their integration, powered by advancements in machine learning, particularly deep learning. The focus is on integrating traditional image reconstruction algorithms with deep learning, enabling data-driven and task-driven imaging algorithms for a holistic approach. The significance and future of computational imaging in life sciences and medicine research is also discussed.
• Format : Talk at Waseda University
• Author(s) :
  • Bin Dong (Peking University)

[EM011] Decentralized Optimization Over the Stiefel Manifold

• Session Date & Time : 2E (Aug.22, 17:40-19:20) @A208
• Type : Talk in Embedded Meeting
• Abstract : We study the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network. The objective is an average of d local functions, which are privately held by d agents in the network. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. Our algorithm DESTINY only invokes a single round of communications per iteration and has guaranteed convergence and promising numerical performance.
• Format : Talk at Waseda University
• Author(s) :
  • Xin Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Lei Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

[EM012] Diversified sample selection via predictive inference

• Session Date & Time : 2E (Aug.22, 17:40-19:20) @A208
• Type : Talk in Embedded Meeting
• Abstract : We consider how to obtain informative individuals that are characterized by their unobserved responses with a given budget. We propose an optimal subsampling procedure that can maximize the diversity of the selected subsample and control the false selection rate simultaneously, allowing us to explore reliable information as much as possible. Further, we extend the algorithm to the online setting, where one encounters a possibly infinite sequence of individuals collected by time with covariate information available.
• Format : Talk at Waseda University
• Author(s) :
  • Xiaoyang Wu (Nankai University)
  • Yuyang Huo (Nankai University)
  • Haojie Ren (Shanghai Jiao tong University)
  • Changliang Zou (Nankai University)
  
  
  

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  MS [02440] Advances in Optimization I

  room : A502

  • [04479] Breaking the quadratic gap for strongly polynomial solvers to combinatorial linear programs
    • Format : Talk at Waseda University
    • Author(s) :
      • Bento Natura (Georgia Tech)
    • Abstract : Recent years have seen tremendous progress in high-accuracy solvers for Maximum Flow, Minimum-Cost Flow and general Linear Programs (LP). Progress on strongly polynomial solvers for combinatorial LP on the other hand has stalled. For combinatorial LP beyond directed graphs this gap between exact and high-accuracy solvers is currently quadratic. We finally break the quadratic gap and design a strongly polynomial interior-point-method for combinatorial LP, which reduces the gap to only a linear factor.
  • [03172] Computational challenges in Flag Algebra proofs
    • Format : Talk at Waseda University
    • Author(s) :
      • Aldo Kiem (Zuse Institute Berlin)
      • Sebastian Pokutta (ZIB / TUB)
      • Christoph Spiegel (Zuse Institute Berlin)
    • Abstract : Introduced by Razborov in 2007, flag algebras are a potent tool for computer-assisted proofs in extremal combinatorics. They combine first-order logic, model theory, and semidefinite programming to tackle classical Turán and Ramsey theory problems. This talk explores computational challenges, symmetry exploitation, and optimization ideas to broaden the method's scope. We'll demonstrate its practical application by determining the 4-color Ramsey multiplicity of triangles.
  • [03673] Improving Lower Bounds for Large Scale QAPs
    • Format : Talk at Waseda University
    • Author(s) :
      • Koichi Fujii (tokyo institute of technology)
    • Abstract : We report our progress on the project for solving large scale quadratic assignment problems (QAPs). Our main approach to solve QAPs is a parallel branch-and-bound method using the Ubiquity Generator framework (UG), utilizing Newton-bracketing method to solve doubly nonnegative cone (DNN) relaxations. In this talk, we present some preliminary numerical results of DNN-based branch-and-bound method and report the result that we have succeeded to update the lower bounds of instances in QAPLIB.
  • [03941] Closing Nonzero Duality Gaps in SDPs through Perturbations
    • Format : Talk at Waseda University
    • Author(s) :
      • Takashi Tsuchiya (National Graduate Institute for Policy Studies)
      • Bruno Lourenço (Institute of Statistical Mathematics)
      • Masakazu Muramatsu (The University of Electro-Communication)
      • Takayuki Okuno (Seikei University)
    • Abstract : Consider a primal-dual pair of SDP with nonzero duality gap. There are arbitrary small perturbations to make the pair strongly feasible with a common primal-dual optimal value $v$, say, zeroing duality gap. $v$ is not well-defined at zero (unperturbed problem) since the primal and dual have different optimal values, but it is continuous elsewhere. We analyze properties of $v$ around zero to demonstrate a few surprising and beautiful properties and establish connections to interior-point methods.
  
  
  

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  MS [02545] Challenges and Recent Advances in Phylogenetics

  room : A508

  • [04303] Phylogenetic X-cactuses
    • Format : Talk at Waseda University
    • Author(s) :
      • Taoyang Wu (University of East Anglia)
    • Abstract : In this talk we discuss X-cactus, a type of phylogenetic network which is essentially a cactus graph in which some vertices are labelled by elements from a set X of species. In this talk, we present a way to encode X-cactuses in terms of certain collections of X-partitions, and discuss a partial order on the set of X-cactuses, including an analysis of some properties of its least upper and greatest lower bounds.
  • [05034] On the Sackin index of galled trees
    • Format : Talk at Waseda University
    • Author(s) :
      • Michael Fuchs (National Chengchi University)
      • Bernhard Gittenberger (TU Wien)
    • Abstract : We will compute the Sackin index of some classes of phylogenetic networks that belong to so-called galled trees. In particular, we consider level-1 networks as well as the closely related one-component galled trees. The Sackin index is the sum of the vertex heights. The method we approach the problem is specifying the networks in terms of combinatorial structures and performing a singularity analysis on the resulting generating functions.
  • [04250] Distribution of patterns in ranked tree-child networks
    • Format : Talk at Waseda University
    • Author(s) :
      • Michael Fuchs (National Chengchi University)
      • Hexuan Liu (National Sun Yat-sen University )
      • Tsan-Cheng Yu (National Chengchi University)
    • Abstract : In this talk, I will first review tree-child networks and ranked tree-child networks (RTCN), and then explain our results on the distributional behavior of certain patterns in random RTCNs. These results extend the limit law for cherries and give rise to a conjecture for general patterns. This is the first such study for a class of phylogenetic networks.
  • [04323] Counting phylogenetic networks with the component graph method
    • Format : Talk at Waseda University
    • Author(s) :
      • Michael Fuchs (National Chengchi University)
    • Abstract : The component graph method was proposed by Louxin Zhang in order to solve algorithmic problems for tree-child networks, galled networks, reticulation-visible networks and extensions. Moreover, the method was also used to obtain exact counting results of the number of networks with n leaves and k reticulations. In this talk, we will explain how we used the method to prove asymptotic counting results for tree-child networks with a fixed number of reticulation nodes and galled networks.
  
  
  

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  MS [00286] Low-Reynolds-number swimming: modelling, analysis and applications

  room : A510

  • [03303] Nonlinear dynamics, bifurcations and stability transitions in motion of periodically-actuated micro-swimmers
    • Format : Online Talk on Zoom
    • Author(s) :
      • Yizhar Or (Mechanical Engineering, Technion)
    • Abstract : We study simple models of robotic-like microswimmers with periodic actuation. We start from the well-known Purcell’s three-link swimmer model, and modify it in order to add realistic effects of passive elasticity and/or mechanical actuation, rather than kinematic control. We also focus on minimal models of magnetically-actuated microswimmers. We show that the nonlinear dynamics of such models include bifurcations and stability transitions of periodic solutions, which can be analyzed both numerically and analytically using asymptotic methods.
  • [05278] Low-Reynolds-number swimming via reinforcement learning
    • Format : Online Talk on Zoom
    • Author(s) :
      • Alan C. H. Tsang (University of Hong Kong)
      • Yangzhe Liu (University of Hong Kong)
      • Zonghao Zou (Cornell University)
      • Ali Gurbuz (Santa Clara University)
      • On Shun Pak (Santa Clara University)
    • Abstract : The application of machine learning methods in the development of microswimmers has garnered significant interest recently. In particular, reinforcement learning has proven to be valuable in empowering microswimmers to learn effective propulsion strategies through their interactions with the environment. In this talk, we will discuss our latest progress in integrating reinforcement learning techniques into the design of smart microswimmers capable of performing complex tasks relevant to their biomedical applications.
  • [03505] Controllability of microswimming systems with and without drift
    • Format : Talk at Waseda University
    • Author(s) :
      • Clement Moreau (RIMS, Kyoto University)
    • Abstract : In this talk, I will discuss the controllability properties of microswimmer models, i.e. their capacity to reach a given target, depending on important assumptions such as the way the swimmer's deformation is controlled and its environment. I will focus on the example of a magneto-elastic swimmer to present a result on the local controllability of control-affine systems with a drift.
  • [03844] Recent trends in micro-swimming
    • Format : Talk at Waseda University
    • Author(s) :
      • Marta Zoppello (Politecnico di Torino)
      • Marco Morandotti (Politecnico di Torino - P. IVA 00518460019)
    • Abstract : Inertialess hydrodynamics is notorious for its time-reversibility constraint, which leads to the well known "Scallop Theorem”. One way to overcome it is to couple two or more micro-swimmer units. In this talk we will show some recent results about the controllability of more than one micro-swimmer immersed in a viscous fluid, highlighting the crucial role of hydrodynamic interaction in achieving it.
  
  
  

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

  room : A511

  • [01465] Screening cell-cell communication in spatial transcriptomics via collective optimal transport
    • Author(s) :
      • Yanxiang Zhao (George Washington University)
    • Abstract : Spatial transcriptomic technologies and spatially annotated single cell RNA-sequencing (scRNA-seq) datasets provide unprecedented opportunities to dissect cell-cell communication (CCC). How to incorporate the spatial constraints and other physical processes when inferring CCC computationally remains a major challenge. Here we present COMMOT to infer CCC in spatial transcriptomics accounting for the competition among different ligand and receptor species and cells or spots, and enforcing spatial constraints. A novel collective optimal transport method is developed to handle these complex interactions and constraints. Further downstream analysis tools on spatial signaling directions and signaling-regulated genes are then developed using machine learning models. We validate the method with simulation data and one spatially annotated scRNA-seq dataset. We show that COMMOT effectively infers spatial CCC using datasets by three popular spatial transcriptomic technologies. Finally, COMMOT reveals connections between CCC and skin development in a case study of human epidermal development. The method will have broad application in uncovering ligand-receptor mediated CCC using spatial genomics datasets.
  • [04188] A Novel Tool for Enhanced Single-cell RNA Sequencing Data Preprocessing and Dimensionality Reduction
    • Author(s) :
      • Hyun Kim (Institute for basic science)
      • JaeKyoung Kim (Korea Advanced Institute of Science and Technology, Institute for basic science)
      • Jong-Eun Park (Korea Advanced Institute of Science and Technology)
      • Minseok Seo (Korea University)
    • Abstract : Single-cell RNA sequencing (scRNA-seq) has revolutionized various cellular research applications, including cellular phenotyping and gene regulatory network reconstruction. However, data analysis remains challenging due to sparsity, high dimensionality, bias, skewed data distribution, and technological noise. In addition, conventional preprocessing methods, such as log-normalization and user-driven dimensionality reduction techniques, often introduce subjectivity and signal distortion, leading to decreased data dimension accuracy. To address these limitations, we developed a novel tool that effectively filters out data noise and corrects signal distortion during preprocessing. This approach significantly improves the accuracy of dimensionality reduction and overcomes the drawbacks associated with current methodologies. Our solution was tested on 53 real and simulated datasets and demonstrated superior performance compared to ten widely-used tools, including Seurat, Scanpy, and Monocle3. The enhanced performance of our tool offers promise for advancing scRNA-seq data analysis and facilitating more accurate downstream analyses.
  • [00602] Adaptive immune discrimination of antigen risks by predictive coding
    • Author(s) :
      • Kana Yoshido (Graduate School of Biostudies, Kyoto University)
      • Honda Naoki (Graduate School of Integrated Sciences for Life, Hiroshima University)
    • Abstract : Immune system induces appropriate responses depending on the risk of antigens: Strong responses to harmful antigens and weak or no responses to harmless antigens. To reveal the mechanism, we modeled T cell population dynamics with memory formation based on predictive coding. By the simulation, we found antigen concentration- and input rapidness- dependent discrimination between harmful and harmless antigens. Furthermore, we reproduced temporal change of discrimination as seen in the onset and therapy of allergy.
  
  
  

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  MS [00794] Mathematical Modelling and Disease

  room : A512

  • [01627] Transboundary management of ecological systems with applications to diseases
    • Format : Talk at Waseda University
    • Author(s) :
      • Julie Blackwood (Williams College)
    • Abstract : Human migration and infectious diseases often span multiple administrative jurisdictions that might have different systems of government and management objectives. I'll introduce two examples in which spatial coordination may be critical for disease control. First, I’ll demonstrate that spatial interactions of vampire bats likely play a key role in driving rabies persistence. Second, I’ll describe a more general infectious disease in humans and show that successful management may depend on the actions of multiple managers.
  • [04446] Separating Populations in Flow Cytometry Experiments: A Probabilistic Approach
    • Format : Talk at Waseda University
    • Author(s) :
      • Danielle J Middlebrooks (National Institute of Standards and Technology)
    • Abstract : Flow cytometry (FC) is used in many areas of clinical testing, measuring cell characteristics of roughly one million cells. Data analysis is critical for interpreting FC measurements, but traditional techniques are often time-consuming and subjective. Our methodology identifies an unknown population by constructing probability density functions of specific biomarker expression levels in a sample. Once we estimate the unknown distribution, we compute the relative fraction of the unknown population and estimates of the uncertainty.
  • [04840] Case Studies in Modeling and Optimization for Diagnostics
    • Format : Talk at Waseda University
    • Author(s) :
      • Prajakta Purushottam Bedekar (National Institute of Standards and Technology)
      • Paul Patrone (National Institute of Standards and Technology)
      • Anthony Kearsley (National Institute of Standards and Technology)
    • Abstract : We demonstrate that modeling and optimization are crucial tools for interpretation of diagnostic measurements through case studies. First we model the errors in dilution and find a best-fit to minimize variability of biological antibody measurements, enabling us to compare results across experiments. Secondly, we use optimal decision theory to develop a time-dependent, probabilistic classification and adaptive prevalence estimation scheme using antibody testing measurements. We demonstrate the results by using SARS-CoV-2 datasets.
  • [03298] Optimal Bandwith Selection in Bio-FET Measurements
    • Format : Talk at Waseda University
    • Author(s) :
      • Luis Melara (Shippensburg University)
    • Abstract : The use of stochastic regression to separate signal from noise produced by Bio-FETs will be discussed in this talk. The noise realized by BioFETs interferes with quantitative and qualitative analysis, thus determining optimal bandwidth associated with experimental Bio-FET data measurements is an important task. Presented results suggest consistent across aspect rations and a choice of stochastic regression kernel function and yield what appear to be good results.
  
  
  

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  MS [02537] Structured Low-Rank Matrices and Their Applications

  room : A601

  • [05551] Dynamic Rupture Simulation Using FDP Method Accelerated by Lattice H-matrices
    • Author(s) :
      • Takumi Miyajima (The University of Tokyo)
      • Akihiro Ida ( Japan Agency for Marine-Earth Science and Technology )
      • Ryosuke Ando (The University of Tokyo)
    • Abstract : Dynamic rupture simulation with the spatiotemporal boundary integral equation method requires N × N dense matrices in a naive method. In order to reduce the memory consumption and computational cost, we propose a new approximation method called “FDP=LH matrices method” by incorporating travel time approximation into H matrices. In this minisymposium, we will talk about the algorithm and simulation results.
  
  
  

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  MS [00420] Painlevé equations, Applications, and Related Topics

  room : A617

  • [04366] On the bilinear equations of the Painlev\'e transcendents
    • Format : Talk at Waseda University
    • Author(s) :
      • Hidetaka Sakai (University of Tokyo)
      • Tatsuya Hosoi (University of Tokyo)
    • Abstract : The sixth Painlev\'e equation is a basic equation with three fixed singular points, corresponding to Gauss's hypergeometric differential equation among linear equations. Similar to hypergeometric equation, for nonlinear equations, we would like to determine the equation from the local behavior around the three singularities. In this talk, the sixth Painlev\'e equation is derived by imposing the condition that it is of type (H) at each three singular points for quadratic 4th-order differential equation.
  • [04932] Large-degree asymptotics of Generalized Hastings-McLeod functions
    • Format : Talk at Waseda University
    • Author(s) :
      • Robert Buckingham (University of Cincinnati)
    • Abstract : The Generalized Hastings-McLeod functions form an infinite sequence of solutions to the inhomogeneous Painleve-II equation. The functions have recently arisen in a variety of random matrix and interacting particle system problems. Using Riemann-Hilbert analysis and the nonlinear steepest-descent method, we establish the leading-order asymptotic behavior inside and outside the pole region as the inhomogeneous term tends to infinity. This is joint work with Kurt Schmidt.
  • [04515] Spaces of initial values for equations with the quasi-Painleve property
    • Format : Online Talk on Zoom
    • Author(s) :
      • Thomas Kecker (University of Portsmouth)
    • Abstract : Considering differential equations and Hamiltonian systems with the property that all movable singularities of all their solutions in the complex plane are algebraic poles (quasi-Painlevé property), we generalise the concept of the Okamoto's space of initial values for these types of equations. Starting from a general equation with analytic coefficient functions, the construction of this space yields certain differential conditions on these functions that are equivalent to the resonances found e.g. by the (quasi-)Painlevé test.
  • [02754] On the (quasi-)Painleve equations
    • Format : Online Talk on Zoom
    • Author(s) :
      • Galina Filipuk (University of Warsaw)
    • Abstract : Painleve equations are second order nonlinear differential equations solutions of which have no movable critical points. They appear in many applications. For solutions of quasi-Painleve equations algebraic singularities are allowed. The so-called geometric approach may help in many cases to understand the nature of singularities. In this talk I shall present some recent results on the geometric approach for the Painleve and quasi-Painleve equations. This is a joint work with A. Stokes.
  
  
  

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