MS and CT list / Aug. 22, 15:30-17:10.

MS [01107] Efficient methods for Isogeometric Analysis

room : G301

• [04261] Matrix free weighted quadrature IgA applied to heat transfer problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Joaquin Eduardo Cornejo Fuentes (INSA Lyon)
    • Thomas Elguedj (Lamcos)
    • Arnaud Duval (Lamcos)
    • David Dureisseix (Lamcos)
  • Abstract : IsoGeometric Analysis was introduced as an extension of Finite Element Method to represent the geometry and the solution field. However, the algorithms commonly used in FEM represented a major challenge from a computational point of view in IgA. This communication focuses on novel techniques applied to heat transfer problems which take advantage of the tensor structure of the shape functions, improve computation time of matrix-vector products and enhance the convergence rate of the iterative solver.
• [04410] Solving boundary value problems via the Nystrom method using spline Gauss rules
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Barton
    • Ali Hashemian (BCAM)
    • Hanna Sliusarenko (BCAM)
    • Sara Remogna (University of Torino)
    • Domingo Barrera (University of Granada)
  • Abstract : We propose to use spline Gauss quadrature rules for solving boundary value problems~(BVPs) using the Nystrom method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nystrom method, which involves the use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts.
• [05302] An efficient solver for space–time isogeometric Galerkin methods for parabolic problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gabriele Loli (Università di Pavia )
    • Monica Montardini (Università di Pavia )
    • Giancarlo Sangalli (Università di Pavia )
    • Mattia Tani (University of Pavia)
  • Abstract : We present an efficient solver for a Galerkin space–time isogeometric discretization of the heat equation. In particular, we propose a preconditioner that is the sum of Kronecker products of matrices and that can be efficiently applied thanks to an extension of the classical Fast Diagonalization method. The preconditioner is robust w.r.t. the polynomial degree of the spline space and the time required for the application is almost proportional to the number of degrees-of-freedom.
• [05187] Singularity extraction and efficient numerical integration for isogeometric BEM
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tadej Kanduc (University of Ljubljana)
  • Abstract : Quadrature rules to evaluate governing (weakly singular) integrals that appear in boundary integral equations for 3D potential problems are presented. The rules are described by two main features: a higher order isoparametric singularity extraction technique and a spline-based quasi-interpolation technique. Uniform distribution of quadrature nodes is preferable to improve the implementation efficiency. The integration scheme has high order converge rates and since it is tailored for spline integrands, it perfectly fits in the isogeometric framework.

MS [00654] Poset Combinatorics

room : G302

• [02151] The operad of finite posets acts on zeta values
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Dolores Cuenca (Yonsei University)
  • Abstract : Consider Riemann zeta function $\zeta(k)=\sum_{n=1}^\infty\frac{1}{n^k}$. We develop a theory in which the zeta values and the order polytopes share the same combinatorial information. More precisely, we show that the operad of finite posets acts on Stanley order polynomials, and the aforementioned operad acts on a set of numbers generated by zeta values. To demonstrate that the action of the operad on zeta values is not trivial, we explicitly compute a quaternary associative non commutative operation.
• [01777] What is -Q for a poset Q?
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiko Yoshinaga (Osaka University)
  • Abstract : In the context of combinatorial reciprocity, it is a natural question to ask what "−Q" is for a poset Q. In a previous work, the definition "−Q:=Q×R with lexicographic order" was proposed based on the notion of Euler characteristic of semialgebraic sets. In fact, by using this definition, Stanley's reciprocity for order polynomials was generalized to an equality for the Euler characteristics of certain spaces of increasing maps between posets. The purpose of this paper is to refine this result, that is, to show that these spaces are homeomorphic if the topology of Q is metrizable.
• [04172] A new expression for the order polynomial
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fengming Dong (Nanyang Technological University )
  • Abstract : In 1970s, Stanley introduced the order polynomial of a poset $P$. For a poset $P$, a mapping $\sigma: P\rightarrow [m]$ is said to be order-preserving if $u\preceq v$ implies that $\sigma(u)\le \sigma(v)$. The order polynomial $\Omega(P,x)$ is defined to be the function which counts the number of order-preserving mappings $\sigma:P\rightarrow [m]$ whenever $x=m$ is a positive integer. In this talk, I will introduce an expression for $\Omega(P,x)$, and an expression for the chromatic polynomial of a graph by applying this new result on order polynomial.
• [02099] Polychrony as chinampas
  • Format : Online Talk on Zoom
  • Author(s) :
    • José Antonio Arciniega-Nevárez (Universidad de Guanajuato)
  • Abstract : In this talk, we will discuss the effect of stimulating some nodes at certain time (initial condition) in a signal flow path with auto-edges. The stimuli are applied at different times. The effect of these stimuli propagates through the vertices of the path, causing other nodes, which we will call secondary nodes, to cascade. We are interested in cascades in which the initial stimuli are less than or equal to the number of secondary vertices. This can be transferred to the study of a graph with weights, these weights being the times at which a signal travels from the output vertex to the arrival vertex. We are interested in knowing the time at which a node will be activated under a certain initial condition. The problem is nonlinear, so to deal with time, we propose to study a latiz, where, vertically, the time is described and horizontally, the vertices of the path are repeated. In this way, a vertex of the latiz will be connected to another one to which it was already connected in the path but at a different height, depending on the time. If the time is always t=1, the problem becomes to study an automaton, where a cell at time t lives depending on the cells alive at time t-1, in particular we are interested in the rule 192 with the difference that the automaton is reactivated at different times (with the initial condition). The generated automata,that we call chinampas, have topological and combinatorial properties that allow us to solve the initial problem. Moreover, we can characterize automata in which the number of cells outside the initial condition are equal to or one more than those of the initial condition. For the case in which we have more than one of these cells, we have translated the problem to one of triangular series with order conditions. These series can be obtained from partially ordered sets (posets). We have noted that the series obtained are known as generalizations of Stanley polynomials whose coefficients count the different ways of labeling a poset preserving the order. The problem was inspired by the behavior of a neural network so this work is related to those who study such neural networks as polychrony groups, in fact, this is a particular case of polychrony.

MS [00410] Recent advances in Bayesian optimal experimental design

room : G304

• [04376] A transport map approach for Bayesian optimal experimental design
  • Format : Talk at Waseda University
  • Author(s) :
    • Karina Koval (Heidelberg University)
    • Roland Herzog (Heidelberg University)
    • Robert Scheichl (Heidelberg University)
  • Abstract : Solving the Bayesian optimal experimental design (BOED) problem requires optimizing an expectation of a utility function or optimality criterion that assesses the quality of each design. For Bayesian inverse problems with non-Gaussian posteriors, a closed-form expression for the criterion is typically unavailable. Thus, access to a computationally efficient approximation is crucial for numerical solution of the optimal design problem. We propose a flexible approach for approximating the expected utility function and solving the BOED problem that is based on transportation of measures. The key to our method is the approximation of the joint density on the design, observation and inference parameter random variables via the pushforward of a simple reference density under an inverse Knothe-Rosenblatt (KR) rearrangement. This KR map exposes certain conditional densities which enables approximation of the optimality criterion for any design choice. We present our approach and assess the effectiveness of the resulting optimal designs with some numerical examples.
• [04957] Accelerating A-Optimal Design of Experiments Using Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinwoo Go (Georgia Institute of Technology)
    • Peng Chen (Georgia Institute of Technology)
  • Abstract : Designing experiments for large-scale problems demands significant computational resources, and Partial Differential Equation (PDE) surrogates have emerged as a widely-adopted approach to address this challenge. This study enhances this methodology by independently training PDE surrogates and their Jacobians. Leveraging the trained Jacobian of PDEs, we approximate the posterior covariance matrix. Subsequently, we compute the trace of this matrix and evaluate the reduction in uncertainty resulting from executing the experimental setup.
• [05059] Stability of Bayesian optimal experimental design in inverse problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Tapio Helin (LUT University)
    • Jose Rodrigo Rojo Garcia (LUT University)
    • Duc-Lam Duong (LUT University)
  • Abstract : In this talk, I will explore the stability properties of Bayesian optimal experimental design towards misspecification of distributions or numerical approximations. Specifically, I will present a framework for addressing this problem in a non-parametric setting, and demonstrate a stability result for the expected utility with respect to likelihood perturbations. To provide a more concrete illustration, I will then consider non-linear Bayesian inverse problems with Gaussian likelihood, where the forward mapping is replaced by an approximation.
• [05080] Quasi-Monte Carlo methods for Design of Experiment
  • Format : Talk at Waseda University
  • Author(s) :
    • Claudia Schillings (FU Berlin)
    • Vesa Kaarnioja (Free University of BerlinFU Berlin)
  • Abstract : Bayesian experimental design aims to optimize the placement of measurements in an experiment such that information about unknown quantities is maximized (w.r. to a suitable criterion). The optimization problem requires the evaluation of the information gain, which corresponds to the evaluation of an integral w.r. to the posterior distribution. We will explore the use of quasi-Monte Carlo methods for Bayesian design problems in this talk and present convergence results.

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

room : G305

• [01891] Criteria for Grobner bases and degenerations by structure of signatures
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuta Kambe (Mitsubishi Electric Corporation)
  • Abstract : The F5 algorithm was presented by Faugere in 2002 and variants of the F5 algorithm have been proposed by various researchers called signature based algorithms (SBAs). The concept of signatures was revised by Arri-Perry in 2011 as normal monomials for syzygies and Vaccon-Yokoyama presented an implementable SBA in 2017 with the concept of guessed signatures. The speaker will talk about these new concepts and his new criterion theorem for Grobner bases and degenerations.
• [01876] On signature-based algorithm for tropical Groebner bases on Weyl algebra
  • Format : Talk at Waseda University
  • Author(s) :
    • Ari Dwi Hartanto (Department of Mathematics, Universitas Gadjah Mada)
    • Katsuyoshi Ohara (Faculty of Mathematics and Physics, Kanazawa University)
  • Abstract : The computational aspect of tropical Groebner basis for polynomial rings introduced by A.W.Chan is extended to the Weyl algebras over fields with valuations. A term order with valuation is designed to be a generalization of the tropical term orders studied by A.W.Chan and by T.Vaccon. Although it is not well-ordering, a signature-based algorithm can still be developed. The minimal natural signature of a polynomial exists. The F5 criterion is then adopted for this context.
• [01898] Algorithms for bivariate lexicographic Groebner bases
  • Format : Talk at Waseda University
  • Author(s) :
    • Xavier DAHAN (Tohoku UniversityTohoku University)
  • Abstract : The lexicographic monomial order for Groebner bases is fundamental since it holds the elimination property. This also implies strong structural properties, as shown by Lazard in 1985 in the case of two variables. Yet these properties have not been fully exploited. I will explain how they allow to perform Chinese Remainder Theorem like operations in several situations, as well as the difficulties in remaining cases. I will also discuss extensions to more than two variables.
• [01885] An algebraic approach to factor analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryoya Fukasaku (Kyushu University)
    • Kei Hirose (Kyushu University)
    • Yutaro Kabata (Nagasaki University)
    • Keisuke Teramoto (Hiroshima University)
  • Abstract : When the maximum likelihood method is used in factor analysis, it is not uncommon for an unique variance less than or equal to zero to be generated, which is known as the improper solution problem. Although numerical approaches have been made to this problem, algebraic approaches have not. Therefore, we aim to exactly describe the solution space associated with the maximum likelihood method in factor analysis by making use of computational algebraic methods such as Gröbner bases and cylindrical algebraic decomposition.

MS [02392] Low-Rank Models in Data Science

room : G306

• [03939] Bures-Wasserstein Methods in Matrix Recovery
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tyler Maunu (Brandeis University)
  • Abstract : We revisit the problem of recovering a positive semidefinite matrix from a linear map using tools from optimal transport. More specifically, we connect a variational formulation of this problem to the computation of Wasserstein barycenters. This new perspective enables the development of efficient first-order geometric methods. Experiments demonstrate the advantages of our new methodology over existing methods. We also discuss extensions to recovery in other settings of restricted positive semidefinite matrices.
• [05442] Improved Global Guarantees for Low-Rank Models via Rank Overparameterization
  • Format : Talk at Waseda University
  • Author(s) :
    • Richard Y Zhang (University of Illinois at Urbana-Champaign)
  • Abstract : We consider minimizing a twice-differentiable, $L$-smooth, and $\mu$-strongly convex objective $\phi$ over an $n\times n$ positive semidefinite matrix $M\succeq0$, under the assumption that the minimizer $M^{\star}$ has low rank $r^{\star}\ll n$. Following the Burer--Monteiro approach, we instead minimize the nonconvex objective $f(X)=\phi(XX^{T})$ over a factor matrix $X$ of size $n\times r$. This substantially reduces the number of variables from $O(n^{2})$ to as few as $O(n)$ and also enforces positive semidefiniteness for free, but at the cost of giving up the convexity of the original problem. In this talk, we prove that if the search rank $r\ge r^{\star}$ is overparameterized by a \emph{constant factor} with respect to the true rank $r^{\star}$, namely as in $r>\frac{1}{4}(L/\mu-1)^{2}r^{\star}$, then despite nonconvexity, local optimization is guaranteed to globally converge from any initial point to the global optimum. This significantly improves upon a previous rank overparameterization threshold of $r\ge n$, which is known to be sharp if $\phi$ is allowed to be nonsmooth and/or non-strongly convex, but would increase the number of variables back up to $O(n^{2})$. Conversely, without rank overparameterization, we prove that such a global guarantee is possible if and only if $\phi$ is almost perfectly conditioned, with a condition number of $L/\mu<3$. Therefore, we conclude that a small amount of overparameterization can lead to large improvements in theoretical guarantees for the nonconvex Burer--Monteiro factorization.
• [04377] Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric
  • Format : Talk at Waseda University
  • Author(s) :
    • Ke Wei (Fudan University)
  • Abstract : Low-rank tensor completion problem is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix case to the tensor case. The first-order and second-order quotient geometry of the manifold of fixed tensor train rank tensors under this metric is studied in detail. Algorithms, including Riemannian gradient descent, Riemannian conjugate gradient, and Riemannian Gauss-Newton, have been proposed for the tensor completion problem based on the quotient geometry. It has also been shown that the Riemannian Gauss-Newton method on the quotient geometry is equivalent to the Riemannian Gauss-Newton method on the embedded geometry with a specific retraction. Empirical evaluations on random instances as well as on function-related tensors show that the proposed algorithms are competitive with other existing algorithms in terms of completion ability, convergence performance, and completion quality.
• [04975] Iteratively Reweighted Least Squares for Low-Rank Optimization: Optimality & Convergence Rates
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Kümmerle (University of North Carolina at Charlotte)
  • Abstract : Convex or non-convex matrix functions such as Schatten-p (quasi-)norms have been successfully used as surrogates of the rank objective. Iteratively Reweighted Least Squares (IRLS) has emerged as a suitable algorithmic framework to scalably optimize such rank surrogates. We review the formulation, optimality and empirical data-efficiency of MatrixIRLS. We show that the algorithm, which optimizes Schatten-type objectives, exhibits a local superlinear convergence rate with a large basin of attraction, and linear convergence rates in the convex case.

MS [00170] Integrable systems, orthogonal polynomials and asymptotics

room : G401

• [05494] Orthogonal polynomials on elliptic curves and Painlevé VI equation.
  • Author(s) :
    • Harini Desiraju (University of Sydney)
    • Pieter Roffelsen (University of Sydney)
    • Tomas Latimer (University of Sydney)
  • Abstract : Elliptic orthogonal polynomials are a family of special functions that satisfy certain orthogonality condition with respect to a weight function on an elliptic curve. Building up on several recent works on the topic, we establish a framework using Riemann-Hilbert problems to study such polynomials. When the weight function is constant, these polynomials relate to the elliptic form of the sixth Painleve equation. This talk is based on a recent work with Tomas Latimer and Pieter Roffelsen (arXiv: 2305.04404).
• [04872] On q-Painlevé VI and the geometry of affine Segre surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Pieter Roffelsen (University of Sydney)
  • Abstract : A famous result by M. Jimbo (1982) relates Painlevé VI to a family of affine cubic surfaces via the Riemann-Hilbert correspondence. In recent work with Nalini Joshi, a $q$-analog of this result was obtained, relating $q$-Painlevé VI to a family of affine Segre surfaces. I will explain this result and show how the geometry of these surfaces is reflected in the asymptotic expansions of solutions around the two critical points of $q$-Painlevé VI.
• [05564] Riemann-HIlbert problem on the q-Painleve equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yousuke Ohyama (Tokushima University)
  • Abstract : We study monodromy spaces of $q$-Painleve equations. We apply the Riemann-Hilbert correspondence to analytic studies on $q$-Painleve equations.
• [05591] A 3×3 Lax form for the q-P(E_6^{(1)})
  • Format : Talk at Waseda University
  • Author(s) :
    • Kanam Park (Toba college)
  • Abstract : For the q-Painlevé equation with the affine Weyl group symmetry of type E_6^{(1)}, a 2×2 matrix Lax form and a second order scalar lax form were known. In this talk, we give a 3×3 matrix Lax form and a third order scalar equation related to it. We also give its continuous limit. These Lax form and a scalar equation seems to be new.

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

room : G402

• [04203] Multiple timescales in reaction networks and the parametrisation method
  • Format : Talk at Waseda University
  • Author(s) :
    • Martin Wechselberger (University of Sydney)
    • Ian Lizarraga (University of Sydney)
    • Bob Rink (Vrije Universiteit Amsterdam)
  • Abstract : Many biochemical reaction network problems display distinct temporal features, which can be attributed to processes taking place on multiple timescales. In mathematical terms, such multiple timescale models are in fact singular perturbation problems. We present a parametrisation method for computing slow manifolds and their fast fibre bundles in such singular perturbation problems. In particular, we highlight the emergence of hidden timescales and show how our method can uncover these surprising multiple timescale structures.

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

room : G404

• [05314] The geodesic deviation equation for null geodesics in the Schwarzschild black-hole
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan José Morales-Ruiz (Universidad Politécnica de Madrid)
    • Alvaro Pérez-Raposo (Universidad Politécnica de Madrid)
  • Abstract : The Schwarzschild black-hole is an integrable Hamiltonian system with four degrees of freedom. The geodesic deviation equations are the variational equations for this Hamiltonian system. By a joint theorem with Ramis, these equations can be solved in closed form in the framework of the differential Galois theory. This talk will be devoted to give the solutions of these equations around some null geodesics. This a joint work with Álvaro Pérez-Raposo.
• [03161] Non-integrability of a model of two tethered satellites
  • Format : Talk at Waseda University
  • Author(s) :
    • Thierry Combot (Universite de Bourgogne)
  • Abstract : We study the integrability of a model of two tethered satellites whose centre of mass moves in a circular Keplerian orbit around a gravity centre. When tether rest length is zero, the model is integrable and even superintegrable for selected values of the parameters. For positive rest length, the system is non-integrable. Obstructions to integrability are obtained through study of the differential Galois group of an irreducible symplectic variational equation in dimension 4.
• [04393] Obstructions to integrability of nearly integrable dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shoya Motonaga (Ritsumeikan University)
  • Abstract : We study necessary conditions for the existence of real-analytic first integrals and real-analytic integrability for perturbations of integrable systems including non-Hamiltonian ones in the sense of Bogoyavlenskij. Moreover, we compare our results with the classical results of Poincar\'{e} and Kozlov for systems written in action and angle coordinates and discuss their relationships with the Melnikov methods for periodic perturbations of single-degree-of-freedom Hamiltonian systems. This is joint work with Kazuyuki Yagasaki at Kyoto University.
• [04873] A Tale of Two Polytopes related to geodesic flows on spheres
  • Format : Talk at Waseda University
  • Author(s) :
    • Holger Rainer Dullin (University of Sydney)
    • Diana Nguyen (University of Sydney)
    • Sean Dawson (University of Sydney)
  • Abstract : Separation of variables for the geodesic flows on round spheres leads to a large family of integrable systems whose integrals are defined through the separation constants. Reduction by the periodic geodesic flow leads to integrable systems on Grassmanians. Specifically for the geodesic flow on the round $S^3$ the reduced system defines a family of integrable systems on $S^2\times S^2$. We show that the image of these systems under a continuous momentum map defined through the action variables has a triangle as its image. The image is rigid and does not change when the integrable system is changed within the family. Each member of the family can be identified with a point inside a Stasheff polytope. Corners of the polytope correspond to toric systems (possibly with degenerations), edges correspond to semi-toric systems (in various meanings of the word), and the face corresponds to ``generic'' integrable systems. A fundamental difference of this momentum map to that of a toric or semi-toric system is that the number of tori in the preimage of a non-critical point may be 1, 2, or 4. The momentum map is continuous but not smooth along the images of hyperbolic singularities. The corresponding quantum problem and generalisations to higher dimensional spheres will be discussed.

MS [01188] Recent Developments in Fluid Dynamics

room : G405

• [04242] Small scale creation for the 2D Boussinesq Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Kiselev (Duke university)
    • Yao Yao (National University of Singapore)
    • Jaemin Park (University of Basel)
  • Abstract : In this talk, we study long-time behaviors of the two- dimensional incompressible Boussinesq equations without thermal diffusion. While the 2D Boussinesq equations is known to possess global solutions with the presence of viscos- ity, it remains a outstanding open problem whether the inviscid case can exhibit a finite-time blow up. In the viscous case, we established algebraic growth of the Sobolev norms of the solu- tions for all time. For the inviscid case, we obtained the growth of the gradient of the temperature, assuming that the global so- lution exists for all time. The initial data under consideration in this work is not too restrictive. More precisely, we only require certain symmetry and sign conditions. The key ingredient of the proof is to derive a norm-inflation from the decay of an anisotropic Sobolev norm of the temperature, which can be ob- served in the conservation of energy. This work is a joint work with A. Kiselev and Y. Yao.
• [05046] On the motion of an internal wave in two-dimensional viscous flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Rafael Granero-Belinchon (Universidad de Cantabria)
  • Abstract : In this talk we will review some recent results concerning the motion of an internal wave in two-phase viscous flow. In particular we will establish the local and global well-posedness of the free boundary problem associated to this physical situation. Finally, we will also prove an exponential instability result. These results were obtained in a joint work with Francisco Gancedo and Elena Salguero.
• [03025] Smooth imploding solutions for 3D compressible fluids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gonzalo Cao Labora (Massachusetts Institute of Technology (MIT))
  • Abstract : We will talk about singularity formation for the 3D isentropic compressible Euler and Navier-Stokes equations for ideal gases. We will construct a new family of self-similar profiles corresponding to larger self-similar exponents than what was previously known. In particular, this will show singularity formation for all adiabatic constants, giving the first known singularity formation result for monoatomic gases. These results are joint work with Tristan Buckmaster and Javier Gomez-Serrano.

MS [00278] Nonlocal Modeling, Analysis, and Computation

room : G406

• [01086] Machine-learning based coupling of local and nonlocal models
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Diehl (LSU)
    • Noujoude Nader (LSU)
    • Serge Prudhomme (PolyMTL)
  • Abstract : This talk will present a machine-learning coupling approach for local and nonlocal models. We will identify when to switch two the coupled system and where to place the nonlocal region within the local region. We will present some one-dimensional and two-dimensional examples to showcase the applicability of the approach.
• [01235] Nonlocal Neural Operators for Learning Complex Physical Systems with Momentum Conservation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yue Yu (Lehigh University)
  • Abstract : Neural operators have recently become popular tools for learning responses of complex physical systems. Nevertheless, their applications neglects the intrinsic preservation of fundamental physical laws. Herein, we introduce a novel integral neural operator architecture, to learn physical models with conservation laws of linear and angular momentums automatically guaranteed. As applications, we demonstrate our model in learning complex material behaviors from both synthetic and experimental datasets, and show that our models achieves state-of-the-art accuracy and efficiency.
• [03023] A Numerical Study of the Peridynamic Differential Operator Discretization of Incompressible Navier-Stokes Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Burak Aksoylu (Texas A&M University-San Antonio)
    • Fatih Celiker (Wayne State University)
  • Abstract : We study the incompressible Navier-Stokes equations using the Projection Method. The applications of interest are the classical channel flow problems such as Couette, shear, and Poiseuille. In addition, we consider the Taylor-Green vortex and lid-driven cavity applications. For discretization, we use the Peridynamic Differential Operator (PDDO). The main emphasis of the paper is the performance of the PDDO as a discretization method under these flow problems. We present a careful numerical study with quantifications and report convergence tables with convergence rates. We also study the approximation properties of the PDDO and prove that the $N$-th order PDDO approximates polynomials of degree at most $N$ exactly. As a result, we prove that the PDDO discretization guarantees the zero row sum property of the arising system matrix.
• [03546] An efficient peridynamics-based coupling method for composite fracture
  • Format : Talk at Waseda University
  • Author(s) :
    • Zihao Yang (Northwestern Polytechnical University)
  • Abstract : In this talk, we will introduce a peridynamics-based statistical multiscale framework and related numerical algorithms to predict the fracture of composite structure with randomly distributed particles. The heterogeneities of composites, including the shape, spatial distribution and volume fraction of particles, are characterized within the representative volume elements, and their impact on structure failure are extracted as two types of peridynamic parameters, namely, statistical critical stretch and equivalent micromodulus. Two- and three-dimensional numerical examples illustrate the validity, accuracy and efficiency of the proposed method.

MS [00068] Models for collective behavior and emergent phenomena

room : G501

• [03562] Emergence of Biological Transportation Networks as a Self-Regulated Process
  • Format : Talk at Waseda University
  • Author(s) :
    • Simone Portaro (KAUST)
  • Abstract : Our purpose is to investigate self-regulating processes modeling biological transportation networks by writing formal $L^2$-gradient flow for a tensor valued diffusivity $D$. We will explore a broad class of entropy dissipations associated with a purely diffusive model and investigate the formal $L^2$-gradient flow of the Fokker-Planck equation. It derives an integral formula for the second variation of the dissipation functional, proving convexity, and couples the Poisson equation for electric potential obtaining the Poisson-Nernst-Planck system. Numerical results are also presented.
• [03929] Bifurcations in collective dynamics: ordered and disordered behaviour
  • Format : Talk at Waseda University
  • Author(s) :
    • Sara Merino-Aceituno (University of Vienna)
    • Raphael Winter (University of Vienna)
    • Christian Schmeiser (University of Vienna)
    • Pierre Degond (University of Toulouse)
  • Abstract : In this talk, I will review some questions that arise around the classical Vicsek model - which is a model for collective dynamics where agents move at a constant speed while trying to adopt the averaged orientation of their neighbours, up to some noise. I will discuss the emergence of bifurcations leading to disordered and ordered motion, depending on the local density of the agents. This is a very interesting phenomenon: it showcases how two completely different observed behaviours can appear simultaneously from agents that interact following the same rules.
• [04259] A new approach to upscaling of KTEs modelling cell migration
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Zhigun (Queen’s University Belfast)
    • Christina Surulescu (University of Kaiserslautern-Landau)
  • Abstract : A new approach to upscaling of a class of kinetic transport equations that can, e.g. model cell migration in a fibrous environment under the influence of attractants will be presented. It doesn’t rely on a Hilbert space setting and provides a unified and transparent way of obtaining both parabolic and hyperbolic scalings. Formal computations are mimicked by rigorous operations with Radon measures. A key tool is a PDE that connects zero and second order moments.
• [04922] Asymptotic limits of transient patterns in a continuous-space interacting particle system.
  • Format : Talk at Waseda University
  • Author(s) :
    • Dietmar B Oelz (University of Queensland)
    • Cecilia Gonzalez Tokman (University of Queensland)
  • Abstract : We study a discrete-time interacting particle system with continuous state space. The process has applications in the modeling of actin filament turnover in biological cells through branching and subsequent rapid debranching. In continuous phase space, it can be interpreted as a voter model and as a step-wise mutation model. Its solutions are characterized by transient clusters reminiscent of either actin filament assemblies in the cell cortex or of the formation of opinion clusters. We reformulate the process in terms of the inter-particle distances and focus on their marginal and joint distributions. We construct a recurrence relation for the associated characteristic functions and pass to the large population limit reminiscent of the Fleming-Viot super-processes. The precise characterization of all marginal distributions established in this work opens the way to a detailed analysis of cluster dynamics. We also obtain a recurrence relation which enables us to compute the moments of the asymptotic single particle distribution characterizing the transient aggregates. Our results indicate that aggregates have a fat-tailed distribution.

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

room : G502

• [04385] Gamma-convergence and stochastic homogenisation for phase-transition models
  • Format : Talk at Waseda University
  • Author(s) :
    • Roberta Marziani (TU Dortmund)
  • Abstract : In this talk we discuss the gamma-convergence of general phase-transition functionals of Modica-Mortola type whose integrands depend both on the space variable and on the regularization parameter (which represents the characteristic length scale of phase transition). In particular we show that the limit is a surface functional whose integrand is characterized by the limit of a suitable cell formula. We then extend our analysis to the case of stochastic homogenization and prove a gamma-convergence result for stationary random integrands.
• [05141] Anomalous diffusion of a passive tracer advected by the curl of the GFF in 2D
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Morfe (Max Planck Institute, Leipzig)
    • Georgiana Chatzigeorgiou (Max Planck Institute, Leipzig)
    • Lihan Wang (Max Planck Institute, Leipzig)
    • Felix Otto (Max Planck Institute, Leipzig)
  • Abstract : I will discuss the long-time asymptotics of the displacement of a passive tracer in a (time-independent) turbulent flow, where the velocity field equals the curl of the GFF, in two dimensions. Physicists long ago predicted that the mean-squared displacement scales like time with a logarithmic correction. In our contribution, we prove that this is indeed the case via a novel iterative argument that exploits fundamental ideas from the theory of stochastic homogenization.
• [04734] Variance reduction methods in random homogenization by using surrogate models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Frederic Legoll (Ecole des Ponts ParisTech and Inria)
    • Sebastien Brisard (Ecole des Ponts ParisTech)
    • Michael Bertin (Ecole des Ponts ParisTech and Inria)
  • Abstract : We consider the homogenization of elliptic PDEs with random coefficients. The associated corrector problem is set on the entire space, and is thus practically intractable. A standard approximation consists in restricting this problem to a large but bounded domain. The obtained effective coefficients are random. It is thus natural to consider several realizations. To improve the accuracy on the expectation of the effective coefficients, we introduce a variance reduction approach based on a surrogate model.

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

room : G601

• [02382] Control of advection-diffusion equations on networks and singular limits
  • Format : Talk at Waseda University
  • Author(s) :
    • Nicola De Nitti (FAU Erlangen-Nürnberg )
  • Abstract : We consider advection-diffusion equations posed on a tree-shaped network with suitable transmission conditions at the junctions. We study the asymptotic behavior of the cost of the null-controllability as the diffusivity parameter vanishes: we show that it decays for a sufficiently large time and explodes for short times with an exponential rate.
• [02297] A second order model of traffic with organization marker
  • Format : Talk at Waseda University
  • Author(s) :
    • Abraham Sylla (University of Milano-Bicocca)
  • Abstract : We present a toy model for self-organized road traffic taking into account the state of orderliness in drivers’ behavior. The model is reminiscent of the wide family of generalized second-order models of road traffic. The orderliness marker is evolved along vehicles’ trajectories and it influuences the fundamental diagram of the traffic flow. The coupling we have in mind is nonlocal, leading to a kind of "weak decoupling" of the resulting $2 \times 2$ system.
• [02293] Limiting flow in atrial-ventricular function
  • Format : Talk at Waseda University
  • Author(s) :
    • Javier Murillo (I3A, University of Zaragoza,)
    • Juan Mairal (I3A, University of Zaragoza,)
    • Pilar García-Navarro (I3A, University of Zaragoza,)
  • Abstract : To date, no methodology is available for coupling 1D blood flow to models of the peripheral vasculature, valves, or heart when the flow regime is other than subsonic. When modeling complex fluid networks using 1D approaches, boundary conditions can be imposed using 0D models. An application case is the modeling of the human circulation using closed-loop models. These can be considered a tool to investigate short-term transient hemodynamic responses to postural changes in atrial-ventricular function.

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

room : G602

• [02834] Segmentation-based tracking of macrophages in microscopy videos
  • Format : Talk at Waseda University
  • Author(s) :
    • Seol Ah Park (Slovak University of Technology in Bratislava)
    • Tamara Sipka (University of Montpellier)
    • Zuzana Kriva (Slovak University of Technology in Bratislava)
    • Georges Lutfalla (University of Montpellier)
    • Mai Nguyen-Chi (University of Montpellier)
    • Karol Mikula (Slovak University of Technology in Bratislava)
  • Abstract : We propose an algorithm to achieve automatic cell tracking in macrophage videos. First, we design a segmentation method employing space-time filtering, local Otsu's threshold, and the SUBSURF method. Then, the partial trajectories are extracted when segmented cells overlap in time. Finally, the extracted trajectories are linked by considering their direction of movement. The automatic tracking achieved 97.4% of accuracy for macrophage data under challenging situations, feeble fluorescent intensity, irregular shapes, and motion of macrophages.
• [02927] Model-aware learning for super-resolution in fluorescence microscopy
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Calatroni (CNRS)
  • Abstract : In this talk, I will present image super-resolution approaches for fluorescence microscopy applications based on the use of combined model-based and data-driven learning methods. Namely, I will show how generative adversarial training and plug-and-play learning methods can be effectively used as new paradigms for obtaining precise reconstructions with guarantees beyond the use of purely model-based approaches. Numerical results on both simulated and challenging real-world data will be presented.
• [02833] Macrophages trajectories smoothing by evolving curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Giulia Lupi (Slovak University of Technology in Bratislava)
    • Karol Mikula (Slovak University of Technology in Bratislava)
    • Seol Ah Park (Slovak University of Technology in Bratislava)
  • Abstract : We present a mathematical model and numerical method based on evolving open-plane and 3D curve approach in the Lagrangian formulation. The model contains three terms: the curvature term, the attracting term, and the tangential redistribution. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve.
• [02718] Limited memory restarted lp-lq minimization methods using generalized Krylov subspaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessandro Buccini (University of Cagliari)
    • Lothar Reichel (Kent State University)
  • Abstract : Regularization of certain linear discrete ill-posed problems, as well as of certain regression problems, can be formulated as large-scale, possibly nonconvex, minimization problems, whose objective function is the sum of the p-th power of the lp-norm of a fidelity term and the q-th power of the lq-norm of a regularization term, with 0 < p, q ≤ 2. We describe new restarted iterative solution methods that require less computer storage and execution time than the methods described by [Huang et al.,Majorization-minimization generalized Krylov subspace methods for lp-lq optimization applied to image restoration. BIT (2017)]. The reduction in computer storage and execution time is achieved by periodic restarts of the method. Computed examples illustrate that restarting does not reduce the quality of the computed solutions.

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

room : G605

• [04439] On the boundary controllability of conservation laws with boundary and source controls
  • Format : Talk at Waseda University
  • Author(s) :
    • Fabio Ancona (University of Padova)
    • Khai Tien Nguyen (North Carolina State University)
  • Abstract : We will discuss local and global controllability results for hyperbolic conservation laws on a bounded domain, where the control acts through a time dependent source term in combination with the boundary controls. We shall investigate first this problem for scalar conservation laws with a not necessarily convex flux. Next, we shall address the problem of extending these results to the case of rich systems of conservation laws.
• [02947] Advances on structural controllability of ensembles
  • Format : Talk at Waseda University
  • Author(s) :
    • Bahman Gharesifard (UCLA)
  • Abstract : Ensemble control studies the problem of steering the state of a large population of systems, or a continuum, using a finite number of controllers. The problem has historic ties to control of partial differential equations, with many applications including quantum ensembles in spectroscopy, control of large limits of complex networks with few inputs, and recently in the study of universal approximation of neural networks. The purpose of this talk is to study a suit of structural controllability results for linear ensemble systems, where the objective is to identify structural properties that generically render the state of the ensemble — or some statistical properties of the profile over the parametrization space, for instance the average or higher moments — controllable. The latter provides a necessary and critical complement to full structural ensemble controllability which is hard to achieve in multiparameter settings. For the case where the statistical property of interest is the average, we provide a graph-theoretic characterization of structural controllability. Along the way of establishing this result, we hint at a conjecture on minimal ``complexity’’ controllers and relate it a conjecture on invertibility of a sparse version of Hilbert matrices, which is open for most parts.
• [03282] Second microlocalization and optimal decay for the Bouendi-Grushin damped wave equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Chenmin Sun (CNRS(Université Paris Est Créteil))
    • Victor Arnaiz (Nantes Université)
  • Abstract : The Bouendi-Grushin damped-wave operator is a hypoelliptic operator with a distributional damping. This presentation introduces the second microlocalization method for obtaining the optimal resolvent estimate for the operator under varying damping conditions.
• [04573] Controls on Networks: Modeling, Learning and Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Yue Wang (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : This talk is an introduction of controllability properties and methods for networked 1D hyperbolic systems based on results obtained by the speaker and her collaborators in recent years. Modelling, analysis of the underlying dynamics and exact controllability of several physical models will be presented at first. Some recent numerical experiments with Physics-Informed Neural Networks (PINNs) show interesting possibilities for future research on the interface between control and machine learning.

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

room : G701

• [00364] Surface localized resonances and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongyu Liu (City University of Hong Kong)
  • Abstract : In this talk, I shall discuss our recent discoveries on certain novel surface localized resonances which were inspired by the surface plasmon resonance. These localized resonances generate a variety of interesting applications.
• [01244] Spectral structure of the Neumann-Operator on thin domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyeonbae Kang (Inha University)
  • Abstract : The Neumann-Poincare operator on thin domains, such as thin rectangles, thin prolate spheroids, flat oblate ellipsoids, exhibits interesting spectral structure. In this talk we review recent development on this topic.
• [00730] A unified approach to the field concentration problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Sanghyeon Yu (Korea University)
  • Abstract : Composite materials shows the high field concentration when the inclusions have geometric singularities in their boundaries. This phenomenon has many practical applications in imaging, spectroscopy, and meta-materials. In this talk, we discuss a new way of tackling the field concentration problem via the spectral analysis of the Neumann-Poincare operator. We focus on two kinds of important singularities: nearly touching surfaces and high curvature points.

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

room : G702

• [04654] On a kinetic Elo rating model for players with dynamical strength
  • Format : Talk at Waseda University
  • Author(s) :
    • Bertram Düring (University of Warwick)
  • Abstract : We discuss a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann-type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments.
• [04235] Nonlocal approximation of nonlinear diffusion equations and cross-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Antonio Esposito (University of Oxford)
    • Martin Burger (University of Hamburg)
    • José Antonio Carrillo (University of Oxford)
    • Jeremy S.-H. Wu (UCLA)
  • Abstract : In this talk I will discuss the connection between a class of nonlocal PDEs and nonlinear diffusion equations, including porous medium PDEs and cross-diffusion systems. As byproduct of this link, one can obtain a rigorous deterministic particle approximation for the PDEs considered. The analysis is based on a suitable regularisation of the associated free energy using gradient flow techniques. However, the strategy proposed relies on a discretisation scheme, so-called JKO, which can be slightly modified in order to extend the results to PDEs without gradient flow structure. In particular, it does not require convexity of the associated energies. The talk is based on two joint works with M. Burger (FAU Erlangen-Nuremberg), and J. A. Carrillo (Oxford) and J. Wu (UCLA).
• [04374] Kinetic models for multi-agent systems with multiple microscopic states
  • Format : Talk at Waseda University
  • Author(s) :
    • Nadia Loy (Politecnico di Torino)
  • Abstract : In this talk we present a class of kinetic models describing interactions among individuals having multiple microscopic states. We shall consider microscopic states evolving according to both stochastic dependent and independent processes. In particular, we shall consider interacting agents who are divided into multiple sub-populations. As such, the agents are not indistinguishable, as classically assumed in kinetic theory, within the whole population. A general framework allowing to describe binary interactions and transfers among different sub-groups by deriving the model from microscopic stochastic processes will be presented. We shall discuss formal results concerning existence, uniqueness and equilibria. Moreover, we shall illustrate applications to wealth exchange models with migration.
• [03362] Modelling coevolutionary dynamics in heterogeneous SI epidemiological systems across scales
  • Format : Talk at Waseda University
  • Author(s) :
    • Elisa Paparelli (Politecnico di Torino)
    • Tommaso Lorenzi (Politecnico di Torino)
    • Andrea Tosin (Politecnico di Torino)
  • Abstract : We present a new structured compartmental epidemiological model for the coevolutionary dynamics between susceptible and infectious individuals. Specifically, continuous structuring variables capture interindividual variability in resistance to infection and viral load. The model comprises a system of integro-differential equations providing a Boltzmann-type kinetic description of corresponding stochastic particle dynamics. We discuss a formal derivation of this model from the underlying particle dynamics and present analytical and numerical results on the long-time behaviour of its solutions.

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

room : G703

• [04677] Aadaptive mesh atmospheric model development
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jinxi Li (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Fangxin Fang (Imperial College London)
    • Pu Gan (Chengdu University of Information Technology)
    • Christopher Pain (Imperial College London)
    • Xiaofei Wu (Chengdu University of Information Technology)
    • Zifa Wang (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Jie Zheng (Institute of Urban Environment, Chinese Academy of Sciences)
    • Jiang Zhu (Institute of Atmospheric Physics, Chinese Academy of Sciences)
  • Abstract : This study presents the development of a three-dimensional unstructured adaptive finite-element model (Fluidity-Atmosphere) for atmospheric research. To improve the computational efficiency, a LSTM-based three-dimensional unstructured mesh generator is proposed to predict the evolution of the adaptive mesh. To evaluate the performance of adaptive meshes and physical parameterisations in Fluidity-Atmosphere, a series of idealized test cases have been setup and the unstructured tetrahedral meshes are adapted automatically with the specified fields in time and space.

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

room : G704

• [04545] Special self-similar class in Rayleigh-Taylor interfacial mixing
  • Format : Talk at Waseda University
  • Author(s) :
    • Snezhana Abarzhi (University of Western Australia)
  • Abstract : Rayleigh-Taylor mixing governs a broad range of processes in nature and technology. We discover special self-similar class in Rayleigh-Taylor mixing with variable accelerations, by exploring its symmetries, scaling laws, correlations and fluctuations. We find that Rayleigh-Taylor mixing can vary from super-ballistics to sub-diffusion depending on the acceleration and retain memory of deterministic conditions for any acceleration. We explain high Reynolds number experiments in Rayleigh-Taylor mixing and provide new insights for processes driven by the mixing.
• [04164] Compressible Kelvin-Helmholtz and Rayleigh-Taylor Instabilities
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasuhide Fukumoto (Kyushu University)
    • Rong Zou (Zhejiang Normal University)
    • Kazuo Matsuura (Ehime University)
    • Nobutaka Taniguchi (University of Tokyo)
  • Abstract : For an incompressible fluid, an interface of tangential-velocity discontinuity suffers from the Kelvin-Helmholtz instability (KHI), with growth rate proportional to velocity discontinuity. Compressibility acts to stabilize KHI and, if limited to two dimensions, suppresses KHI for the Mach number larger than √8. We extend this analysis to include the gravity effect, with allowance made for density discontinuity and surface tension. Numerical simulations of a compressible mixing layer, being desingularization, exhibit complex vortical structures in turbulence.
• [03293] Interaction between a particle and a liquid surface
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Nepomnyashchy (Technion - Israel Institute of Technology)
  • Abstract : The interaction of a particle with a liquid interface takes place in many engineering processes. We consider the motion of a spherical particle rising in a viscous fluid towards the interface. The particle mobility can be significantly modified by a surfactant adsorbed on the interface. Upon the particle attachment to the interface, the spatial inhomogeneity of the wetting properties on the particle surface strongly enhance the duration of the system equilibration.

MS [00913] Geometric Mechanics and Related Topics

room : G710

• [05487] Feedback Integrators for Mechanical Systems with Holonomic Constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Joris Vankerschaver (Ghent University Global Campus)
    • Dong Eui Chang (Korea Advanced Institute of Science and Technology)
    • Matthew Perlmutter (Universidade Federal de Minas Gerais)
  • Abstract : We present a straightforward method for the numerical integration of the equations of motion of mechanical systems with holonomic constraints, to produce numerical trajectories that remain in the constraint set and preserve the values of constrained quantities. Our method only requires changes to the vector field and can be used in conjunction with any numerical integration scheme. This talk will describe the theoretical foundations of the method and compare its performance with other integrators.
• [04689] Geometric Integrators for Neural Symplectic Forms
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuhan Chen (Kobe University)
    • Takashi Matsubara (Osaka University)
    • Takaharu Yaguchi (Kobe University)
  • Abstract : The neural symplectic form is a deep physical model for general Hamiltonian systems in arbitrary coordinates. A primal application of deep physical models is physical simulations; however, when general numerical integrators are used for discretization, the physical properties are destroyed. Structure-preserving numerical methods are effective to address this problem. Typical integrators are symplectic integrators, which can be derived as variational integrators. In this study, we show that variational integrators are available for neural symplectic forms.
• [04691] Structure-Preserving Learning for GENERIC systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Baige Xu (Kobe University)
    • Yuhan Chen (Kobe University)
    • Takashi Matsubara (Osaka University)
    • Takaharu Yaguchi (Kobe University)
  • Abstract : GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) formulation is a key theory of non-equilibrium thermodynamics, with systems described by it having a unique geometric structure. We propose a neural network model that infers the equations of motion from observed data while preserving this geometric structure by applying the neural symplectic forms and introducing an equivalence relation between the models.
• [05507] A discretization of Dirac structures and Lagrange-Dirac dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroaki Yoshimura (Waseda University)
    • Linyu Peng (Keio University)
  • Abstract : Various physical systems such as circuits, nonholonomic systems, as well as nonequilibrium thermodynamic systems can be formulated as a Lagrange-Dirac dynamical systems, in which an induced Dirac structure that is constructed by the canonical two-form and a distribution plays an essential role. In this talk, we show a discretization of such an induced Dirac structure and then we demonstrate how the associated discrete Lagrange-Dirac systems can be developed ,consistently with the discrete Lagrange-d’Alembert principle.

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

room : G801

• [00596] Forward and inverse homogenization for quasiperiodic composites
  • Author(s) :
    • Elena Cherkaev (University of Utah)
    • Sébastien Guenneau (Imperial College London)
    • Niklas Wellander (Swedish Defence Research Agency )
  • Abstract : From quasicrystalline alloys to twisted bilayer graphene, materials with a quasiperiodic structure exhibit unusual properties that drastically differ from those with periodic structures. Quasiperiodic geometries can be modeled using the cut-and-projection method restricting a periodic function in a higher-dimensional space to a lower-dimensional subspace cut at an irrational projection angle. The talk will discuss the homogenized equations for quasiperiodic materials and an inverse problem of recovering information about microstructural parameters from known effective properties.
• [00609] Studying Stefan problems with internal heat generation using sharp interface models
  • Format : Talk at Waseda University
  • Author(s) :
    • Lyudmyla L. Barannyk (University of Idaho)
    • John C. Crepeau (University of Idaho)
    • Patrick Paulus (University of Idaho)
    • Alexey Sakhnov (Kutateladze Institute of Thermophysics SB RAS)
    • Sidney D. V. Williams (Georgia Institute of Technology)
  • Abstract : We study the evolution of the solid-liquid interface during melting and solidification of a material with constant internal heat generation with prescribed temperature and heat flux conditions at the boundary of an infinite cylinder. We derive a nonlinear differential equation for the motion of the interface, which involves Fourier-Bessel series. The problem is also solved numerically by the front catching into a space grid node method as well as the enthalpy-porosity method to validate results.
• [00623] Capturing Quasistatic Fracture Evolution with Nonlocal Models
  • Author(s) :
    • Robert Lipton (Louisiana State University)
    • Debdeep Bhattacharya (Louisiana State University)
  • Abstract : Nonllocal quasistatic fracture evolution for interacting cracks is developed. The approach is implicit and based on local stationarity and fixed point methods. It is proved that the fracture evolution decreases the stored elastic energy with each load step; provided the load increments are taken sufficiently small. Existence theory for the fracture evolution is proved rigorously. Numerical examples include capturing the crack path propagating inside an L-shaped domain, and two offset inward propagating cracks.
• [00631] The Lippmann Schwinger Lanczos algorithm for inverse scattering problems
  • Author(s) :
    • Shari Moskow (Drexel University)
    • Vladimir Druskin (WPI)
    • Mikhail Zaslavsky (Southern Methodist University)
  • Abstract : We combine data-driven reduced order models with the Lippmann- Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced. This internal solution is then used in the Lippmann-Schwinger equation, in a direct or iterative framework. The approach also allows us to process more general transfer functions, i.e., to remove the main limitation of the earlier versions of the ROM based inversion algorithms. We also describe how the generation of internal solutions simplifies in the time domain and give examples of its use given mono static data, targeting synthetic aperture radar.

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

room : G802

• [04798] Quantum Dynamics of Incommensurate System
  • Format : Talk at Waseda University
  • Author(s) :
    • Diyi Liu (University of Minnesota, Twin Cities)
  • Abstract : Motivated by the need to develop accurate numerical methods for computing the electronic properties of twisted bilayer graphene, we consider the problem of numerically computing the dynamics of a general aperiodic discrete (tight-binding) Schrödinger equation in an infinite domain. We prove that, under appropriate conditions, these dynamics can be rigorously approximated by those of a finite-dimensional truncated model. The key role in the proof is played by speed of propagation estimates derived from Combes-Thomas estimates. Besides the general aperiodic medium, we further improve our truncation analysis and Combes-Thomas Estimate for aperiodic medium with low dimensional structure, general van der Waal heterostructures. We then present a range of numerical experiments showing the effectiveness of our analysis.
• [04339] On the kinetic description of the objective molecular dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Kunlun Qi (University of Minnesota)
    • Li Wang (University of Minnesota)
  • Abstract : In this talk, we will introduce a multiscale hierarchy framework for objective molecular dynamics (OMD), a reduced molecular dynamics with certain symmetry, that connects it to the statistical kinetic equation, and the macroscopic hydrodynamic model. In the mesoscopic regime, we exploit two interaction scalings that lead to either a mean-field type or a Boltzmann-type equation. At the macroscopic level, we also derive the corresponding reduced Euler and Navier-Stokes systems by conducting a detailed asymptotic analysis.

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

room : G808

• [00236] On plasmon modes in multi-layer structures
  • Format : Talk at Waseda University
  • Author(s) :
    • Youjun Deng (Central South University)
  • Abstract : We consider the plasmon resonances in multi-layer structures. We show the plasmon modes are equivalent to the eigenvalue problem of a matrix, whose order is the same to the number of layers. For any number of layers, the exact characteristic polynomial is derived by a conjecture, which is verified by using induction. It is shown that all the solutions to the characteristic polynomial are real and exist in the span [-1, 2]. Numerical examples are presented for finding all the plasmon modes.
• [00405] Uniqueness and non-uniqueness for inverse source problems of elliptic equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yi-Hsuan Lin (Department of Applied Mathematics, National Yang Ming Chiao Tung University)
  • Abstract : We study inverse source problems associated to second order elliptic equations on a bounded domain. We demonstrate both uniqueness and non-uniqueness for inverse source problems of different type elliptic equations.
• [00361] Mathematical analysis of microscale hydrodynamic cloaking and shielding using electro-osmosis
  • Format : Talk at Waseda University
  • Author(s) :
    • Guang-Hui Zheng (Hunan University)
  • Abstract : Rendering objects invisible by cloaking them with metamaterials have made rapid progress in the past decade. However, the difficulties of metamaterials manufacturing have limited its development. In this talk, we discuss the mathematical analysis of hydrodynamic cloaking and shielding via electro-osmosis in a microfluidic chamber that does not rely on metamaterials. Based on layer potential technique, the conditions that can ensure the occurrence of the microscale hydrodynamic cloaking and shielding are established. Finally, several numerical examples are served to validate our theoretical analysis. (joint works with Hongyu Liu (CityU) and Zhiqiang Miao (HNU))
• [00920] Regularizing Effect of Damping Mechanisms in Inverse Problems of Evolution Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Sakthivel Kumarasamy (Indian Institute of Space Science and Technology )
    • Alemdar Hasanov Hasanoglu (Kocaeli University, Turkey)
    • Anjuna Dileep (Indian Institute of Space Science and Technology )
  • Abstract : It is known that the undamped evolution models, such as the Euler-Bernoulli beam, and Kirchhoff-Love plate, don’t support the unique determination of unknown spatial load from the measured displacement at the final time. We solve this issue by introducing the viscous external damping and Kelvin-Voigt damping effects in the basic governing equations. The damping terms play a pivotal role in getting more regular solutions with less regular data on the direct problem, while in the context of inverse problems, it has a similar effect to a regularization term in the Tikhonov functional of the quasi-solution approach.

MS [01935] Advances in Inverse Problems and Imaging

room : G809

• [04288] Recovering an infinite rough surface by acoustic measurements
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiaqing Yang (Xi'an Jiaotong University)
  • Abstract : In this talk, I will report some recent advances on inverse scattering by rough surfaces, where new uniqueness results and inversion algorithms will be presented to recover the shape and location of the rough surface from the near-field measurements associated with incident point sources. Moreover, several numerical examples will be provided to illustrate the effectiveness of the algorithms.
• [03405] Uniqueness on recovering coefficients from localized Dirichlet-to-Neumann map for piecewise homogeneous piezoelectricity
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiang Xu (Zhejiang University)
  • Abstract : In this talk, we present an inverse problem on determining coefficients of piecewise homogeneous piezoelectric equations from a localized Dirichlet-to-Neumann map on partial boundaries. Assume the bounded domain can be divided into finite subdomains, in which the unknown coefficients including the anisotropic elastic tensor, the piezoelectric tensor, and the dielectric tensor are constants. Two different cases are considered: the subdomains are either known and Lipschitz or unknown and subanalytic. For both cases, the unknown coefficients can be uniquely determined from a given localized Dirichlet-to-Neumann map.

MS [02474] Applied and Computational Dynamics

room : F308

• [03364] Connectedness of graphs of dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • James A Yorke (Univ. Of Maryland )
    • Roberto De Leo (Howard Univ.)
  • Abstract : We have been developing the general theory of graphs of maps or differential equations that works for maps, ordinary differential equations and parabolic partial differential equations. We have a complete theory for the logistic map. We have created axioms for graphs that can be used to prove results about graphs, axioms that hold for all of the standard definitions. We prove that the graph is connected under mild hypotheses.
• [03770] Changes in basin of attraction by homoclinic and heteroclinic tangencies in passive dynamic walking
  • Format : Talk at Waseda University
  • Author(s) :
    • Kota Okamoto (Kyoto University)
    • Ippei Obayashi (Okayama University)
    • Hiroshi Kokubu (Kyoto University)
    • Kei Senda (Kyoto University)
    • Kazuo Tsuchiya (Kyoto University)
    • Shinya Aoi (Osaka University)
  • Abstract : In the passive dynamic walking that walks down a shallow slope without any control or input, countless sudden changes appear in the basin of attraction depending on the slope angle. An infinite number of periodic solutions also appear. We investigated the mechanism of the sudden changes in the basin of attraction of the passive dynamic walking based on the homoclinic and heteroclinic tangencies of the manifolds of the periodic solutions.
• [04997] A novel bifurcation in hybrid dynamical systems: a model of human locomotion and its generalization
  • Format : Talk at Waseda University
  • Author(s) :
    • Hidetoshi Morita (Shitennoji University)
    • Shinya Aoi (Osaka Univeristy)
    • Kazuo Tsuchiya (Kyoto University)
    • Hiroshi Kokubu (Kyoto University)
  • Abstract : Aiming to understand the coexistence of walk and run in human locomotion, we study a simpler vertical motion of inverted spring-mass model. We observe the coexistence of two limit cycles between which no unstable periodic orbit lies, unlike the usual coexistence of attractors. We analyze the mechanism of this novel type of coexistence. We further consider a generalized hybrid dynamical systems model, and analyze the corresponding, as well as yet other, behaviors.
• [03723] Coupled Hopf bifurcations: interaction between Fitzhugh-Nagumo neurons
  • Format : Talk at Waseda University
  • Author(s) :
    • Fátima Drubi (University of Oviedo)
    • Santiago Ibáñez (University of Oviedo)
    • Diego Noriega (University of Oviedo)
  • Abstract : Coupled dynamical systems allow to model a wide range of phenomena. We are interested in models where identical pieces with simple dynamics are coupled through simple mechanisms, wondering about the complexity that interaction may imply. The coupling of identical families of vector fields exhibiting a Hopf bifurcation is paradigmatic. After discussing a general model, we will focus on the interaction between two Fitzhugh-Nagumo planar systems and study the appearance of Hopf-Pitchfork and Hopf-Hopf bifurcations.

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

room : F309

• [01338] Random dynamical systems and multiplicative ergodic theorems
  • Format : Talk at Waseda University
  • Author(s) :
    • Cecilia Gonzalez Tokman (University of Queensland)
  • Abstract : Random dynamical systems are flexible mathematical models for the study of complicated systems whose evolution is affected by external factors, such as seasonal cycles and random effects. This talk will start with a broad introduction to the area, with an emphasis on multiplicative ergodic theory. Then, we will review recent advances in the field, which provide fundamental information for the study of transport phenomena in such systems.
• [05504] Compound Poisson Statistics for Random Dynamical Systems via Spectral Perturbation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jason Atnip (University of Queensland)
    • Gary Froyland (UNSW Sydney)
    • Cecilia Gonzalez Tokman (University of Queensland)
    • Sandro Vaienti (Aix Marseille Universite)
  • Abstract : In this talk we discuss recent results concerning the return time statistics for deterministic and random dynamical systems. Taking a perturbative approach, we consider a decreasing sequence of holes in phase space which shrink to a point. For systems satisfying a spectral gap, we show that limiting distribution of return times to these shrinking holes is a compound Poisson distribution. We provide specific examples of classes of transformations for which the limiting distribution is Polya-Aeppli.
• [01905] Entropy and pressure formulas for conditioned random dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Maximilian Engel (Free University of Berlin)
    • Tobias Hurth (Free University of Berlin)
  • Abstract : Building upon recent results on Lyapunov eponents for memoryless random dynamical systems with absorption --- see Castro et al. 2022 ---, we establish the notion of metric entropy for this setting. We further discuss the relation between entropy, positive Lyapunov exponents and escape rates for such conditioned RDS, where the main example concerns the local dynamics of stochastic differential equations on bounded domains with escape through the boundary. This is joint work with Tobias Hurth.

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

room : F310

• [03722] Dirac points for the honeycomb lattice with impenetrable obstacles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Junshan Lin (Auburn University)
  • Abstract : Dirac points are special vertices in the band structure when two bands of the spectrum for the operator touch in a linear conical fashion, and their investigations play an important role in the design of novel topological materials. In this talk, I will discuss Dirac points for the honeycomb lattice with impenetrable obstacles arranged periodically in a homogeneous medium. I will discuss both the Dirichlet and Neumann eigenvalue problems and prove the existence of Dirac points for both eigenvalue problems at crossing of the lower band surfaces as well as higher band surfaces. In addition, quantitative analysis for the eigenvalues and the slopes of two conical dispersion surfaces near each Dirac point will be presented by a combination of the layer potential technique and asymptotic analysis.
• [03675] Electronic Structure of Incommensurate 2D Heterostructures with Mechanical Relaxation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Daniel Massatt (Louisiana State University)
  • Abstract : Momentum space transformations for incommensurate 2D electronic structure calculations are fundamental for reducing computational cost and for representing electronic structure data in a more physically motivating format, as exemplified in the Bistritzer-MacDonald model. However, these transformations can be difficult to implement in more complex systems such as when mechanical relaxation patterns are present. In this work, we aim for two objectives. Firstly, we strive to simplify the understanding and implementation of this transformation by rigorously writing the transformations between the four relevant spaces, which we denote real space, configuration space, momentum space, and reciprocal space. This provides a straight-forward algorithm for writing the complex momentum space model from the original real space model. Secondly, we implement this for twisted bilayer graphene with mechanical relaxation affects included. We also analyze the convergence rates of the approximations, and show the tight-binding coupling range increases for smaller relative twists between layers, demonstrating that the 3-nearest neighbor coupling of the Bistritzer-MacDonald model is insufficient when mechanical relaxation is included for very small angles. We quantify this and verify with numerical simulation.
• [03832] Structural Symmetry and Fabry-Perot Bound States in the Continuum: A Numerical Study
  • Format : Talk at Waseda University
  • Author(s) :
    • Zitao MAI (City University of Hong Kong)
    • Ya Yan LU (City University of Hong Kong)
  • Abstract : Fabry-Perot BIC is a special type of BIC occurs in systems with two parallel identical structures acting as ideal mirrors. Similar phenomena may arise in two-layer periodic dielectric structures by tuning different parameters such as the spacing between two layers. In our study, structures with different symmetry properties are used to verify the existence of Fabry-Perot BIC, and the minimum number of tuning parameters required is also examined.

MS [00063] Recent Advances on Nonlocal Interaction Models

room : F311

• [00105] Deterministic particle approximation for a nonlocal interaction equation with repulsive singular potential
  • Format : Talk at Waseda University
  • Author(s) :
    • Marco Di Francesco (University of L'Aquila)
    • Markus Schmidtchen (TU Dresden)
  • Abstract : We consider a variant of a deterministic particle approximation for a nonlocal interaction equation with repulsive Morse potential in 1d, which is not covered by previous similar results in the literature. We prove convergence in a weak sense towards solutions to the corresponding continuum PDE. We prove our scheme is able to capture L^p contractivity and a smoothing effect which allows to extend the result to initial data in the set of probability measures.
• [00155] Nonlocal deterministic and stochastic models for collective movement in biology
  • Format : Talk at Waseda University
  • Author(s) :
    • Raluca EFTIMIE (University of Franche-Comté)
  • Abstract : The collective movement of animals occurs as a result of communication between the members of the community. However, inter-individual communication can be affected by the stochasticity of the environment, leading to changes in the perception of neighbours and subsequent changes in individual behaviour, which then influence the overall behaviour of the animal aggregations. To investigate the effect of noise on the overall behaviour of animal aggregations, we consider a class of nonlocal hyperbolic models for the collective movement of animals. We show numerically that for some sets of model parameters associated with individual communication, strong noise does not influence the spatio-temporal pattern (i.e., travelling aggregations) observed when all neighbours are perceived with the same intensity (i.e., the environment is homogeneous). However, when neighbours ahead/behind are perceived differently by a reference individual, noise can lead to the destruction of the spatio-temporal pattern.
• [00117] Zero-Inertia Limit: from Particle Swarm Optimization to Consensus-Based Optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Huang (University of Graz)
  • Abstract : Large systems of interacting particles are widely used to investigate self-organization and collective behavior. They have also been used in metaheuristic methods, which can provide empirically robust solutions to tackle hard optimization problems with fast algorithms. In this talk, we will focus on two examples of metaheuristics, i.e. Particle Swarm Optimization $(PSO)$ and Consensus-Based Optimization $(CBO)$. In particular, we shall provide a rigorous derivation of CBO from PSO through the limit of zero inertia. This is also related to the problems of overdamped limit and large-friction limit.
• [00093] Many-spike limits of reaction-diffusion systems of PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Theodore Kolokolnikov (Dalhousie University)
  • Abstract : Many reaction-diffusion have solutions consisting of spots or spikes. We consider the problem of describing the density distribution of these spikes when the number of spikes is large. This naturally leads to integral equation for spike density.

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

room : F312

• [00392] Asymptotic analysis of a parabolic problem with a rough fast oscillating interface
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrizia Donato (Univ Rouen Normandie, France)
    • Editha Carreon Jose (University of the Philippines Los Banos)
    • Daniel Onofrei (University of Houston)
  • Abstract : In this talk, we will discuss the well posedness and prove several homogenization results for a parabolic problem with an imperfect contact on the rough fast oscillating interface separating a domain occupied by heterogeneous materials. The complexity of the domain geometry and the imperfect contact on the interface create interesting multiscale phenomena with different macroscale behaviors depending on model parameters.
• [00417] A decomposition result for thin domains with rough boundary
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Casado-Díaz (University of Seville)
    • Manuel Luna-Laynez (University of Seville)
    • Francisco Javier Suárez-Grau (University of Seville)
  • Abstract : We prove a decomposition result for the pressure of a fluid in a thin domain. This result extends to the linear elasticity framework, providing better estimates for the Korn constant and fine decompositions for the elastic deformations. We show how these results, which give additional compactness properties, apply to study the asymptotic behaviour of some problems in fluid mechanics and elasticity, posed in thin domains with rough boundaries.
• [00412] Derivation of coupled Stokes-Plate-Equations for fluid flow through thin porous elastic layers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Maria Neuss-Radu (Friedrich-Alexander-Universität Erlangen-Nürnberg)
    • Markus Gahn (University Heidelberg)
    • Willi J\"ager (University Heidelberg)
  • Abstract : We consider two fluid-filled bulk domains separated by a thin porous elastic layer with thickness and periodicity $\epsilon$. The fluid flow is described by an instationary Stokes-system, and the solid via linear elasticity. By rigorous homogenization and dimension reduction methods, we derive for $\epsilon \to 0$ an effective model consisting of the Stokes-equations in the bulk domains coupled to a time dependent plate equation with homogenized coefficients on the effective interface separating the bulk regions.
• [00416] Homogenization of a two-component domain with an oscillating thick interface
  • Format : Online Talk on Zoom
  • Author(s) :
    • Klas Pettersson (Freelance)
    • Patrizia Donato (Univ Rouen Normandie, France)
  • Abstract : The homogenization of an elliptic boundary value problem is considered in a finite cylindrical domain that consists of two components separated by a periodically oscillating thick interface. On the interface, the flux is assumed to be continuous, and the jump of the solution to be proportional to the flux through the interface. By means of the periodic unfolding method, we derive the homogenized system, and prove the convergence of the solutions and their energies.

MS [00640] Variational Analysis: Theory and Applications

room : F401

• [01896] Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient
  • Format : Talk at Waseda University
  • Author(s) :
    • Puya Latafat (KU Leuven)
    • Andreas Themelis (Kyushu University)
    • Lorenzo Stella (Amazon Berlin)
    • Panagiotis Patrinos (KU Leuven)
  • Abstract : Gradient-based proximal algorithms have traditionally being bound to global Lipschitz differentiability requirements. Attempts to widen their applicabilty or reduce conservatism typically involve wasteful trial-and-error backtracking routines. Extending recent advancements in the smooth setting, we show how for convex problems it is possible to avoid backtrackings altogether and retrieve stepsizes adaptively without function evaluations. We demonstrate this with an adaptive primal-dual three-term splitting method that includes proximal gradient as special case.
• [02427] Level proximal subdifferential and its resolvent
  • Format : Talk at Waseda University
  • Author(s) :
    • Ziyuan Wang (University of British Columbia)
    • shawn xianfu wang (University of British Columbia)
  • Abstract : In this talk, we introduce a new subdifferential whose resolvent completely represents the associated proximal operator. After illustrating that the usual limiting subdifferential representation is only valid when the given function is weakly convex, we propose level proximal subdifferential, which is a careful refinement of the well-known proximal subdifferential. As such, its resolvent always coincides with the associated proximal operator regardless of weak convexity. Besides this pleasant identity, we also investigate several useful properties of level proximal subdifferential. Finally, numerous examples are given to further illustrate our results.
• [02993] On quasidifferentiability and optimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • VIVEK LAHA (Banaras Hindu University)
  • Abstract : The talk presents suitable optimality conditions based on some recent works in fractional programming and variational inequaliites in terms of quasidifferentials. The presentation deals with Fritz-John and Karush-Kuhn-Tucker type necessary optimality conditions at an optimal point in the framework of the quasidifferentiable analysis. Further, several other applications of the results are investigated in different fields of optimization like mathematical programs with equilibrium constraints and/or vanishing constraints.

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

room : F402

• [03439] Eikonal methods applied to image segmentation
  • Format : Talk at Waseda University
  • Author(s) :
    • Laurent D. Cohen (CEREMADE, Universite Paris dauphine, PSL, CNRS)
  • Abstract : Minimal paths have been used for long as an interactive tool to find contours or segment tubular and tree structures, like vessels in medical images. These minimal paths correspond to minimal geodesics according to some relevant metric defined on the image domain. Finding a geodesic distance and geodesic paths can be solved by the Eikonal equation using the fast and efficient Fast Marching method. We will present various applications to image segmentation.
• [04713] Casualty and anisotropy in the design of eikonal solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • Jean-Marie Mirebeau (Centre Borelli, CNRS, ENS Paris-Saclay)
  • Abstract : The eikonal equation characterizes the arrival time of a front, propagating at a speed which is locally dictated by the front position and normal direction, and which crucially is always positive. The causality property is the discrete counterpart of the monotonic progression of the front, and is at the foundation of efficient numerical solvers of the eikonal equation such as the fast marching method. I will describe an eikonal solver enjoying this property and applying to the tilted transversely anisotropy encountered in some geological media, as well as recent efforts on the formalization of the causality property, and its application to models which advect a state.
• [03987] Learning to Measure Distances: High Order Accurate Efficient Eikonal Solvers on Surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Ron Kimmel (Technion - Israel Institute of Technologyn )
  • Abstract : The intimate relation between Eikonal equations and distance maps would be our starting point. When introducing a numerical solver, the balance between accuracy and complexity is at the core of computer science and a measure of quality of our solution. We will present a high accuracy deep learning method for approximating geodesic distances on surfaces at linear computational complexity. For training an accurate local solver a bootstrapping mechanism is employed.
• [03578] An Artificial Neural Network Approach for Re-distancing Implicit Surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Yesom Park (Seoul National University)
    • Chang hoon Song (Seoul National University)
    • Jooyoung Hahn (Slovak University of Technology in Bratislava)
    • Myungjoo Kang (Seoul National University)
  • Abstract : Following the success of machine learning tasks, the use of neural networks for solving PDEs has begun to show promising results. In this talk, we introduce a deep-learning-based method for recovering the signed distance function (SDF) from an implicit level set function representation of the hypersurface. By exploiting one of the main advantages of neural network approaches which is flexibility in network design and optimization objectives, our developments have two-fold: First, in order to increase the expressiveness of the network, we propose an augmented network that parameterizes the SDF together with the gradient of SDF as an auxiliary output while keeping the number of parameters. Second, we introduce a new objective that exploits a more global property and regularizes the singularity of the SDF by harnessing the geometric properties of the SDF. Numerical experiments on a diverse range of interfaces on two and three-dimensional domains validate the effectiveness and accuracy of the proposed method.

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

room : F403

• [01367] Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Braxton Osting (University of Utah)
  • Abstract : Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary minimal surface, i.e., a surface contained in the ball that has (i) zero mean curvature and (ii) meets the boundary of the ball orthogonally. In this talk, I'll discuss numerical methods that use this connection to realize free boundary minimal surfaces. Namely, on a compact surface, $\Sigma$, with genus $\gamma$ and $b$ boundary components, we maximize $\sigma_j(\Sigma,g) \, L(\partial \Sigma, g)$ over a class of smooth metrics, $g$, where $\sigma_j(\Sigma,g)$ is the $j$-th nonzero Steklov eigenvalue and $L(\partial \Sigma, g)$ is the length of $\partial \Sigma$. Our numerical method involves (i) using conformal uniformization of multiply connected domains to avoid explicit parameterization for the class of metrics, (ii) accurately solving a boundary-weighted Steklov eigenvalue problem in multi-connected domains, and (iii) developing gradient-based optimization methods for this non-smooth eigenvalue optimization problem. Eigenfunctions corresponding to the extremal Steklov eigenvalues are used to generate a free boundary minimal surface. This is joint work wtih Chiu-Yen Kao and Èdouard Oudet.
• [05329] Capturing surfaces using differential forms
  • Format : Talk at Waseda University
  • Author(s) :
    • Stephanie Wang (University of California, San Diego)
    • Albert Chern (University of California, San Diego)
  • Abstract : Exterior calculus has been an important tool in solving numerical PDEs by representing physical quantities as differential forms. In this talk we expand the usage of differential forms to a whole new way of representing curves and surfaces. By doing so we reformulate the classical nonconvex Plateau minimal surface problem into a convex optimization problem, and introduce a new implicit surface representation that permits nonempty boundaries.
• [05617] Nonlocal approximations of anisotropic surface energies on partitions
  • Format : Talk at Waseda University
  • Author(s) :
    • Selim Esedoglu (University of Michigan)
  • Abstract : Nonlocal energies approximating the perimeter of sets and, in the multiphase case, partitions, arise in many settings. In particular, they play an important role in the study of threshold dynamics, an algorithm for multiphase mean curvature motion. Ensuring the convergence of nonlocal energies in the multiphase, anisotropic setting turns out to be tricky but essential for the correct behavior of these numerical methods. I will discuss conditions that guarantee convergence of the anisotropic energies.
• [05463] On some extensions and applications of thresholding schemes
  • Format : Talk at Waseda University
  • Author(s) :
    • Karel Svadlenka (Kyoto University)
  • Abstract : In this talk, I will present two examples of application of suitably modified thresholding schemes, which were originally developed by Merriman, Bence and Osher, and later generalized by Esedoglu and Otto. First example concerns elucidating cell pattern formation in morphogenesis of sensory epithelia, and the other example concerns understanding evolution of anisotropic particles on solid substrate. I will also touch on the mathematical background of the schemes and their numerical implementation.

MS [00384] Origami Engineering (1/2)

room : F411

• [01360] Farthest point map on the double cover of a parallelotope
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshikazu Yamagishi (Ryukoku University)
    • Sayaka Ueda (Ryukoku University)
  • Abstract : We describe the source unfolding on the double cover of a parallel polytope of dimension n. Suppose two persons p,q play the squash in a parallelotope. Where is the farthest point q from a given point p? What happens if they keep playing the squash by choosing the farthest points? It is shown that the limit set is a union of quadratic curves.
• [01518] Deployable earwig fan dome with the algorithmic design tool
  • Format : Talk at Waseda University
  • Author(s) :
    • Chisaki KITAJIMA (Kyushu University)
    • Kazuya Saito (Kyushu University)
  • Abstract : Earwigs can fold their wing most compactly of all insects, therefore the characteristics have potential for engineering applications. In previous studies, we have already revealed how to design the crease pattern of the earwigs fan. Here we show a method to create three-dimensional forms from the folding simulation of the earwig fan with an algorithmic design tool. Furthermore, we propose to design compactly foldable dome-shape structures based on crease pattern of earwig fan.
• [01519] Geometry and mechanics of molting in snakes and caterpillars
  • Format : Talk at Waseda University
  • Author(s) :
    • Taiju Yoneda (Kyushu University)
    • Kazuya Saito ( Kyushu University)
  • Abstract : Snakes and caterpillars have longer bodies and grow by molting, but the molting process is different. Snakes molt by reversing the front and back of their skin. In the molting of caterpillars, their skin is folded with buckling. Which mode is expected to be determined by geometric factors such as thickness and mechanical factors such as friction. We quantify these boundary conditions using a combination of buckling experiments and finite element method with cylindrical shell models.
• [01523] Linear transformation of crease pattern boundaries preserving internal graph isomorphisms
  • Format : Talk at Waseda University
  • Author(s) :
    • Yohei Yamamoto (University of Tsukuba)
    • Jun Mitani (University of Tsukuba)
  • Abstract : A crease pattern whose boundaries are similar before and after flat-folding can be tiled to create larger origami works. In order to increase the variation, linearly transforming the boundary shape is a useful approach, but if the entire crease pattern is transformed, the flat-foldability is not maintained. We propose a method for linear transformation of the boundaries while preserving internal graph isomorphisms. The characteristics of generated crease patterns and the folded states are discussed.

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

room : F412

• [04865] Topological Representation Learning for Biomedical Image Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Chen (Stony Brook University)
  • Abstract : Modern analytics is facing highly complex and heterogeneous data. While deep learning models have pushed our prediction power to a new level, they are not satisfactory in some crucial merits such as transparency, robustness, data-efficiency, etc. In this talk, I will focus on our recent work on combining topological reasoning with learning to solve problems in biomedical image analysis. In biomedicine, we encounter various complex structures such as neurons, vessels, tissues and cells. These structures encode important information about underlying biological mechanisms. To fully exploit these structures, we propose to enhance learning pipelines through the application of persistent homology theory. This inspires a series of novel methods for segmentation, generation, and analysis of these topology-rich biomedical structures. Complex structures also arise in many other contexts beyond biomedicine. We will also briefly introduce how topological reasoning can be used to strengthen graph neural networks and to improve the robustness of deep neural networks against noise and against backdoor attacks.
• [05110] New Algorithms for Random Graph Embeddings
  • Format : Talk at Waseda University
  • Author(s) :
    • Jason H Cantarella (University of Georgia)
    • Clayton Shonkwiler (Colorado State University)
    • Henrik Schumacher (Technische Universitat Chemnitz)
    • Tetsuo Deguchi (Ochanomizu University)
    • Erica Uehara (Kyoto University)
  • Abstract : We discuss the problem of randomly embedding graphs in $R^d$, which often arises in machine learning. Given an arbitrary probability distribution on each edge, we condition the joint distribution on the graph type (loops of edges must close). The key idea is to use an unusual version of cohomology to encode embedding data. Our method is particularly well suited to embeddings with fixed edge lengths, which arise in polymer science and robotics.
• [05318] Topological Deep Learning: Going Beyond Graph Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Mustafa Hajij (university of San Francisco)
    • Ghada Zamzmi (University of South Florida)
    • Theodore Papamarkou (University of Manchester)
    • Nina Miolane (University of Californian Santa Barbara)
    • Aldo Saenz (IBM)
    • Karthikeyan Natesan Ramamurthy (IBM)
    • Tolga Birdal (Imperial College London)
    • Tamal Krishna Dey (Purdue University)
    • Soham Mukherjee (Purdue University)
    • Shreyas Samaga (Purdue University)
    • Neal Livesay (Northeastern University)
    • Robin Walters (Northeastern University)
    • Paul Rosen (University of Utah)
    • Michael Schaub (RWTH Aachen University)
  • Abstract : Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

MS [01494] Queues and Related Stochastic Models

room : E501

• [02929] Strategic revenue management for discriminatory processor sharing queues
  • Format : Talk at Waseda University
  • Author(s) :
    • Dieter Fiems (Ghent University)
  • Abstract : We consider revenue management for discriminatory processor sharing (dps) queues. The server receives revenue per customer, as well as a fee if customers opt for premium service. We study the optimal parameter allocation of the dps discipline, assuming that customers rationally select between premium and non-premium service. It is shown that the optimal dps discipline is a strict priority discipline when customers cannot balk, while a non-degenerate dps discipline is optimal with balking.
• [03027] Bounding performance of stochastic models for server virtualization in cloud computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Ken'ichi Kawanishi (Gunma University)
  • Abstract : In recent years, ICT systems are constructed with virtual servers on the cloud computing by virtualization technology. The cloud computing is based on a huge number of physical servers in data centers. One of the important issues is to reduce server power consumption while ensuring performance. In this talk, we consider stochastic models for server virtualization in cloud computing and propose a method to evaluate performance bounds while suppressing computational costs even in large-scale systems.
• [03114] Strategic behaviour of reserved customers in a queueing model with multiple reservation zones
  • Format : Talk at Waseda University
  • Author(s) :
    • Yutaka Sakuma (Department of Computer Science, National Defense Academy of Japan)
    • Emiko Fukuda (Department of Industrial Engineering and Economics, Tokyo Institute of Technology)
    • Hiroyuki Ichihara (Deptartment of Management Synthesis, Chubu University)
    • Hiroyuki Masuyama (Graduate School of Management, Tokyo Metropolitan University)
  • Abstract : We consider the strategic behavior of customers in a queueing system with multiple reservation zones. In this system, customers are assigned to the reservation zones, and they face the problem of when to arrive within their reservation zone, where early arrival is allowed. The customers are assumed to be homogeneous and non-cooperative, and they try to find a mixed strategy that minimizes their expected waiting time. We propose a numerical algorithm to obtain the customers' mixed strategy in equilibrium for each reservation zone.
• [02958] Analysis of time-dependent queues with generally distributed retrials
  • Format : Talk at Waseda University
  • Author(s) :
    • Raik Stolletz (University of Mannheim)
    • Ömer Özümerzifon (University of Mannheim)
    • Benjamin Legros (EM Normandie)
  • Abstract : Time-dependent queueing systems are present in various service systems. Often customers leave the queue before being served due to a lack of patience. However, impatient users may join the system after the so-called retrial time. We analyze the time-dependent performance of multi-server queues with generally distributed retrial times and develop a stationary backlog-carryover (SBC) approach. The numerical study analyzes the reliability of the approach and demonstrates the impact of retrial time distributions on performance measures.

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

room : E502

• [02085] Almost sure averaging for fast-slow stochastic differential equations via controlled rough path
  • Format : Talk at Waseda University
  • Author(s) :
    • Bin PEI (Northwestern Polytechnical University)
    • Yong Xu (Northwestern polytechnical university)
  • Abstract : We apply the averaging method to a coupled system consisting of two differential equations which has a slow component driven by fractional Brownian motion (FBM) with the Hurst parameter $\frac13 < H_1 \leq \frac12$ and a fast component driven by additive FBM with the Hurst parameter $\frac13 < H_2 \leq \frac12$. The main purpose is to show that the slow component of such a couple system can be described by a stochastic differential equation with averaged coefficients. Our main result deals with an averaging procedure which proves that the slow component converges almost surely to the solution of the corresponding averaged equation using the approach of time discretization and controlled rough path. To do this we generate a stationary solution by a exponentially attracting random fixed point of the random dynamical system generated by the fast component.
• [01488] Discrete-time Approximation of Partially Observed Stochastic Optimal Control Problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Yunzhang Li (Fudan University)
  • Abstract : In this talk, we study a class of stochastic optimal control problems under partial observation by discrete-time control problems. To establish a convergence result, we adapt the weak convergence technique together with the notion of relaxed control rule. With a well chosen discrete-time control system, we provide an implementable numerical algorithm to approximate the value. We illustrate our convergence result by numerical experiments on a partially observed control problem in a linear quadratic setting.
• [03981] Large deviations for a slow-fast McKean-Vlasov model with jumps
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoyu YANG (Northwestern Polytechnical University)
    • Yong Xu (Northwestern polytechnical university)
  • Abstract : We aim to investigate large deviations for a slow-fast McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system. Different from the general case, the controlled system is related to the distribution of the original system, which causes difficulties. To solve it, the combination of asymptotic of original system and averaging principle is employed efficiently.
• [02182] Recent advances in stochastic nonlinear dynamics: modeling, data analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zi-Fei Lin (Xi 'an University of Finance and Economics)
    • Yan-Ming liang (Xi 'an University of Finance and Economics)
    • Jia-Li Zhao (Xi 'an University of Finance and Economics)
    • Jiao-Rui Li (Xi 'an University of Finance and Economics)
    • Kapitaniak Tomasz (Lodz University of Technology)
  • Abstract : Predicting strongly noise-driven dynamic systems has always been a difficult problem due to their chaotic properties. In this study, we investigated the prediction of dynamic systems driven by strong noise intensities, which proves that deep learning can be applied in diverse fields. This is the first study that uses deep learning algorithms to predict dynamic systems driven by strong noise intensities. We examined the effect of hyperparameters in deep learning and introduced an improved algorithm for prediction. Several numerical examples are presented to illustrate the performance of the proposed algorithm, including the Lorenz system and the Rossler system driven by noise intensities of 0.1, 0.5, 1, and 1.25. All the results suggest that the proposed improved algorithm is feasible and effective for predicting strongly noise-driven dynamic systems. Furthermore, the influences of the number of Neurons, the Spectral Radius, and the Regularization Parameters are discussed in detail. These results indicate that the performances of the machine learning techniques can be improved by appropriately constructing the neural networks.

contributed talk: CT080

room : E503

[02398] Mixed-precision Paterson--Stockmeyer method for evaluating matrix polynomials

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E503
• Type : Contributed Talk
• Abstract : The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximants, for example, those for computing transcendental matrix functions. We derive a mixed-precision version of the Paterson--Stockmeyer method that can be faster and use less memory than its fixed-precision counterpart while delivering the same level of accuracy.
• Classification : 65G50, 65F45, 65F60
• Format : Talk at Waseda University
• Author(s) :
  • Nicholas J. Higham (The University of Manchester)
  • Xiaobo Liu (The University of Manchester)

[02453] Allee effects, Evolutionary game, and Ideal free strategies in Partial Migration Population

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E503
• Type : Contributed Talk
• Abstract : Allee effect is a density-dependent phenomenon in which population growth or individual components of fitness increase as population density increases. Understanding the density-dependent effect is vital to elucidate how populations evolve and to investigate evolutionary stability. Partial migration, where a proportion of a population migrates while other individuals remain resident, is widespread across most migratory lineages. However, the mechanism is still poorly understood in most taxa, especially those experiencing positive density-dependent effects. In this talk we discuss the evolutionary stability of partial migration population with the only migrant population experiencing Allee effects. Using the Evolutionary Game Theoretic (EGT) approach, we show the existence and uniqueness of a evolutionary stable strategy (ESS). We also show that the ESS is the only Ideal Free distribution (IFD) that arises in the context of a partially migrating population.
• Classification : 39A60, 92D25, 91A22
• Format : Talk at Waseda University
• Author(s) :
  • Yogesh Trivedi (Bits-Pilani, K.K Birla Goa Campus)
  • Ram Singh (Bits-Pilani, K.K Birla Goa Campus)
  • Anushaya Mohapatra (Bits-Pilani, K.K Birla Goa Campus)

[00516] Parameters Estimation For Car Following Models Using Bayesian Inference

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E503
• Type : Contributed Talk
• Abstract : Car following (CF) models play an important role in traffic simulation software. Estimating their parameters is necessary to enhance predictive performance and is traditionally accomplished through optimisation. In this research, we adopted Bayesian inference which is advantageous for uncertainty quantification. As the CF model depends on its parameters through solution of a delay differential equation, the likelihood is analytically intractable so we employed an adaptive Markov chain Monte Carlo algorithm to sample from the posterior.
• Classification : 62F15, 65Cxx
• Format : Talk at Waseda University
• Author(s) :
  • Samson Ting (The University of Western Australia)
  • Michael Small (The University of Western Australia)
  • Thomas Stemler (The University of Western Australia)
  • Chao Sun (The University of Western Australia)
  • Thomas Lymburn (The University of Western Australia)

[01648] Parameter identifiability for extensions of the Fisher-KPP model

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E503
• Type : Contributed Talk
• Abstract : The Fisher-KPP model is one of the simplest partial differential equation models exhibiting travelling wave behaviour, and has been widely used to model the growth and spread of populations in biology. When applying the model to experimental data, it is often tempting to generalize the model with additional parameters to obtain a better fit. However, this increase in model complexity also increases the difficulty of estimating the parameter values. In this study, we use a profile likelihood approach to investigate parameter identifiability in extensions of the Fisher-KPP model on both simulated data, and experimental data from a cell invasion assay. We focus on the effects of the forms of the kinetic terms, model misspecifications, and amount of data. We also quantify the amount of data required to justify a more complex model, and explore ways to design experiments to yield data more useful for parameter identification.
• Classification : 62fxx, 62p10, 92cxx
• Format : Online Talk on Zoom
• Author(s) :
  • Yue Liu (University of Oxford)
  • Philip K Maini (University of Oxford)
  • Ruth E Baker (University of Oxford)

[00058] Thermocapillary dynamics of viscous droplet driven by internal thermal singularity

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E503
• Type : Contributed Talk
• Abstract : In a non-isothermal Poiseuille flow, we investigate the impact of an internal thermal singularity on the migration of a viscous immiscible droplet. The migration velocity strongly depends upon the type of thermal singularity and where it is located inside the droplet. In $Re \to 0$ and $Pe \to 0$ limits, this mathematical model provides a control mechanism for droplet migration, which may be useful in a variety of microfluidics as well as industrial applications.
• Classification : 76T06
• Format : Online Talk on Zoom
• Author(s) :
  • Arindam Basak (Indian Institute of Technology Kharagpur)
  • Rajaram Lakkaraju (Indian Institute of Technology Kharagpur)
  • Raja Sekhar G P (Indian Institute of Technology Kharagpur India)

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

room : E504

• [05189] Time fractional gradient flows: Theory and numerics
  • Author(s) :
    • Abner J Salgado (University of Tennessee)
    • Wenbo Li (Chinese Academy of Sciences)
  • Abstract : We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, lower semicontinuous energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals the so-called Caputo derivative of the state. We introduce the notion of energy solutions, for which we provide existence, uniqueness and certain regularizing effects. We also consider Lipschitz perturbations of this energy. For these problems we provide an a posteriori error estimate and show its reliability. This estimate depends only on the problem data, and imposes no constraints between consecutive time-steps. On the basis of this estimate we provide an a priori error analysis that makes no assumptions on the smoothness of the solution.
• [05258] Semiconvexity estimates for integro-differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Marvin Weidner (Universitat de Barcelona)
  • Abstract : The Bernstein technique is a classical tool to establish derivative estimates for solutions to a large class of elliptic and parabolic equations. It is based on the maximum principle applied to suitable auxiliary functions. We explain how the Bernstein technique can be extended to integro-differential equations. As an application, we establish semiconvexity estimates for solutions to the nonlocal obstacle problem, the optimal regularity of the solution and the regularity of the free boundary. Based on a joint work with Xavier Ros-Oton and Damià Torres-Latorre.
• [05644] Gradient flow for symmetric nonlocal Lévy operators
  • Format : Talk at Waseda University
  • Author(s) :
    • Guy Foghem (Technische Universität Dresden )
    • Markus Schmidtchen (Technische Universität Dresden)
    • David Padilla-Garza (Technische Universität Dresden)
  • Abstract : We study a nonlocal continuity equation for the probability density with pressure driven by a symmetric nonlocal Lévy operator. The class of nonlocal operators under consideration appear as a generalization of the classical fractional Laplace operator. We construct weak solutions with respect to the associated homogeneous nonlocal Sobolev space using the minimizing movement scheme technique. The lack of interpolation techniques brings up some difficulties and renders our approach different from the usual interpolation techniques.
• [04692] The Spatially Variant Spectral Fractional Laplacian: Analytical Aspects and Parameter Selection
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carlos Rautenberg (George Mason University)
    • Andrea Ceretani (University of Buenos Aires)
  • Abstract : We consider a variational definition for the spatially variant (spectral) fractional Laplacian and study the well-posedness of the associated Poisson’s equation. The state space for the elliptic problem relies on non-standard Sobolev spaces with weights that are not of Muckenhoupt-type. The increased regularity of solutions is established together with the effectiveness of the fractional operator as a regularization for inverse problems. The latter leads to the optimal selection of the fractional order in image reconstruction.

contributed talk: CT094

room : E505

[02520] A direct method for solving a structured Sylvester equation

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E505
• Type : Contributed Talk
• Abstract : In this talk, we will present a pseudospectral method for 2D advection operators. After discretizing the 2D advection operator by the Legendre-Gauss-Lobatto pseudospectral methods, we obtain a Sylvester equation. The Sylvester equation is equivalent to a block tridiagonal liner system of equations. We propose a URV approach to solve the linear system.
• Classification : 65F05, 65N35
• Format : Talk at Waseda University
• Author(s) :
  • Yung-Ta Li (Fu Jen Catholic University)

[01042] Preconditioners of Reduced Dimension for Vector Field Problems

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E505
• Type : Contributed Talk
• Abstract : When designing preconditioners based on domain decomposition methods, the coarse space plays a key role. In order to keep the scalability, the coarse space of low computational complexity is essential. We introduce a new coarse space of reduced dimension for vector field problems. Numerical results for the problems in three dimensions are also presented.
• Classification : 65F08, 65F10, 65N30, 65N55
• Format : Talk at Waseda University
• Author(s) :
  • Duk-Soon Oh (Chungnam National University)

[01183] Development of algebraic preconditioners based on multiscale domain decomposition methods

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E505
• Type : Contributed Talk
• Abstract : This work presents a new algebraic formulation for the Multiscale Robin Coupled Method - MRCM. This domain decomposition method generalizes other mixed multiscale methods by imposing Robin-type boundary conditions on the local problems. The MRCM is flexible and accurate, obtaining near-optimal scalability up to billions of unknowns in high-performance simulations. We propose a new algebraic formulation, allowing the construction of multiscale-based preconditioners for solving non-symmetric linear systems with Krylov subspace methods, such as GMRES.
• Classification : 65F08, 65N55, 65N08, 76S05
• Format : Talk at Waseda University
• Author(s) :
  • Fabricio Simeoni de Sousa (University of Sao Paulo)
  • Franciane F. Rocha (Wikki Brazil)
  • Luca Meacci (Università degli Studi di Firenze)
  • Rafael T. Guiraldello (Piri Technologies LLC)
  • Roberto F. Ausas (University of Sao Paulo)
  • Gustavo C. Buscaglia (University of Sao Paulo)
  • Felipe Pereira (The University of Texas at Dallas)

[00544] Quantification of Entangled Bipartite Systems

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E505
• Type : Contributed Talk
• Abstract : Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low-rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk.
• Classification : 65F10, 15A24, 65H10, 15A72, 58D19
• Author(s) :
  • Matthew M. Lin (National Cheng Kung University)
  • Moody T. Chu (North Carolina State University)

contributed talk: CT090

room : E506

[02532] Stochastic pseudo-symplectic explicit Runge-Kutta methods for Hamiltonian Systems

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
• Type : Contributed Talk
• Abstract : We propose a systematic approach, based on colored trees and B-series, to construct explicit Runge-Kutta pseudo-symplectic schemes for stochastic Hamiltonian systems in the sense of Stratonovich. Numerical experiments are presented to verify our theoretical analysis and illustrate the long-term accuracy of these methods. Overall, these schemes offer a good compromise between computational time and accuracy, because they are more accurate than the explicit Itô-Taylor approximation methods and less computationally expensive than the implicit symplectic schemes.
• Classification : 65C30, 60H35
• Format : Talk at Waseda University
• Author(s) :
  • cristina adela anton (MacEwan University)

[02361] A unified framework for convergence analysis of stochastic gradient algorithms with momentum: a linear two-step approach

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
• Type : Contributed Talk
• Abstract : From the viewpoint of weak approximation, the stochastic gradient algorithm and stochastic differential equation are closely related. In this talk, we develop a systematic framework for the convergence of stochastic gradient descent with momentum by exploring the stationary distribution of a linear two-step method applied to stochastic differential equations. Then we prove the convergence of two stochastic linear two-step methods, which are associated with the stochastic heavy ball method and Nesterov's accelerated gradient method.
• Classification : 65C30, 60H35
• Format : Online Talk on Zoom
• Author(s) :
  • Qian Guo (Shanghai Normal University)
  • Fangfang Ma (Shanghai Normal University)

[01104] Generation of $hp$-FEM Massive Databases for Deep Learning Inversion

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
• Type : Contributed Talk
• Abstract : Deep Neural Networks are employed in many geophysical applications to characterize the Earth’s subsurface. However, they often need to solve hundreds of thousands of complex and expensive forward problems to produce the training dataset. This work presents a robust approach to producing massive databases at a reduced computational cost. In particular, we build a single $hp$-adapted mesh that accurately solves many FEM problems for any combination of parameters within a given range.
• Classification : 65N30, Finite Element Method, Deep Neural Networks, Goal-Oriented Adaptivity
• Format : Talk at Waseda University
• Author(s) :
  • Julen Alvarez-Aramberri (University of the Basque Country (UPV/EHU))
  • Vincent Darrigrand (CNRS-IRIT, Toulouse)
  • Felipe Vinicio Caro (Basque Center for Applied Mathematics (BCAM), University of the Basque Country (UPV/EHU))
  • David Pardo (University of the Basque Country (UPV-EHU), Basque Center for Applied Mathematics (BCAM), Ikerbasque)

[02305] Simulating First Passage Times for Ito Diffusions

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
• Type : Contributed Talk
• Abstract : We are interested in the mechanism of olfactory receptor neuron responses in moths. A neuron's processing of information is represented by spike trains, collections of spikes, short and precisely shaped electrical impulses. Mathematically, these can be modeled as the first passage times of solutions to certain stochastic differential equations, describing the membrane voltage, to a threshold. Classical numerical methods like the Euler-Maruyama method and the Milstein scheme approximate hitting times as a ‘by-product’ and are not very good if we perform them on a large interval of time. For that reason, we study an algorithm that simulates the exact discretized grid of a class of stochastic differential equations. It uses an acceptance-rejection scheme for the simulation of that grid at random time intervals; later, the whole path can be completed independently of the target process by interpolation of the Brownian or Bessel bridge. This method is very effective in the sense that it neither simulates the whole path nor focuses on a fixed time interval. We further examine the different numerical methods with the help of an example.
• Classification : 65C30, 60H99, 92-10, First Passage Times, Exact Simulations, Applications in Neuroscience
• Format : Talk at Waseda University
• Author(s) :
  • Evelyn Buckwar (Johannes Kepler University)
  • Devika Khurana (Johannes Kepler University)

[02215] Solving Fokker-Planck Equation in High Dimensions via Milestoning

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
• Type : Contributed Talk
• Abstract : We propose a novel method for solving Fokker-Planck-type equations via the Feynman-Kac formula, closely related to rare events sampling. A family of trajectories is maintained between each pair of milestones while new samples are drawn based on an importance-sampling principle. We also show a probabilistic estimate of the sampling error which explains why, so-called, milestoning can significantly speed up molecular dynamics simulations.
• Classification : 65C35, 65C30, 60H35
• Format : Talk at Waseda University
• Author(s) :
  • Ziheng Chen (University of Texas at Austin)
  • Bjorn Engquist (University of Texas at Austin)

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

room : E507

• [04530] Photonic reservoir computing with small networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Joseph David Hart (US Naval Research Laboratory)
    • Thomas Carroll (US Naval Research Laboratory)
    • Francesco Sorrentino (University of New Mexico)
    • Joel Q Grim (US Naval Research Laboratory)
    • Allan Bracker (US Naval Research Laboratory)
  • Abstract : The model-free training permitted by reservoir computing makes it particularly attractive for implementation in analog physical hardware, which can offer significant improvements in speed and power requirements over digital hardware. In many cases, however, it can be difficult or undesirable to build a large, tunable analog network. In this talk, we will present recent results using photonic analog hardware to implement reservoir computers made up of small networks.
• [04854] Latent GP-ODEs with Informative Priors
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ilze Amanda Auzina (University of Amsterdam)
    • Cagatay Yildiz (University of Tuebingen)
    • Efstratios Gavves (University of Amsterdam)
  • Abstract : We propose a novel framework by combining a generative and a Bayesian nonparametric model which learns a physically meaningful latent representation and solves an ODE system in latent space. The model is able to account for uncertainty as well as to be constrained with informative physical priors. The method demonstrates its ability to learn dynamics from high dimensional data and we obtain state-of-the-art performance compared to earlier nonparametric ODE models on dynamic forecasting.
• [04314] A Framework for Hyperparameter Optimization for Randomized Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Oliver Dunbar (Division of Geological and Planetary Sciences, California Institute of Technology)
    • Nicholas Nelsen (California Institute of Technology)
    • Maya Mutic (Princeton University)
  • Abstract : Randomization can be used to replace layers of neural networks or kernel matrices of Gaussian processes. This approach accelerates numerical methods and converts training to a least-squares problem. In practice however, necessary hyperparameter optimization becomes more challenging, as optimization objective functions are non-deterministic. In the context of the random features, we present a framework and algorithm based on the ensemble Kalman filter, that can automate this optimization, and demonstrate practical performance through illustrative examples.

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

room : E508

• [04594] PSCTOOLKIT: Parallel Sparse Computation Toolkit
  • Format : Talk at Waseda University
  • Author(s) :
    • Fabio Durastante (University of Pisa)
    • Pasqua D'Ambra (Institute for Applied Computing (IAC)-National Research Council of Italy (CNR))
    • Salvatore Filippone (University of Rome "Tor Vergata")
  • Abstract : In this talk, we will describe a software framework for solving large and sparse linear systems on hybrid architectures, from small servers to high-end supercomputers, embedding multi-core CPUs and Nvidia GPUs. The framework has a tripartite modular structure, which separates basic functionalities for distributed sparse matrices and sparse matrix computations involved in Krylov methods, eventually exploiting multi-threading and CUDA-based programming models, from the setup and application of different types of preconditioners.
• [04611] Recent Developments in Two-level Schwarz Domain Decomposition Preconditioners in Trilinos
  • Format : Talk at Waseda University
  • Author(s) :
    • Ichitaro Yamazaki (Sandia National Labs)
    • Alexander Heinlein (Delft University of Technology (TU Delft))
    • Sivasankaran Rajamanickam (Sandia National Labs)
  • Abstract : Domain decomposition methods are used to build a class of effective parallel solvers for sparse linear systems arising from the discretization of partial differential equations. FROSch is a software package, which implements GDSW type Two-level Schwarz Domain Decomposition preconditioners in Trilinos. In this talk, we present several recent developments made in FROSch.
• [05152] Preparing Algebraic Multigrid Solvers in hypre for Exascale Computers
  • Format : Talk at Waseda University
  • Author(s) :
    • Rui Peng Li (LLNL)
  • Abstract : The emerging exascale computers provide opportunities to perform much larger scale simulations to obtain more accurate solutions than ever before. The increasing complexities of heterogeneous accelerators on such platforms have made the development of sparse linear solvers challenging to achieve high performance. In this talk, we will discuss the porting strategies, new developments and performance optimizations of the multigrid solvers in hypre in preparation for the exascale computers with the results from real application codes.
• [04535] JXPAMG: an auto-tuning parallel AMG solver for extreme‑scale numerical simulations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaowen Xu (IAPCM)
    • Silu Huang (IAPCM)
    • Xiaoqiang Yue (Xiangtan University)
    • Runzhang Mao (IAPCM)
  • Abstract : JXPAMG is a parallel algebraic multigrid (AMG) solver for solving the extreme-scale sparse linear systems on modern supercomputers. It is designed follows the auto-tuning mechanisms allow JXPAMG to use different AMG strategies for different application features and architecture features, and thereby JXPAMG becomes aware of changes in these features. This talk introduces the algorithms, implementation techniques, auto-tuning mechanisms and applications of JXPAMG.

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

room : E603

• [01505] Eigen-decomposition and Fast Solvers for Maxwell's Equations for 3D Photonic Crystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiexiang Li (Southeast University)
    • Heng Tian (Sichuan University of Science and Engineering)
    • Xing-Long Lyu (Southeast University)
    • Wen-Wei Lin (National Yang Ming Chiao Tung University)
  • Abstract : In this article, we propose the Fast Algorithms for Maxwell's Equations FAME package for solving Maxwell's equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform FFT-based matrix-vector multiplications to solve the generalized eigenvalue problems GEPs arising from the oblique Yee's discretization. Numerical results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.
• [01246] Projected Gradient Method for Volume-Measure-Preserving Optimal Mass Transportation Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsung-Ming Huang (National Taiwan Normal University)
    • Wei-Hung Liao (National Yang Ming Chiao Tung University)
    • Wen-Wei Lin (National Yang Ming Chiao Tung University)
    • Mei-Heng Yueh (National Taiwan Normal University)
    • Shing-Tung Yau (Tsinghua University)
  • Abstract : Volumetric stretch energy minimization (VSEM) has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models. In this talk, based on the VSEM algorithm, we propose a projected gradient method for the computation of the volume/mass-preserving optimal mass transport map with a guaranteed convergence rate of O(1/m). Numerical experiments are presented to justify the theoretical convergence behavior for various examples drawn from known benchmark models. Moreover, these numerical experiments show the effectiveness and accuracy of the proposed algorithm, particularly in the processing of 3D medical MRI brain images.
• [01095] Multitask kernel-learning Gaussian process regression parameter prediction method and its application in matrix splitting iteration methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan Zhang (Xiangtan University)
  • Abstract : In this talk, we present a multitask kernel-learning Gaussian process regression (GPR) parameter prediction method, and apply it in matrix splitting iteration methods. The first application is developing a general alternating direction implicit (ADI) framework, which can put most existing ADI methods into a unified framework and offer more new ADI approaches. Using the GPR method, the splitting parameter selection of this framework can be solved. The second application is for solving time-dependent linear systems, we give a new matrix splitting Kronecker product method, which can unify the existing Kronecker product schemes. Using the Multitask kernel-learning method, simultaneous multiple splitting parameters prediction and data-driven kernel learning can all be achieved. Based on Bayesian inference, the GPR method only requires a small training data set for learning the regression prediction mapping, and has sufficient accuracy and high generalization capability. We apply our developed methods to solving (time-dependent) convection-diffusion equations and (differential) Sylvester matrix equations. Numerical results illustrate our methods can solve large sparse linear systems more efficiently compared with existing methods.
• [01322] Breakdown Avoidance Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yueh-Cheng Kuo (National university of Kaohsiung)
  • Abstract : Structure-Preserving Doubling Algorithms (SDAs) are efficient algorithms for solving Riccati-type matrix equations. However, the breakdown may happen in the SDA. To avoid the breakdown, we first introduce the class of $\Omega$-symplectic forms, $\Omega$-SF, consisting of symplectic matrix pairs with Hermitian parametric matrix $\Omega$. Based on the $\Omega$-SF, we developed modified SDAs, called MSDAs, for solving the Riccati-type equations. The MSDA generates a sequence of symplectic matrix pairs in $\Omega$-SF and can avoid the breakdown by employing a suitable Hermitian matrix $\Omega$. In addition, we show that the Hermitian matrix $\Omega$ in MSDAs can be chosen as a real diagonal matrix which can reduce the computational complexity. In this case, MSDA and SDA have the same computational complexity.

MS [02448] Verified Numerical Computations and Applications

room : E604

• [05276] Lower Bounds for Smallest Singular-Values of Asymptotic Diagonal Dominant Matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Shin'ichi Oishi (Waseda University)
  • Abstract : This article presents three classes of real square matrices. They are models of coefficient matrices of linearized Galerkin's equations of first order nonlinear delay differential equations with smooth nonlinearity. This paper shows results of computer experiments stating that the minimum singular values of these matrices are unchanged even if orders of matrices are increased. A theorem is presented based on the Schur complement. Through it, tight lower bounds are derived for the minimum singular values of such three matrices. It is proved that these lower bounds are unchanged even if orders of matrices are increased.
• [05029] Error estimation for the FEM solution with a few bad elements
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenta Kobayashi (Hitotsubashi University)
  • Abstract : In conventional error analysis for the finite element method, even one bad element results in poor error estimation. However, numerical results suggest that a few bad elements do not lead to an increase in error. We have provided theoretical proof for this fact, together with the error estimation, that under certain conditions, the presence of a few bad elements does not worsen the error of the finite element method.
• [03173] Verified Numerical Computations for multiple solutions of the Henon equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Taisei Asai (Waseda University)
    • Kazuaki Tanaka (Waseda University)
    • Shin'ichi Oishi (Waseda University)
  • Abstract : In this talk, we describe a numerical verification of the Henon equation in which some asymmetric solutions arise due to the nonlinear term. The existence of multiple solutions is verified on various domains, and the relationship between the domain and the symmetry of the solution will be discussed.
• [05290] Rigorous solution-enclosures of elliptic boundary value problems between piecewise linear functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazuaki Tanaka (Waseda University)
  • Abstract : Sub- and super-solutions are useful for obtaining stable solutions of elliptic boundary value problems. However, their conventional definition requires smoothness, which makes it difficult to construct sub- and super-solutions using piecewise linear functions. To overcome this issue, we propose a definition that uses a variational inequality and constrained test functions. We show that the generalized sub- and super-solutions enclose the desired solutions, and that even a simple difference method can construct sub- and super-solutions that enclose the true solutions.

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

room : E605

• [04070] Conductivity imaging using deep neural networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bangti Jin (Chinese University of Hong Kong)
  • Abstract : Conductivity imaging from various observational data represents one fundamental task in medical imaging. In this talk, we discuss numerical methods for identifying the conductivity parameters in elliptic PDEs. Commonly, a regularized formulation consists of a data fidelity and a regularizer is employed, and then it is discretized using finite difference method, finite element methods or deep neural networks in practical computation. One key issue is to establish a priori error estimates for the recovered conductivity distribution. In this talk, we discuss our recent findings on using deep neural networks for this class of problems, by effectively utilizing relevant stability results.
• [04396] Model-corrected learned primal-dual models for fast photoacoustic tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Andreas Hauptmann (University of Oulu)
  • Abstract : Learned iterative reconstructions hold great promise to accelerate tomographic imaging with empirical robustness to model perturbations. Adoption for photoacoustic tomography is hindered by the computational expensive forward model. Computational feasibility can be obtained by the use of fast approximate models, but model errors need to be compensated. In this talk we discuss conceptual difficulties and present methodological advances for model corrections in learned image reconstructions by embedding the model correction in a learned primal-dual framework.
• [03165] Learning the Regularisation Parameter for Inverse Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sebastian Scott (University of Bath)
    • Matthias Ehrhardt (University of Bath)
    • Silvia Gazzola (University of Bath)
  • Abstract : Solving linear inverse problems via variational regularisation involves the use of unknown regularisation parameters. In order to attain a meaningful reconstruction, these parameters must be carefully chosen. This work will cover bilevel learning, a framework in which one is able to learn appropriate parameter values via a machine learning approach.
• [04247] Lipschitz Training for Adversarially Robust Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Tim Roith (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : Adversarial examples have revealed the vulnerability of neural networks, making stability and robustness key concerns. To address this, we explore the role of the Lipschitz constant in adversarial machine learning. I will present an algorithm that employs an approximate Lipschitz constant as a regularizer. In each training step, we compute points that aim to maximize a difference quotient. Finally, I will discuss the conceptual limits of methods enforcing a low Lipschitz constant of neural networks.

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

room : E606

• [04291] A learned conservative semi-Lagrangian finite volume scheme for transport simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei Guo (Texas Tech University)
    • Yongsheng Chen (Zhejiang University)
    • Xinghui Zhong (Zhejiang University)
  • Abstract : Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many. In this talk, we introduce a novel machine learning-assisted approach to accelerate the conventional SL finite volume schemes. The proposed scheme avoids the expensive tracking of upstream cells but attempts to learn the SL discretization from the data by incorporating specific inductive biases in the neural network, significantly simplifying the algorithm implementation and leading to improved efficiency.
• [03990] A new type of simplified inverse Lax-Wendroff boundary treatment for hyperbolic conservation laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Shihao Liu (University of Science and Technology of China)
    • Tingting Li (Henan University)
    • Ziqiang Cheng (Hefei University of Technology)
    • Yan Jiang (University of Science and Technology of China)
    • Chi-Wang Shu (Brown University)
    • Mengping Zhang (University of Science and Technology of China)
  • Abstract : In this talk, we will introduce a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh, in which both scalar equations and systems are considered. This new ILW method decomposes the construction of ghost points into two steps: interpolation and extrapolation. At first, we approximate some special points value through interpolation polynomial given the interior points near boundary. Then, we will construct a Hermite extrapolation polynomial based on those special point values and spatial derivatives at boundary obtained through ILW process. This extrapolation polynomial will give us the approximation of the the ghost points value. Eigenvalue analysis shows that the new method can improve the computational efficiency on the premise of maintaining accuracy and stability. Numerical tests for one- and two-dimensional problems indicate that our method has high order accuracy for smooth solutions and non-oscillatory property for shock solution near boundary.
• [02713] Transmission Dynamics of Tuberculosis with Age-specific Disease Progression
  • Format : Talk at Waseda University
  • Author(s) :
    • Wing-Cheong Lo (City University of Hong Kong)
  • Abstract : In this talk, we develop a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of the disease stage. We determine the basic reproduction number and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. This is joint work with Yu Mu, Tsz-Lik Chan, and Hsiang-Yu Yuan.
• [02985] Extended-release Pre-Exposure Prophylaxis and Drug Resistant HIV
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanping Ma (Loyola Marymount University)
    • Yeona Kang (Howard University)
    • Angelica Davenport (Florida State University)
    • Jennifer Aduamah (University of Delaware)
    • Kathryn Link (Pfzier)
    • Katharine Gurski (Howard University)
  • Abstract : We present a within-host, mechanistic Differential Equation model of the HIV latency and infection cycle in CD4+ T-cells to investigate drug-resistant mutations. We develop a pharmacokinetic/pharmacodynamic model for long-acting cabotegravir (CAB-LA, injectable PrEP) to relate the inhibitory drug response to the drug concentration in plasma and rectal, cervical, and vaginal fluids and tissue. And we will report some of our important findings in the talk.

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

room : E701

• [04343] Energy stability of variable step higher order ETD-MS scheme for gradient flows
  • Author(s) :
    • Xiaoming Wang (Missouri University of Science and Technology)
  • Abstract : We present a family of ETD-MS based variable-step higher order numerical schemes for a family of gradient flows. We demonstrate the energy stability of this family of numerical algorithms. Numerical examples will be provided to show the effectiveness of the schemes.
• [04034] Energy Dissipation of Time-Fractional Phase-Field Equations: Analysis and Numerical methods
  • Author(s) :
    • Jiang Yang (Southern University of Science and Technology)
  • Abstract : There exists a well defined energy dissipation law for classical phase-field equations, i.e., the energy is non-increasing with respect to time. However, it is not clear how to extend the energy definition to time-fractional phase-field equations so that the corresponding dissipation law is still satisfied. In this work, we will try to settle this problem for phase-field equations with Caputo time-fractional derivative, by defining a nonlocal energy as an averaging of the classical energy with a time-dependent weight function. To deal with this, we propose a new technique on judging the positive definiteness of a symmetric function, that is derived from a special Cholesky decomposition. Then, the nonlocal energy is proved to be dissipative under a simple restriction of the weight function. Within the same framework, the time fractional derivative of classical energy for time-fractional phase-field models can be proved to be always nonpositive. At the discrete level, a fast L2-1$_\sigma$ method on general nonuniform meshes is employed. The global-in-time $H^1$-stability is established via the same framework.
• [02973] A Spectral Element in Time Method for Nonlinear Gradient Systems
  • Author(s) :
    • Shiqin Liu (University of Chinese Academy of Sciences)
    • Haijun Yu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : We present a spectral element in time method for large scale nonlinear gradient systems, with the phase-field Allen-Cahn equation as an example. Different to commonly-used spectral in time methods that employ Petrov-Galerkin or weighted Galerkin approximations, the present method employs a natural variation Galerkin form that maintains volume conservation and energy dissipation property of the continuous dynamical systems. Explicit extrapolation is applied to handle the nonlinear term, which makes the method efficient. The explicit method can be improved by a few Picard iterations to obtain superconvergence. Numerical experiments confirm that the method outperforms the popular BDF4 scheme and the ETD-RK4 method.
• [02987] Energy stability and error analysis of high-precision algorithms for two-phase incompressible flows
  • Author(s) :
    • Xiaoli Li (Shandong University)
  • Abstract : In this talk, we will first present several efficient and high-precision schemes for the two-phase incompressible flows. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. We carry out a rigorous error analysis for the first-order scheme, establishing optimal convergence rate for all relevant functions in different norms. Next we shall discuss the consistent splitting GSAV approach for the Navier-Stokes equations and carry out theoretical analysis.

contributed talk: CT102

room : E702

[01848] A Higher Order Schwarz Domain Decomposition Method for Singularly Perturbed Differential Equation

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : We consider a fourth order singularly perturbed differential equation. To solve the problem, the differential equation is transformed into a coupled system of singularly perturbed differential equations. The original domain is divided into three overlapping subdomains. On the regular subdomain, a hybrid scheme is used, while a compact fourth order difference scheme is used on the two boundary layer subdomains on a uniform mesh. We demonstrate that proposed scheme is nearly fourth order uniformly convergent.
• Classification : 65M06
• Format : Talk at Waseda University
• Author(s) :
  • AAKANSHA AAKANSHA (Indian Institutes of Technology (Banaras Hindu University) Varanasi)

[01248] Reduction of Computational Cost with Optimal Accurate Approximation for Boundary Layer Originated Two Dimensional Coupled System of Convection Diffusion Reaction Problems

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : In this talk, I will consider a generalized form of a coupled system of time dependent convection diffusion reaction problems having arbitrary small diffusion terms, which lead to boundary layers. The numerical approximations of these problems require adaptive mesh generation for uniformly convergent approximation. In the present talk, I will provide an algorithm which will reduce the computational cost of the system solver by converting the system of discrete equations to a tridiagonal matrix form. This approach together with an adaptive mesh generation technique will preserve the optimal convergence accuracy. This convergence is proved to be independent of diffusion terms magnitude.
• Classification : 65M06, 65M50, 65N50, Computational Cost Reduction, Error Analysis, Adaptive Mesh Generation, Coupled System of Time Dependent PDEs, Two Dimension
• Format : Online Talk on Zoom
• Author(s) :
  • Pratibhamoy Das (Indian Institute of Technology Patna)
  • Pratibhamoy Das (Indian Institute of Technology Patna)
  • Shridhar Kumar (Indian Institute of Technology Patna)

[02229] Efficient numerical methods for time-fractional Black-Scholes equation arising in finance

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : Two numerical schemes to solve time-fractional Black-Scholes PDE governing European options. are proposed. First, fractional derivative is discretized by L1-scheme and spatial derivatives by cubic spline method on uniform mesh. Secondly, we discretize temporal variable by L1-scheme on non-uniform mesh and spatial derivatives by NIPG method on uniform mesh. Stability, convergence and numerical results are carried out. Three European options are priced as application and impact of time-fractional derivative order on option price is shown.
• Classification : 65M06, 65M12, 65M15
• Format : Online Talk on Zoom
• Author(s) :
  • Jaspreet Kaur Anand (Indian Institute of Technology Guwahati, Guwahati, Assam)
  • Natesan Srinivasan (Indian Institute of Technology Guwahati, Guwahati, Assam)

[01742] A signed distance function preserving scheme for mean curvature flow and related applications

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : Mean curvature flow is an important research topic in geometry, applied mathematics, and the natural sciences. In this talk, we propose a scheme for solving mean curvature flow and some related problems efficiently and accurately on Cartesian grids. Our method uses the sign distance function defined in a narrowband near the moving interface to represent the evolution of the curve. We derive the equivalent evolution equations of distance function in the narrowband. The novelty of the work is to determine the equivalent evolution equation on Cartesian girds without extra conditions or constraints. The proposed method extends the differential operators appropriately so that the solutions on the narrowband are the distance function of the solution to the original mean flow solution. Furthermore, the extended solution carries the correct geometric information, such as distance and curvature, on Cartesian grids. Consequently, it is possible to adapt the existing numerical methods, for instance, finite difference or WENO scheme, that are developed on the Cartesian grids to solve PDEs on curves. The computational domain is a thin narrowband whose widths are a small constant multiple of uniform Cartesian grid spacing. Some experiments confirm that the proposed method is convergent numerically.
• Classification : 65M06
• Author(s) :
  • Chia-Chieh Jay Chu (National Tsing Hua UniversityB)

[01634] Mimetic schemes applied to the convection diffusion equation: A numerical comparison.

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : Mimetic Finite Difference Schemes (DFM) are increasingly present in the numerical resolution of transient problems [1] since they are more precise than traditional Finite Difference (DF) schemes. However, there are methods in DF that use appropriate combinations of schemes in different nodes in order to eliminate the numerical spread of the method, [2]. In these cases, DF methods are more accurate than DFM. In this work, we start from the equation of convection-diffusion of an incompressible fluid ∂u/∂t+v·∇u=∇·(K∇u), (1) where u(x, t) represents the unknown of the problem, v(x, t) is the velocity, K is the diffusion tensor, and DFM is defined that eliminates the numerical diffusion presented by traditional DFM schemes. To measure the effectiveness of the mimetic schemes, for different configurations of (1), they are compared with the equivalent schemes in DF with the same order of precision as the DFM; for this purpose, the second-order schemes proposed by [2, 3] are taken. Finally, different comparisons are made to verify the results obtained by the given schemes. References: [1] Castillo J. and Grone R.D. A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law. SIAM J. Matrix Anal. Appl., 25(1):128– 142, 2003. [2] Mehdi Dehghan. Weighted finite difference techniques for the one-dimensional advection-diffusion equation. Applied Mathematics and Computation, 147(2):307–319, 2004. [3] Mehdi Dehghan. Quasi-implicit and two-level explicit finite-difference procedures for solving the one-dimensional advection equation. Applied Mathematics and Computation, 167(1):46–67, 2005.
• Classification : 65M06, 65M99
• Author(s) :
  • Jorge Ospino (Universidad del Norte)
  • Giovanni Calderon (Universidad Industrial de Santander)
  • Jorge Villamizar (Universidad Industrial de Santander)

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

room : E703

• [04124] Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods
  • Format : Online Talk on Zoom
  • Author(s) :
    • Paola Francesca Antonietti (Politecnico di Milano)
    • Mattia Corti (Politecnico di Milano)
    • Luca Dede' (Politecnico di Milano)
    • Alfio Quarteroni (Politecnico di Milano)
  • Abstract : In this talk we introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark β-method for the momentum equation and a θ-method for the pressure equations. We present verification numerical results and perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. We also present a simulation in a three-dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model perfusion in the brain.
• [03151] Cell-average based Neural Network method for time dependent PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Changxin Qiu (Ningbo University)
    • Jue Yan (Iowa State University)
  • Abstract : Motivated by finite volume scheme, a cell-average based neural network method is proposed. The method is based on the integral or weak formulation of partial differential equations. Offline supervised training is carried out to obtain the optimal network parameter set, which uniquely identifies one finite volume like neural network method. Once well trained, the network method is implemented as a finite volume scheme and can adapt large time step size for solution evolution.
• [04606] A non-overlapping Schwarz algorithm for the HDG method
  • Format : Talk at Waseda University
  • Author(s) :
    • Issei Oikawa (University of Tsukuba)
  • Abstract : This talk is concerned with a non-overlapping Schwarz algorithm for the hybridizable discontinuous Galerkin (HDG) method for the steady-state diffusion problem. We present several iterative algorithms based on the non-overlapping Schwarz domain decomposition method and their numerical results.
• [03898] Adaptive methods for fully nonlinear PDE
  • Format : Online Talk on Zoom
  • Author(s) :
    • Iain Smears (University College London)
  • Abstract : Hamilton--Jacobi--Bellman and Isaacs equations are important classes of fully nonlinear PDE with applications from stochastic optimal control and two player stochastic differential games. In this talk, we present our recent proof of the convergence of a broad family of adaptive nonconforming DG and $C^0$-interior penalty methods for the class of these equations that satisfy the Cordes condition in two or three space dimensions. The adaptive mesh refinement is driven by reliable and efficient a posteriori error estimators, and convergence is proven in $H^2$-type norms without higher regularity assumptions of the solution. A foundational ingredient in the proof of convergence is the concept of the limit space used to describe the limiting behaviour of the finite element spaces under the adaptive mesh refinement algorithm. We develop a novel approach to the construction and analysis of these nonstandard function spaces via intrinsic characterizations in terms of the distributional derivatives of functions of bounded variation. We provide a detailed theory for the limit spaces, and also some original auxiliary function spaces, that resolves some foundational challenges and that is of independent interest to adaptive nonconforming methods for more general problems. These include Poincare and trace inequalities, a proof of the density of functions with nonvanishing jumps on only finitely many faces of the limit skeleton, symmetry of the Hessians, approximation results by finite element functions and weak convergence results.

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

room : E704

• [04076] Local approximation of operators
  • Format : Talk at Waseda University
  • Author(s) :
    • HRUSHIKESH N MHASKAR (Claremont Graduate University)
  • Abstract : We study the question of approximation of an operator $\mathfrak{F}$ from one metric space $X$ to another, $Y$. The input $f\in X$ and $\mathfrak{F}(f)$ are encoded in terms of a point on a sphere $S^d$ ($S^D$), Local approximation techniques are developed to achieve approximation of properly defined smooth function in a tractable manner.
• [04141] Neural operator surrogates for Gaussian inputs
  • Format : Talk at Waseda University
  • Author(s) :
    • Jakob Zech (Universität Heidelberg)
  • Abstract : In this talk we discuss the use of operator surrogates to approximate smooth maps between infinite-dimensional Hilbert spaces. Such surrogates have a wide range of applications in uncertainty quantification and parameter estimation problems. The error is measured in the $L^2$-sense with respect to a Gaussian measure on the input space. Under suitable assumptions, we show that algebraic and dimension-independent convergence rates can be achieved.
• [03497] Derivative-Informed Neural Operators for Scalable and Efficient UQ
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas O'Leary-Roseberry (The University of Texas at Austin)
    • Omar Ghattas (The University of Texas at Austin)
    • Peng Chen (Georgia Tech)
    • Umberto Villa (The University of Texas at Austin)
    • Dingcheng Luo (The University of Texas at Austin)
    • Lianghao Cao (The University of Texas at Austin)
  • Abstract : We present a novel operator learning methodology "derivative-informed neural operators" (DINOs) that can accurately represent both operator maps and their derivatives in function spaces. DINOs are built using advanced adjoint methods and dimension reduction techniques, resulting in efficient computation of derivative quantities that can facilitate fast and scalable UQ. We showcase the potential of DINOs in two applications: Bayesian inversion using data from the 2011 Tōhoku earthquake, and optimal control of PDEs under uncertainty.
• [05169] Deep Operator Network Approximation Rates for Lipschitz Operators
  • Format : Online Talk on Zoom
  • Author(s) :
    • Christoph Schwab (ETH Zurich)
  • Abstract : We establish expression rate bounds for neural Deep Operator Networks (DON) emulating Lipschitz continuous maps G between (suitable subsets of) separable Hilbert spaces X and Y. The DON architecture uses linear encoders E and decoders D via Riesz bases of X, Y, and an approximator network of a parametric coordinate map that is Lipschitz continuous on the sequence space. The present results require mere Lipschitz (or Holder) continuity of G.

MS [00201] Data-Driven Methods for Rough PDEs

room : E705

• [03744] GMsFEM based multiscale model learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric Chung (The Chinese University of Hong Kong)
    • Yiran Wang (Purdue University)
    • Shubin Fu (Eastern Institute for Advanced Study)
  • Abstract : In this talk, we present a deep learning based reduced order modeling method for stochastic flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate mapping from the stochastic parameter space that characterizes the possible highly heterogeneous media to the solution space of a stochastic flow problem. The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Projects: 14305222 and 14304021).
• [03131] Multilevel Picard Approximation Algorithm for Semi-linear Integro-differential Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Ariel Neufeld (Nanyang Technological University)
    • Sizhou Wu (Nanyang Technological University)
  • Abstract : We introduce a multilevel Picard approximation algorithm for semi-linear parabolic partial integro-differential equations (PIDEs). We prove that the numerical approximation scheme converges to the unique viscosity solution of the PIDE under consideration. To that end, we derive a nonlinear Feynman-Kac formula. Furthermore, we show that the algorithm does not suffer from the curse of dimensionality, i.e., the computational complexity of the algorithm is bounded polynomially in the dimension and the reciprocal of the prescribed accuracy.
• [03090] Exponentially Convergent Multiscale Finite Element Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Yixuan Wang (California Institute of Technology)
  • Abstract : Exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation is proposed. ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.
• [05179] Learning Solutions to Elliptic PDEs with Discontinuous Multiscale Parameters
  • Format : Talk at Waseda University
  • Author(s) :
    • Margaret Katherine Trautner (California Institute of Technology)
  • Abstract : Elliptic partial differential equations with discontinuous coefficients arise in modeling dynamics of solid materials. When these coefficients are also multiscale, homogenization theory eliminates the rapidly-varying stiff variable. The bottleneck of this approach is solving an associated cell problem whose discontinuous parameters make solving computationally expensive. Thus, we aim to learn the cell problem solution via data-driven means. In this talk, we describe rigorous theory underpinning these learning methods and numerical experiments that validate the theory.

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

room : E708

• [03198] Simulating solid-state dewetting of thin films: a phase-field approach
  • Author(s) :
    • Wei Jiang (Professor)
  • Abstract : TBA
• [03625] Modeling and simulation for solid-state dewetting problems
  • Author(s) :
    • Quan Zhao (University of Regensburg)
  • Abstract : Deposited thin films are unstable and could dewet to form isolated islands on the substrate in order to minimize the total surface energy. I will introduce a sharp-interface model and a diffuse-interface model for describing the dewetting of solid thin films with anisotropic surface energies. The relationship between the two models is established via the asymptotic analysis. Numerical results are presented to validate the asymptotic results and to demonstrate the anisotropic effects in the evolution.
• [02975] Modeling and Energy Stable Numerical Schemes of Network Development in Biology Gels
  • Author(s) :
    • BOYI WANG (TU Wien)
  • Abstract : In this paper, we focus on the modeling and simulation of the network development in biological gels. A thermodynamically consistent model with homogenous Neumann or periodic boundary condition is derived based on the Rayleighian method. Two fully discrete numerical schemes are proposed to solve the problem. Energy stability is achieved at the discrete level for both schemes. Positivity-preserving property can be shown for the model with the Flory—Huggins potential at continuous and discrete level.
• [03582] The mixed finite element method applied to cavitation in incompressible nonlinear elasticity
  • Author(s) :
    • Weijie Huang (Beijing Jiaotong University)
  • Abstract : In this talk, I will introduce a mixed finite element method for solving cavitation problem for 2D incompressible nonlinear elastic materials. The method is analytically proved to be locking-free and convergent, and it is also shown to be numerically accurate and efficient by numerical experiments. Furthermore, the newly developed accurate method enables us to find an interesting bifurcation phenomenon in multi-cavity growth.

contributed talk: CT110

room : E709

[02444] Pricing American XVA with stochastic default intensity

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : We derive a PDE model for American derivatives' pricing including the valuation adjustment (XVA), assuming mean-reverting default risk for the counterparty, and constant default risk for the self-party. There are two nonlinear source terms, one from the American constraint and one from the XVA, handled by a double-penalty iteration. We also derive asymptotic approximations to the XVA price and to the free boundary. We present numerical experiments to study the accuracy and effectiveness of the 2D PDE and asymptotic approximations.
• Classification : 65Mxx, 65Nxx, 91Gxx
• Format : Talk at Waseda University
• Author(s) :
  • Christina Christara (University of Toronto)
  • Yuwei Chen (University of Toronto)

[00365] Advancing Computerized Tomography: Deep-Learning based Regularization in Diffuse Optical Tomography

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : X-rays Computed Tomography is a main pillar of medical imaging which at present is experiencing a strong innovation phase. While new tomographic systems try to minimize X-rays exposure, non-trivial challenges exist, mainly increased noise levels and the need for dealing with low and high contrast regions. In this talk we will refer about our research on new algorithms able to efficiently deal with this trade–off, with specific reference to Diffuse Optical Tomography.
• Classification : 65Z05, 65N20, 65N80, 68T07
• Format : Talk at Waseda University
• Author(s) :
  • Paola Causin (University of Milano )
  • Andrea Aspri (University of Milano )

[00651] Parallel Coordinate Descent Methods for Full Configuration Interaction

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : Solving the time-independent Schrödinger equation gives us full access to the chemical properties of molecules. Among all the ab-initio methods, full configuration interaction (FCI) provides the numerically exact solution under a predefined basis set. However, the FCI problem scales factorially with respect to the number of bases and electrons and suffers from the curse of dimensionality. The FCI problem could be reformulated as an unconstraint minimization problem. This work proposes a novel algorithm to address the minimization problem. The algorithm introduces an extra search dimension to enable the exact linesearch for the multi-coordinate descent method, which could be fully parallelized. Hence, the proposed algorithm benefits from both exact linesearch and parallelization. Numerically, we demonstrate the parallel efficiency of the algorithm. The algorithm achieves better energy and parallelism on systems with approximately a hundred electrons than other existing methods.
• Classification : 65Z05, 68Q12
• Format : Talk at Waseda University
• Author(s) :
  • Yuejia Zhang (Fudan University)
  • Yingzhou Li (Fudan University)

[00393] Mathematical Modelling of Bilayered Cathodes for Lithium-Ion Batteries

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : Bilayered cathodes are promising candidates to improve lithium-ion battery performance by optimising the electrode design. In this work, lithium iron phosphate and nickel manganese cobalt chemistries are connected in two discrete layers within a cathode, which improves the C-rate performance above 2C compared to uniform cells. To inform the design process we create mathematical model to accommodate multilayers. The model is solved numerically, validated against data and explains how each layer acts.
• Classification : 35Qxx, 37Nxx
• Format : Talk at Waseda University
• Author(s) :
  • Eloise Tredenick (University of Oxford)

[01172] Spatio-structural partial differential equation (PDE) modelling for single-cell cancer data

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : Melanoma routinely develops resistance to targeted therapies, leading to unfavourable prognosis for patients. We introduce a novel approach to modelling single-cell RNA-seq data obtained from melanoma tumours, using partial differential equations (PDEs) to represent the tumour as a spatio-structural population. We show how non-spatial data can be used to predict spatially heterogeneous distributions of cell types, within the tumour, and explore combination therapies and treatment strategies to overcome traditional patterns of resistance.
• Classification : 35Q92, 37N25, 62P10, 92-10, 35G20, Mathematical Oncology, PDEs
• Author(s) :
  • Arran Hodgkinson (Queen's University Belfast)
  • Arran Hodgkinson (Queen's University Belfast)
  • Dumitru Trucu (University of Dundee)
  • Matthieu Lacroix (Institut de Recherche en Cancerologie de Montpellier)
  • Laurent Le Cam (Institut de Recherche en Cancerologie de Montpellier)
  • Ovidiu Radulescu (Universite de Montpellier)

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

room : E710

• [04946] A conforming finite element method for a nonisothermal fluid-membrane interaction
  • Format : Talk at Waseda University
  • Author(s) :
    • Ricardo Oyarzúa (Universidad del Bio-Bio)
  • Abstract : We propose a conforming finite element method for a nonisothermal fluid-membrane interaction problem. The governing equations are given by a Navier-Stokes/Darcy system for the fluid variables and a convection-diffusion model for the temperature. Both systems are coupled through buoyancy terms and a set of transmission conditions on the fluid-membrane interface given by mass conservation, balance of normal forces, the Beavers-Joseph-Saffman law, and the continuity of the heat flux and the fluid temperature.
• [05072] Multipoint mixed finite elements for Biot poroelasticity using a rotation-based formulation
  • Format : Talk at Waseda University
  • Author(s) :
    • Wietse Boon (Politecnico di Milano)
    • Alessio Fumagalli (Politecnico di Milano)
    • Anna Scotti (Politecnico di Milano)
  • Abstract : We propose a discretization method for Biot poroelasticity that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The solid rotation and fluid flux are introduced as auxiliary variables and subsequently removed from the system using a local quadrature rule, leading to a multipoint rotation-flux mixed finite element method. By analyzing the method in terms of weighted norms, we additionally obtain parameter-robust preconditioners.
• [05593] Application of CutFEM to the modeling of coastal processes through vegetation
  • Author(s) :
    • Chris Kees (Louisiana State University)
    • Wen-Huai Tsao (Louisiana State University)
  • Abstract : We consider viscous and depth-averaged models of non-hydrostatic coastal wave propagation through vegetation. Our aim is to model wave height attenuation and momentum dissipation through marsh vegetation. Each model requires a significantly different set of numerical methods to achieve higher-order accuracy in a robust manner, and we will discuss several of these, including CutFEM and multiscale methods. Finally we present results on experimental data obtained from physical models of wave/structure interaction.

MS [02423] Non-standard finite element methods

room : E711

• [04728] Adaptive FEM for Helmholtz equation with large wave number
  • Author(s) :
    • Haijun Wu (Nanjing University)
    • Songyao Duan (Nanjing University)
  • Abstract : A posteriori upper and lower bounds are derived for the finite element method (FEM) for the Helmholtz equation with large wavenumber. It is proved rigorously that the standard residual type error estimator seriously underestimates the true error of the FE solution for the mesh size $h$ in the preasymptotic regime, which is first observed by [Babuska,~et~al., A posteriori error estimation for finite element solutions of Helmholtz equation. Part I, Int. J. Numer. Meth. Engrg. 40, 3443--3462 (1997)] for a one dimensional problem. By establishing an equivalence relationship between the error estimators for the FE solution and the corresponding elliptic projection of the exact solution, an adaptive algorithm is proposed and its convergence and quasi-optimality are proved under the condition that $k^{2p+1}h_0^{2p}$ is sufficiently small, where $k$ is the wavenumber, $h_0$ is the initial mesh size.
• [03581] Stable Finite Element Scheme for Dynamic Ginzburg-Landau Equations
  • Author(s) :
    • Limin Ma (Wuhan University)
  • Abstract : We propose a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. The maximum bound principle of the order parameter and the energy dissipation law in the discrete sense are proved, which can guarantee the stability and validity of the numerical simulations, and further facilitate the adoption of adaptive time-stepping strategy. An optimal error estimate of the proposed scheme is also proved and verified by numerical examples.
• [03508] Local bounded commuting projection operators for discrete finite element complexes
  • Author(s) :
    • Ting Lin (Peking University)
  • Abstract : Local bounded commuting projection operators are an important tool in the analysis of finite element exterior and mixed finite element methods. However, so far only those of the standard finite element spaces have been discussed. In this talk, I will introduce the construction of local bounded commuting projection operators of the discrete finite element complexes, with some possible applications. The techniques developed here also give us a new perspective on the construction of finite element complexes.
• [04168] The weak Galerkin method for elliptic eigenvalue problems
  • Author(s) :
    • Qilong Zhai (Jilin University)
  • Abstract : In this report, we propose and analyze the elliptic eigenvalue problems by using the weak Galerkin method. In contrast to the conforming finite element method, the lower bounds of eigenvalues are considered. We prove that the weak Galerkin method produces asymptotic lower bounds by using the high order polynomials, and produces guaranteed lower bounds by using the lowest order polynomials. Some numerical acceleration techniques are also applied to the weak Galerkin method, and the numerical experiments are presented to verify the theoretical analysis.

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

room : E802

• [03920] Displacement-only Partitioned Equations for Structures without Lagrange Multipliers
  • Format : Talk at Waseda University
  • Author(s) :
    • K. C. Park (University of Colorado)
  • Abstract : A new formulation for the Displacement-only Partitioned (DP) equations of motion for linear structures is presented, which employs: the partitioned displacement and applied force (u, f), the partitioned block diagonal mass and stiffness matrices (M, K); and, the coupling projector (P), yielding the partitioned coupled equations of motion: M ü =P( f – K u) The proposed DP formulation contains no Lagrange multipliers and offers wide practical applications as well as intellectual pleasure.
• [04749] Displacement-based dynamic analysis of partitioned structural systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • José Ángel González Pérez (Universidad de Sevilla)
    • K. C. Park (University of Colorado)
  • Abstract : An unconditionally stable implicit-explicit time integration algorithm is presented, which employs the displacement-only partitioned formulation for structures. The displacement-only partitioned equations of motion for linear and nonlinear structures are expressed in terms of the partitioned displacements, partitioned velocities, and partitioned accelerations, and are devoid of interface Lagrange multipliers and associated variables. Numerical examples illustrate both unconditional stability of the proposed algorithm, second-order accuracy, as well as computational simplicity and efficiency.
• [04659] Partitioned Damage Identification of Structural Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyeon-Jun Kim (KAIST)
    • Yong-Hwa Park (KAIST)
    • K. C. Park (University of Colorado)
  • Abstract : This study proposes a damage identification procedure by employing a recently developed displacement-only partitioned equations of motion for structures. Damage is identified by detecting changes in partitioned or elemental stiffness. Applications of the proposed damage identification procedure to sample problems show that the proposed procedure captures damage locations through numerical examples.

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

room : E803

• [01736] Improving reproducibility, trustworthiness and fairness for diverse applications of machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirotaka Takahashi (Tokyo City University)
  • Abstract : Machine learning is applied to a diverse set of problems in our group. For example, research on gravitational wave physics and astronomy, development of traffic safety training and skills education methods, athlete support system of various sports, application to education to collaborate between teachers and machine learning etc.. In this presentation, we would like to focus on various applications and discuss how we can improve reproducibility, trustworthiness and fairness in machine learning.
• [01850] Multi-domain & Multi-task Generalisation on Real-World Clinical Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Kreuter (University of Cambridge)
    • Samuel Tull (University of Cambridge)
  • Abstract : Machine learning models have been holding the promise to revolutionise healthcare for several years. However, we rarely see promising approaches translate into deployment in the clinic. Often, this is due to an unexpected drop in performance when deploying the model on unseen test data due to domain shift. Our novel "Disentanglement Autoencoder" approach allows for multiple domains and tasks, both continuous and categorical, creating a disentangled embedding which can be used for multiple classification tasks.
• [02239] Software engineering for data science
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sören Dittmer (Uni Cambridge)
  • Abstract : Despite democratized data science tools, developing a trustworthy and effective data science system (DSS) is becoming increasingly challenging. The lack of software engineering (SE) skills and perverse incentives are among the root causes. We analyze why SE and building large complex systems, in general, is hard. We identify how SE addresses those difficulties and discuss how to adapt the insides to DSSs. We emphasize two key development philosophies: incremental growth and feedback loops.
• [02340] ShearletX: A Mathematical Approach Towards Explainability
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gitta Kutyniok (LMU Munich)
    • Stefan Kolek (LMU Munich)
    • Robert Windesheim (LMU Munich)
    • Hector Andrade Loarca (LMU Munich)
    • Ron Levie (Technion)
  • Abstract : Automated decision making using machine learning, in particular deep learning, is becoming an increasingly important component of modern technical systems and often affects humans directly. In this talk, we will present an explainability approach, coined ShearletX, based on a combination of information theory and applied harmonic analysis, which not only often outperforms state-of-the-art methods, but is also accessible to a mathematical analysis.

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

room : E804

• [03467] Multi-scale Neural Networks for High Frequency Problems in Regressions and PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei Cai (Southern Methodist University)
    • Lizuo Liu (Southern Methodist University)
    • Bo Wang (LCSM(MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China.)
  • Abstract : In this talk, we will introduce multiscale deep neural networks (MscaleDNNs) in order to overcome the spectral bias of deep neural networks when approximating functions with wide-band frequency information. The MscaleDNN uses a radial scaling in the frequency domain, which converts the problem of learning high frequency contents in regression problems or PDE’s solutions to one of learning lower frequency functions. As a result, the MscaleDNN achieves fast uniform convergence over multiple scales as demonstrated in solving regression problems and highly oscillatory Navier-Stokes flows. Moreover, a diffusion equation model in the frequency domain is obtained based on the neural tangent kernel, which clearly shows how the multiple scales in the MscaleDNN improves the convergence of the training of neural networks over wider frequency ranges with more scales, compared with a traditional fully connected neural network.
• [05449] Implicit bias in deep learning based PDE solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • Tao Luo (Shanghai Jiao Tong University)
    • Qixuan Zhou (Shanghai Jiao Tong University)
  • Abstract : We will discuss some recent development on the theory of deep learning based PDE solvers. We would like to mention some new ideas on modeling and analysis of such algorithms, especially some related phenomenon observed during the training process. For the theorectical part, both optimization and approximation will be considered.
• [05655] Coupling Deep Learning with Full Waveform Inversion
  • Author(s) :
    • Wen Ding (Stripe)
    • Kui Ren (Columbia University)
    • Lu Zhang (Rice University)
  • Abstract : In recent years, there has been increasing interest in applying deep learning to geophysical/medical data inversion. However, the direct application of end-to-end data-driven approaches to inversion has quickly shown limitations in practical implementation. Indeed, due to the lack of prior knowledge about the objects of interest, the trained deep learning neural networks very often have limited generalization. This talk presents a new methodology for coupling model-based inverse algorithms with deep learning for full waveform inversion. In particular, we present an offline-online computational strategy that couples classical least-squares-based computational inversion with modern deep learning-based approaches for full waveform inversion to achieve benefits that cannot be achieved by either component alone.

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

room : E811

• [04523] Are randomized NLA algorithms numerically stable?
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuji Nakatsukasa (University of Oxford)
    • Joel A. Tropp (Caltech)
  • Abstract : We develop algorithms for linear systems and eigenvalue problems that apply fast randomized sketching to accelerate standard subspace projection methods, such as GMRES and Rayleigh-Ritz. This modification allows for incorporating nontraditional bases for the approximation subspace. When the basis is numerically full rank, these algorithms have accuracy similar to classic methods but run faster. We illustrate a 70x speedup over gmres. Time (and progress) permitting, I will discuss recent developments in related topics.
• [05547] Randomized orthogonalization process
  • Format : Online Talk on Zoom
  • Author(s) :
    • Laura Grigori (EPFL and PSI)
  • Abstract : In this talk we will review recent progress on deriving algorithms for orthogonalizing a set of vectors. We will discuss then how this algorithms could be used to solve linear systems of equations and eigenvalue problems. We will conclude with numerical experiments that show the numerical stability of the proposed algorithms.
• [04952] A robust randomized indicator method for accurate symmetric eigenvalue detection
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhongyuan Chen (Medical College of Wisconsin)
    • Jiguang Sun (Michigan Technological University)
    • Jianlin Xia (Purdue University)
  • Abstract : We propose a robust randomized indicator method for accurate eigenvalue detection for symmetric matrices $A$, which gives a novel way to use randomization to design eigensolvers for finding interior eigenvalues. An indicator detects the existence of eigenvalues inside an interval based on some statistical norm estimators for a spectral projector. Previous work on eigenvalue indicators relies on a threshold which is only heuristically chosen, thus often resulting in spurious or missed eigenvalues. In this work, we use rigorous statistical analysis to guide the design of a robust indicator. Multiple randomized estimators for a contour integral operator in terms of $A$ are analyzed. In particular, when $A$ has eigenvalues inside a given interval, we show that the failure probability (for the estimators to return very small estimates) is extremely low. This enables to design a robust rejection indicator based on the control of the failure probability. We then illustrate how the indicator method may potentially be used to develop new randomized symmetric eigensolvers, where fast indicator evaluation via shifted linear system solution is employed in a bisection scheme. Unlike previous indicator methods that only produce eigenvalues, our method can conveniently reuse computations from indicator evaluations to find eigenvectors with little extra cost.
• [05321] The Adversarially Robust Generalized Eigenvalue Problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ming Gu (UC Berkeley)
    • Jiaming Wang (UC Berkeley)
  • Abstract : In this talk, we will introduce novel algorithms for solving the adversarially robust generalized eigenvalue problem, a highly non-convex optimization problem that has long eluded traditional optimization solvers. We will first discuss the rank-one case and then move on to the general-rank case. We will also show the potential applications of our algorithms in robust adaptive beamforming.

MS [00432] Empirically Driven Deep Learning Theory

room : E812

• [02983] How different optimizers select the global minimizer in deep learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Weinan E (Peking University)
  • Abstract : It has been observed in deep learning that different optimization process converges to different global minimum. We analyze this process by studying the stability of the minimum for the optimization algorithm. We find numerically that in practice, the numerical solutions often live at the so-called "edge of stability". We also study the relationship between the "sharpness" and "non-uniformity" of the global minimum. We present arguments that confirm the hypothesis that flat solution tends to generalize better. This is joint work with Chao Ma of Stanford University and Lei Wu of Peking University.
• [03263] A Law of Data Separation in Deep Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Hangfeng He (University of Rochester)
    • Weijie Su (University of Pennsylvania)
  • Abstract : While deep learning has enabled significant advances in many areas of science, its black-box nature hinders architecture design for future artificial intelligence applications and interpretation for high-stakes decision makings. We addressed this issue by studying the fundamental question of how deep neural networks process data in the intermediate layers. Our finding is a simple and quantitative law that governs how deep neural networks separate data according to class membership throughout all layers for classification. This law shows that each layer improves data separation at a constant geometric rate, and its emergence is observed in a collection of network architectures and datasets during training. This law offers practical guidelines for designing architectures, improving model robustness and out-of-sample performance, as well as interpreting the predictions.
• [03057] Neural Collapse in Deep Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Vardan Papyan (University of Toronto)
  • Abstract : In this talk, we'll delve into Neural Collapse - a recently discovered phenomenon in deep learning that emerges in the final phase of model training. Additionally, we'll explore how this phenomenon relates to the interpretability, robustness, and generalization performance of deep learning models.
• [03168] Memorization-Dilation: A Novel Model for Neural Collapse in Deep Neural Network Classifiers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gitta Kutyniok (LMU Munich)
    • Duc Anh Nguyen (---)
    • Ron Levie (Technion)
    • Julian Lienen (University of Paderborn)
    • Eyke Hüllermeier (LMU Munich)
  • Abstract : The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. In this talk, we introduce a more realistic mathematical model than the classical layer-peeled model, which takes both the positivity of the features and the limited expressivity of the network into account. For this, we then show results about the performance of the trained network in the sense of generalization properties.

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

room : E817 -> A715 (changed)

• [04425] Few-Shot Learning for Leaf and Vein Segmentation
  • Format : Talk at Waseda University
  • Author(s) :
    • John Lagergren (Oak Ridge National Laboratory)
  • Abstract : Plant phenotyping is a primary bottleneck in understanding plant adaptation and the genetic architectures underlying complex traits at population scale. We address this challenge by leveraging few-shot learning with convolutional neural networks (CNNs) to segment the leaf body and visible venation of P. trichocarpa leaf images obtained in the field. Biological traits are extracted from the resulting segmentations, validated using real-world measurements, and used to conduct a genome-wide analysis to identify genes controlling the traits.
• [04513] Analysis of spatial transcriptomics using deep learning and optimal transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Zixuan Cang (North Carolina State University)
  • Abstract : The emerging single-cell and spatial genomics techniques allow us to elucidate the governing rules of multicellular systems with unprecedented resolution and depth. These datasets are often high-dimensional, complex, and heterogeneous. Mathematical tools are needed to extract biological insights from such data. In this talk, we will discuss several computational methods for exploring tissue structures, temporal signatures, and cell-cell communication processes on spatial transcriptomics data as well as supervised optimal transport motivated by the biological applications.
• [04520] Applied Machine Learning for Overhead Imagery
  • Format : Talk at Waseda University
  • Author(s) :
    • Adam Attarian (Pacific Northwest National Laboratory)
  • Abstract : Applying machine learning techniques to collected overhead imagery presents many challenges not normally encountered in traditional object detection and classification problems. Complex sensing geometries, small target size, and lack of sufficient training data are all problems that must be mitigated. In this talk, we provide an overview of machine learning approaches and techniques to derive meaningful information from overhead imagery.
• [05238] Solving inverse and forward problems in the water quality model by neutral networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Quy Muoi Pham (The University of Danang - University of Science and Education)
  • Abstract : In this talk, we study the forward and inverse problems in BOD-DO models and present the Physic Inform Neural Network method to solve these problems. We first introduce the fully deep neural network and some well-known results about the approximation of fully deep neural networks to functions of classes. Then, we present the Physic Inform Neural Network method to solve the forward and inverse problems in BOD-DO models. We apply the method to solve some specific numerical examples. The method can be generalized for complex river quality models, e.g., 2D or 3D BOD-DO models or river quality models with more than two indicators. For complex river systems, we can use segmentation techniques to divide the river into some segments and in each segment, we can use the proposed method to solve the forward and inverse problems.

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

room : E818

• [03635] Learning reduced-order operators with Bayesian inference and Gaussian processes
  • Author(s) :
    • Mengwu Guo (University of Twente)
  • Abstract : Credible real-time simulation is a critical enabling factor for digital twin technology, and data-driven model reduction is a natural choice for achieving it. In this talk, we will discuss a probabilistic strategy for the learning of reduced-order representations of high-dimensional dynamical systems, with which a significantly reduced dimensionality guarantees improved efficiency, and the endowed uncertainty quantification certifies computational reliability. The strategy is based on Bayesian reduced-order operator inference, a data-driven method that inherits the formulation structure of projection-based reduced-state governing equations yet without requiring access to full-order solvers. The reduced-order operators are estimated using Bayesian inference with Gaussian priors, and two fundamentally different strategies of likelihood definition will be discussed – one formulated as linear regression, and the other through Gaussian processes. Given by posterior Gaussian distributions conditioning on solution data, the reduced-order operators probabilistically define a low-dimensional dynamical system for the predominant latent states, and provide an inherently embedded Tikhonov regularization together with a quantification of modeling uncertainties.
• [04330] Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting
  • Author(s) :
    • Chuanqi Chen (University of Wisconsin-Madison)
    • Nan Chen (University of Wisconsin-Madison)
    • Jinlong Wu ((University of Wisconsin-Madison)
  • Abstract : Online nonlinear system identification with sequential data has recently become important in many applications, e.g., extreme weather events, climate change, and autonomous systems. In this work, we developed a causation entropy boosting (CEBoosting) framework for online nonlinear system identification. For each sequential data batch, this framework calculates the causation entropy that evaluates the contribution of each function in a large set of candidate functions to the system dynamics. The causation entropies based on multiple data batches are then aggregated to identify a few candidate functions that have significant impacts on the system dynamics. With the identified sparse set of functions, the framework further fits a model of the system dynamics. The results show that the CEBoosting method can capture the regime switching and then fit models of system dynamics for various types of complex dynamical based on a limited amount of sequential data.
• [05255] ClimaX: A foundation model for weather and climate
  • Author(s) :
    • Johannes Brandstetter (Microsoft Research)
  • Abstract : Most state-of-the-art approaches for weather and climate modeling are based on physics-informed numerical models of the atmosphere. These approaches aim to model the non-linear dynamics and complex interactions between multiple variables, which are challenging to approximate. Additionally, many such numerical models are computationally intensive, especially when modeling the atmospheric phenomenon at a fine-grained spatial and temporal resolution. Recent data-driven approaches based on machine learning instead aim to directly solve a downstream forecasting or projection task by learning a data-driven functional mapping using deep neural networks. However, these networks are trained using curated and homogeneous climate datasets for specific spatiotemporal tasks, and thus lack the generality of numerical models. We develop and demonstrate ClimaX, a flexible and generalizable deep learning model for weather and climate science that can be trained using heterogeneous datasets spanning different variables, spatio-temporal coverage, and physical groundings. ClimaX extends the Transformer architecture with novel encoding and aggregation blocks that allow effective use of available compute while maintaining general utility. ClimaX is pre-trained with a self-supervised learning objective on climate datasets derived from CMIP6. The pre-trained ClimaX can then be fine-tuned to address a breadth of climate and weather tasks, including those that involve atmospheric variables and spatio-temporal scales unseen during pretraining. Compared to existing data-driven baselines, we show that this generality in ClimaX results in superior performance on benchmarks for weather forecasting and climate projections, even when pretrained at lower resolutions and compute budgets.

MS [00065] Recent Advances on Stochastic Hamiltonian Dynamical Systems

room : E819

• [00862] A parameterization method for quasi-periodic systems with noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Lei Zhang (Dalian University of Technology)
    • Pingyuan Wei (Beijing International Center for Mathematical Research, Peking University)
  • Abstract : This work is devoted to studying the existence of invariant tori for a class of quasi-periodically forced systems with stochastic noise, and implementing an efficient method to compute the tori as well as Lyapunov exponents. These systems are skew-product systems driven by small perturbations. Two very common cases of noise included in our treatment are continuous stationary stochastic process and white noise. The existence of invariant tori is established by developing a parameterization method in random setting and applying an elementary fixed point theorem in Banach spaces. Based on this, we describe a numerical algorithm for the computation of them. Moreover, by considering the reducibility for random manifold, we also propose a numerical algorithm for the computation of the corresponding Lyapunov exponents.
• [04265] Parametric Resonance for Enhancing the Rate of Metastable Transition
  • Format : Talk at Waseda University
  • Author(s) :
    • Ying Chao (Xi’an Jiaotong University)
    • Molei Tao (Georgia Inistitute of Technology)
  • Abstract : In this talk, we will introduce a way to quantify how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit expression for approximating the rate change is provided, and the corresponding transition mechanism can also be approximated. Unlike the majority of existing relevant works, these results apply to kinetic Langevin equations with high-dimensional potentials and nonlinear perturbations. They are obtained based on a higher-order Hamiltonian formalism and perturbation analysis for the Freidlin-Wentzell action functional. This tool allowed us to show that parametric excitation at a resonant frequency can significantly enhance the rate of metastable transitions. Numerical experiments for both low-dimensional toy models and a molecular cluster are also provided. For the latter, we show that vibrating a material appropriately can help heal its defect, and our theory provides the appropriate vibration.
• [04127] An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable Lévy noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Cheng Fang (Huazhong University of Science and Technology)
    • Yubin Lu (Illinois Institute of Technology)
    • Ting Gao (Huazhong University of Science and Technology)
    • Jinqiao Duan (Great Bay University)
  • Abstract : Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, lots of log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios which could have high error and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by $\alpha$-stable Lévy noise from only random pairwise data. Our innovations include: (1) designing a deep learning approach to learn both drift and diffusion coefficients for Lévy induced noise with $\alpha$ across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, (3) proposing an end-to-end complete framework for stochastic systems identification under a general input data assumption, that is, $\alpha$-stable random variable. Finally, numerical experiments and comparisons with the non-local Kramers-Moyal formulas with moment generating function confirm the effectiveness of our method.

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

room : E820

• [03958] Space-time domain decomposition approach for Stoke flow coupled with poroelasticity
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyesuk Lee (Clemson University)
    • Hemanta Kunwar (Clemson University)
  • Abstract : We consider decoupling iterative algorithms based on domain decomposition for the time-dependent Stokes-Biot model, in which different time steps can be used in the flow region and the poroelastic medium. The coupled system is formulated as a space-time interface problem based on interface conditions. The interface problem is then solved by an iterative method which involves the parallel solution of time-dependent homogeneous Stokes and Biot problems. Consequently, local discretization in both space and time can be used to handle multiphysics systems efficiently. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed methods.
• [04129] Two-field any-order finite element solvers for poroelasticity problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiangguo James Liu (Colorado State University )
  • Abstract : In this talk, we present a family of 2-field finite element solvers for poroelasticity problems based on weak Galerkin (WG) spatial discretizations and the backward differentiation formulas (BDF) temporal discretization. In particular, both primal variables (fluid pressure and solid displacement) are approximated by WG degree k>=0 (scalar or vector) polynomial shape functions defined separately in element interiors and on edges of a quadrilateral mesh. The discrete weak gradients of WG basis functions are constructed in certain broken Arbogast-Correa spaces (of vectors or matrices). The discrete weak gradients, strains, and divergences will be utilized to approximate their continuous counterparts in the variational formulations. Degree-k WG polynomials and BDF(k+1) are combined to develop time-marching schemes for linear poroelasticity. This combination results in a good balance of spatial and temporal discretizations. Numerical experiments on benchmarks will be presented to demonstrate the efficiency and flexibility of these new solvers. Extension to nonlinear poroelasticity problems will be discussed also. This is a joint work with Simon Tavener (Colorado State University, USA), Ruishu Wang (Jilin University, China), and Zhuoran Wang (Sun Yat-sen University, China).
• [04672] A mathematical framework for poro-viso-elastic models
  • Format : Talk at Waseda University
  • Author(s) :
    • Justin Thomas Webster (University of Maryland, Baltimore County)
  • Abstract : Recent works in poroelasticity have included viscous structural effects. Here, we clarify mathematical properties of linear, quasi-static Biot systems with the addition of Kelvin-Voigt viscoelasticity. We demonstrate time-regularization and dissipative effects of viscoelasticity through a priori estimates. We use the full system, as well as the framework of implicit, degenerate evolutions. Precise statements of admissible initial conditions in each scenario are given.
• [04316] An energy stable second-order method for three-phase flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Catalin Trenchea (University of Pittsburgh)
    • Giselle Sosa Jones (Oakland University)
  • Abstract : We present a time-stepping scheme for the numerical approximation of a thermodynamically consistent model of incompressible and immiscible three-phase flow in porous media, with an intrinsic free energy dissipation law. The model consists of three nonlinear degenerate parabolic equations for the saturations of each phase. We prove that the proposed scheme is second-order accurate, and preserves the discrete free energy dissipation.

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

room : D101

• [03035] System-Wide Coupling Communication for Heterogeneous Computing Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shinji Sumimoto (The University of Tokyo)
    • Takashi Arakawa (CliMTech Inc.)
    • Yoshio Sakaguchi (Fujitsu Ltd.)
    • Hiroya Matsuba (Hitachi Ltd.)
    • Satoshi Ohshima (Kyushu University)
    • Hisashi Yashiro (National Institute for Environmental Studies)
    • Toshihiro Hanawa (The University of Tokyo)
    • Kengo Nakajima (The University of Tokyo/RIKEN)
  • Abstract : This talk presents a system-wide coupling communication library to couple multiple MPI programs for heterogeneous coupling computing called h3-Open-SYS/WaitIO (WaitIO for short). WaitIO provides an inter-program communication environment among MPI programs and supports different MPI libraries with various interconnects and processor types. We have developed the WaitIO communication library to realize the environments. We present how WaitIO works and performs in such heterogeneous computing environments.
• [03261] h3-Open-UTIL/MP: a coupling library for heterogeneous computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Arakawa (The University of Tokyo)
    • Shinji Sumimoto (The University of Tokyo)
    • Hisashi Yashiro (National Institute for Environmental Studies)
    • Kengo Nakajima (The University of Tokyo/RIKEN)
  • Abstract : Heterogeneous computing is one of the main topics for recent high-performance computing. The reason is that role of HPC has expanded beyond not only simple simulation but also to large-scale data analysis and machine learning. Based on these backgrounds, we are developing a heterogeneous coupling library h3-Open-UTIL/MP. In our presentation, we will describe the structure and function of h3-Open-UTIL/MP and discuss the results of performance measurements and application examples.
• [03652] Modernizing the weather prediction model ICON for extreme-scale computing, a librarization effort
  • Format : Talk at Waseda University
  • Author(s) :
    • Yen-Chen Chen (Karlsruhe Institute of Technology)
    • Terry Cojean (Karlsruhe Institute of Technology)
    • Jonas Jucker (CSCS Swiss National Supercomputing Centre)
    • Pradipta Samanta (German Climate Computing Centre)
    • Florian Prill (Deutscher Wetterdienst)
    • Sergey Kosukhin (Max-Planck-Institute for Meteorology)
    • Luis Kornblueh (Max-Planck-Institute for Meteorology)
    • Will Sawyer (CSCS Swiss National Supercomputing Centre)
    • Jörg Behrens (German Climate Computing Centre)
    • Claudia Frauen (German Climate Computing Centre)
  • Abstract : The weather and climate prediction model ICON was operated since 1999 and has become the forecasting model of more than 30 national weather services. However, the legacy Fortran code restricts its portability to GPU clusters and hinders its parallel performance on modern exascale clusters. The ICON consolidated (ICON-C) project and several related projects aim to make ICON more modular, portable, and suitable for modern extreme-scale parallel computing. This talk focuses on a librarization effort of ICON-C.
• [03776] Performance Modeling Challenges in Extreme Scale Computing
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ayesha Afzal (Erlangen National High Performance Computing Center (NHR@FAU))
  • Abstract : In extreme scale computing, analytic performance modeling using first-principles is pre-eminent for optimization. However, it is challenging since the implicit presumption of strict synchronization among all processes is not necessarily accurate. Therefore, for programs with rare synchronization points, simply summing the runtimes predicted by computation and communication performance models is often erroneous. In my talk, I will highlight the most intriguing insights about intricate hardware-software interactions emerging from this model failure. Interestingly, the hardware bottlenecks permits for non-intuitive spontaneous asynchronicity that helps to get the most of the systems' capabilities and mitigates the communication overhead.

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

room : D102

• [02962] Internal waves, Coriolis force and undercurrents
  • Format : Talk at Waseda University
  • Author(s) :
    • Rossen I. Ivanov (Technological University Dublin)
    • David J. Henry (University College Cork)
  • Abstract : We study the linear and nonlinear differential equations modelling the interacting surface and internal waves of two fluid layers with different densities over a flat bed. Other effects such as underlying currents and Coriolis force are also included. We use the Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Specific weakly nonlinear long-wave regimes are structure-enhancing and the dynamics is described by integrable Hamiltonian equations. Consequently, integrable models and their soliton solutions will be presented.
• [05173] On three dimensional models of equatorial ocean flows
  • Format : Talk at Waseda University
  • Author(s) :
    • BISWAJIT BASU (Trinity College Dublin)
  • Abstract : A recently developed three dimensional model of equatorial ocean flow is presented in this paper. The model is inspired by the work of Constantin and Johnson and provides some explicit solution of velocity fields. The effect of density variation is discussed alongwith the influence of undercurrent. Some additional insights are provided based on conservation of potential vorticity.
• [03835] Eddy viscosities and ageostrophic wind-speed profiles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tony Lyons (South East Technological University)
  • Abstract : Wind speed profiles in the Ekman layer are used to deduce corresponding variable eddy coefficients. These eddy coefficients are parameterized in terms of a deflection angle, the geostrophic wind speed, and the transfer rate of horizontal momentum in the vertical direction. The classical Ekman flow has deflection angle $45^\circ$, while incorporating variable eddy coefficients changes this deflection angle. This deviation of deflection angle is used to estimate the depth of the Ekman layer.

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

room : D401

• [01485] A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Alina Chertock (North Carolina State University)
    • Alexander Kurganov (Southern University of Science and Technology)
    • Michael Redle (North Carolina State University)
    • Kailang Wu (Southern University of Science and Technology)
  • Abstract : This talk presents a new second-order unstaggered path-conservative central-upwind scheme for ideal and shallow water MHD equations. The new scheme locally preserves the divergence-free constraint, does not rely on Riemann problem solvers, and robustly produces high-resolution and non-oscillatory results. The derivation of the scheme is based on the Godunov-Powell nonconservative modifications of the studied systems and by augmenting it with the evolution equations for the corresponding derivatives of the magnetic field components.
• [01517] Geometric Quasilinearization (GQL) for Bound-Preserving Schemes of Hyperbolic PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kailiang Wu (Southern University of Science and Technology)
    • Chi-Wang Shu (Brown University)
  • Abstract : Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by the speed of light, etc. As widely realized, it is crucial to develop bound-preserving numerical methods that preserve such intrinsic constraints. Exploring provably bound-preserving schemes has attracted much attention and is actively studied in recent years. This is however still a challenging task for many systems especially those involving nonlinear constraints. Based on some key insights from geometry, we systematically propose a novel and general framework, referred to as geometric quasilinearization (GQL), which paves a way for studying bound-preserving problems with nonlinear constraints. The essential idea of GQL is to equivalently transfer all nonlinear constraints into linear ones, through properly introducing some free auxiliary variables. We establish the fundamental principle and general theory of GQL via the geometric properties of convex regions, and propose three simple effective methods for constructing GQL. We apply the GQL approach to a variety of partial differential equations, and demonstrate its effectiveness and remarkable advantages for studying bound-preserving schemes, by diverse challenging examples and applications which cannot be easily handled by direct or traditional approaches.
• [01722] An improved non-hydrostatic shallow-water type model for the simulation of landslide generated tsunamis
  • Format : Talk at Waseda University
  • Author(s) :
    • Manuel J Castro Diaz (University of Málaga)
    • Tomas Morales de Luna (Universidad de Malaga)
    • Cipriano Escalante Sanchez (Universidad de Málaga)
    • Jorge Macías Sanchez (University of Málaga)
    • Enrique D Fernandez Nieto (University of Sevilla)
  • Abstract : In this talk we present an improved version of a non-hydrostatic shallow-water system coupled with a granular landslide shallow-water type model for the numerical simulation of tsunamis generated by landslides. The system is discretized by means of a high-order WB finite volume scheme. Some numerical tests with laboratory experiments and real events will be presented to show the capabilities of the proposed model.
• [01949] A New Approach for Designing Well-Balanced Schemes for the Shallow Water Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Remi Abgrall (University of Zurich)
    • Yongle Liu (University of Zurich)
  • Abstract : In this talk, I will introduce a new approach for constructing robust well-balanced numerical methods for one-dimensional Saint-Venant system. We combine the conservative and non-conservative formulations of the studied hyperbolic system in a natural way. The solution is globally continuous and described by a combination of point values and average values, which will be evolved by two different forms of PDEs. We demonstrate the behavior of the new scheme on a number of challenging examples.

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

room : D402

• [02792] Viscous fingers in a Hele-Shaw cell under an electric field
  • Format : Talk at Waseda University
  • Author(s) :
    • Meng Zhao (Huazhong University of Science and Technology)
  • Abstract : We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate numerical method for solving a coupled integral equation system. Our nonlinear results reveal that currents are able to promote/suppress the interface dynamics depending on its direction. When no fluid is injected, and a negative current is utilized, the interface tends to approach the origin and break up into several drops.
• [02813] Computing viscoelastic and elastoplastic deformations induced by volumetric growth
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Wu (Worcester Polytechnic Institute)
  • Abstract : Based on a discretized energy formulation, I will present a numerical method to solve various nonlinear mechanical systems involving finite elastic deformation, Maxwell-type viscoelasticity, or elastoplasticity. I will show its application to simulate deformations of living and nonliving soft materials during volumetric growth with free boundaries. These simulations can give insight into swelling gel experiments, in vitro wound closure dynamics, and cell and tissue morphogenesis.
• [02818] Disturbance flow generated by particles in linear viscoelastic fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaofan Li (Illinois Institute of Technology)
    • Hualong Feng (California State Univ, Bakersfield)
    • Amlan Barua (Indian Institute of Technology Dharwad)
    • Shuwang Li (Illinois Institute of Technology)
  • Abstract : Studying effects of moving particles on fluids is of fundamental importance for understanding particle dynamics and binding kinetics. We compute the fluid dynamics using an accurate boundary integral method with 3rd order accuracy in space. A unique feature of our method is that we can calculate the stress on the particle surface for a prescribed particle velocity profile. It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. When the flow becomes viscoelastic, however, the boundary layers are fundamentally different than those observed in Newtonian fluids.
• [02820] Mathematical Modeling and Computation of Tumor Growth
  • Format : Online Talk on Zoom
  • Author(s) :
    • Min-Jhe Lu (University of California, Irvine)
    • John Lowengrub (University of California, Irvine)
    • Chun Liu (Illinois Tech)
    • Shuwang Li (Illinois Tech)
    • Yiwei Wang (University of California, Riverside)
  • Abstract : The building of the mechano-chemical tumor models aims to understand how the mechanical interaction and the biochemical reactions can influence the dynamics of tumor growth. The mechanical interaction within cells produces stress and the biochemical reactions involve chemical species supplying tumor with nutrients. In this talk I will demonstrate how we build the tumor models with energetic variational approaches and the numerical simulation results in both sharp interface and diffuse interface formulation will also be given.

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

room : D403

• [03443] Accelerating Pressure-Temperature Flash Calculations with Physics-informed Neural Networks
  • Author(s) :
    • Yuanqing Wu (Dongguan University of Technology)
  • Abstract : Pressure-Temperature (PT) flash calculations are a performance bottleneck of compositional-flow simulations. With physics-informed neural networks, the two heavy-burden routines of PT flash calculations: the successive substitution technique and stability analysis are be avoided in the offline stage, and therefore the computing burden in the offline stage is removed. After training, the phase condition and the compositions can be output by the neural network, which costs much less time than the PT flash calculations.
• [03499] The numerical CFD-DEM model for polymer flooding in weakly consolidated porous media
  • Author(s) :
    • Yerlan Amanbek (Nazarbayev Univesity)
    • Daniyar Kazidenov (Nazarbayev Univesity)
    • Sagyn Omirbekov (Nazarbayev Univesity)
  • Abstract : The study of sand production from the oil and gas reservoirs is an essential for ensuring the long-term viability and profitability of hydrocarbon production operations. In this talk, we present numerical model of polymer flooding using CFD coupled DEM for sand production in 3D. The Navier-Stokes equation is solved using CFD approach, and the DEM approach is based on the second Newton’s law to simulate the behavior of individual particles in the porous medium. The modified JKR model is used to represent the weakly consolidated sandstone. The rheology of the injected polymer is described by the power law model. The laboratory experiment was conducted considering the polymer flooding. Numerical model was validated by the sand production rate of the laboratory experiment in the normalized setting.
• [03503] Physics-Preserving Semi-Implicit Schemes for Porous Media Flow with Capillary Heterogeneity
  • Author(s) :
    • Shuyu Sun (KAUST)
  • Abstract : Two-phase flow commonly occurs in environmental engineering and petroleum industry. We present our work on semi-implicit algorithms for two-phase flow in porous media with capillary heterogeneity; in particular, different capillary pressure functions are used for different rock types. Our proposed algorithms, derived from our novel splitting of variables, are locally conservative for both phases, handle capillary heterogeneity well, and are unbiased. The algorithms are also numerically more stable than classical approaches, demonstrated using numerical examples.
• [04169] Efficient numerical methods for thermodynamically consistent model of two-phase flow in porous media
  • Author(s) :
    • Huangxin Chen (Xiamen University)
  • Abstract : In this talk we will introduce a thermodynamically consistent mathematical model for incompressible and immiscible two-phase flow in porous media with rock compressibility. An energy stable numerical method will be introduced, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and bounds of porosity and saturations. Numerical results are given to verify the features of the proposed methods.

contributed talk: CT148

room : D404

[01286] Radiation effect of ND–Ni nanocomposite, water-filled multiport cavity

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : The control of the thermal radiation influence on free convection of a multiple-port open cavity packed with water supported nanocomposite nanofluid is investigated numerically . One inlet port and two outlet ports are situated on the perpendicular walls. The remaining cavity walls are adiabatic. The heated thin baffle is located inside the cavity. The cavity is crammed with the water-supported nanodiamond–nickel nanocomposite. The governing Navier–stokes equations are written in the term of vorticity stream function transport. An ADI scheme-based finite difference process is used for discretization of the governing equations. The results are discussed graphically with the various parameters of radiation parameter, Reynolds number, Rayleigh number, solid volume fraction, widths of the opening, and locations of baffle position. It reveals that the average heat transfer rate reduces with the baffle placed far from the inlet.
• Classification : 76Sxx, 76Rxx, 76Mxx
• Format : Talk at Waseda University
• Author(s) :
  • muthtamilselvan murugan (Bharathiar university)

[02505] Modelling capture and storage of gases in porous media

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : An accurate description of reactive mass transport in porous media is of paramount importance in a multitude of environmental applications. In this talk, we will present mathematical models of gas transport in porous media for applications in contaminant removal and hydrogen storage. The models will be simplified via dimensional analysis and solved analytically in some limiting cases. Numerical solutions of the full models will also be presented. All solutions will be compared with experimental data.
• Classification : 76S05, 80A19, 35B40, 76M50
• Format : Talk at Waseda University
• Author(s) :
  • Francesc Font (Universitat Politècnica de Catalunya, CIF: Q0818003F, C. Jordi Girona, 31, 08034 Barcelona, Barcelona)
  • Tim G. Myers (Centre de Recerca Matemàtica)
  • Maria Aguareles (Universitat de Girona)
  • Esther Barrabés (Universitat de Girona)

[01021] A mixed finite element approach to a non-isothermal flow vegetation model

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : We consider a vegetation root-soil model which couples Richards PDE in the soil domain and saturated flow in the roots domain. Scenarios when the flow depends on soil temperature is included. A mixed finite element method is applied to obtain numerical solutions, and the well-posedness for its weak formulation and error estimates are studied. We provide numerical examples using tomography data of root domains and study convergence errors to validate our theoretical results.
• Classification : 76Sxx, 65Mxx
• Format : Talk at Waseda University
• Author(s) :
  • Malgorzata Peszynska (Oregon State University)
  • Nachuan Zhang (Oregon State University)

[02189] Improved viscous flow between expanding or contracting permeable walls

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : Solutions to transport models of fluid in contracting/expanding porous vessels remain unknown, and the problem has been restricted to the “slow” expansion/contraction of the walls. I partially address these gaps by generating explicit solutions and improving approximations without the “slowness” dilation rate. Indeed, the homogeneous differential equation is completely solved and this exact solution may be leveraged to form more precise approximations to the flow via perturbation techniques when the Reynolds number is small.
• Classification : 76S05, 34B15
• Format : Online Talk on Zoom
• Author(s) :
  • Christopher C. Tisdell (University of New South Wales (UNSW))

[02224] Numerical simulation of convective flow models in porous media using deep learning technique

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : The outstanding computational ability of artificial neural networks (ANN) makes the deep learning (DL) branch more robust for solving various simple and complex convective models $\left(2D ~and~3D\right)$ in porous media. Moreover, it is an unsupervised learning approach in the DL that uses randomly sampled spatial and boundary collocation points as training data for ANN. A loss function according to the governing and boundary conditions is formulated and enforced to minimize at the sampled collocation points through the backpropagation algorithm using suitable optimization techniques. Eventually, a fine-tuned ANN is achieved after a sufficiently large number of training processes, and the tunned ANN is used to replicate the solution quickly.
• Classification : 76S05, 68T07
• Author(s) :
  • Sumant Kumar (Defence Institute of Advanced Technology, Pune)
  • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
  • Somanchi V.S.S.N.V.G. Krishna Murthy (Defence Institute of Advanced Technology, Pune)

MS [00462] Mathematical and applicable studies on quantum walks

room : D405

• [03456] Resonance expansion for quantum walks
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenta Higuchi (Ehime University)
  • Abstract : We study long time behavior of "open" quantum walks by introducing resonances and the resonance expansion. Eigenvalues on the unit circle characterize the localization of quantum walkers. However, an open quantum walk does not have eigenvalues but may have resonances inside the unit circle. Then the decay rate of the quantum walker in any bounded region is described by the modulus of resonances. The eigenstate expansion is generalized to the resonance expansion.
• [04207] Spectral scattering theory for quantum walks
  • Format : Talk at Waseda University
  • Author(s) :
    • Akito Suzuki (Shinshu university)
  • Abstract : Spectral scattering theory works to understand the dynamics of quantum walks and obtain the limit distribution of the asymptotic velocity of the walker, which gives a quantum version of the central limit theorem. In this talk, I would like to talk about the recent development of spectral scattering theory for one-dimensional quantum walks.
• [04051] Quantum Walk-Based Maze-Solving with Absorbing Holes
  • Format : Talk at Waseda University
  • Author(s) :
    • Leo Matsuoka (Hiroshima Institute of Technology)
    • Kenta Yuki (Freelancer)
    • Hynek Lavicka (STTech GmbH)
    • Etsuo Segawa (Yokohama National University)
  • Abstract : We propose a strategy for finding the shortest path on a bipartite graph maze using a discrete-time quantum walk with absorbing holes. Our numerical analysis shows that the chain of maximum trapped densities detects the shortest paths in most cases. Furthermore, we discuss the speed of the algorithm and propose a strategy for accelerating it using numerical analysis. Our results offer a potential model for autonomous maze-solving optimization by harnessing natural phenomena.
• [03689] Distinguishability and Complexity in Non-Unitary Boson Sampling Dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ken Mochizuki (RIKEN)
  • Abstract : We show that quantum walks of many photons are closely related to the boson sampling problem and computational complexity. In addition, we consider non-unitary quantum walks, which correspond to photonic dynamics in open quantum systems with post selection. We clarify that the distribution of photons can approach that of distinguishable particles in the long time limit, which makes the non-unitary boson sampling problem easy. Ken Mochizuki and Ryusuke Hamazaki, Physical Review Research 5 013177 (2023).

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

room : D407

• [05193] A model for territorial dynamics: from particle to continuum
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alethea Barbaro (TU Delft)
    • Abdulaziz Alsenafi (Kuwait University)
  • Abstract : Many species, including our own, demonstrate territoriality, with individuals or groups marking their territories either chemically or visually. Here, we present an agent-based lattice model for territorial development. In this model, there are several groups; agents from each group put down that group’s territorial markings as they move on the lattice. Agents move away from areas with territorial markings which do not belong to their own group. The model was motivated by gangs expressing territoriality through graffiti markings, though the model itself could be applicable in any chemo-repellent situation. We show that this model undergoes a phase transition between well-mixed dynamics and the formation of distinct territories as parameters are varied. We formally derive a system of coupled convection-diffusion equations from this model. The system is cross-diffusive due to the avoidance of other groups’ markings. Using the PDE system, we pinpoint the critical value for the phase transition.
• [04662] A variational approach for an existence result for a cross-diffusion model
  • Format : Talk at Waseda University
  • Author(s) :
    • Havva Yoldaş (Delft University of Technology)
    • Filippo Santambrogio (Université Claude Bernard - Lyon 1)
    • Romain Ducasse (Université Paris Cité)
  • Abstract : In this talk, we look at a cross-diffusion system consisting of two Fokker-Planck equations where the gradient of the density for each species acts as a potential for the other one. The system is the gradient flow for the Wasserstein distance of a functional which is not lower semi-continuous, and the system is not well-posed. We compute the convexification of the integral and provide an existence proof in a suitable sense for the gradient flow of the corresponding relaxed functional.
• [04745] A degenerate cross-diffusion system as the inviscid limit of a nonlocal tissue growth model
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomasz Dębiec (University of Warsaw)
  • Abstract : In recent years, there has been a spike in interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law or Darcy's law. While each of these velocity-pressure relations has been studied in the literature, little emphasis has been placed on the fine relationship between them. In this talk, we want to address this dearth of results in the literature, providing a rigorous argument that bridges the gap between a viscoelastic tumour model (of Brinkman type) and an inviscid tumour model (of Darcy type).
• [04637] Proposing a Finite Volume Method for a Kinetic Model for Interacting Species
  • Format : Talk at Waseda University
  • Author(s) :
    • Julia Ines Mareike Hauser (TU Dresden)
  • Abstract : We consider a system of two kinetic equations coupled by non-local interaction terms which are used to describe systems of indistinguishable agents such as flocks of birds. In this talk we propose an upwind finite volume method for this model. The method is constructed in such that mass is preserved and positivity is maintained. We show the convergence of the method and we provide explicit error estimates. Finally, we underline our theoretical results with simulations.

MS [00378] Mathematical Methods in System Reliability

room : D408

• [01455] New exactly solvable architecture for system reliability and safety
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Tanguy (Orange)
  • Abstract : Network reliability is a crucial performance index for telecommunication operators. In the general case, the calculation of the two-terminal reliability is known to be #P-complete, even for identical links and perfect nodes of the network's underlying graph. Exact solutions have nonetheless been found for a few recursive architectures. We present a new example of such an architecture, which could be of interest to reliability practitioners and graph theorists.
• [01469] Application of Logic Differential Calculus in Reliability Analysis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michal Mrena (University of Zilina)
  • Abstract : Logic differential calculus – specifically logic derivatives – provides an efficient way to investigate the reliability of systems described by a structure function. The structure function captures the topology of the system and the derivatives describe the behavior of the system when the state of a component changes. Consequently, they allow us to calculate importance measures for individual components. In this contribution, we present a comprehensive framework for the evaluation of various system reliability characteristics.
• [03092] Stochastic comparisons of coherent systems with active redundancy at component level and system level
  • Format : Talk at Waseda University
  • Author(s) :
    • Pradip Kundu (XIM University, Bhubaneswar)
    • Arindam Panja (Indian Statistical Institute)
    • Biswabrata Pradhan (Indian Statistical Institute)
  • Abstract : An effective way to increase system reliability is to use redundancies (spares) into the systems. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provides better system reliability than that of the system with another set of redundancy, with respect to some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model.

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

room : D501

• [03278] A semismooth Newton stochastic proximal point algorithm with variance reduction
  • Format : Talk at Waseda University
  • Author(s) :
    • Andre Milzarek (The Chinese University of Hong Kong, Shenzhen)
    • Fabian Schaipp (Technical University of Munich)
    • Michael Ulbrich (Technical University of Munich)
  • Abstract : We present an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account. Finally, numerical experiments are shown illustrating that SPP competes favorably with other state-of-the-art methods.

MS [01671] Financial Modeling

room : D502

• [05403] Insurance design for the loss of epidemic outbreaks involving the Cramer -Lundberg model
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoyuki Ishimura (Chuo University)
    • Chenwei Sun (Chuo University)
    • Koichiro Takaoka (Chuo University)
  • Abstract : We consider the insurance design for the loss of epidemic outbreaks such as COVID-19. The new point of our model is to involve the Cramer-Lundberg process in the risk theory. Utilizing the standard time-discrete SIR model, we propose how to compute the insurance coverage due to the damage of epidemic bursts. The comparison between our theory and the empirical study employing the daily data of Tokyo area will be also discussed.
• [02749] Micro-foundations of some financial models with bubbles
  • Format : Talk at Waseda University
  • Author(s) :
    • Naohiro Yoshida (Keiai University)
  • Abstract : This presentation will discuss the micro-foundation of some financial models with bubbles. The micro-foundation discussed is the excess demand model. In other words, the amount of demand for and supply of a security by each investor in the market are formulated, and the price of the security is determined so that they satisfy the market-clearing condition. The main objective of this presentation is to propose some excess demand models of financial models with bubbles. We will discuss what characteristics of investor's demand and supply cause bubbles.
• [02787] An Ito-Wentzell Formula for SDE Conditional Measure Flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Nizar Touzi (CMAP, Ecole Polytechnique)
    • Assil Fadle (CMAP, Ecole Polytechnique)
  • Abstract : We provide general Ito and Ito-Wentzell formulas for functions of conditional measure flows of continuous semimartingales, using functional linear derivatives and standard stochastic analysis results. We provide applications for mean field optimal control and mean field optimal stopping with common noise.
• [04500] A Generalized Cram{¥'e}r-Lundberg Model Driven by Mixed Poisson Processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Masashi Tomita (Meiji Yasuda Life Insurance Company)
    • Koichiro Takaoka (Chuo University)
    • Motokazu Ishizaka (Chuo University)
  • Abstract : We propose a generalized Cram{\'e}r-Lundberg model of the risk theory of non-life insurance and discuss several mathematical properties including the ruin probability. Our model is an extension of that of Dubey (1977) to the case of multiple insureds, where the counting process is a mixed Poisson process and the continuously varying premium rate is determined by a Bayesian rule on the number of claims.

MS [00715] Recent Trends in Market Design

room : D505

• [01693] Mechanism Design Powered by Social Interactions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dengji Zhao (ShanghaiTech University)
  • Abstract : Mechanism design has traditionally assumed that the participants are fixed and independent. However, in reality, the participants are well-connected (e.g., via their social networks) and we can utilize their connections to power the design. One interesting trend is to incentivize the existing participants to use their connections to invite new participants. This helps to form larger games in auctions, coalitional games, matching etc., which is not achievable with the traditional solutions. The challenge is that the participants are competitors and they would not invite each other by default. Solving this is well-coupled with the existing challenges. For example, in auctions, solving it may require revenue monotonicity and false-name-proofness, which were proved impossible to achieve under certain sensible conditions. In matching, this cannot get along with standard optimality and stability. Hence, we believe there is an important theoretical value to discover and the study will stimulate many interesting applications, especially under decentralized systems with blockchain.
• [01426] Tract housing, the core, and pendulum auctions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andrew Mackenzie (∗Department of Microeconomics and Public Economics, Maastricht University)
    • Yu Zhou (Graduate School of Economics, Kyoto University )
  • Abstract : We consider a model of tract housing where buyers and sellers have (i) wealth constraints, and (ii) unit demand over identical indivisible objects represented by a valuation. First, we characterize the strong core. Second, we characterize the bilateral weak core, or the weak core allocations with no side-payments. Finally, when buyer wealth constraints and valuations are private information and when transfers are discrete, we introduce two families of pendulum auctions, both of which consist of obviously strategy-proof implementations of the bilateral weak core. The buyer-optimal pendulum auctions are preferred by the buyers but are inefficient when side-payments are possible, while the efficient pendulum auctions are efficient.
• [01327] Mechanism Design with Uncertainty
  • Format : Talk at Waseda University
  • Author(s) :
    • Taiki Todo (Kyushu University)
  • Abstract : My research is summarized as mechanism design with uncertainty. Traditional mechanism design focuses on static environments where all the (possibly probabilistic) information about the agents are observable by the mechanism designer. In practice, however, it is possible that the set of participating agents and/or some of their actions are not observable a priori. We therefore focused on various kinds of uncertainty in mechanism design and developed/analyzed several market mechanisms that incentivize agents to behave in a sincere way.
• [01620] Multi-Unit Bilateral Trade
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bart de Keijzer (King's College London)
  • Abstract : We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting. Joint work with Matthias Gerstgrasser, Paul Goldberg, Philip Lazos, and Alexander Skopalik. Based on a paper published in the Proceedings of AAAI 2019.

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

room : D514

• [03167] Incentive to shape equilibria in double auction markets
  • Format : Talk at Waseda University
  • Author(s) :
    • Thibaut Mastrolia (UC Berkeley)
    • Mathieu Rosenbaum (Ecole Polytechnique)
    • Joffrey Derchu (Ecole Polytechnique)
  • Abstract : We study a toy two-player game for periodic double auction markets with imperfect information between the players. It allows us to link market spreads with signal strength. We first derive some market statistics related to the model studied. Then, we characterize Nash equilibria in cases with or without incentives from the exchange. This enables us to derive new insights about price formation and incentives design.
• [04566] On time-consistent equilibrium stopping under aggregation of diverse discount rates
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiacheng Zhang (UC Berkeley)
    • Shuoqing Deng (The Hong Kong University of Science and Technology)
    • Xiang Yu (The Hong Kong Polytechnic University)
  • Abstract : This paper studies the central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with a smooth aggregation preference to incorporate all heterogeneous discount rates with an attitude function that reflects the aggregation rule in the same spirit of ambiguity aversion in the smooth ambiguity preference proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibria as fixed points of an operator in the setting of one-dimensional diffusion processes. We provide some sufficient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium in which the attitude function becomes equivalent to the linear aggregation rule as of diversity neutral. When the sufficient condition of the attitude function is violated, we can illustrate by various examples that the characterization of the optimal equilibrium may differ significantly from some existing results for an individual agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates.
• [02775] CONVERGENCE OF POLICY IMPROVEMENT FOR ENTROPY-REGULARIZED STOCHASTIC CONTROL PROBLEMS
  • Format : Talk at Waseda University
  • Author(s) :
    • Yu-Jui Huang (University of Colorado, Boulder)
    • Zhenhua Wang (University of Michigan)
    • Zhou Zhou (University of Sydney)
  • Abstract : For a general entropy-regularized stochastic control problem on an infinite horizon, we prove that a policy improvement algorithm (PIA) converges to an optimal relaxed control. Contrary to the standard stochastic control literature, classical Hölder estimates of value functions do not ensure the convergence of the PIA, due to the added entropy-regularizing term. To circumvent this, we carry out a delicate estimation by moving back and forth between appropriate Hölder and Sobolev spaces. This requires new Sobolev estimates designed specifically for the purpose of policy improvement and a nontrivial technique to contain the entropy growth. Ultimately, we obtain a uniform Hölder bound for the sequence of value functions generated by the PIA, thereby achieving the desired convergence result. Characterization of the optimal value function as the unique solution to an exploratory Hamilton– Jacobi–Bellman equation comes as a by-product.
• [03347] Continuous time q-learning for McKean-Vlasov control problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoli Wei (Tsinghua Shenzhen International Graduate School)
    • Xiang Yu (The Hong Kong Polytechnic University)
  • Abstract : For continuous time McKean-Vlasov control problems, we study the continuous time version of Q-learning for reinforcement learning under entropy regularization. Due to the complexity of distribution dependence, the counterpart of the martingale characterization of q-function in the single-agent control problem fails in our framework. To resolve the challenge, we introduce two distinct q-functions, which share the same integral under all test stochastic policies. The first q-function is associated to the optimal policy and policy improvement, and the second q-function can be used to develop the weak martingale characterization of some related processes under all test stochastic policies. Based on the weak martingale characterization and the relationship between two q-functions, we can design some q-learning algorithms for the learning McKean-Vlasov control problems and present several financial applications.

MS [00989] Structure and dynamics in complex biological systems

room : D515

• [01961] Network topology determines robustness and flexibility in chemical reaction systems
  • Format : Talk at Waseda University
  • Author(s) :
    • TAKASHI OKADA (Kyoto Univ)
  • Abstract : In living cells, biochemical reactions form complex networks. Conventional sensitivity analysis is limited by the need for detailed reaction kinetics and parameters, which are often not available for living systems. Our new method, structural sensitivity analysis, determines qualitative sensitivity solely from network structures. Based on this framework, we established a topological theorem that determines the extent to which the perturbation of a parameter affects chemical concentrations and fluxes within the network.
• [01937] Simplifying complex chemical reaction networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuji Hirono (Asia Pacific Center for Theoretical Physics)
  • Abstract : Understanding the behavior of complex biochemical reaction networks is an important and challenging problem. To ease the analysis, it is desirable if we can simplify a complex reaction network while preserving its important features. In this talk, we discuss a method for the reduction of chemical reaction networks. We identify topological conditions on its subnetworks, reduction of which preserves the original steady state exactly.
• [01907] Multistationarity conditions for polynomial systems in biology
  • Format : Talk at Waseda University
  • Author(s) :
    • Carsten Conradi (HTW Berlin)
  • Abstract : Polynomial Ordinary Differential Equations are an important tool in quantitative biology. Often parameters vary in large intervals. Consequently one is interested in parameter conditions that guarantee multistationarity and further constrain parameter values. The focus of this talk are mass action ODEs that admit a monomial parameterization of positive steady states. For such systems it is straightforward to derive a parameterization of rate constants where multistationarity exists. Multisite phosphorylation systems are of this type.
• [02165] Global Attractor Conjecture, Persistence Conjecture, and Toric Differential Inclusions
  • Format : Talk at Waseda University
  • Author(s) :
    • Gheorghe Craciun (University of Wisconsin-Madison)
  • Abstract : The Global Attractor Conjecture can be regarded as a far-reaching generalization of Boltzmann’s H-theorem for finite dimensional systems. The related Persistence Conjecture is even more general, and essentially says that solutions of weakly reversible systems cannot go extinct. We will discuss some of these connections, and we focus especially on introducing Toric Differential Inclusions as a tool for proving these conjectures. We also describe implications for biochemical mechanisms for noise filtering and cellular homeostasis.

contributed talk: CT187

room : A201

[00809] Mathematical Aspects of Metaheuristics in Medical Imaging and Pattern Recognition

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @A201
• Type : Contributed Talk
• Abstract : Medical imaging and pattern recognition have very important applications in the health and other industrial sectors. In this talk, we will be focusing on the mathematical model that deals with high-order graph matching using a metaheuristic technique. This model has been tested real-life images including identifying white blood cells in human blood. The models work on the idea of artificial intelligence and have a high level of efficiency with good results. The role of AI is in terms of AI-based metaheuristics which are used as search and optimization techniques to address aforementioned problems.
• Classification : 68W50, 68U10, 68T42, 68T10, 68T05, Evolutionary Algorithms, Agent Based Systems, Graph Matching
• Format : Talk at Waseda University
• Author(s) :
  • Anupam Yadav (Dr BR Ambedkar National Institute of Technology Jalandhar)

[00078] A higher order numerical scheme to a nonlinear McKendrick-Von Foerster equation with singular mortality

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @A201
• Type : Contributed Talk
• Abstract : In this paper, higher-order numerical schemes to the McKendrick-Von Foerster equation are presented when the death rate has singularity at the maximum age. The third, fourth-order schemes that are proposed are based on the characteristics, which are non-intersecting lines in this case, and are multi-step methods with appropriate corrections at each step. In fact, the convergence analysis of the schemes is discussed in detail. Moreover, numerical experiments are provided to validate the orders of convergence of the proposed third-order and fourth-order schemes.
• Classification : 92D25, 65M25, 65M12
• Format : Talk at Waseda University
• Author(s) :
  • Joydev Halder (School of Mathematics and Statistics, University of Hyderabad)
  • Suman Kumar Tumuluri (School of Mathematics and Statistics, University of Hyderabad)

[00655] Finite-time fault-tolerant robust control design for parabolic partial differential equations

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @A201
• Type : Contributed Talk
• Abstract : In this paper, a finite-time fault-tolerant robust control design for parabolic partial differential equations in the presence of uncertainties, actuator faults and external disturbances is discussed. The main aim is to design a non-fragile fault-tolerant control to ensure the robust stabilization of the considered PDEs. By employing Lyapunov method, a novel set of conditions is obtained to ensure the required result. Finally, simulations are provided to demonstrate the effectiveness of the developed control design.
• Classification : 93D15, 93D05, 93D40, Robust Control Theory
• Author(s) :
  • Sakthivel Rathinasamy (Bharathiar University)

[01059] EVENT-TRIGGERED CONTROL FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH CYBER-ATTACKS

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @A201
• Type : Contributed Talk
• Abstract : An event-triggered control for parabolic-type partial differential equations subject to disturbances and cyber-attacks is addressed in this talk. To attenuate the disturbances an H∞ performance is considered. By designing an appropriate Lyapunov-Krasovskii functional the stabilization conditions for the considered parabolic type partial differential equations are obtained in the form of linear matrix inequalities. Finally, a numerical example is provided to verify the efficiency of the derived theoretical results.
• Classification : 93D05, 93D09, 93D15, Lyapunov Stability, event-triggered control
• Format : Online Talk on Zoom
• Author(s) :
  • Parivallal Arumugam (Sungkyunkwan University)

[01008] EID estimator-based Control Design for Singular Polynomial Fuzzy Systems

• Session Time & Room : 2D (Aug.22, 15:30-17:10) @A201
• Type : Contributed Talk
• Abstract : This paper studied the disturbance rejection problem for singular polynomial fuzzy system based on equivalent-input-disturbance-estimator-based control approach. The proposed approach is used to compensate the influences of unknown lumped disturbance. To cope the robust stability problems, the augmented closed-loop system is constructed that includes dynamics of the system, observer, and low-pass filter. Lyapunov stability theory is used to develop stability conditions for the resulting system. Finally, numerical examples are provided to validate the theoretical result.
• Classification : 93D09, 93D15, 93D25, Robust stability, Lyapunov stability theory, Stabilization of systems by feedback
• Format : Online Talk on Zoom
• Author(s) :
  • Selvaraj Palanisamy (Chungbuk National University)
  • Kwon Oh-Min (Chungbuk National University)

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

room : A206

• [02141] Machine Learning for Scientific Discovery, with Examples in Fluid Mechanics
  • Format : Talk at Waseda University
  • Author(s) :
    • Steven Brunton (University of Washington)
  • Abstract : This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system.
• [02075] Hamiltonian structure-preserving non-intrusive operator inference for predictive digital twins
  • Format : Talk at Waseda University
  • Author(s) :
    • Anthony Gruber (Sandia National Laboratories)
    • Irina Tezaur (Sandia National Laboratories)
    • Max Gunzburger (University of Texas at Austin)
  • Abstract : To serve as reliable predictive tools, digital twins require dimensionality-reduction techniques that preserve key properties of the underlying equations. This talk presents a novel non-intrusive structure-preserving model reduction technique for canonical and non-canonical Hamiltonian systems based on operator inference. The method reduces to a straightforward linear solve given snapshot data and “gray-box” knowledge of the underlying problem. We demonstrate that, unlike traditional reduction methods, the proposed approach delivers stable, accurate, energy-conserving and robust reduced-order models.
• [01631] Weakly supervised learning for power grid state estimation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jochen Lorenz Cremer (TU Delft)
    • Elvin Isufi (TU Delft)
    • Benjamin Habib (TU Delft)
  • Abstract : In this talk, I present a novel approach for Distribution System State Estimation (DSSE) called the Deep Statistical Solver for Distribution System State Estimation (DSS^2). This approach, based on graph neural networks (GNNs) and weakly-supervised learning, addresses the challenges of lack of observability and high density in the distribution system. DSS$^2$ uses hypergraphs to represent the heterogeneous components of the distribution system and updates their latent representations via a node-centric message-passing scheme. Our approach allows for the training of DSS$^2$ using noisy and corrupted measurements, alleviating the need for ideal labelled data. The results of our experiments on various sizes of power networks showed DSS2 outperforms the conventional Weighted Least Squares algorithm in terms of accuracy, convergence, and computational time and is more robust to noisy, erroneous, and missing measurements. Our approach demonstrates the potential of weakly-supervised learning in DSSE and the ability to respect the physical constraints of the distribution system while learning from noisy measurements.
• [03438] Data-driven Balancing for Acoustical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Art J.R. Pelling (TU Berlin)
    • Ennes Sarradj (TU Berlin)
  • Abstract : Constructively modelling acoustical systems is difficult due to unknown material and domain properties and complexity of dynamics. Although measurement data is abundantly available, reduced order modelling is not well-established in the field. We showcase recent system identification methods from the mathematical community and analyze their aptitude and performance in real applications that involve high-dimensional measurement data. Amongst others, we consider head-related transfer functions that are used for auralization in virtual reality applications.

MS [00616] Continuous optimization: theoretical and algorithmic trends

room : A207

• [03943] On the Inexact Restoration approach for adaptive sample size in finite sum minimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefania Bellavia (University of Florence)
    • Natasa Krejic (University of Novi Sad)
    • Benedetta Morini (University of Florence)
    • Simone Rebegoldi (University of Florence)
  • Abstract : In this talk we discuss recent advances in the inexact restoration approach combined with stochastic trust-region methods for finite-sum minimization problems. At each iteration, the proposed methods approximate the function and the derivatives by subsampling. The choice of the function sample size is ruled by the Inexact Restoration approach, whereas the derivatives approximations are computed averaging in smaller sets. We report worst-case complexity results in expectation and numerical results showing the advantages of adaptive approaches.
• [03290] Block coordinate descent and the close enough traveling salesman problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Ernesto G. Birgin (University of São Paulo)
  • Abstract : At each iteration of a Block Coordinate Descent method one minimizes a constrained approximation of the objective function with respect to a generally small set of variables. In this work we address the problem in which block constraints are not defined by global sets of equations and inequations. An algorithm is defined and convergence and complexity are proved. The proposed method is used to solve a generalization of the close enough traveling salesman problem.
• [02948] Sequential optimality conditions: how to stop optimization algorithms
  • Format : Talk at Waseda University
  • Author(s) :
    • Paulo J. S. Silva (University of Campinas)
  • Abstract : Optimality conditions, like KKT, play essential roles in modern optimization. They may be used as a starting point to develop algorithms or as a condition to accept an approximate solution. This dynamic aspect, led to the development of sequential optimality conditions that try to capture the iterative approximation nature of computed sequences. In this talk, we will present how this development enlightened the convergence requirements and termination criteria of algorithms in nonlinear optimization.

CSIAM

room : A208 -> D604 (changed)

[EM005] Deep adaptive sampling for numerical PDEs

• Session Date & Time : 2D (Aug.22, 15:30-17:10) @A208
• Type : Talk in Embedded Meeting
• Abstract : In this talk, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
• Format : Talk at Waseda University
• Author(s) :
  • Tao Tang (BNU-HKBU United International College)

[EM006] Energy transfer and Generalized Fermi's Golden Rule in Hamiltonian nonlinear Klein-Gordon equations

• Session Date & Time : 2D (Aug.22, 15:30-17:10) @A208
• Type : Talk in Embedded Meeting
• Abstract : More than 20 years ago, Soffer-Weinstein proved that spatially localized and time-periodic solutions of the linear Klein-Gordon problem are destroyed by generic nonlinear Hamiltonian perturbations via slow radiation of energy to infinity, via energy transfer from the discrete to continuum modes, under the condition that the discrete modes are close to the continuous spectral modes. Since then, a long-standing open question is to study the corresponding small eigenvalues problem, which will be reported in this talk.
• Format : Talk at Waseda University
• Author(s) :
  • Zhen Lei (Fudan University)
  • Jie Liu (Fudan University)
  • Zhaojie Yang (Fudan University)

[EM007] The weak Galerkin finite element method for elliptic eigenvalue problems

• Session Date & Time : 2D (Aug.22, 15:30-17:10) @A208
• Type : Talk in Embedded Meeting
• Abstract : This talk is devoted to studying eigenvalue problem by the weak Galerkin finite element method with an emphasis on obtaining lower bounds. We demonstrate that the WG methods can achieve arbitrary high order convergence. This is in contrast with classical nonconforming finite element methods which can only provide the lower bound approximation by linear elements. We also presented the guaranteed lower bound for k=1 order polynomials and some acceleration techniques are applied to WG method.
• Format : Talk at Waseda University
• Author(s) :
  • Ran Zhang (Peking University)
  • Hehu Xie (LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Zhimin Zhang (Beijing Computational Science Research Center)
  • Qilong Zhai (Jilin University)
  • Carsten Carstensen (Department of Mathematics, Humboldt-Universit)

[EM008] PMLs for scattering problems in complex media

• Session Date & Time : 2D (Aug.22, 15:30-17:10) @A208
• Type : Talk in Embedded Meeting
• Abstract : Perfectly matched layer (PML) provides a very efficient method for solving exterior scattering problems by designing a layer of artificial material which damps outgoing waves exponentially. The research on PML methods is still very rare for inhomogeneous background media. In this talk, I will focus on the stability and exponential convergence of PML methods for acoustic and electromagnetic scattering problems in two-layered media and half spaces with step-like boundaries.
• Format : Talk at Waseda University
• Author(s) :
  • Weiying Zheng (Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

MS [02440] Advances in Optimization I

room : A502

• [04074] Some Recent Developments on Solving Variational Inequality Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuzhong Zhang (University of Minnesota)
  • Abstract : In this talk, we will present several solution methods for solving non-monotone VI problems. As the VI formulation is generalized from the optimality condition for optimization, the results are immediately applicable to nonconvex and constrained continuous optimization. The focus is placed on the conditions of the non-monotone VI models, under which the newly designed solution algorithms would converge with guaranteed rates of convergence.
• [05227] Monotone Variational Inequality (VI) for estimation and learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Yao Xie (Georgia Institute of Technology)
  • Abstract : We propose a new computational framework for estimating parameters in generalized generalized linear models (GGLMs), inspired by Juditsky and Nemirovsky's recent work. First, we extend GLMs to spatio-temporal data by accounting for dependencies among observations while using a monotone operator-based variational inequality method. We also present online instance-based bounds using martingale concentration inequalities and apply our algorithm to wildfire and police datasets. In addition, we demonstrate our approach to training neural networks.
• [04577] Implementation of Interior Point Method for Nonlinear Programming for Real-life Applications.
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahito Tanabe (NTTDATA Mathematical Systems Inc.)
  • Abstract : In the modeling of real-life applications, we encounter some non-linearity. In such a case, interior-point algorithm is one approach to choose because it is good at finding locally optimal solutions quickly for large-scale mildly nonlinear problems. In this talk, we discuss some implementation issues related to interior-point method that originates from non-linearity, and review some applications.
• [04650] Tropical convexity: application to linear programming and mean-payoff games
  • Format : Talk at Waseda University
  • Author(s) :
    • Stephane Louis Gaubert (INRIA and Ecole polytechnique)
  • Abstract : Tropical geometry sets up a bridge between linear programming and mean-payoff games, exploiting a correspondence between generic convex semi-algebraic programs over nonarchimedean fields and different classes of zero-sum repeated games. We will discuss the application of this correspondence to the complexity analysis of interior point methods, showing in particular that no self-concordant barrier interior point method is strongly polynomial. This is based on a series of works with Allamigeon, Benchimol, Joswig and Vandame.

MS [02545] Challenges and Recent Advances in Phylogenetics

room : A508

• [05365] Minimum Number of Leaf-Covering Subtrees Covering Phylogenetic Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Yoshida (The University of Tokyo)
  • Abstract : Several deviation measures of non-tree-based phylogenetic networks from tree-based have been defined and their characteristics have been studied. One of the measures is the minimum number of leaf-covering subtrees which cover the phylogenetic network. In this talk, I suggest the first polynomial-time and efficient algorithm to compute both the minimum number and the covering subtrees. This algorithm is based on flow algorithms on several networks transformed from the network used to compute another deviation measure.
• [04243] Proximity measures for phylogenetic network classes
  • Format : Talk at Waseda University
  • Author(s) :
    • Yukihiro Murakami (TU Delft)
    • Leo van Iersel (TU Delft)
    • Mark Jones (TU Delft)
    • Esther Julien (TU Delft)
  • Abstract : Orchard networks represent the evolutionary history of species as a tree structure with horizontal arcs. In this talk, we will explore the extent to which a network departs from being orchard. We will examine this deviation through varying graph operations such as adding leaves and removing arcs, as well as via vertex labeling. To provide context, we will compare these findings to proximity measures for other classes of networks, including tree-based and tree-child networks.
• [03534] Data reduction rules to compute distances between phylogenetic trees
  • Format : Online Talk on Zoom
  • Author(s) :
    • Simone Linz (University of Auckland)
    • Steven Kelk (Maastricht University)
    • Ruben Meuwese (Maastricht University )
    • Simone Linz (University of Auckland)
  • Abstract : In evolutionary biology, phylogenetic trees are widely used to unravel the ancestral history of entities such as species or viruses. However, it is not uncommon to obtain different trees for the same data set. For example this can be due to methodological reasons. These tree incongruences motivate the use of distance measures in phylogenetics to quantify the dissimilarities between two phylogenetic trees. One popular distance between phylogenetic trees is called the tree bisection and reconnection (TBR) distance. Although this distance is NP-hard to compute, it is also fixed-parameter tractable. In this talk, we describe a series of results on the size of the TBR kernel, i.e. the size of two phylogenetic trees after pre-processing.
• [03576] Parsimony and the rank of phylogenetic flattenings
  • Format : Online Talk on Zoom
  • Author(s) :
    • David Bryant (University of Otago)
  • Abstract : The standard models of sequence evolution on a phylogeny determine probabilities for every character or site pattern. A flattening is an arrangement of these probabilities into a matrix, with rows corresponding to all possible site patterns for one set of taxa and columns corresponding to all site patterns for another. Flattenings have been used to prove difficult results in phylogenetic mathematics and form the basis of several methods of phylogenetic inference. We provide an exact formula for the rank of these matrices based on parsimony scores.

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

room : A510

• [03028] Results on Classical Elastohydrodynamics for a Swimming Filament
  • Format : Talk at Waseda University
  • Author(s) :
    • Laurel A Ohm (University of Wisconsin--Madison)
  • Abstract : We consider two models of an immersed inextensible filament undergoing planar motion: (1) the classical elastohydrodynamic model using resistive force theory and Euler-Bernoulli beam theory, and (2) a novel curve evolution incorporating effects of linear viscoelasticity. We mention our recent PDE results on these models and highlight how this analysis can help to understand undulatory swimming at low Reynolds number. This includes the development of a novel numerical method to simulate inextensible swimmers.
• [04238] A limiting model for a low Reynolds number swimmer with N passive elastic arms
  • Format : Talk at Waseda University
  • Author(s) :
    • Jessie Levillain (CMAP, Ecole Polytechnique)
    • François Alouges (Centre Borelli, École Normale Supérieure Paris-Saclay)
    • Aline Lefebvre-Lepot (CMAP, École polytechnique)
  • Abstract : We study a simple model of artificial microswimmer, consisting of a rigid extensible arm followed by an $N$-mass-spring system. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Numerical experiments show performances of the displacement in terms of frequency or amplitude of the oscillation of the active arm.
• [05406] Activation processes of flagellated micro-swimmers
  • Format : Online Talk on Zoom
  • Author(s) :
    • Irene Anello (SISSA)
    • Jessie Levillain (CMAP, Ecole Polytechnique)
    • François Alouges (Centre Borelli, Ecole Normale Supérieure Paris-Saclay)
    • Aline Lefebvre-Lepot (CMAP, Ecole Polytechnique)
    • Antonio De Simone (SISSA)
  • Abstract : We study the activation processes of flagellated micro-swimmers investigating microscopic details inside the flagellum. The flagellum is composed of a structure called axoneme, composed of nine filament pairs along which are disposed force-generating elements called molecular motors. After describing the biology behind it, we first model these motors individually before introducing a mathematical representation of the whole system. The aim is to couple this microscopic description with a macroscopic beam equation for flagellated swimmers.
• [02171] Emergent rheotaxis of shape-changing swimmers in Poiseuille flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Benjamin Benjamin Walker (University of Bath)
    • Kenta Ishimoto (Kyoto University)
    • Clement Moreau (RIMS, Kyoto University)
    • Eamonn Gaffney (University of Oxford)
    • Mohit Dalwadi (University College London)
  • Abstract : The complexity of microscale swimming has driven the development of simple, representative models. In this talk, we'll examine an apparently simple model of a swimming cell in a channel and reveal a surprisingly complex dynamics that evolves on three distinct timescales. Through an asymptotic analysis, we'll show how the long-time behaviours of this system can be reduced to the study of a single ordinary differential equation, whose evolution turns out to be remarkably simple.

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

room : A511

• [03206] Network design principle for biological dual functions
  • Author(s) :
    • Lei Zhang (Peking University)
  • Abstract : Biological systems are capable of performing complex functions with a remarkable degree of accuracy, reliability, and robustness. We postulate that behind the celebrated diversity of the biological world lie “universal” principles that emerge at various levels of organization. For example, many signaling systems execute adaptation under noisy circumstances, and transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. In this talk, we will explore two dual functions: one is adaptation and noise attenuation, and the other one is oscillation and noise attenuation. By analyzing and computing three-node or four-node networks, we reveal essential network design principles for biological dual functions, which can be utilized in synthetic biology.
• [03385] Density Physics-Informed Neural Network infers an arbitrary density distribution for non-Markovian system
  • Author(s) :
    • Hyeontae Jo (Institute for Basic Science)
    • Hyukpyo Hong (KAIST)
    • Hyung Ju Hwang (Pohang University of Science and Technology)
    • Won Chang (University of Cincinnati)
    • Jae Kyoung Kim (KAIST)
  • Abstract : In this talk, we developed Density-PINN (Physics-Informed Neural Networks), a method capable of estimating the probability density function embedded within a differential equation. While conventional PINNs have focused on determining the solutions or parameters of differential equations that can explain observed data, we introduce a specialized approach for estimating the probability density function contained within the equation. Specifically, when dealing with a limited number of stochastic time series as observed data, and where only the average of the data satisfies the solution of the differential equation, we have constructed a mean-generating model using Variational Autoencoders. By applying our method to single-cell gene expression data from 16 promoters in response to antibiotic stress, we discovered that promoters with slower signaling initiation and transduction exhibit greater cell-to-cell heterogeneity in response intensity.
• [02263] Integrating different layers of biological data to enhance prediction
  • Author(s) :
    • Suoqin Jin (Wuhan University)
  • Abstract : The rapid advances of single-cell technologies have been attracting more attention. Recently we made some efforts to enhance biological prediction and discovery from single-cell RNA sequencing. By integrating single-cell RNA-seq with single-cell epigenomic data, bulk data or prior knowledge, we were able to dissect cellular heterogeneity and communication more comprehensively, and prioritize clinically-relevant cell subsets and prognostic signatures, which cannot be fully explained by single-cell genomics only, and highlights the valuable role of data integration.
• [03677] Physics of Furrow Ingression in C. elegans Zygote
  • Author(s) :
    • Masatoshi Nishikawa (Hosei University)
  • Abstract : Cleavage furrow ingression is asymmetric in the first cleavage of Caenorhabditis elegans zygote. The asymmetric ingression gives rise to the symmetry breaking in terms of dorsal-ventral axis establishment, but its underlying mechanisms are largely unexplored. We will demonstrate that the distribution of cortical tension generator in the contractile ring becomes asymmetric as the curvature change at the ingression site and cortical flow toward the ring, suggesting the feedback between cell shape, contractility and flow.

MS [00643] Stochastic modeling in cell biology

room : A512

• [02211] Optimal curvature and directional sensing in long-range cell-cell communication
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Allard (University of California Irvine)
    • Sohyeon Park (University of California Irvine)
    • Dae Seok Eom (University of California Irvine)
    • Hyunjoong Kim (University of Pennsylvania)
  • Abstract : Cells in tissue can communicate long-range via diffusive signals. In addition, another class of cell-cell communication is by long, thin cellular protrusions that are $\sim 100$ microns in length, i.e., many cell-lengths, and $\sim 100$ nanometers in width, i.e., below traditional microscope resolution. These protrusions have been recently discovered in many organisms, including nanotubes humans and airinemes in zebrafish. But, before establishing communication, these protrusions must find their target cell. Here we demonstrate airinemes in zebrafish are consistent with a finite persistent random walk model. We study this model by stochastic simulation, and by numerically solving the survival probability equation using Strang splitting. The probability of contacting the target cell is maximized for a balance between ballistic search and diffusive highly curved, random search. We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme’s source, finding the experimentally observed parameters to be at a Pareto optimum balancing directional sensing with contact initiation.
• [04467] Centrosome asymmetry in the early C. elegans embryo
  • Format : Talk at Waseda University
  • Author(s) :
    • Adriana Dawes (Ohio State University)
    • Shayne Plourde (The Ohio State University)
    • David Ignacio (The Ohio State University)
    • Andrew Cohen (The Ohio State University)
  • Abstract : Centrosome positioning, which determines where a cell divides, is mediated by microtubules, biopolymers nucleated at the centrosomes, and the motor protein dynein. Using stochastic and continuum models along with a measure of centrosome movement, we identify key proteins involved in regulating centrosome movement in early embryos of the nematode worm C. elegans, and demonstrate the parallel role of cell geometry in proper positioning of the centrosomes.
• [04462] Modeling and tracking random motion in micrometer-scale living systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jay Mack Newby (University of Alberta)
  • Abstract : We study stochastic motion of objects in micrometer-scale living systems: tracer particles in living cells, pathogens in mucus, and single cells foraging for food. We use stochastic models and state space models to track objects through time and infer properties of objects and their surroundings. For example, we can calculate the distribution of first passage times for a pathogen to cross a mucus barrier, or we can spatially resolve the fluid properties of the cytoplasm in a living cell. Recently developed computational tools, particularly in the area of Markov Chain Monte Carlo, are creating new opportunities to improve multiple object tracking. The primary remaining challenge, called the data association problem, involves mapping measurement data (e.g., positions of objects in a video) to objects through time. I will discuss new developments in the field and ongoing efforts in my lab to implement them. I will motivate these techniques with specific examples that include tracking salmonella in GI mucus, genetically expressed proteins in the cell cytoplasm, active transport of nuclei in multinucleate fungal cells, and raphid diatoms in seawater surface interfaces.
• [04071] Stochastic effects in molecular motor teams under detachment and reattachment
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Kramer (Rensselaer Polytechnic Institute)
    • Joseph Klobusicky (The University of Scranton)
    • John Fricks (Arizona State University)
  • Abstract : We revisit two paradigms of cooperative action by kinesin molecular motors involving a coupling of the detachment and reattachment processes with the stochastic spatial dynamics. First, for two dissimilar types of kinesin transporting a common cargo, we provide approximate analytical characterizations for how incorporating slack in the tether model affects the cooperative dynamics. Secondly, we extend consideration of gliding assays to a situation where microtubules are crosslinked while being crowdsurfed by immobilized kinesin.

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

room : A601

• [05519] Hierarchical Lowrank Arithmetic with Binary Compression
  • Author(s) :
    • Ronald Kriemann (Max Planck Institute for Math. i.t.S.)
  • Abstract : With lowrank approximation the storage requirement for dense data is reduced to linear levels. However, the lowrank factors are often stored using double precision. Newer approaches exploit the different IEEE754 floating point formats in a mixed precision approach. Since these formats show a significant storage (and accuracy) gap, we look beyond the standard formats and use an adaptive precision scheme to further increase the storage efficiency and investigate its effects on the arithmetic of H-matrices.
• [05545] Parallel Factorization of Hierarchical Matrices
  • Author(s) :
    • Wagih Halim Boukaram (Lawrence Berkeley National Lab)
  • Abstract : Hierarchical matrices allow for memory efficient representation of the data sparse matrices that often appear in scientific applications. The open source H2Opus library provides distributed CPU and GPU implementations of several key operations using the H2-variant of hierarchical matrices, where nested row and column bases allow for asymptotically optimal memory storage requirements. In this talk, we discuss the details of a newly developed parallel hierarchical factorization algorithm using skeletonization.
• [05552] Parallel Low-Rank Approximation of High-Dimensional Multivariate Normal Probabilities on Manycore Systems
  • Author(s) :
    • Xiran Zhang (KAUST)
    • Sameh Abdulah (KAUST)
    • Hatem Ltaief (KAUST)
    • Ying Sun (KAUST)
    • Marc Genton (KAUST)
    • David Keyes (KAUST)
  • Abstract : The multivariate normal (MVN) probabilities frequently appear in statistics to support applications requiring, for example, the computation of skewed probability density functions or Bayesian spatial probit problems. In the literature, the separation-of-variable (SOV) technique is commonly used to compute the MVN probability by converting the integration region to the unit hypercube, allowing a faster convergence rate. However, the SOV techniques require the computation of the Cholesky factorization of an n x n matrix with O(n^3) computation and O(n^2) space complexity. The computing of the Cholesky factorization operation in higher dimensions is prohibitive in dense structures. Thus, several studies have proposed to include an approximation technique that can help perform the Cholesky factorization faster while preserving the required accuracy. Another direction is to rely on high-performance computing techniques to allow intensive computing on modern parallel systems. In this work, we aim to couple the computing power and the hierarchical approximation to allow faster computation of the MVN probability of high-dimensional problems. We rely on state-of-the-art parallel hierarchical linear algebra algorithms and runtime systems to provide high performance and scalability in computing the MVN probability. We also include a block reordering technique to allow a faster convergence rate than the dense algorithm. Moreover, we assess the performance and the accuracy of the provided method using simulations and real air pollution data.
• [05590] A geometry oblivious H-matrix approximation scheme for rectangular matrices
  • Author(s) :
    • George Biros (The University of Texas at Austin)
  • Abstract : We propose a novel method for compressing dense matrices. Our method is based on a hierarchical-matrix (H-matrix) approximation. H-matrix approximations have been popular in science and engineering applications. They combine the notion of singular value decomposition (SVD) with appropriate block permutations and recursion. H-matrices are applicable to problems in which the matrix entries correspond to pairwise interactions between sets of points, as for example in kernel matrices. Here we generalize this approximation to arbitrary dense matrices. Our method comprises of a randomized low-rank approximation of permuted blocks along with approximate leverage scores computations that are used to find such permutations. We introduce theoretical analysis, complexity analysis, and experimental results on kernel matrices.

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

room : A615

• [04826] Learning high-dimensional feedback laws for collective dynamics control
  • Format : Talk at Waseda University
  • Author(s) :
    • Dante Kalise (Imperial College London)
    • Giacomo Albi (University of Verona)
    • Sara Bicego (Imperial College London)
  • Abstract : We discuss the control of collective dynamics for an ensemble of high-dimensional particles. The collective behaviour of the system is modelled using a kinetic approach, reducing the problem to efficiently sampling binary interactions between controlled agents. However, as individual agents are high-dimensional themselves, the controlled binary interactions correspond to large-scale dynamic programming problems, for which we propose a supervised learning approach based on discrete-time State-dependent Riccati Equations and recurrent neural networks.
• [05378] Sparse Kernel Flows for Learning 132 Chaotic Dynamical Systems from Data
  • Format : Talk at Waseda University
  • Author(s) :
    • Boumediene Hamzi (Caltech)
    • Lu Yang (Nanjing University of Aeronautics and Astronautics)
    • Xiuwen Sun (Nanjing University of Aeronautics and Astronautics)
    • Houman Owhadi (California Institute of Technology)
    • Naiming Xie (NUAA)
  • Abstract : Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. As shown in previous work, a simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a data-adapted kernel which can be learned by using Kernel Flows. The method of Kernel Flows is a trainable machine learning method that learns the optimal parameters of a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used. The objective function could be a short-term prediction or some other objective. However, this method is limited by the choice of the base kernel. In this paper, we introduce the method of Sparse Kernel Flows in order to learn the “best” kernel by starting from a large dictionary of kernels. It is based on sparsifying a kernel that is a linear combination of elemental kernels. We apply this approach to a library of 132 chaotic systems. Presentation based on https://arxiv.org/pdf/2301.10321.pdf
• [05395] Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Sebastian Peitz (Universität Paderborn)
    • Jan Stenner (Universität Paderborn)
    • Vikas Chidananda (Universität Paderborn)
    • Steven Brunton (UW)
    • Kunihiko Taira (UCLA)
  • Abstract : We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of partial differential equations (PDEs). Exploiting translational invariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents' environment can be drastically reduced using a convolution operation over the state space of the PDE. In this setting, the complexity can be flexibly adjusted via the kernel width or using a stride greater than one. A central question in this framework is the definition of the reward function, which may consist of both local and global contributions. We demonstrate the performance of the proposed framework using several standard PDE examples with increasing complexity, where stabilization is achieved by training a low-dimensional DDPG agent with small training effort.

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

room : A617

• [04296] The Identification Problem for Discrete Painlevé Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Anton Dzhamay (University of Northern Colorado and BIMSA)
  • Abstract : We describe a refined version of the discrete Painlevé equations identification problem. We emphasize that, in addition to determining the surface type of the equation, it is important to determine the actual translation element, up to conjugation, and to keep in mind possible special point configurations that can affect the symmetry group of the equation. We illustrate this by a variety of examples that appear in applications, especially in the theory of orthogonal polynomials.
• [04597] Orthogonal polynomials and discrete Painlevé equations on the $D_5^{(1)}$ Sakai surface
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Stokes (The University of Tokyo)
    • Anton Dzhamay (University of Northern Colorado)
    • Galina Filipuk (University of Warsaw)
  • Abstract : We show that two recurrences coming from the theory of orthogonal polynomials are transformable to discrete Painlevé equations, which share the same surface type $D_5^{(1)}$ in the Sakai classification scheme but are non-equivalent. The surfaces associated with these recurrences do not have the full parameter freedom for their type, and we find the symmetry groups of these examples as subgroups of the extended affine Weyl group of type $A_3^{(1)}$ from the generic case.
• [03019] Orthogonal polynomials, Schur flow and Painlevé equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Walter Van Assche (KU Leuven)
  • Abstract : We give a brief introduction to orthogonal polynomials on the unit circle and show how an exponential modification of the weight function leads to the Ablowitz-Ladik lattice equations for the recurrence coefficients (Verblunsky coefficients) of these polynomials. As shown by Periwal and Shevitz (1990) these orthogonal polynomials appear in unitary matrix models. The Verblunsky coefficients satisfy the discrete Painlevé II equation and the ratio of these coefficients satisfy Painlevé III. The Lax pair can be written in terms of the CMV matrix, which is a pentadiagonal infinite matrix similar to the Jacobi matrix for orthogonal polynomials on the real line.
• [04527] Symmetries of discrete Nahm systems and Normalizers in Coxeter groups
  • Format : Online Talk on Zoom
  • Author(s) :
    • yang shi (Flinders university)
    • Giorgio Gubbiotti (Universita degli Studi di Milano)
  • Abstract : It is known that discrete Nahm systems arise as autonomous versions of Sakai's classification of discrete Painlev\e equations. Here we study the groups of symmetries of these systems using the theory of normalizers of Coxeter groups developed by Brink and Howlett (Invent. Math, 1999).

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

room : A618

• [05645] Test like you train in implicit deep learning
  • Author(s) :
    • Pierre Ablin (Apple)
  • Abstract : Implicit deep learning relies on expressing some components of deep learning pipelines implicitly via a root equation. The training of such a model is thus a bi-level optimization. In practice, the root equation is solved using a fixed number of iterations of a solver. We discuss the effect of having a different number of iterations at test time than at train time, challenging a popular assumption that more iterations at test time improve performance.