MS and CT list / Aug. 25, 13:20-15:00.

MS [02591] Recent advances in data-driven modeling and computational methods

room : G301

• [02896] Topological Data Analysis Experience in Malaysia: A Survey
  • Format : Talk at Waseda University
  • Author(s) :
    • Fatimah Abdul Razak (Universiti Kebangsaan Malaysia)
    • Mohd Salmi Md Noorani (Universiti Kebangsaan Malaysia)
  • Abstract : Topological Data Analysis (TDA) is used to detect qualitative features in datasets. It is often combined with techniques from Machine Learning, Time Series Analysis as well as Complex Network Analysis to achieve better predictions and classifications. This presentation outlines our experiences of using TDA to investigate several Malaysian data sets in order to predict floods and financial crises, classify different levels of air quality within a certain time window as well as detecting critical transitions.
• [03038] A Reaction Network Analysis of Insulin Signaling
  • Format : Talk at Waseda University
  • Author(s) :
    • Angelyn Lao (De La Salle University)
  • Abstract : The insulin signaling system is an important metabolic system that initiates the uptake of glucose into the cell. This reduced ability of cells to use available insulin for energy metabolism is viewed as a common factor in diseases such as obesity, type 2 diabetes, metabolic syndrome, and cancer, and more recently to brain insulin resistance in connection with mild cognitive impairment and Alzheimer’s disease (AD). The complexity of the insulin signaling system, both in terms of the number of molecular components involved as well as the intricate combination of positive and negative feedback loops, clearly warrants the application of mathematical modeling and computational tools. This talk presents the construction of the insulin signaling reaction network and the analysis of its robustness and stability using Chemical Reaction Network Theory.
• [03583] Comparing Lagrangian Particle Dispersion Models in Turbulent Flows: A Data-Driven Approach
  • Format : Talk at Waseda University
  • Author(s) :
    • Nurul Huda Mohd Ramli (Universiti Brunei Darussalam)
    • Haziq Jamil (Universiti Brunei Darussalam)
  • Abstract : This talk introduces a data-driven method for comparing two Lagrangian stochastic particle models in turbulent flows: the random flight model (RFM) and the simpler random displacement model (RDM). The RFM offers a more realistic representation of eddy velocities but can pose computational challenges. Using a Bayesian approach to infer the models' parameters, the objective is to provide a better understanding of their dynamics and assist researchers in selecting the appropriate model for their specific needs.
• [03912] Error estimates of numerical methods for the Dirac equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Ying Ma (Beijing University of Technology)
    • Jia Yin (Lawrence Berkeley National Laboratory)
    • Yue Feng (Sorbonne Université)
    • Lizhen Chen (Beijing Computational Science Research Center)
  • Abstract : The Dirac equation is a relativistic wave equation which plays an important role in relativistic quantum physics and provides a natural description of relativistic spin-1/2 particles. In this talk, we present numerical methods including several finite difference methods, the symmetric and asymmetric exponential wave integrator Fourier pseudospectral methods and establish the error estimates for the discretization of the Dirac equation in different regimes. Extensive numerical results are reported to support our error estimates.

contributed talk: CT005

room : G302

[00979] Optimal radio channel assignment to transmitters in a network by graph labeling approach

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G302
• Type : Contributed Talk
• Abstract : An optimal radio channel assignment to transmitters in a network is modelled by graph labeling approach. A radio labeling of a graph $G$ is a mapping $f : V(G) \rightarrow \{0,1,2,\ldots\}$ satisfying $|f(u)-f(v)| \geq diam(G)+1-d(u,v)$ for all $u,v \in V(G)$. The radio number $rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling $f$ with $\max\{f(v) : v \in V(G)\}=k$. We present our recent results on optimal radio labelings of graphs.
• Classification : 05C78, 05C15, 05C12
• Format : Talk at Waseda University
• Author(s) :
  • Devsi Dudabhai Bantva (Lukhdhirji Engineering College, Morbi)

[00511] Metapopulation network models explain non-Poissonian statistics of intercontact times

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G302
• Type : Contributed Talk
• Abstract : Intercontact times in empirical data obtained from humans and animals typically obey heavy-tailed distributions as opposed to exponential distributions that would correspond to Poisson processes. We show that this phenomenon is a mathematical property of a most basic metapopulation network model used in epidemiology and ecology modeling, in which individuals move from a patch to another according to the simple or other types of random walks. Our results hold true for any network structure.
• Classification : 05C82, 60K20
• Format : Talk at Waseda University
• Author(s) :
  • Elohim Fonseca dos Reis (State University of New York at Buffalo)
  • Naoki Masuda (State University of New York at Buffalo)

[00451] Transmission problems for composite layered elastic structures containing interfacial cracks

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G302
• Type : Contributed Talk
• Abstract : We investigate mixed transmission problems of the generalized thermo-electro-magneto elasticity theory for complex elastic multi-layered structures containing interfacial cracks. We apply the potential method and the theory of pseudodifferential equations and analyze smoothness properties and asymptomatic behaviour of solutions near the edges of cracks and near the curves where different type boundary conditions collide. We describe the stress singularity exponents explicitly.
• Classification : 74A15, 74H35, 74F05, 74F15
• Format : Talk at Waseda University
• Author(s) :
  • David Natroshvili (Georgian Technical University)

[00902] Influence of the statistical parameters of random particulate materials on wave propagation

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G302
• Type : Contributed Talk
• Abstract : Current models predicting the effective properties of random particulate materials neglect the correlation between the particles positions by using the hole correction approximation. A recent method which predicts more than one effective wavenumber is adapted in order to take into account these correlations. The method is validated against Monte-Carlo simulations and the influence of the correlations is demonstrated with computed effective wavenumbers.
• Classification : 74A40, 78A48, 82D30
• Format : Talk at Waseda University
• Author(s) :
  • Kevish Kumar Napal (University of Sheffield)
  • ARTUR LEWIS GOWER (University of Sheffield)
  • Paulo Sergio Piva (The University of Sheffield)
  • Aristeidis Karnezis (The University of Sheffield)

MS [00652] Recent Advances in Quasi-Monte Carlo Methods and Related Topics

room : G304

• [03343] High dimensional approximation and the curse of dimensionality
  • Format : Talk at Waseda University
  • Author(s) :
    • Ian Hugh Sloan (UNSW Sydney)
  • Abstract : This talk, joint work with Kuo and Kaarnioja, extends a 2022 result with Kazashi and Nobile. It uses periodic kernels located at lattice points. The lattice points and the kernels depend on parameters called “weights”. Using new “serendipitous” weights, the cost grows linearly with both dimension and number of lattice points, allowing practical computations in 1,000 dimensions, and no curse of dimensionality.
• [01697] QMC and sparse grids beyond uniform distributions on cubes
  • Format : Talk at Waseda University
  • Author(s) :
    • Ilja Klebanov (Free University of Berlin)
    • Tim Sullivan (University of Warwick)
  • Abstract : While Monte Carlo and MCMC methods are generally applicable and have a dimension-independent convergence rate, this rate is rather slow and unfeasible for many applications. Sparse grids and Quasi Monte Carlo methods provide better convergence rates under certain assumptions, but have only been constructed for uniform distributions on cubes and several other very specific distributions such as Gaussians. In this talk, I will show how these methods can be generalized to mixtures of such specific distributions, e.g. Gaussian mixtures, by means of a properly constructed transport map, which is a crucial step towards combining QMC and sparse grids methods with state of the art importance sampling algorithms, that are often based on such mixtures. I will avoid technical details and present lots of illustrations and videos instead.
• [02052] Can hyperinterpolation part with quadrature exactness?
  • Format : Online Talk on Zoom
  • Author(s) :
    • Congpei An (Southwestern University of Finance and Economics)
    • Hao-Ning Wu (The Hong Kong University)
  • Abstract : We discuss the approximation of continuous functions on the unit sphere by spherical polynomials of degree n via hyperinterpolation. Hyperinterpolation of degree n is a discrete approximation of the L2-orthogonal projection of degree n with its Fourier coefficients evaluated by a positive-weight quadrature rule that exactly integrates all spherical polynomials of degree at most 2n. This talk aims to bypass this quadrature exactness assumption by replacing it with the Marcinkiewicz--Zygmund property. Consequently, hyperinterpolation can be constructed by a positive-weight quadrature rule--not necessarily with quadrature exactness. This scheme is called unfettered hyperinterpolation. We provide a reasonable error estimate for unfettered hyperinterpolation. The error estimate generally consists of two terms: a term representing the error estimate of the original hyperinterpolation of full quadrature exactness and another introduced as compensation for the loss of exactness degrees. A guide to controlling the newly introduced term in practice is provided. In particular, if the quadrature points form a quasi-Monte Carlo design, then there is a refined error estimate. Numerical experiments verify the error estimates and the practical guide.
• [04553] Quasi-Monte Carlo-Based Algorithms for Deep Learning with Applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaoqun Wang (Tsinghua University)
  • Abstract : Deep learning methods are now used to solve (stochastic) partial differential equations in high dimensions, where the loss functions are defined as mathematical expectations. Traditional method to approximate the expectation is Monte Carlo (MC) method. We propose novel deep learning algorithms based on quasi-Monte Carlo (QMC) method, which is a deterministic version of MC method. We prove that the theoretical convergence order of QMC-based deep learning algorithms is asymptotically higher than that of MC-based algorithms. Numerical experiments demonstrate the substantial superiority of QMC-based algorithms in various applications.

MS [00505] Structured matrices with applications in sciences and engineering

room : G305

• [05539] Bundles of matrix pencils under strict equivalence
  • Format : Talk at Waseda University
  • Author(s) :
    • FERNANDO DE TERÁN (Universidad Carlos III de Madrid)
    • Froilán Martínez Dopico (Universidad Carlos III de Madrid)
  • Abstract : Bundles of matrix pencils are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are a union of orbits under strict equivalence). This notion was introduced in the 1990’s, following the one for matrices under similarity (from Arnold, 1971). In this talk, we provide a characterization for the inclusion relation between closures of bundles and prove that bundles are open in their closure (in the standard topology) .
• [05542] Row completion of polynomial matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Alicia Roca (Universitat Politècnica de València / IMM, Valencia, Spain)
    • Agurtzane Amparan (Universidad del País Vasco UPV/EHU)
    • Itziar Baragaña (Universidad del País Vasco UPV/EHU)
    • Silvia Marcaida (University of the Basque CountryUniversidad del País Vasco UPV/EHU)
  • Abstract : Perturbation problems arise frequently in applications, as in structural changes of the dynamics of a system or in pole placement problems in control theory. Perturbation problems of matrices are closely related to completion problems. We present a solution to the row-completion problem of a polynomial matrix, prescribing the eigenstructure of the resulting matrix and maintaining the degree.
• [01819] Computational Techniques for the Mittag-Leffler Function of a Matrix Argument
  • Format : Talk at Waseda University
  • Author(s) :
    • João R. Cardoso (Polytechnic Institute of Coimbra – ISEC)
  • Abstract : It is well-known that the two-parameter Mittag-Leffler function plays a key role in Fractional Calculus. In this talk, we address the problem of computing this function, when its argument is a square matrix. Effective methods for solving this problem involve the computation of successive derivatives or require the use of mixed precision arithmetic. We provide an alternative method that is derivative-free and can work entirely using IEEE standard double precision arithmetic. Our method starts with a reordered Schur decomposition of the argument matrix, so that the problem reduces to the computation of the Mittag-Leffler function of a triangular matrix with ``close'' eigenvalues. Theoretical and numerical issues regarding the performance of the method are investigated. A set of numerical experiments show that our novel approach is competitive with the existing ones, in terms of accuracy and computational cost.
• [05653] Classification of edges due to the change in multiplicity of an eigenvalue
  • Format : Talk at Waseda University
  • Author(s) :
    • KENJI TOYONAGA (Toyohashi University of Technology)
  • Abstract : We give possible classifications of edges in a general undirected graph in terms of the change in multiplicity of an eigenvalue by removing the edge. Further, we give a characterization of Parter vertices associated with the downer branch mechanism in general graphs. When the graph is a tree, the existence of a downer branch at a Parter vertex has been known in the previous work. We clarify the downer branch mechanism, Then we give the effect for the classifications of other edges or vertices in the remaining graph by removing a 2-downer edge.

contributed talk: CT020

room : G401

[00177] Bifurcations of Limit Cycles and Multistability in Polynomial Dynamical Systems

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G401
• Type : Contributed Talk
• Abstract : We study global limit cycle bifurcations and multistability in 2D polynomial dynamical systems, namely, in: the general Liénard polynomial system, the Euler-Lagrange-Liénard mechanical system, Leslie-Gower ecological or biomedical systems, and a reduced quartic Topp system which models the dynamics of diabetes. We study also 3D polynomial dynamical systems and, in particular, complete the strange attractor bifurcation scenarios in Lorenz type systems connecting globally the homoclinic, period-doubling, Andronov-Shilnikov, and period-halving bifurcations of limit cycles.
• Classification : 34C05, 34C07, 34C23, 37G10, 37G15
• Format : Talk at Waseda University
• Author(s) :
  • Valery A. Gaiko (United Institute of Informatics Problems, National Academy of Sciences of Belarus)

[00492] Asymptotic convergence of heterogeneous first-order aggregation models: from the sphere to the unitary group

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G401
• Type : Contributed Talk
• Abstract : We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value and furthermore that each oscillator converges to a possibly different stationary point. In order to establish the desired results, we introduce a novel method, called dimension reduction method that can be applied to a specific situation when the degree of freedom of the natural frequency is one. In this way, we would say that although a small perturbation is allowed, convergence toward an equilibrium of the gradient flow is still guaranteed. Several first-order aggregation models are provided as concrete examples by using the dimension reduction method to study the structure of the equilibrium, and numerical simulations are conducted to support theoretical results.
• Classification : 34C15, 34D06, 34C40
• Format : Talk at Waseda University
• Author(s) :
  • Dohyun Kim (Sungkyunkwan University)
  • Dohyun Kim (Sungshin Women's University)

[02588] Synchronization in a model system of two bubbles

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G401
• Type : Contributed Talk
• Abstract : We develop a model system of ODEs describing motions of bubbles interacting through the emission of sound waves of finite speed. In particular of the case of two bubbles, they fall into a state of synchronization, where the limit phase difference is 0 or $\pi$ depending on the distance of the bubbles. We elucidate the mechanism by the analysis of the phase coupling function, and from the physical viewpoint.
• Classification : 34E13, 35Q31, 76N30
• Format : Talk at Waseda University
• Author(s) :
  • Masashi Ohnawa (Tokyo University of Marine Science and Technology)

[02043] Almost Automorphic Solution of a Leslie-Gower Prey-Predator Model on Time Scales

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G401
• Type : Contributed Talk
• Abstract : A general non-autonomous Leslie-Gower prey-predator model on time scales with control input terms is examined. The significant property permanence is established along with the existence of almost automorphic solution of the model system. By constructing a suitable Lyapunov functional, presence of a one of a kind all-around attractive positive almost automorphic solution of the system is obtained. Two numerical examples are given to demonstrate the effectiveness of our hypothetical outcomes with simulations.
• Classification : 34C27, 34C60, 34C25
• Format : Online Talk on Zoom
• Author(s) :
  • Soniya NA (Rajiv Gandhi Institute of Petroleum Technology Jais India)

[00130] THE DYNAMICS OF THE MONKEYPOX VIRUS IN THE PRESENCE OF ENVIRONMENTAL TRANSMISSION

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G401
• Type : Contributed Talk
• Abstract : A deterministic model for the environmental transmission dynamics of monkeypox with the presence of quarantine and vaccination is presented. The analysis of the model presented three important equilibrium states namely; monkeypox-free equilibrium (MPXV-FE), infected rodent-free endemic equilibrium (IRF-EE) and coexistence equilibrium (CO-EE). The local and global stability of the equilibrium states is established in terms of the basic reproduction number, $\mathcal{R}_0.$ For global stability, the Comparison theory is used for MPXV-FE while the Voltera-Lyapunov matrix theory is used for both IRF-EE and CO-EE. Sensitivity analysis is performed using the Latin Hypercube sampling method with the results showing that environmental transmission parameters are the main driver of infection in the dynamics of monkeypox infection. This is further supported by numerical simulations to show the impact of environmental transmission on monkeypox infection and also the validity of the theoretical analysis presented. Based on the results, it is recommended that health practitioners and policy-makers should constitute control strategies that will focus on reducing environmental transmission and shedding of the virus in the environment while increasing the environmental decay rate of the monkeypox virus. This will complement the quarantine and vaccination strategies in place. 34C60, 92B05, 34D23, 34D20
• Classification : 34CXX, 34DXX
• Format : Online Talk on Zoom
• Author(s) :
  • Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria )

MS [02017] Recent progress in theory and applications of time-delay systems

room : G402

• [04187] Blow-up of solutions to some delay differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Tetsuya Ishiwata (Shibaura Institute of Technology)
    • Yukihiko Nakata (Aoyama Gakuin University)
  • Abstract : Time lags sometimes play an essential role in the phenomena, and it is also well-known that the delay effects cause instability or oscillation. In this talk, we consider the effects of time delay for such instabilities from the viewpoint of a finite time blow-up of the solutions and treat some delay differential equations. We show mathematical results on the blow-up of solutions and give numerical observations.
• [03602] Absolute stability and absolute hyperbolicity in systems with time-delays
  • Format : Online Talk on Zoom
  • Author(s) :
    • Serhiy Yanchuk (Potsdam Institute for Climate Impact Research)
  • Abstract : We present criteria for the absolute stability of DDEs. For a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. For multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have bifurcations.
• [03557] Delay-dependent stability switches in delay differential systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Hideaki Matsunaga (Osaka Metropolitan University)
  • Abstract : We will summarize some recent results on the stability properties of linear differential systems with delays. Some examples are provided to illustrate the delay-dependent stability switches for a system with delay in the diagonal terms. The proof technique is based on careful analysis of the existence and the transversality of characteristic roots on the imaginary axis. This is a joint work with Yuki Hata.
• [05023] Stabilization of periodic orbits with complex characteristic multipliers via DFC
  • Format : Talk at Waseda University
  • Author(s) :
    • Rinko Miyazaki (Shizuoka Univ.)
    • Dohan Kim (Seoul National University)
    • Jong Son Shin (Shizuoka University)
  • Abstract : The delayed feedback control (DFC) proposed by Pyragas (Pyhs. Lett. A, 1992) is a method to stabilize an unstable periodic orbit by using delayed terms. Recently we have succeeded in proving a stabilization regime under certain constraints. In this talk, we will focus on the case where the characteristic multiplier is complex.

MS [01140] Modelling and simulation of electro-chemo-mechanical processes in batteries and fuel cells

room : G404

• [03277] A Model Framework for Lithium Ion Intercalation Cells
  • Format : Talk at Waseda University
  • Author(s) :
    • Manuel Landstorfer (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))
    • Alireza Selahi (Weierstrass Institute for Applied Analysis and Stochastics (WIAS))
  • Abstract : We present a model framework for Lithium-ion batteries based on non-equilibrium thermodynamics. It emphasizes thermodynamic consistency, especially for reaction rates and concentration-dependent diffusion coefficients. A coupled two-scale PDE system is derived using periodic homogenization. Numerical simulations are finally shown, predicting the cell voltage during cycling at different C-Rates. We compare single- and many-particle electrode models and discuss the impact of material functions, diffusion coefficients, and reaction rate models based on numerical simulations.
• [02810] Asymptotic reduction of a model for mechanical stresses in cylindrical batteries
  • Format : Talk at Waseda University
  • Author(s) :
    • Jon Chapman (University of Oxford)
    • Robert Timms (University of Oxford)
    • Steven Psaltis (Queensland University of Technology)
    • Colin Please (University of Oxford)
  • Abstract : Macroscopic mechanical stresses in lithium-ion batteries are known to significantly affect the long-term degradation mechanisms. These stresses are created by expansion and contraction of the different parts of the structure, due both to thermal variations and lithiation state. Predicting the resulting stresses using numerical techniques is made difficult due to the small-scale geometry of current collectors, separator and regions of active material. Here we use the methods of boundary layer analysis and homogenisation, exploiting the small-scale periodic structure of a spirally-wound cylindrical battery, to derive a reduced-order model to determine approximations to the resulting stresses.
• [04382] Modeling Solid Oxide Fuel Cells based on Electrode Microstructure Information
  • Format : Talk at Waseda University
  • Author(s) :
    • Masashi Kishimoto (Kyoto University)
    • Hiroshi Iwai (Kyoto University)
  • Abstract : Understanding the effect of the porous microstructure of SOFC electrodes on the electrochemical performance is essential in predicting their macroscopic performance and thereby optimizing electrode microstructure. We present several numerical simulation models of SOFCs with quantitative information of the electrodes obtained by 3D imaging technique based on focused ion beam scanning electron microscope (FIB-SEM). Typical results of microscopic distribution within the electrodes and macroscopic performance, such as overpotential and impedance characteristics, are overviewed.
• [03013] Exploring non-isothermal effects in all-vanadium redox flow batteries through advanced numerical models
  • Format : Talk at Waseda University
  • Author(s) :
    • Marcos Vera (Universidad Carlos III de Madrid)
    • Vanesa Muñoz-Perales (Universidad Carlos III de Madrid)
    • Santiago E. Ibáñez (Repsol)
    • Enrique García-Quismondo (IMDEA Energy)
    • Sabrina Berling (IMDEA Energy)
    • Jesús Palma (IMDEA Energy)
  • Abstract : Redox flow batteries are a promising electrochemical technology for large-scale stationary energy storage that still requires further development to increase its profitability and energy market penetration. Continuous macroscopic models enable the optimization of new architectures and operational strategies without extensive fabrication and experimental procedures. This work presents a non-isothermal two-dimensional steady-state model of a unit-cell all-vanadium redox flow battery. The model integrates state-of-the-art descriptions of the fundamental physical phenomena along with new features, such as local mass transfer coefficients for the active species, precise sulfuric acid dissociation kinetics, and experimentally determined electrochemical parameters and electrolyte properties. The model is validated at different states of charge, flow rates, and operating temperatures using polarization, conductivity, and open circuit voltage measurements. Then, the contribution of operating conditions to battery performance is studied by analyzing its separate effect on the various phenomena that affect cell performance, such as local pore mass transfer limitations, parasitic hydrogen evolution reactions, crossover, and self-discharge fluxes. After model calibration, a parametric study is carried out to explore the role of the operating temperature, deconvoluting the different contributions to cell heating and providing practical guidance about the thermal effects induced by operating conditions. The results reveal that i) increasing the cell temperature enhances species mass transfer but negatively affects activation losses, ii) the cell suffers higher overheating during charge than during discharge, and iii) cell heating increases proportionally with cell length. Lastly, we propose using asymmetric electrolyte temperatures as a performance improvement strategy for electrochemical storage systems hybridized with thermal energy storage. The resulting model is a reliable tool that can be used to assess the relevance of the coupled phenomena that take place simultaneously within the reaction cell. This vital information is critical to optimize cell components, reactor design and selecting optimal operating conditions.

MS [00084] Asymptotic approaches to multi-scale PDEs in mathematical physics

room : G405

• [05460] Local smooth solvability for the Relativistic Vlasov-Maxwell system.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Slim IBRAHIM (UNIVERSITY OF VICTORIA)
    • Christophe Cheverry (University of Rennes)
  • Abstract : This talk is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies (and its long time version for small data). This result is derived from a representation formula decoding how the momentum spreads, and showing that the domain of influence in momentum is controlled by mild information. We do so by developing a Radon Fourier analysis on the RVM system, leading to the study of a class of singular weighted integrals. In the end, we implement our method to construct smooth solutions to the RVM system in the regime of dense, hot and strongly magnetized plasmas. This is done by investigating the stability properties near a class of approximate solutions. This is a joint work with C. Cheverry.
• [04487] Incompressible limit for tumor growth models with convective effects
  • Format : Talk at Waseda University
  • Author(s) :
    • Noemi David (Université de Lyon)
    • Tomasz Dębiec (University of Warsaw)
    • Benoit Perthame (Sorbonne Université)
    • Markus Schmidtchen (Technische Universität Dresden)
  • Abstract : Both compressible and incompressible models have been used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a bridge between density-based models and free boundary problems where saturation holds. I will present the study of the incompressible limit for advection-porous medium equations and discuss the convergence rate of solutions of the compressible model to solutions of the limit Hele-Shaw problem.
• [03628] Construction of weak solutions to Compressible Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Piotr B. Mucha (University of Warsaw)
  • Abstract : We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures, and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable loss allows us to fit market data for multiple S&P 500 and VIX maturities. A one-factor Markovian stochastic local volatility model is shown to fit both smiles and VIX futures within bid-ask spreads. The joint calibration actually makes it a pure path-dependent volatility model, confirming the findings in (Guyon, 2022, The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew).

MS [00545] Waves in complex and multiscale media

room : G406

• [04940] Bounds on the Quality-factor of Two-phase Quasi-static Metamaterial Resonators and Optimal Microstructure Designs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kshiteej Deshmukh (University of Utah)
    • Graeme Milton (University of Utah)
  • Abstract : Material resonances are fundamentally important in the field of nano-photonics and optics. So it is of great interest to know what are the limits to which they can be tuned. The bandwidth of the resonances in materials is an important feature which is commonly characterized by using the quality (Q) factor. We present bounds on the quality factor of two-phase quasi-static metamaterial resonators evaluated at a given resonant frequency by introducing an alternative definition for the Q-factor in terms of the complex effective permittivity of the composite material. Optimal metamaterial microstructure designs achieving points on these bounds are presented. The most interesting optimal microstructure, is a limiting case of doubly coated ellipsoids, consisting of a dilute suspension of ellipsoids near resonance sandwiched between layers. It attains points on the lower bound for the Q-factor. We also obtain bounds on Q for three dimensional, isotropic, and fixed volume fraction two-phase quasi-static metamaterials. Some almost optimal isotropic microstructure geometries are identified.
• [04245] Band structure and Dirac points of real-space quantum optics in periodic media
  • Format : Talk at Waseda University
  • Author(s) :
    • Erik Orvehed Hiltunen (Yale University)
    • John Schotland (Yale University)
    • Michael Weinstein (Columbia University)
    • Joseph Kraisler (Columbia University)
  • Abstract : The field of photonic crystals is almost exclusively based on a Maxwell model of light. While often an effective model, it is natural to study such systems under a quantum-mechanical photon model instead. In the real-space parametrization, interacting photon-atom systems are governed by a system of \emph{nonlocal} partial differential equations. In this talk, we study resonant phenomena of such systems. Using integral equations, we phrase the resonant problem as a nonlinear eigenvalue problem. In a setting of high-contrast atom inclusions, we obtain fully explicit characterizations of resonances, band structure, and Dirac cones. Additionally, we present a strikingly simple relation between the Green's function of the nonlocal equation and that of the local (Helmholtz) equation. Based on this, we are able to achieve highly efficient numerical calculations of band structures of interacting photon-atom systems.
• [03889] Mathematics of in-gap interface modes in photonic/phononic structures in one dimension
  • Format : Talk at Waseda University
  • Author(s) :
    • Hai Zhang (HKUST)
    • Junshan Lin (Auburn University)
  • Abstract : The developments of topological insulators have provided a new avenue for creating interface modes (or edge modes) in photonic/phononic structures. Such created modes have the distinct property of being topologically protected and are stable with respect to perturbations in certain classes. In this talk, we will report recent results on the existence of an in-gap interface mode that is bifurcated from a Dirac point in a photonic/phononic structure in one dimension.
• [04807] Recent advances in the theory of field patterns
  • Format : Talk at Waseda University
  • Author(s) :
    • Ornella Mattei (San Francisco State University)
    • Vincenzo Gulizzi (University of Palermo)
  • Abstract : Field pattern materials are spatial composites whose properties are modulated in time in such a way that disturbances propagate along locally periodic networks of characteristic lines, called field patterns. Depending on the material properties, modes can be propagating or can blow up (decay) in time. Here we show how to design the spatial geometry of one- and two-dimensional field pattern materials, so that modes are always stable.

MS [00316] Dynamics of patterns and traveling waves arising from reaction-diffusion systems

room : G501

• [02140] Some Progress on the spreading properties of two-species Lotka-Volterra competition-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Chang-Hong Wu (National Yang Ming Chiao Tung University)
  • Abstract : The Lotka-Volterra competition-diffusion system is a well-established model for understanding the interactions between competing species. In particular, the two-species case has been extensively studied, revealing the existence of traveling waves that can provide insight into the spreading behaviors of the species. In this presentation, we will present some recent progress on the spreading properties of this system.
• [02366] Weak interaction between traveling wave solutions in the three-species competition-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Chueh-Hsin Chang (National Chung Cheng University, Department of Mathematics)
  • Abstract : In this talk we consider the weak interaction between two trivial three-species traveling wave solutions (one component is trivial) of the threes-species Lotka-Volterra competition-diffusion systems. By the asymptotic behavior of the trivial threes-species waves and the existence results of the three-species waves from gluing bifurcation approaches in our previous results, we can observe the dynamics of the distance between the trivial three-species waves. The interaction between the two trivial three-species waves are attractive or repulsive due to different conditions of parameters. We let the growth rate of the third species as the bifurcation parameter.
• [04983] Defects in the segmented pattern for oscillated reaction-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ayuki Sekisaka (Meiji university)
  • Abstract : In this talk, the existence and stability of the modulated waves of a certain three-component reaction-diffusion system will be discussed. The modulated waves appearing in this equation are called defects, and their formulation and basic properties have been investigated by Sandstede and Scheel. In this talk, we will discuss the basic properties of the deffects appearing in the equations and their stability using the infinite dimensional Evans function.
• [04560] Linearized eigenvalue problems in a mass-conserved reaction-diffusion compartment model
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsubasa Sukekawa (Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University Institute for Advanced Study, Kyoto University)
  • Abstract : In a mass-conserved reaction-diffusion system, we can observe by numerical simulations that a transient pattern such as a stripe one converges to a spatially monotone pattern. To understand the dynamics theoretically, we introduce a reaction-diffusion compartment model. This model equation is defined on multiple regions (compartments), and each compartment is connected by diffusive coupling. In this talk, we analyze linearized eigenvalue problems of spatially non-monotone stationary solutions in mass-conserved reaction-diffusion compartment model.

contributed talk: CT035

room : G502

[00722] Scalar auxiliary variable schemes for Cahn-Hilliard systems with mass source

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G502
• Type : Contributed Talk
• Abstract : The scalar auxiliary variable approach presents a novel way to discretize a large class of dissipative systems. We consider a general Cahn-Hilliard system with mass source that may not admit a known dissipative structure, and so the stability of discrete solutions is not immediate. With a bounded mass source, we show stability and convergence of time discrete solutions for a first-order scheme, and apply our ideas to systems in tumour growth, image inpainting and segmentation.
• Classification : 35K35, 35K55, 65M12, 65Z05
• Format : Talk at Waseda University
• Author(s) :
  • Andrew Lam (Hong Kong Baptist University)
  • Ru Wang (Hong Kong Baptist University)

[00937] Asymptotic and numerical approaches to degeneracies in Stefan problems

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G502
• Type : Contributed Talk
• Abstract : This talk discusses how asymptotic analysis and numerics can be combined to devise computational schemes to moving boundary $($Stefan$)$ problems more accurately; in particular, this relates to degenerate situations where the solution domain is initially of zero extent, or where a domain that was initially present disappears completely. A further subtlety concerns whether a new domain starts to form instantaneously or after some delay time.
• Classification : 35K40, 35K65, 35K60
• Format : Talk at Waseda University
• Author(s) :
  • Michael Vynnycky (University of Limerick)
  • Sarah Mitchell (University of Limerick)

[02483] Existence and uniqueness of traveling wave solutions for competition-diffusion systems

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @G502
• Type : Contributed Talk
• Abstract : In this talk, we will consider the existence and uniqueness of traveling wave solutions for a class of competition-diffusion models. We find a necessary and sufficient condition for the existence of non-decreasing traveling wave solutions connecting trivial and positive equilibria. Moreover, with the help of the asymptotic behaviors of such solutions at positive infinity, we also prove that traveling wave solutions are unique up to translations.
• Classification : 35K40, 35K57, 35B35
• Format : Talk at Waseda University
• Author(s) :
  • Jian-Jhong Lin (National Taipei University of Technology)

MS [00220] Reaction-Diffusion Systems and Applications in life Sciences

room : G601

• [01484] Recent Progress on Reaction-Diffusion Systems and Applications in Life Sciences
  • Format : Talk at Waseda University
  • Author(s) :
    • Hong-Ming Yin (Washington State University)
  • Abstract : Reaction-diffusion equations and systems are the backbone of many mathematical models in biological, ecological, health and medical sciences. In this talk I will first give a short survey on some recent progress about the global solvability for general reaction-diffusion systems. Then I will focus on a class of nonlinear reaction-diffusion systems with balanced mass. Some new results will be reported in the talk. Finally, I will show how the general result is used to establish the global solvability for two models arising from life sciences.
• [04053] Effect of density-dependent dispersal on the predator-prey system
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhi-An Wang (The Hong Kong Polytechnic University )
  • Abstract : This talk is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. By our analysis results, we pinpoint the positive role of density-dependent dispersal on the predator-prey dynamics for the first time and show that the density-dependent dispersal is a beneficial strategy promoting the coexistence of species in the predator-prey system by increasing the chance of predator's survival.
• [04100] Nonlinear Stefan problem with a certain class of multi-stable nonlinearity
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Matsuzawa (Kanagawa University)
    • Yuki Kaneko (Kanto Gakuin University)
    • Yoshio Yamada (Waseda University)
  • Abstract : I will discuss the long-time dynamical behavior of solutions to a nonlinear Stefan problem for a reaction-diffusion equation with a positive bistable type nonlinearity. I will show that the asymptotic behavior of the solutions is classified into four cases: vanishing, small spreading, big spreading, and transition. In particular, I will show that for transition occurs, the solution converges to an equilibrium solution that is radially symmetric, radially decreasing, and centered at some point as $t\to\infty$.
• [01531] Some results on a haptotaxis model of cancer invasion
  • Format : Online Talk on Zoom
  • Author(s) :
    • Feng Dai ( Huazhong University of Science and Technology)
  • Abstract : In this talk, we will report some results on a haptotaxis model of cancer invasion. Under appropriate regularity assumptions on initial data, the global solvability of the corresponding homogeneous Neumann initial-boundary value problem is established. In addition, an optimal control problem for this cancer invasion model with chemotherapy is investigated to balance the therapeutic benefits with its side effects.

MS [00135] Nonlinear PDEs and related diffusion phenomena

room : G602

• [03548] Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yohei Fujishima (Shizuoka University)
  • Abstract : We discuss the global in time existence of solutions for a superlinear heat equation. In particular, we determine the critical decay rate of initial functions for the global existence of solutions by introducing a quasi self-similar solution for the problem.
• [03604] Stochastically perturbed log diffusion equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Reika Fukuizumi (Waseda University)
  • Abstract : We will present a result on the existence and uniqueness of the solution for the stochastic fast logarithmic equation with a Stratonovich multiplicative noise in R^d for d \ge 3. We overcome several technical difficulties due to the degeneracy properties of the logarithm and to the fact that the problem is treated in an unbounded domain. This is a joint work with Ioana Ciotir (INSA Rouen, France) and Dan Goreac (Univ Paris Est, France and Shandong University, China).
• [03225] Spreading and extinction of solutions to ​the logarithmic diffusion​ with a logistic reaction​
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiko Shimojo (Tokyo Metropolitan University)
    • Eiji Yanagida (University of Tokyo)
    • Harunori Monobe (Osaka Metropolitan University)
  • Abstract : Logarithmic diffusion is observed in several fields of science, such as the central limit approximation of Carleman’s model based on the Boltzmann equation, a model for long Van-der-Waals interactions in thin fluid films, and the evolution of conformal metric under the Ricci flow on the plane. We focus on the spreading and extinction phenomena of the solution to the logarithmic diffusion equation on a line, in the presence of a logistic reaction term. A Liouville-type theorem will be introduced to understand the extinction and interfacial phenomena from the point of entire solutions.
• [03474] Characterization of F-concavity preserved by the Dirichlet heat flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Asuka Takatsu (Tokyo Metropolitan University)
    • Paolo Salani (University of Florence)
    • Kazuhiro Ishige (The University of Tokyo)
  • Abstract : F-concavity is a generalization of power concavity and, actually, the largest available generalization of the notion of concavity. We characterize the F-concavities preserved by the Dirichlet heat flow in convex domains on Euclidean space, and complete the study of preservation of concavity properties by the Dirichlet heat flow, started by Brascamp and Lieb in 1976 and developed in some recent papers.

MS [02671] Recent advances on the analysis of hyperbolic balance laws

room : G605

• [03611] Existence and Stability of Traveling Waves of Boussinesq-Burgers Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kyle Kun Zhao (Tulane University)
    • Anita Yang (Chinese University of Hong Kong)
    • Zhian Wang (Hong Kong Polytechnic University)
  • Abstract : We introduce rigorous mathematical results concerning the existence and stability of traveling wave solutions to the Cauchy problem of the one-dimensional Boussinesq-Burgers equations modeling the propagation of weak tidal bores. Existence of traveling waves is obtained by means of phase plane analysis and geometric singular perturbation. Local stability of traveling waves with arbitrary strength is proven by spatially weighted energy methods.
• [04963] Global dynamics and photon loss in the Kompaneets equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Hailiang Liu (Iowa State University )
  • Abstract : The Kompaneets equation governs dynamics of the photon energy spectrum in certain high temperature (or low density) plasmas. We present several results concerning the long-time convergence of solutions to Bose–Einstein equilibria and the failure of photon conservation due to shock formation at the zero-energy boundary. This talk is based on a joint work with J. Ballew, G. Iyer, D. Levermore and R. Pego.
• [03629] HYPOCOERCIVITY OF STOCHASTIC GALERKIN FORMULATIONS FOR STABILIZATION OF KINETIC EQUATIONS
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Yu (Tsinghua University)
    • Stephan Gerster (Universit`a degli Studi dell’Insubria)
    • Michael Herty (RWTH Aachen University)
  • Abstract : We consider the stabilization of linear kinetic equations with a random relaxation term. The well-known framework of hypocoercivity by J. Dolbeault, C. Mouhot and C. Schmeiser (2015) ensures the stability in the deterministic case. This framework, however, cannot be applied directly for arbitrarily small random relaxation parameters. Therefore, we introduce a Galerkin formulation, which reformulates the stochastic system as a sequence of deterministic ones. We prove for the gamma-distribution that the hypocoercivity framework ensures the stability of this series and hence the stochastic stability of the underlying random kinetic equation. The presented approach also yields a convergent numerical approximation.
• [04154] Traveling Wave Solutions in Keller-Segel Models of Chemotaxis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tong Li (The University of Iowa)
  • Abstract : We study global existence and long-time behavior of solutions for hyperbolic-parabolic PDE models of chemotaxis. We show the existence and the stability of traveling wave solutions to systems of nonlinear conservation laws derived from the Keller-Segel model. We construct biologically relevant oscillatory traveling wave solutions to an attractive chemotaxis system of mixed-type. Traveling wave solutions of chemotaxis models with growth are also investigated.

MS [02613] Advances in Variational and Hemivariational Inequalities: Modeling, Analysis, and Applications

room : G606

• [04032] The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiali Qiu (Xi'an Jiaotong University)
    • Fei Wang (Xi'an Jiaotong University)
    • Min Ling (School of Mathematical Sciences, Peking University)
    • Jikun Zhao (Zhengzhou University)
  • Abstract : We develop the interior penalty virtual element method (IPVEM) for solving a Kirchhoff plate contact problem, which can be described by a fourth-order elliptic hemivariational inequality (HVI). With certain assumptions, the well-posedness of the discrete problem is proved. Furthermore, a priori error estimation is established for the IPVEM for the fourth-order elliptic HVI, and we show that the lowest-order VEM achieves optimal convergence order. Finally, some numerical examples are presented to support the theoretical results.
• [03325] Virtual element method for a frictional contact problem with normal compliance
  • Format : Talk at Waseda University
  • Author(s) :
    • Bangmin Wu (Xinjiang University)
  • Abstract : We study the virtual element method for solving the frictional contact problem with the normal compliance condition, which can be modeled by a quasi-variational inequality. Existence and uniqueness results are obtained for the discretized scheme. Furthermore, a priori error analysis is established, and an optimal order error bound is derived for the lowest order virtual element method. One numerical example is given to show the efficiency of the method and to illustrate the theoretical error estimate.
• [03328] Well-posedness and Numerical Analysis of a Stokes Hemivariational Inequality
  • Format : Online Talk on Zoom
  • Author(s) :
    • Min Ling (School of Mathematical Sciences, Peking University)
  • Abstract : This talk is devoted to the development and analysis of a pressure projection stabilized mixed finite element method, with continuous piecewise linear approximations of velocities and pressures, for solving a hemivariational inequality of the stationary Stokes equations with a nonlinear non-monotone slip boundary condition. We present an existence result for an abstract mixed hemivariational inequality and apply it for a unique solvability analysis of the numerical method for the Stokes hemivariational inequality. An optimal order error estimate is derived for the numerical solution under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence order.
• [03157] Well-posedness of parabolic variational-hemivariational inequalites with unilateral constraints
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stanislaw Migorski (Jagiellonian University in Krakow)
    • Dong-ling Cai (School of Mathematical Sciences, University of Electronic Science and Technology of China)
  • Abstract : In this talk we discuss a novel class of variational-hemivariational inequalites with a unilateral constraint of parabolic type. Results on existence, uniqueness and the continuous dependence of the weak solution with respect to perturbations in the data are proved. As an application we examine a mathematical model of nonsmooth quasistatic viscoelastic frictional contact problem with the Signorini unilateral contact condition and a generalization of the static Coulomb law of dry friction.

MS [00086] Recent advances in the theory of rogue waves: stability and universality of wave pattern formation

room : G701

• [04902] Rogue waves of infinite order and their properties, Part 1
  • Author(s) :
    • Deniz Bilman (University of Cincinnati)
  • Abstract : In a study of high-order fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation, a new limiting object termed the rogue wave of infinite order was found in a high-order near-field limit. Subsequently it has been shown that this same limiting object, itself a solution of the focusing nonlinear Schrödinger equation in rescaled variables that also solves differential equations in the Painlevé-III hierarchy, also arises in numerous other settings such as high-order solitons, semiclassical asymptotics, iterated Bäcklund transformations of arbitrary backgrounds, and even other related nonlinear systems. This talk will describe this story and introduce the rogue wave of infinite order and some generalizations of it. This is joint work with Peter D. Miller.
• [04895] Rogue waves of infinite order and their properties, Part 2
  • Author(s) :
    • Peter David Miller (University of Michigan)
  • Abstract : The general rogue wave of infinite order is a family of exact solutions of the focusing nonlinear Schr\"odinger equation that also solve ordinary differential equations related to Painlev\'e-III and while being highly-transcendental, nonetheless arise in several natural limits. From their Riemann-Hilbert representation we deduce some elementary properties, detailed asymptotics for large values of the independent variables, and a double-scaling limit. This is joint work with Deniz Bilman.
• [05529] Universality and rogue waves in semi-classical sine-Gordon equation
  • Author(s) :
    • Bingying Lu (SISSA)
    • Peter David Miller (University of Michigan)
  • Abstract : We study the semiclassical sine-Gordon equation with below threshold pure impulse initial data of Klaus-Shaw type. The system exhibits both phase transition and a gradient catastrophe in finite time. Near the gradient catastrophe point, the asymptotics are universally described by the Painlevé I tritronquée solution away from the poles and the rogue wave solutions of sG near the poles; away from the gradient catastrophe, the phase transition exhibits another type of universality.
• [05518] Large order breathers of the nonlinear Schodinger equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoen Zhang (Shandong University of Science and Technology)
  • Abstract : Multi-soliton and high-order soliton solutions are famous in the integrable focusing nonlinear Schrodinger equation. The dynamics of multi-solitons have been well known to us since the 70s of the last century by the determinant analysis. However, there is little progress in the study of high-order solitons. In this work, we would like to analyze the large-order asymptotics for the high-order breathers, which are special cases of double high-order solitons with the same velocity. To analyze the large order dynamics, we first convert the representation of Darboux transformation into a framework of the Riemann-Hilbert problem. Then we show that there exist five distinct asymptotic regions by the Deift-Zhou nonlinear steepest descent method. More importantly, we first find a novel genus-three asymptotic region, which uncovers that the maximal genus is connected with the number of spectral parameters. All results of the asymptotic analysis are verified by the numerical method.

MS [00215] Mathematical Advances in the nonlinear PDEs from physics

room : G702

• [04667] Vacuum free boundary problems in ideal compressible MHD
  • Format : Talk at Waseda University
  • Author(s) :
    • Tao Wang (Wuhan University)
  • Abstract : We present the joint works with Professor Yuri Trakhinin on the local well-posedness of vacuum free boundary problems in ideal compressible magnetohydrodynamics (MHD) with or without surface tension.
• [01253] Well-posedness of some free boundary problems in compressible fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenbin Zhao (Peking University)
  • Abstract : In this talk, we will discuss some free boundary problems in compressible fluids. We derive the evolution equation of the free surface and identify the stability condition of the problem. This method gives a unified approach to treat both incompressible and compressible fluids.
• [04043] Long time instability of compressible symmetric shear flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Xianpeng Hu (City University of Hong Kong)
    • Andrew Yang (City University of Hong Kong)
  • Abstract : It is well-known that at high Reynolds numbers, the linearized Navier-Stokes equations around the inviscid stable shear profile admit growing mode solutions due to the destabilizing effect of small viscosities. This phenomenon, which is related to Tollmien-Schlichting instability, has been rigoriously justified by Grenier-Guo-Nguyen [Adv. Math. 292 (2016); Duke J. Math. 165 (2016)] on incompressible Navier-Stokes equations. In this work, we aim to construct the Tollmien-Schlichting waves for the compressible Navier-Stokes equations over symmetric shear flows in a channel. We will also discuss the effect of temperature fields on the stability of these shear flows.

MS [01152] Recent trends in the mathematical theory for incompressible fluids

room : G703

• [02208] Local Nonuniqueness for Stochastic Transport Equations with Deterministic Drift
  • Format : Talk at Waseda University
  • Author(s) :
    • Andre Schenke (Courant Institute of Mathematical Sciences at New York University)
  • Abstract : We study the incompressible hypodissipative Navier--Stokes equations with dissipation exponent $0 < \alpha < \frac{1}{2}$ on the three-dimensional torus perturbed by an additive Wiener noise term and prove the existence of an initial condition for which distinct probabilistic weak solutions exist. To this end, we employ convex integration methods to construct a pathwise probabilistically strong solution, which violates a pathwise energy inequality up to a suitable stopping time. This paper seems to be the first in which such solutions are constructed via Beltrami waves instead of intermittent jets or flows in a stochastic setting.
• [02509] Restoration of well-posedness of 2D fluid dynamics equations by transport noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Lucio Galeati (EPFL)
    • Dejun Luo (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : A longstanding problem in fluid dynamics is whether solution to 2D Euler with $L^p$-valued vorticity are unique, for some $p<\infty$. A related question on the probabilistic side is whether one can find a physically meaningful noise that can restore such uniqueness. Here I will present some recent progress, concerning other closely related 2D equations, for which we can provide a positive answer. Based on a joint work with Dejun Luo.
• [04785] Finite-time blowup for a 3D hypo-dissipative Navier-Stokes model equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Evan Miller (University of British Columbia)
    • Johannes Haubner (University of Graz)
    • Bastian Zapf (University of Oslo)
  • Abstract : In this talk, I will discuss a new blowup result for a model equation for the 3D hypo-dissipative Navier-Stokes equation based on considering a restricted constraint space. When imposing the right geometric conditions on initial data, involving planar stretching at the origin, this allows a forward energy cascade that generates finite-time blowup. This model equation respects both the energy equality and the identity for enstrophy growth.
• [05631] Nonlinear Landau damping for the Vlasov-Poisson system in the whole space around Penrose-stable equilibria
  • Author(s) :
    • Quoc Hung Nguyen (Academy of Mathematics and Systems Science,)
    • Lingjia Huang (Fudan University, Shanghai)
  • Abstract : In this talk, I will present recent results on the nonlinear asymptotic stability of the stable equilibria among solutions of the Vlasov-Poisson system in $\mathbb{R}^3/\mathbb{R}^2$.

MS [00674] Modern numerical methods for PDE-constrained optimization and control

room : G704

• [04310] Optimal Control of Some Nonlocal PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Roland Herzog (Heidelberg University)
    • Masoumeh Hashemi (Heidelberg University)
  • Abstract : Partial differential equations (PDEs) with nonlocal effects pose various challenges in the analysis as well as the numerical solution. This is all the more true for optimal control problems involving nonlocal PDEs. In this presentation, we will discuss examples of optimal control problems for nonlocal PDEs and exhibit the numerical challenges posed by the associated blocks in the optimality systems.
• [01642] Decentralized strategies for coupled shape and parameter inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Abderrahmane HABBAL (University Cote d'Azur Inria)
  • Abstract : We present a novel family of algorithms framed within game theory setting and dedicated to solve ill-posed inverse problems, where unknown shapes -obstacles or inclusions- or sources are to be reconstructed as well as missing boundary conditions, for steady Stokes fluids. Some theoretical results and several numerical experiments are provided that corroborate the ability of the approch to tackle harsh problems.
• [04057] Stability-exploiting adaptive finite elements for optimal control
  • Format : Talk at Waseda University
  • Author(s) :
    • Manuel Schaller (Technische Universität Ilmenau)
  • Abstract : Optimal control problems often exhibit a particular stability property which, for time-dependent problems, manifests itself, e.g., by means of a turnpike property. The latter states that optimal solutions to dynamic problems reside close to a particular steady state for the majority of the time. Such a stable behavior can be shown under stabilizability and detectability-like assumptions and in particular also can be shown to hold when the uncontrolled equations are unstable. In this talk, we will show how this stability leads to locality of discretization errors which can be exploited by means of adaptive finite-element methods, leading to a significant reduction in computational expenses, e.g., in a Model Predictive Controller.

MS [01229] Cauchy problem for Deterministic and Stochastic nonlinear dispaersive equations

room : G709

• [03890] The well-posedness of the stochastic nonlinear Schrödinger equations in H^2
  • Format : Talk at Waseda University
  • Author(s) :
    • Shunya Hashimoto (Saitama university)
  • Abstract : We consider the well-posedness of $H^2$-solutions in initial value problems for the stochastic nonlinear Schrödinger equations with power-type nonlinear terms with multiplicative noise. For the proof, we use the rescaling approach, which transforms the stochastic equation into a random equation in which no white noise appears. Unlike $L^2$- and $H^1$-solution, there are two difficulties in the $H^2$-solution: first, the lack of the smoothness of nonlinear functions, and second, the treatment of white noise that reappears.
• [04966] Time beharior of solutions to nonlinear Schr\"odinger equation with a potential
  • Format : Talk at Waseda University
  • Author(s) :
    • Masaru Hamano (Waseda University)
  • Abstract : In this talk, we deal with the Cauchy problem of a nonlinear Schr\"odinger equation with a potential. In particular, we consider time behavior of solutions to the equation with initial data, whose energy is equal to that of the Talenti function.
• [03584] On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction
  • Format : Talk at Waseda University
  • Author(s) :
    • Noriyoshi Fukaya (Tokyo University of Science)
  • Abstract : We consider existence and stability properties of ground-state standing waves for two-dimensional nonlinear Schrödinger equation with a point interaction. The Schrödinger operator with a point interaction describes a one-parameter family of self-adjoint realizations of the Laplacian with delta-like perturbation. In this talk we consider the stability/instability of standing waves with small and large frequencies. This talk is based on a joint work with Vladimir Georgiev (University of Pisa) and Masahiro Ikeda (RIKEN).
• [05020] Convergence of the intermediate long wave equation from a statistical perspective
  • Format : Talk at Waseda University
  • Author(s) :
    • Guopeng Li (The Maxwell Institute for Mathematical Sciences)
  • Abstract : The intermediate long wave equation (ILW) models water waves of finite depth, connecting the Benjamin-Ono equation (deep-water limit) and the KdV equation (shallow-water limit). Convergence problems of ILW (in both the deep-water and shallow-water limits) have attracted attention from both the applied and theoretical points of view. In this talk, I will discuss convergence problems from a statistical viewpoint. I first consider the convergence problem of the Gibbsian ensembles. In this case, I establish convergence of the Gibbs measures and then also show convergence of invariant Gibbs dynamics to that of the Benjamin-Ono and KdV equations (without uniqueness). ILW is known to be completely integrable and thus possesses infinitely many conservation laws. In the second part of the talk, I consider invariant dynamics for ILW associated with higher order conservation laws. Due to a complicated nature of the dispersion, even the construction of measures associated with higher order conservation laws turns out to be highly non-trivial. By considering a suitable combination of higher order conservation laws, I overcome this issue and construct invariant dynamics for ILW with a fixed depth parameter. In the final part, I will discuss convergence of the invariant dynamics associated with higher order conservation laws. This talk is based on a joint work with Tadahiro Oh (Edinburgh), Guangqu Zheng (Liverpool), and Andreia Chapouto (UCLA).

MS [00615] Nonlinear PDEs & Probability

room : G710

• [03798] A regularity structure for the quasilinear generalized KPZ equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Masato Hoshino (Osaka University)
    • Ismael Bailleul (Universite Rennes 1)
    • Seiichiro Kusuoka (Kyoto University)
  • Abstract : We prove the local well-posedness of a regularity structure formulation of the quasilinear generalized KPZ equation and give an explicit form of the renormalized equation in the full subcritical regime.
• [03415] Gradient continuity of weak solutions for perturbed one-Laplace problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuntaro Tsubouchi (Graduate School of Mathematical Sciences, University of Tokyo)
  • Abstract : This talk is concerned with continuity of a spatial derivative of weak solutions to very singular problems that involve both one-Laplace and $p$-Laplace operators. The main difficulty is that one-Laplacian has both singular and degenerate ellipticity, which makes it difficult to prove Hölder continuity of a spatial gradient across a facet, the degenerate region of a gradient. In this talk, the speaker would like to talk about recent results on gradient continuity across the facet.
• [02739] Asymptotic behavior of geometric flows with contact angle conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Kagaya (Muroran Institute of Technology)
  • Abstract : Several geometric flows were derived from interface phenomena. In this talk, contact angle conditions for the geometric flows are dealt with, motivated by surface tension problems. The asymptotic behavior of the geometric flows depends on the contact angle conditions. In particular, traveling waves have the asymptotic stability if we assume specific contact angle conditions. I will introduce my results related to the asymptotic behavior.
• [05334] Weak-strong uniqueness for volume-preserving mean curvature flow
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tim Laux (University of Bonn)
  • Abstract : I will discuss a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the case without volume preservation recently introduced by Fischer et al. [arXiv:2003.05478]. The first main result shows that any strong solution with certain regularity is calibrated. The second main result consists of a stability estimate in terms of a relative entropy, which is valid in the class of distributional solutions to volume-preserving mean curvature flow.

MS [00778] Analysis, Applications, and Advances in Metamaterials and Composites

room : G801

• [05015] Time domain analysis of resonant plasmonic nano-particles
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre Millien (CNRS)
    • Alice L. Vanel (CERN)
    • Lorenzo Baldassari (RICE)
    • Habib Ammari (ETHZ)
  • Abstract : We study the possible expansion of the electromagnetic field scattered by a strictly convex metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low-frequency regime as a sum of modes oscillating at complex frequencies (diverging at infinity), known in the physics literature as the quasi-normal modes expansion. We show that such an expansion is valid in the static regime and that we can approximate the electric field with a finite number of modes. We then use perturbative spectral theory to show the existence, in a certain regime, of plasmonic resonances as poles of the resolvent for Maxwell's equations with non-zero frequency. We show that, in the time domain, the electric field can be written as a sum of modes oscillating at complex frequencies. We introduce renormalised quantities that do not diverge exponentially at infinity.
• [05234] Active exterior thermal cloaking
  • Format : Talk at Waseda University
  • Author(s) :
    • Trent DeGiovanni (University of Utah)
    • Fernando Guevara Vasquez (University of Utah)
    • Maxence Cassier (CNRS, Institut Fresnel)
    • Sébastien Guenneau (Imperial College London)
  • Abstract : We consider the problem of concealing an object, in the presence of a known probing fielding, from the perspective of thermal measurements. This is achieved using specially designed sources. Such a cloak can be constructed by using the Green identities; however, this requires a continuous strip of sources that encloses the object. In this talk, we demonstrate an alternative approach to this cloaking problem that uses only a few sources.
• [04994] Imaging conductivity with thermal noise induced currents
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fernando Guevara Vasquez (University of Utah)
    • Trent DeGiovanni (University of Utah)
  • Abstract : Thermal fluctuations of charge carriers in a conductive body create small but detectable currents. We show that the variance of such currents can be used to image the conductivity of a body, including for complex conductivities. This is done by relating the stochastic problem to a deterministic inverse problem that is close to one arising in acousto-electric tomography.

MS [00595] Combinatorial topological dynamics

room : G802

• [04935] A combinatorial/homological framework for continuous nonlinear dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Konstantin Mischaikow (Rutgers University)
  • Abstract : Computational science and data-driven science suggests the importance of having finite models of dynamics. This raises three questions: 1. How to go from data to appropriate combinatorial models of dynamics. 2. What computations should be performed on these combinatorial models. 3. How to translate the output from the combinatorial models to structures associated with continuous systems. In this talk we will discuss our attempts to provide a coherent approach to addressing these questions.
• [04988] Computing the Global Dynamics of Parameterized Systems of ODEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Marcio Gameiro (Rutgers University)
  • Abstract : We present a combinatorial topological method to compute the dynamics of a parameterized family of ODEs. A discretization of the state space of the systems is used to construct a combinatorial representation from which recurrent versus non-recurrent dynamics are extracted. Algebraic topology is then used to validate and characterize the dynamics of the system. We will discuss the combinatorial description and the algebraic topological computations and will present applications to systems of ODEs arising from gene regulatory networks.
• [04981] Combinatorics and Topology for Understanding Global Dynamics in Multi-Scale Systems.
  • Format : Talk at Waseda University
  • Author(s) :
    • Ewerton Rocha Vieira (Rutgers University)
  • Abstract : This talk introduces a new approach to analyzing time-varying systems with multi-scale dynamics, which can be challenging due to poorly measured parameters and numerous variables. Traditionally, these systems are modeled using ordinary differential equations (ODE), but this approach can be difficult to apply directly. The proposed approach is based on combinatorics and algebraic topology, and focuses on describing global dynamics in terms of annotated graphs (Morse graphs) and Conley complexes. The method is based on piecewise linear models and offers a more robust, scalable, and computable description of dynamics than classical ODE analysis, with formal mathematical guarantees that extend to a class of ODE with steep sigmoidal nonlinearities. This approach is particularly useful for modeling complex systems, such as biological systems.
• [04843] On the identification of cycling motion using topological tools
  • Format : Talk at Waseda University
  • Author(s) :
    • Ulrich Bauer (Technical University of Munich)
    • David Hien (Technical University of Munich)
    • Oliver Junge (Technical University of Munich)
    • Konstantin Mischaikow (Rutgers University)
  • Abstract : Nonlinear dynamical systems often exhibit complicated recurrent behaviour. We propose to decompose recurrent sets into elementary oscillations and the connections between them. To this end, we use topological tools that are flexible enough to be computed from data while still providing a comprehensive description of the oscillations. We demonstrate this through several examples. In particular, we identify and analyze 6 oscillations in a 4d hyperchaotic attractor.

MS [00696] Scientific Machine Learning for Inverse Problems

room : G808

• [03214] Solving High-dimensional Inverse Problems with Weak Adversarial Networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • yaohua zang
    • Yaohua Zang (Zhejiang University)
    • Gang Bao (Zhejiang University)
    • Xiaojing Ye (Georgia State University)
    • Haomin Zhou (Georgia Institute of Technology)
  • Abstract : We present a weak adversarial network approach to numerically solve a class of inverse problems. The weak formulation of PDE in the inverse problem is leveraged with DNNs and induces a minimax problem. Then, the solution can be solved by finding the saddle points in the network parameters. As the parameters are updated, the network gradually approximates the solution of the inverse problem. Numerical experiments demonstrate the promising accuracy and efficiency of this approach.
• [01482] Automatic discovery of low-dimensional dynamics underpinning time-dependent PDEs for inverse problems resolution
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Regazzoni (MOX, Dipartimento di Matematica, Politecnico di Milano)
    • Matteo Salvador (MOX, Dipartimento di Matematica, Politecnico di Milano)
    • Stefano Pagani (MOX, Dipartimento di Matematica, Politecnico di Milano)
    • Luca Dede' (MOX, Dipartimento di Matematica, Politecnico di Milano)
    • Alfio Quarteroni (MOX, Dipartimento di Matematica, Politecnico di Milano)
  • Abstract : We present a novel Machine Learning technique able to learn differential equations that surrogate the solution of space-time-dependent problems. Our method exploits a finite number of latent variables, providing a compact representation of the system state, automatically discovered during training. It allows building, in a fully non-intrusive manner, surrogate models accounting for the dependence on parameters and time-dependent inputs. As such, our method is suitable to accelerate the resolution of inverse problems.

MS [02277] New regularizing algorithms for solving inverse and ill-posed problems

room : G809

MS [00785] Learning Dynamical Systems by Preserving Symmetries, Energies, and Variational Principles

room : F308

• [02758] Structure-preserving exterior calculus for GNNs: surrogates, physics discovery, and causality
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nathaniel Trask (Sandia National Laboratories)
  • Abstract : We present a graph exterior calculus which may be used to design graph neural network which naturally preserve mathematical and physical structure without resorting to physics-informed regularizers. The calculus provides a framework for proving numerical stability, conservation, preservation of geometric symmetries, thermodynamic consistency, gauge conditions, and other properties more typical of traditional PDE discretization. In this setting we discover Whitney forms encoding physically relevant subdomains, their boundaries, and flux conservation laws for multiphysics/multiscale systems. We introduce ongoing applications work using this to discover structure-preserving surrogates which exhibit 100000x speedup for typical problems while guaranteeing mathematical robustness, and introduce recent extensions discovering causal relationships in scientific datasets.

MS [00965] New mathematical trends in weather prediction and inverse problems

room : F309

• [03741] Gaussian Assimilation of non-Gaussian Image Data via Pre-Processing by Variational Auto-Encoder (VAE)
  • Author(s) :
    • Daisuke Hotta (Meteorological Research Institute, Japan Meteorological Agency)
  • Abstract : Assimilation of image data such as satellite images with conventional data assimilation methods is challenging due to non-Gaussian error distribution, dimensional redundancy, and strong inter-pixel correlations. While several techniques have been proposed to address each of these issues, no single method can simultaneously handle them all. Here we propose to use a Variational AutoEncoder to resolve all three difficulties. A preliminary assessment with a toy model shows promising results.
• [04216] Implementing local ensemble transform Kalman filter to reservoir computing for improving weather forecast
  • Author(s) :
    • Mao Ouyang (Chiba University)
    • Shunji Kotsuki (Chiba University)
  • Abstract : Data assimilation (DA) improves the numerical weather prediction (NWP) by combining the model forecast and observational data. The forecasts were usually obtained from a physical-based model, but recent studies reported that the reservoir computing (RC) could be implemented to surrogate both the small- and intermediate-scale physical models. This study implemented the DA, i.e., local ensemble transform Kalman filter, in both the physic-based and RC-surrogated models and compared their performances in the improvement of forecasts.
• [04315] Sparse optimization of inverse problems regularized with infimal-convolution-type functionals
  • Author(s) :
    • Marcello Carioni (University of Twente)
  • Abstract : The infimal convolution of functionals is a convex-preserving operation that have been used to construct regularizers for inverse problems by optimally combining features of two or more functionals. In this talk, we analyze the infimal convolution regularization from a sparse optimization point of view. First, we discuss optimal transport-type energies. Then, we consider the infimal convolution of a parametrized family of functionals and we develop optimization methods taking advantage of the sparsity in the parameters.
• [04562] Efficient data-driven regularization for ill-posed inverse problems in imaging
  • Author(s) :
    • Subhadip Mukherjee (University of Bath, UK)
    • Marcello Carioni (University of Twente)
    • Ozan Öktem (KTH Royal Institute of Technology)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : In recent years, data-driven regularization has led to impressive performance for image reconstruction problems in various scientific applications, e.g., medical imaging. We propose a new adversarial learning approach for imaging inverse problems by combining an iteratively unrolled network with a deep regularizer using ideas from optimal transport. The resulting unrolled adversarial regularization approach is shown to be provably stable, efficient in terms of image reconstruction time, and competitive with supervised methods in empirical performance.

MS [01074] Approximation Theory, Approximation Methods and Applications (ATAMA)

room : F310

• [05151] Projection Constants for Spaces of Multivariate Polynomials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mieczysław Mastyło (Adam Mickiewicz University, Poznań)
  • Abstract : We study the projection constant of spaces of polynomials with the supremum norm over the unit ball of finite dimensional Banach sequence space including the Hilbert space. We consider the action of topological groups over these spaces of polynomials and provide some integral formulas for their projection constants. This cycle of ideas leads to the asymptotic behaviour of the projection constants of spaces of Dirichlet polynomials and the space of nuclear operators on $\ell_2^n$.
• [05170] Stable high-order randomized cubatures for integration in arbitrary dimension
  • Format : Talk at Waseda University
  • Author(s) :
    • Giovanni Migliorati (Sorbonne Université)
  • Abstract : We present cubature formulae for the integration of functions in arbitrary dimension and arbitrary domain. These cubatures are exact on a given finite-dimensional subpace $V_n$ of $L^2$ of dimension $n$, they are stable with high probability and are constructed using $m$ pointwise evaluations of the integrand function with $m$ proportional to $n \log n$. For these cubatures we provide a convergence analysis showing that the expected cubature error decays as $m^{-1/2}$ times the $L^2$ best approximation of the integrand function in $V_n$.
• [05108] On empirical adequacy of approximations within mathematical models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael A Slawinski (Memorial University)
  • Abstract : We discuss a phenomenological model formulated to study the power applied by a cyclist on a velodrome. The dissipative forces we consider are air resistance, rolling resistance, lateral friction and drivetrain resistance. Also, the power is used to increase the kinetic and potential energy. Following derivations and justifications of expressions that constitute this mathematical model, we discuss them in the context of measurements.
• [05186] On technical considerations of velodrome track design
  • Format : Online Talk on Zoom
  • Author(s) :
    • Theodore Stanoev (Memorial University of Newfoundland)
  • Abstract : We present a novel approach to velodrome track design. The mathematical model uses differential geometry to form a three-dimensional ruled surface. The track is comprised of straight lines, the arcs of circles, and connecting transition curves, whose features are derived from the Frenet-Serret relations. Symmetric and asymmetric designs are obtained using least-squares optimization. The formulation may be used to design velodrome tracks of a wide variety of track geometry specifications.

MS [00746] Variational methods for singularities and concentration on low dimensional sets

room : F312

• [03156] effective geometric motions of Ginzburg--Landau equations with potentials of high-dimensional wells
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuning Liu (NYU shanghai)
  • Abstract : We study the co-dimensional one interface limit and geometric motions of parabolic Ginzburg--Landau systems with potentials of high-dimensional wells. In particular combining modulated energy methods and weak convergence methods, we derive a sharp interface limit and the limiting harmonic heat flows in the inner and outer bulk regions segregated by the sharp interface.
• [02113] Quasistatic evolution problems for models of geomaterials coupling plasticity and damage
  • Format : Talk at Waseda University
  • Author(s) :
    • Vito Crismale (Sapienza Università di Roma)
  • Abstract : I will discuss existence of quasistatic evolutions for a model proposed by Kazymyrenko and Marigo in 2019, which uses a suitable coupling between plasticity and damage to study the behavior of geomaterials under compression.
• [04281] Liquid crystal colloids: from the electrostatic analogy to interaction energies
  • Format : Talk at Waseda University
  • Author(s) :
    • Raghavendra Venkatraman (Courant Institute )
  • Abstract : We discuss some recent progress on nematic liquid crystal colloids, with the goal of deriving simplified descriptions of colloidal suspensions in a liquid crystal matrix. The first half of the talk will provide justification of the so-called "electrostatic analogy" frequently used in physics (and proposed by Brochard and De Gennes in the 70s). The second half will be about interaction energies for paranematic colloids.
• [03855] Evolution of vector fields on flexible curves and surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Georg Dolzmann (University of Regensburg)
  • Abstract : We discuss some recent progress on a model system consisting of a flexible surface and a vector field defined on the surface in the case in which an interaction between the vector field and the conformation of the surface is present. Recent approaches towards the existence of solutions will be reviewed and short time existence will be established. The lecture is based on joint work with Christopher Brand (Regensburg), Julia Menzel (Regensburg) and Alessandra Pluda (Pisa).

MS [00731] Optimal control: methods and applications

room : F401

• [04845] A variational approach for modelling and optimal control of electrodynamic tether motion
  • Format : Talk at Waseda University
  • Author(s) :
    • Yana Valentinova Lishkova (University of Oxfordrsity of Oxford)
    • Mai Bando (Kyushu University)
    • Sina Ober-Blöbaum (Paderborn University)
  • Abstract : We present a novel variational model for 6DOF spacecraft dynamics equipped with an electrodynamic tether in circular restricted three-body environment and use it to perform an optimal orbit transfer with simultaneous orbit and attitude control. We discuss the advantages of the suggested variational approach and develop an alternative multirate formulation of the model and OCP, investigating the extent to which such reformulations can reduce the computational cost of simulating and optimally controlling spacecraft in CR3BP.
• [04761] The Role of Stable Manifolds in Optimal Control under Stochastic Noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Mai Bando (Kyushu University)
    • Shohei Morimitsu (Kyushu University)
    • Takuro Nishimura (Kyushu University)
    • Shinji Hokamoto (Kyushu University)
  • Abstract : This study investigates the optimal control around a hyperbolic fixed point under stochastic noise. For a deterministic system without noise, it is known that the stable manifold of a hyperbolic fixed point is the solution to the minimum-energy problem with infinite horizon. We analyze the structure of the optimal control under a stochastic noise based on path integral approach and investigate the role of the stable manifold of the hyperbolic fixed point.
• [04228] Second-order averaging of time-optimal low-thrust orbital transfers
  • Format : Talk at Waseda University
  • Author(s) :
    • Lamberto Dell'Elce (Inria & Université Côte Azur)
  • Abstract : This work offers a numerical methodology to solve low-thrust orbital transfer problems. After detailing necessary conditions for optimality stemming from the Pontryagin maximim principle, a numerical methodology based on the averaging of the extremal flow of the optimal control hamiltonian is proposed. First, a one-parameter family of averaged solutions is obtained. Second, perturbations of these solutions associated to both short-periodic variations and second-order terms are computed. Finally, the magnitude of the thrust-to-mass ratio is identified by reconstructing a first-order approximation of the fast variables from the averaged solution.
• [03208] Optimization on manifolds by Riemannian gradient methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Sato (Kyoto University)
  • Abstract : In this talk, we will discuss optimization on Riemannian manifolds. After introducing examples of manifold optimization problems, some recent results by the speaker will be presented. In particular, the Riemannian conjugate gradient method is a simple first-order method, which does not use the Hessian but only the gradient of the objective function, and it shows much faster convergence performance than the Riemannian steepest descent method. Reference: H. Sato, Riemannian Optimization and Its Applications, Springer, 2021.

MS [00023] Recent advances on application driven nonlinear optimization

room : F402

• [01475] An Efficient Quadratic-Programming Relaxation Based Algorithm for Large-Scale MIMO Detection
  • Format : Talk at Waseda University
  • Author(s) :
    • Ping-Fan ZHAO (Beijing Institute of Technology)
    • Qing-Na LI (Beijing Insitute of Technology)
    • Wei-Kun CHEN (Beijing Institute of Technology)
    • Ya-Feng LIU (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Massive MIMO has been recognized as a key technology in 5G and beyond communication networks, which can significantly improve the communication performance, but also poses new challenges of solving the corresponding optimization problems due to the large problem size. In this talk, we propose an efficient sparse QP relaxation based algorithm for solving the large-scale MIMO detection problem. With exact recovery guaranteed, the algorithm achieves better detection performance compared with the state-of-art algorithms.
• [01487] Uniform Framework of Convergence Analysis for Nesterov's Accelerated Gradient Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuo Chen (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Nesterov's accelerated gradient method $(\texttt{NAG})$ is one of the most influenced methods used in machine learning and other fields. In this talk, we give a new framework to analyze convergence property of $\texttt{NAG}$ based on the high-resolution differential equation, phase-space representation and Lyapunov functions. New convergence rate for gradient norm is revealed in convex case, while the requirement for stepsize is loosed and the convergence rate is improved for strongly convex objective.
• [01285] Exact continuous relaxations and algorithms for regularized optimization problems
  • Author(s) :
    • Wei Bian (Harbin Institute of Technology)
  • Abstract : In this talk, we consider two classes of regularized optimization problems, in which the group sparsity is considered. Firstly, we give the continuous relaxation models of the considered problem and establish the equivalence of these two problems in the sense of global minimizers. Then, we define a class of stationary points of the relaxation problem, and prove that any defined stationary point is a local minimizer of the considered regularized problem and satisfies a desirable property of its global minimizers. Further, based on the difference-of-convex (DC) structure of the relaxation problem, we design some corresponding algorithms and prove their convergence properties.

MS [00882] Geometric Shape Generation II: Design

room : F403

• [01581] Generation of κ-Space Curve
  • Format : Talk at Waseda University
  • Author(s) :
    • DAN WANG (Shizuoka University)
    • Tadatoshi Sekine (Shizuoka University)
    • Shin Usuki (Shizuoka University)
    • Kenjiro Takai Miura (Department of Mechanical Engineering, Shizuoka University)
  • Abstract : The κ-curve is a recently published interpolating spline which consists of quadratic Bezier segments passing through input points at the loci of local curvature extrema. But their interpolation can only deal with planar curves. Therefore, in this research We propose a method that enables to extend this representation to deal with space curves in a new scheme called κ-space curves
• [01561] The uniqueness theorem on the shape of free-form curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenjiro Takai Miura (Shizuoka University)
    • R.U. Gobithaasan (University Malaysia Terengganu)
    • Md Yushalify Misro (University Science Malaysia)
    • Tadatoshi Sekine (Shizuoka University)
    • Shin Usuki (Shizuoka University)
  • Abstract : We will discuss about the shape uniqueness theorem for curves defined by three or more control points and show several examples of applications ofthe theorem.
• [01775] Construction of κ-Curve Using Fractional Bézier Curve
  • Format : Talk at Waseda University
  • Author(s) :
    • Syed Ahmad Aidil Adha Said Mad Zain (Universiti Sains Malaysia)
    • Md Yushalify Misro (Universiti Sains Malaysia)
    • Kenjiro Takai Miura (Department of Mechanical Engineering, Shizuoka University)
  • Abstract : The $\kappa$-curve is one of the famous curves that has been applied as a curvature pen tool in Adobe Illustrator® and Photoshop®. The $\kappa$-curve has an excellent property where the local maxima of curvature have occurred at the control points. This will prevent the formation of cusps and loops. In this work, the construction of the $\kappa$-curve will be shown by using the fractional Bézier curve with the help of fractional continuity.

MS [00607] Analysis and computation of interface evolution equation and related topics

room : F411

• [03814] A minimizing movement approach to surface constrained interfacial motions
  • Format : Talk at Waseda University
  • Author(s) :
    • Elliott Ginder (Meiji University)
  • Abstract : By extending the applicability of minimizing movements to the surface PDE setting, we will develop threshold dynamics for surface-constrained interfacial motions. In particular, we will show how our approach enables one to approximate multiphase, volume-preserving, curvature flows on surfaces via generalized MBO and HMBO algorithms.
• [02801] Geometric Sobolev gradient flows on spaces of curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Philip Schrader (Murdoch University)
  • Abstract : The curve-shortening flow, which deforms a closed planar curve by moving its points perpendicular to the curve with velocity proportional to curvature, was proposed by Mullins as a model for the motion of grain boundaries in the process of annealing. It can be characterised as the gradient descent of the length functional on curves, when the gradient is taken with respect to a parametrisation invariant $L^2$ inner product. In this talk I will describe some of the gradient flows which result when taking instead the gradient with respect to some Sobolev parametrisation invariant inner products. I will discuss the different kinds of asymptotic behaviour that are possible and also the numerical advantages of $H^1$ products.
• [03938] A Simple Algorithm for the Monge-Ampere Equation on a Sphere
  • Format : Talk at Waseda University
  • Author(s) :
    • Richard Tsai (The University of Texas at Austin)
    • Axel Turnquist (University of Texas at Austin)
  • Abstract : In this talk, we present a novel approach for solving the Monge-Ampere (MA) equation defined on a sphere. Specifically, we extend the MA equation on a sphere to a narrowband around the sphere by formulating an equivalent optimal transport problem. We demonstrate that the extended MA equation can be solved using existing algorithms developed for the MA equation on Euclidean space, making the resulting algorithm simple and easy to implement. Our approach provides a useful tool for solving problems that involve the MA equation defined on or near a sphere, which has a wide range of applications in fields such as computer graphics, image processing, and fluid dynamics.
• [02029] Waiting time effects for the wearing process of a non-convex stone
  • Format : Talk at Waseda University
  • Author(s) :
    • Nao Hamamuki (Hokkaido University)
    • Ryosuke Takahashi (Hokkaido University)
  • Abstract : We investigate evolution of a non-convex stone by the wearing process. Following the formulation introduced by Ishii and Mikami 2001, 2004, we study the unique viscosity solution of a nonlocal Gauss curvature flow equation describing the wearing process and prove that waiting time effects occur on an appropriate subset in a cavity of the stone, that is, any point on the set does not move at all for some positive time.

MS [02408] Recent advances in two-phase flow influenced by thermal fluctuations

room : F412

• [03044] Temperature Effects in Generalized Diffusions
  • Format : Talk at Waseda University
  • Author(s) :
    • Chun Liu (Illinois Tech)
  • Abstract : Abstract: In this work, we will introduce a general framework to derive thermodynamics of a mechanical system, which guarantee the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We will also present some analysis results and difficulties to these systems.
• [04783] Asymptotics of the stochastic Cahn-Hilliard equation with space-time white noise
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lubomir Banas (Bielefeld University)
  • Abstract : We study the sharp interface limit of the stochastic Cahn-Hilliard equation with space-time white noise. We show that for sufficiently strong scaling of the noise the solution of the equation converges to the solution of the deterministic Hele-Shaw problem. We also discuss corresponding results for the numerical approximation of the problem.
• [03980] Weak error analysis for the stochastic Allen-Cahn equation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dominic Breit (TU Clausthal)
    • Andreas Prohl Tuebingen (University of Tuebingen)
  • Abstract : We prove strong rate {\em resp.}~weak rate ${\mathcal O}(\tau)$ for a structure preserving temporal discretization (with $\tau$ the step size) of the stochastic Allen-Cahn equation with additive {\em resp.}~multiplicative colored noise in $d=1,2,3$ dimensions. Direct variational arguments exploit the one-sided Lipschitz property of the cubic nonlinearity in the first setting to settle first order strong rate. It is the same property which allows for uniform bounds for the derivatives of the solution of the related Kolmogorov equation, and then leads to weak rate ${\mathcal O}(\tau)$ in the presence of multiplicative noise. Hence, we obtain twice the rate of convergence known for the strong error in the presence of multiplicative noise.
• [03932] On a convergent SAV scheme for stochastic phase-field equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefan Metzger (FAU Erlangen-Nürnberg)
  • Abstract : In this talk, we discuss the numerical treatment of stochastic Cahn-Hilliard equations with stochastic dynamic boundary conditions. These equations can be used to describe contact line tension effects in two-phase flows. By applying a stochastic version of the SAV method, we derive a stable, fully discrete finite element scheme that is linear with respect to the unknown quantities. Furthermore, we establish convergence of the discrete solutions towards martingale solutions using Skorokhod-type arguments.

MS [00323] Integrating rough paths into domain applications

room : E501

• [00458] Path-Dependent Neural Jump ODEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Florian Krach (ETH Zurich)
    • Marc Nübel (ETH Zurich)
    • Josef Teichmann (ETH Zurich)
  • Abstract : In this talk we discuss the problem of forecasting general stochastic processes using a path-dependent extension of the Neural Jump ODE (NJ-ODE) framework. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time-series, these results were limited to data stemming from It\^o-diffusions with complete observations, in particular Markov processes where all coordinates are observed simultaneously. Here, we first revisit the NJ-ODE and its results and then generalise them to generic, possibly non-Markovian or discontinuous, stochastic processes with incomplete observations, by utilising the reconstruction properties of the signature transform. These theoretical results are supported by empirical studies, where it is shown that the path-dependent NJ-ODE outperforms the original NJ-ODE framework in the case of non-Markovian data.
• [00499] Signature Methods for Outlier Detection
  • Format : Talk at Waseda University
  • Author(s) :
    • Paola Arrubarrena (Imperial College London and DataSig)
    • Terry Lyons (University of Oxford)
    • Thomas Cass (Imperial College University)
    • Maud Lemercier (University of Oxford and DataSIg)
  • Abstract : An anomaly detection methodology is presented that identifies if a given observation is unusual by deviating from a corpus of non-contaminated observations. The signature transform is applied to the streamed data as a vectorization to obtain a faithful representation in a fixed-dimensional feature space. This talk is applied to radio astronomy data to identify very faint radio frequency interference (RFI) contaminating the rest of the data.
• [01312] Path Development Network with Finite-dimensional Lie Group
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hang Lou (University College London)
    • Hao Ni (University College London)
    • Siran Li (Shanghai Jiao Tong University)
  • Abstract : We propose a novel, trainable path development layer that exploits representations of sequential data through finite-dimensional Lie groups. The path development, which originates from rough path theory, inherits useful analytical properties from path signatures while also offering much richer group structures. Empirical results show the superiority of the development layer over signature features in terms of accuracy and dimensionality. The compact hybrid model, which stacks a one-layer LSTM with the development layer, achieves state-of-the-art performance against various RNN and continuous time series models on various datasets.
• [01355] From CCTV video streams to inferring NO2 emissions at city-scale
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mohamed Ibrahim (University of Leeds)
    • Terry Lyons (Oxford university)
  • Abstract : In this talk, we show how we can infer NO2 emissions from CCTV video streams at city-scale through rough path theory. we introduce a framework for mapping objects in CCTV video streams as a stream of paths highlighting the order in which events take place. This temporal representation gives a descriptive summary for video contents which we can maximise: 1) data anonymity, and 2) systematic readability of large-scale video streams.

MS [00672] Efficient inference for large and high-frequency data

room : E502

• [03747] Local asymptotic property for the Euler approximation of SDE driven by a stable Lévy process
  • Format : Talk at Waseda University
  • Author(s) :
    • Emmanuelle Clément (University Gustave Eiffel)
    • Alexandre Brouste (Le Mans University)
    • Thi Bao Trâm Ngô (Le Mans University)
    • Laurent DENIS (Le Mans University )
  • Abstract : We study the stochastic differential equations driven by a symmetric stable Lévy process, in which the joint parametric estimation of the drift coefficient, the scale coefficient and the jump activity of the process based on high frequency observations on a fixed time interval is considered. For these experiments, due to the non-explicit form of the likelihood function, our methodology will be to identify a simpler experiment, where the likelihood function has a traceable form, which is asymptotically equivalent in the Le Cam distance at the process observed at high frequency. To cover all values of jumping activity, the most appropriate experiment is to consider a numerical scheme that combines Euler's approximation of the scale coefficient with the solution of the ordinary equation given by the coefficient of derivative. We therefore prove the LAMN property for this corresponding Euler scheme with the ordinary differential equation. Thanks to the obtained LAMN property, we show that the one-step estimator is efficient. With an easy-to-compute initial estimator with good asymptotic behavior, it can exhibit a performance quite similar to that of the maximum likelihood estimator and reduce a lot of computation time. We illustrate our results by numerical simulations with the one-step procedure.
• [03713] Asymptotics for Student-Lévy regression
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroki Masuda (University of Tokyo)
  • Abstract : We consider the quasi-likelihood analysis for a linear regression model driven by a Student Lévy process with constant scale and arbitrary degrees of freedom. We consider joint estimation of trend, scale, and degrees of freedom when the model is observed at a high frequency over an extending period. The bottleneck in this problem is that the Student distribution is not closed under convolution, making it difficult to estimate all the parameters fully based on the high-frequency time scale. To efficiently deal with that intricate nature, we propose a two-step quasi-likelihood analysis: first, we make use of the Cauchy quasi-likelihood for estimating the regression-coefficient vector and the scale parameter; then, we construct the sequence of the unit-period cumulative residuals to estimate the remaining degrees of freedom. We will present the hopefully asymptotically efficient theoretical behavior of the proposed estimator, which quantitatively clarifies the need for data thinning.
• [01903] High-frequency estimation of pure jump alpha-CIR process
  • Format : Talk at Waseda University
  • Author(s) :
    • Elise Bayraktar (Université Gustave Eiffel)
  • Abstract : We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process defined by $$X_t=x_0+\int_0^t(a-bX_s)ds+\int_0^s\delta X_{s-}^{1/ \alpha}dL^\alpha_s$$ where $(L^\alpha_t)_{t \geq 0}$ is a compensated $\alpha$-stable Lévy process with non-negative jumps and $\alpha \in (1,2).$ We study the joint estimation of drift, scaling and jump activity parameters $(a,b,\delta,\alpha)$ from high-frequency observations of the process on a fixed time period. We prove the existence of a consistent and asymptotic mixed normal estimator based on an approximation of the likelihood function.
• [02309] Local asymptotic properties for the growth rate of a jump-type CIR process
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mohamed Ben Alaya (University of Rouen)
    • Ahmed Kebaier (University of Evry)
    • Gyula Pap (University of Szeged)
    • Ngoc Khue Tran (Hanoi University of Science and Technology)
  • Abstract : In this paper, we consider a one-dimensional jump-type Cox-Ingersoll-Ross pro- cess driven by a Brownian motion and a subordinator, whose growth rate is an unknown parameter. The Lévy measure of the subordinator is finite or infinite. Considering the process observed continuously or discretely at high frequency, we derive the local asymptotic properties for the growth rate in both ergodic and non-ergodic cases. Three cases are distinguished: subcritical, critical and supercritical. Local asymptotic normality (LAN) is proved in the subcritical case, local asymptotic quadraticity (LAQ) is derived in the critical case, and local asymptotic mixed normality (LAMN) is shown in the supercritical case. To do so, techniques of Malliavin calculus and a subtle analysis on the jump structure of the subordinator involving the amplitude of jumps and number of jumps are essentially used.

MS [00193] Adversarial robustness at the interface of analysis, geometry and statistics

room : E503

• [00292] Gamma convergence of a nonlocal perimeter from adversarial machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Leon Bungert (University of Bonn)
    • Kerrek Stinson (University of Bonn)
  • Abstract : Adversarial training is a robust machine learning method which seeks to compute a classifier which is stable with respect to adversarial attacks. Recent analysis has shown that adversarial training admits different reformulations, e.g., as distributionally robust optimization, multi-marginal optimal transport, or geometric regularization problem. In this last context, adversarial training is equivalent to regularized empirical risk minimization $\min_{A\subset\mathbb{R}^d}\mathcal R_\mathrm{emp}(A) + \varepsilon\operatorname{Per}_\varepsilon(A)$ where a nonlocal perimeter $\operatorname{Per}_\varepsilon $ of the classifier is penalized. The nonlocality is parametrized with the so-called “adversarial budget” $\varepsilon>0$ which models the strength of the adversary. In this talk I will discuss local limits of this nonlocal perimeter as the adversarial budget goes to zero. Under generic conditions we prove Gamma convergence of $\operatorname{Per}_\varepsilon$ to a weighted local perimeter as $\varepsilon \to 0$. This is joint work with Kerrek Stinson from the University of Bonn.
• [00313] Provable Adversarial Robustness via Optimal Transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Muni Sreenivas Pydi (Université Paris Dauphine-PSL)
  • Abstract : In this talk, we explore the fundamental limits of adversarially robust classification using optimal transport. We give two characterizations of the best error: as an optimal transport cost between the true data distributions, and as the Bayes error of a minimax hypothesis test involving Wasserstein uncertainty sets. The first characterization leads to a recipe for finding the optimal classifier, and the second leads to the existence of a Nash equilibrium.
• [00277] Adversarial learning and the Wasserstein barycenter problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Matt Jacobs (Purdue University)
  • Abstract : In this talk, I will show that the adversarial training problem is equivalent to a generalized version of the Wasserstein barycenter problem. The connection between these problems allows us to completely characterize the optimal adversarial strategy and to bring in tools from optimal transport to analyze and compute optimal classifiers. We will then use these tools to better understand the regularizing effect of adversarial training.
• [00299] Optimal Adversarial Classification: geometry, regularity, and topology
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryan Murray (North Carolina State University)
  • Abstract : Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be "fooled" using specially constructed adversarial examples. In turn, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will discuss delicate mathematical and geometric information which can inferred about optimal adversarial classifiers. In particular, I will describe types of available regularity theory, and draw connections with non-local isoperimetric problems which have been popular in the variational community. Time permitting, I will also discuss recent algorithmic advances which can detect and track topological changes induced by the presence of an adversary.

MS [00949] Optimal and Efficient Algorithms for Inverse Problems

room : E505

• [05576] Geometric Scattering on Measure Spaces
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael Perlmutter (Boise State University)
  • Abstract : Geometric Deep Learning is an emerging field of research that aims to extend the success of machine learning and, in particular, convolutional neural networks, to data with non-Euclidean geometric structure such as graphs and manifolds. Despite being in its relative infancy, this field has already found great success and is utilized by, e.g., Google Maps and Amazon’s recommender systems. In order to improve our understanding of the networks used in this new field, several works have proposed novel versions of the scattering transform, a wavelet-based model of neural networks for graphs, manifolds, and more general measure spaces. In a similar spirit to the original scattering transform, which was designed for Euclidean data such as images, these geometric scattering transforms provide a mathematically rigorous framework for understanding the stability and invariance of the networks used in geometric deep learning. Additionally, they also have many interesting applications such as the analysis of single-cell data
• [02094] Variable Projection Methods for Solving Separable Nonlinear Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Malena Espanol (Arizona State University)
  • Abstract : Variable projection methods are among the classical and efficient methods to solve separable nonlinear least squares problems. In this talk, I will introduce the variable projection method and its use to solve large-scale blind deconvolution problems.
• [03302] Doubly Noisy Kaczmarz
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Ma (UC Irvine)
    • ELHoucine Bergou ( Mohamed VI Polytechnic University (UM6P))
    • Aritra Dutta (University of Southern Denmark)
    • Soumia Boucherouite ( Mohamed VI Polytechnic University (UM6P))
    • Xin Li (University of Central Florida)
  • Abstract : Large-scale linear systems, Ax=b, frequently arise in inverse problems. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized Kaczmarz algorithm (RK) was studied extensively as an efficient iterative solver for such systems. However, the convergence study of RKA in the noisy regime is limited and considers measurement noise in the right-hand side vector, b. Unfortunately, in practice, that is not always the case; the coefficient matrix A can also be noisy. In this talk, we motivate and discuss the application of RK to doubly noise linear systems, i.e., linear systems with noise in both the measurements and the measurement matrix. The presented work is a joint collaboration with El Houcine Bergou, Soumia Boucherouite, Aritra Dutta, and Xin Li.
• [02096] Geometric Scattering on Measure Spaces
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael Perlmutter (UCLA)
  • Abstract : Geometric Deep Learning is an emerging field of research that aims to extend the success of machine learning and, in particular, convolutional neural networks, to data with non-Euclidean geometric structure such as graphs and manifolds. Despite being in its relative infancy, this field has already found great success and is utilized by, e.g., Google Maps and Amazon’s recommender systems. In order to improve our understanding of the networks used in this new field, several works have proposed novel versions of the scattering transform, a wavelet-based model of neural networks for graphs, manifolds, and more general measure spaces. In a similar spirit to the original scattering transform, which was designed for Euclidean data such as images, these geometric scattering transforms provide a mathematically rigorous framework for understanding the stability and invariance of the networks used in geometric deep learning. Additionally, they also have many interesting applications such as the analysis of single-cell data

MS [01445] Deep Learning, Preconditioning, and Linear Solvers

room : E507

• [03314] Deep Learning, Preconditioning, and Linear Solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • David Hyde (Vanderbilt University)
  • Abstract : We will survey techniques for using learning to accelerate linear solvers and preconditioners. Some methods use learning to determine high-quality initial guesses for iterative systems; other approaches learn parameters for classical preconditioners like algebraic multigrid; further techniques replace the entire role of a preconditioner with learning; and still other works replace entire linear solvers with neural network evaluations. After surveying these approaches, we will suggest some avenues of research, open questions, and opportunities for collaboration.
• [04332] Fourier Neural Solver for Large Sparse Linear Algebraic Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Kai Jiang (Xiangtan University)
  • Abstract : In this talk, we propose an interpretable neural solver, the Fourier neural solver (FNS), to solve sparse linear algebraic systems. Based on deep learning and fast Fourier transformation, FNS combines a stationary iterative method and frequency space correction approach to efficiently eliminate different frequency components of the error. The local Fourier analysis indicates that FNS can detect error components within the frequency domain that cannot be eliminated effectively using stationary methods, even though the error removed by the latter is problem-dependent. Numerical experiments on several classical equations show that the FNS is more efficient and more robust than the existing neural solvers. If time permits, we will update our latest progress in this area.
• [03199] Accelerating multigrid solvers for the acoustic and elastic Helmholtz equation.
  • Format : Talk at Waseda University
  • Author(s) :
    • Rachel Yovel (Ben-Gurion University of the Negev)
    • Eran Treister (Ben-Gurion University of the Negev)
    • Bar Lerer (Ben-Gurion University of the Negev)
  • Abstract : We develop multigrid solvers for the acoustic and elastic Helmholtz equations and accelerate them using deep learning methods. Based on the shifted Laplacian approach, which is typically used for the acoustic version, we build a GPU-friendly geometric multigrid preconditioner for the elastic Helmholtz equation. Moreover, we present a block-acoustic preconditioner for the elastic version and utilize a trained CNN acoustic solver to solve the elastic Helmholtz equation through this reduction.
• [03141] On learning neural operators of PDEs with interfacial jump conditions for accelerating simulations of physical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Pouria Akbari Mistani (NVIDIA Corp)
    • Samira Pakravan (University of California Santa Barbara)
    • Frederic Gibou (University of California Santa Barbara)
  • Abstract : Elliptic (free boundary) problems with jump conditions are commonly used to model multiscale physical systems. Despite the availability of optimal numerical solvers, obtaining solutions over large spatiotemporal scales remains challenging. Pre-trained compact neural operators offer fast inference oracles to accelerate simulations on modern hardware. In this talk we present our work on training accurate neural operators for this class of problems. We also introduce JAX-DIPS, a publicly available library, to promote research in this area.

MS [02178] Efficient computational methods for data matrices: exploiting sparsity and structure

room : E508

• [04795] Exploiting Supernodal Structures in Sparse All Pair Shortest Path Computation.
  • Format : Talk at Waseda University
  • Author(s) :
    • Piyush K Sao (Oak Ridge National Laboratory)
    • Prasun Gera (cerebras)
    • Hao Lu (Oak Ridge National Laboratory)
    • Ramki Kannan (Oak Ridge National Laboratory)
    • Richard W Vuduc (Georgia Institute of Technology)
    • Thomas Potok (Oak Ridge National Laboratory)
  • Abstract : We introduce a novel approach for efficiently solving all-pairs shortest path problems on sparse graphs. We leverage the techniques from sparse Cholesky factorization, including fill-in-reducing ordering, supernodal traversal, and elimination tree parallelism for APSP computation. Our method uses semi-ring notation to express graph algorithms in linear algebraic form and employs BLAS level-III semi-ring operations. Our parallel prototype implementation significantly outperforms a non-sparsity-exploiting Floyd-Warshall algorithm and competes with Dijkstra's algorithm for specific sparse graph classes.
• [04585] Optimizations of H-matirx-vector Multiplication for Many-core Processors
  • Format : Talk at Waseda University
  • Author(s) :
    • Tetsuya Hoshino (Nagoya University)
    • Akihiro Ida (Japan Agency for Marine-Earth Science and Technology)
    • Toshihiro Hanawa (The University of Tokyo)
  • Abstract : Hierarchical matrices (H-matrices) can robustly approximate the dense matrices that appear in the boundary element method (BEM). To accelerate the solving of linear systems in the BEM, we must speed up hierarchical matrix–vector multiplication (HiMV). This presentation discusses optimization methodologies of HiMV for modern multi/many-core CPUs: an H-matrix storage method for efficient memory access, a method that avoids write contentions, an inter-thread load-balancing method, and blocking and sub-matrix sorting methods for cache efficiency.
• [04849] Distributed Graph Neural Network for Billion-Scale Graphs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Israt Nisa (AWS AI)
  • Abstract : GNN models are widely used in recommendation, fraud detection, and search. Real-world graphs from social media and co-purchase networks are large and heterogeneous, posing challenges for scaling training and inference. We demonstrate GraphStorm, a GNN framework that utilizes a distributed hybrid CPU/GPU architecture for efficient graph partitioning, asynchronous computation and data loading, data locality, and hardware utilization (CPU, GPU, network, PCIe).
• [05081] A Framework to Exploit Data Sparsity in Tile Low-Rank Cholesky Factorization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rabab Mohammad Alomairy (King Abdullah University of Science and Technology)
    • Qinglei Cao (University of Tennessee )
    • Yu Pei (University of Tennessee )
    • george bosilca ( University of Tennessee )
    • Hatem Ltaief (King Abdullah University of Science and Technology)
    • David Keyes (King Abdullah University of Science and Technology)
    • Jack Dongarra ( University of Tennessee )
  • Abstract : We accelerate the computations of 3D unstructured mesh deformation based on radial basis function interpolations by exploiting the rank structured property of the matrix. As we increase the accuracy threshold to satisfy the application requirements, the original dense operator gets further compressed and may become sparse enough to switch the dense solver to sparse direct solver. This talk highlights how PaRSEC redistributes the matrix, mitigates the data movement overheads, and copes with the load imbalance.

MS [00581] Analysis, Methods and Applications in Complex Materials

room : E603

• [04090] A framework for a generalization analysis of MLIPs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yangshuai Wang (University of British Columbia)
  • Abstract : I will talk about an analytical (as opposed to statistical) approach to demonstrate the generalization of MLIPs and its application on simulating crystalline defects, explaining how the choice of training data and the accuracy of the fit to that training data affect the accuracy of predictions on materials properties.
• [04086] A Finite Element Configuration Interaction Method for Wigner Localization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xue Quan (Beijing Normal University)
    • Huajie Chen (Beijing Normal University)
  • Abstract : This work proposes a numerical algorithm to study the Wigner localization phenomenon which carefully treats the many-body correlations. The main features are three-fold: (i) a finite element discretization of the one-body space such that the sharp localization can be captured; (ii) a good initial state obtained by exploiting the strongly correlated limit; and (iii) a selected configuration interaction method by choosing the Slater determinants from (stochastic) gradients.
• [05440] Equivariant Tensor Network Potentials
  • Format : Talk at Waseda University
  • Author(s) :
    • Max Hodapp (Materials Center Leoben)
    • Alexander Shapeev (Skoltech)
  • Abstract : The computational cost of many state-of-the-art machine-learning interatomic (MLIPs) potentials increases exponentially with the number of atomic features. Low-rank tensor networks can overcome exponential growth in complexity, however, it is often not easy to encode the model symmetries. Here, we propose a formalism for rank-efficient equivariant tensor networks (ETNs) that remain invariant under actions of SO(3), and, using ETNs, develop a new class of MLIPs that demonstrate superior performance over existing MLIPs.
• [04136] Planewave approximation for electronic structure calculation of incommensurate systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Ting Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences )
  • Abstract : Incommensurate structures come from stacking the single layers of low-dimensional materials on top of one another with misalignment, such as a twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. Under the planewave framework, we provide a numerical scheme to compute the electronic structure of incommensurate systems based on density functional theory.

MS [00295] Estimation problems over groups

room : E604

• [04814] The sample complexity of multireference alignment and cryo-EM
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamir Bendory (Tel Aviv University)
  • Abstract : The problem of multi-reference alignment (MRA) involves retrieving a signal from multiple copies that have been corrupted by noise and transformed by a random group element. MRA is of particular interest in the context of single-particle cryo-electron microscopy (cryo-EM), a prominent technique used to reconstruct biological molecular structures. During this talk, I will examine the sample complexity of both the MRA and cryo-EM models using tools from representation theory, sparse coding, and generative models.
• [04753] Autocorrelation analysis for cryo-EM with sparsity constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamir Bendory (Tel Aviv University)
    • Yuehaw Khoo (The University of Chicago)
    • Joe Kileel (UT Austin)
    • Oscar Mickelin (Princeton University)
    • Amit Singer (Princeton University)
  • Abstract : This work presents new results for the method of moments applied to cryo-electron microscopy. We prove that autocorrelations of noisy tomographic projection images can reconstruct molecular structures that are modeled as sparse sums of Gaussians. This significantly reduces the sample complexity of the problem, compared to previous results. Additionally, we detail a practical ab initio reconstruction algorithm using tools adapted from crystallographic phase retrieval.

MS [02618] Recent Developments in Hyperspectral and Multispectral Imaging

room : E605

• [03524] Multi-Dimensional Signal Alignment using Local All-Pass Filters
  • Format : Talk at Waseda University
  • Author(s) :
    • Christopher Gilliam (University of Birmingham)
  • Abstract : The estimation of a geometric transformation that aligns two or more signals is a problem that has many applications. The problem occurs when signals are either recorded from two or more spatially separated sensors or when a single sensor is recording a time-varying scene, e.g., image registration, motion correction in medical imaging and time-varying delay estimation. In this talk we estimate the transformation by approximating it using a set of local all-pass (LAP) filters.
• [03596] Noise reduction in X-ray microspectroscopy
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jizhou Li (City University of Hong Kong)
  • Abstract : Investigating nanoscale morphological and chemical phase transformations is essential for a wide range of scientific and industrial applications across various disciplines. The emerging TXM-XANES imaging technique combines the strengths of full-field transmission X-ray microscopy (TXM) and X-ray absorption near edge structure (XANES) to generate chemical maps by capturing a series of multi-energy X-ray microscopy images and fitting them accordingly. However, its effectiveness is hindered by low signal-to-noise ratios due to system errors and insufficient exposure illuminations during rapid data acquisition. In this study, we present a straightforward and robust denoising method that capitalizes on the inherent properties and subspace modeling of TXM-XANES imaging data to significantly improve image quality, paving the way for fast and highly sensitive chemical imaging. Comprehensive experiments using both synthetic and real datasets showcase the remarkable performance of our proposed approach.
• [03540] Remote Sensing Image Reconstruction from the Subspace Perspective
  • Format : Talk at Waseda University
  • Author(s) :
    • Jie Lin (University of Electronic Science and Technology of China)
  • Abstract : Remote sensing images cover abundant spatial-spectral information while the images usually suffer from different degradations during the imaging and transmission. Image reconstruction is a fundamental step for subsequent applications. With improved imaging accuracy, the larger sizes of acquired images bring a greatly increased computation burden in reconstruction. In this talk, I will present matrix and tensor subspace-based methods for remote sensing image reconstruction, which enjoy satisfactory effects and lower computational complexity.
• [03879] Nonlocal Self-Similarity-Based Hyperspectral Remote Sensing Image Denoising With 3-D Convolutional Neural Network
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zhicheng Wang (The University of Hong Kong)
    • Michael Kwok-Po NG (The University of Hong Kong)
    • Lina Zhuang (Key Laboratory of Computational Optical Imaging Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing)
    • Lianru Gao (Key Laboratory of Computational Optical Imaging Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing)
    • Bing Zhang (Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China, and also with the University of Chinese Academy of Sciences, Beijing)
  • Abstract : Deep-learning-based denoising methods for hyperspectral images have been comprehensively studied and achieved impressive performance. Compared with deep-learning-based methods, the nonlocal similarity-based methods are more suitable for images containing edges or regular textures. We propose a powerful denoising method, termed non-local 3-D convolutional neural network, combining traditional machine learning and deep learning techniques. The numerical and graphical denoising results of the simulated and real data show that the proposed method is superior to the state-of-the-art methods.

MS [02514] Developing Performance Portable, Scalable and AI enabled Fusion Energy Physics Framework

room : E606

• [04465] Develop next generation CFD tools using AI libraries
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaohu Guo (UKRI STFC Hartree Centre)
  • Abstract : Due to new hardware technologies, increases in computing power and developments in AI software, the benefits of combining AI techniques with traditional numerical methods for solving governing equations of dynamical systems are becoming apparent. This talk introduces a revolutionary approach to the discretization and solution of PDEs. Our approach implements CFD models using neural network with the aim of simplifying the software development and building on the very substantial developments already made in AI software.
• [04652] AI deconvolution operator for plasma turbulent simulations on complex geometries
  • Format : Talk at Waseda University
  • Author(s) :
    • Jony Castagna (UKRI-STFC Hartree Centre)
    • Francesca Schiavello (UKRI-STFC Hartree Centre)
  • Abstract : We use Generative Adversarial Networks (GANs) to model the nonlinear terms in partial differential equations on coarse structured grids. The idea is to reconstruct the high-resolution fields exploring the latent space of the GANs after being properly trained on curvilinear coordinates. The nonlinear terms are then found and mapped back to the coarse structured mesh where the filtered equations are solved. Results for Navier Stokes and Hasagawa-Wakatani plasma equations are presented.
• [04741] Performance and scaling of amrPX: a multiphase CFD framework
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Grant (UKRI STFC Hartree Centre)
    • Xiaohu Guo (UKRI STFC Hartree Centre)
    • Karthikeyan Chockalingam (UKRI STFC Hartree Centre)
  • Abstract : amrPX is a modularised, multi-model adaptive mesh refinement framework built using AMReX. Each model has a common structure with Data, Solver, Physics and Problem containers, with shared utility modules such as numerics or materials, to promote code re-use and ease of development. A compressible multiphase Five-Equation model has been implemented and benchmarked. Performance results and scalability across thousands of CPUs and GPUs is discussed.
• [05229] A highly parallel simulation of patient-specific hepatic flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Zeng Lin (Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences)
  • Abstract : Computational hemodynamics is being developed as an alternative approach for assisting clinical diagnosis and treatment planning for liver diseases. The technology is non-invasive, but the computational time could be high when the full geometry of the blood vessels is taken into account. In this work, we study a highly parallel method for the transient incompressible Navier-Stokes equations for the simulation of the blood flows in the full three-dimensional patient-specific hepatic artery, portal vein and hepatic vein. As applications, we also simulate the flow in a patient with hepatectomy and calculate the portal pressure gradient. One of the advantages of simulating blood flows in all hepatic vessels is that it provides a direct estimate of the portal pressure gradient, which is a gold standard value to assess the portal hypertension. Moreover, the robustness and scalability of the algorithm are also investigated. A 83% parallel efficiency is achieved for solving a problem with 7 million elements on a supercomputer with more than 1000 processor cores.

MS [01605] Recent advances in computational methods for kinetic and hyperbolic equations

room : E702

contributed talk: CT107

room : E703

[01728] C0 IP Methods for Phase Field Crystal Equations

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
• Type : Contributed Talk
• Abstract : A relatively new class of mathematical models known as phase field crystal models has emerged as a way to simulate physical processes where automic- and microscales are tightly coupled. In this talk, we present numerical schemes for two such models which rely on a C0 interior penalty finite element method spatial discretization. We show that the numerical methods are unconditionally energy stable and unconditionally convergent and support our conclusions with a few numerical experiments.
• Classification : 65M60, 65M12
• Format : Talk at Waseda University
• Author(s) :
  • Amanda Emily Diegel (Mississippi State University)
  • Natasha Sharma (University of Texas at El Paso)

[01105] SIPG Method for boundary control problems governed by parabolic PDEs

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
• Type : Contributed Talk
• Abstract : We present a posteriori error analysis of adaptive finite element approximations for parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The discretization is followed by using the symmetric interior penalty Galerkin (SIPG) technique. Both reliable and efficient residual-based error estimators are deduced. The implementation of these error estimators serves as a guide for the adaptive mesh refinement process. The numerical experiment shows the effectiveness of the derived estimators.
• Classification : 65M60, 65M15
• Format : Talk at Waseda University
• Author(s) :
  • Ram Manohar (Indian Institute of Technology Kanpur)
  • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
  • Kedarnath Buda (Indian Institute of Technology Kanpur)
  • Rajen Kumar Sinha (Indian Institute of Technology Guwahati)

[02480] Conservative Timesteppers for Fluid Mechanics via Finite Elements in Time

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
• Type : Contributed Talk
• Abstract : Finite-element-in-time—FET—formulations can be carefully constructed to preserve key structures in time-dependent PDEs, such as energy and helicity dissipation, material conservation, and Hamiltonians. Furthermore, with appropriate trial and test spaces, FET formulations can be solved one timestep at a time, like classical timesteppers. We propose a general auxiliary space concept that connects these ideas, using FET to derive timesteppers up to arbitrary order in time that preserve these structures. We discuss potential future applications of this idea.
• Classification : 65M60, 76D05, 65P10, 76W05, 65M22
• Format : Talk at Waseda University
• Author(s) :
  • Boris Duncan Andrews (University of Oxford)
  • Patrick Emmet Farrell (University of Oxford)
  • Wayne Arter (United Kingdom Atomic Energy Authority)

[00617] Low-regularity exponential-type integrators for the Zakharov system under rough data

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
• Type : Contributed Talk
• Abstract : Two low-regularity exponential-type integrators (LREIs) are proposed and analyzed for the Zakharov system (ZS), including a first-order integrator and a second-order one. To my knowledge, it is the first time to propose such LREIs that achieve the first- and second-order accuracy by requiring one or two additional derivatives for the solutions of ZS, respectively. Numerical comparison with other methods demonstrates the superiority of the newly proposed LREIs for rough data.
• Classification : 65M70, 65M12, 65M15, 65T50
• Format : Talk at Waseda University
• Author(s) :
  • Hang Li (Tsinghua University )
  • Chunmei Su (Tsinghua University)

[01923] Primal hybrid method for quasi-linear parabolic problems

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E703
• Type : Contributed Talk
• Abstract : In this article, a second order quasi-linear parabolic initial-boundary value problem is approximated by using primal hybrid finite element method and Lagrange multipliers. Semi-discrete and backward Euler based fully discrete schemes are discussed and optimal order error estimates are established by applying modified elliptic projection. Optimal order error estimates in maximum norm are also derived. Earlier results on maximum-norm superconvergence of the gradient in piecewise linear finite-element approximations of elliptic and parabolic problems are now carried over to quasi-linear case using primal hybrid method. Finally, the results on numerical experiments confirm our theoretical findings.
• Classification : 65M60
• Author(s) :
  • RAVINA SHOKEEN (The LNM Institute of Information Technology)
  • Ajit Patel (The LNM Institute of Information Technology)
  • Amiya Kumar Pani (BITS Goa)

contributed talk: CT116

room : E705

[00549] On the penalty approach in finite difference methods

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
• Type : Contributed Talk
• Abstract : We introduce a finite difference method with the $H^1$ and $L^2$ penalties to solve the elliptic PDEs over curved complicated domains. The sharp convergence of the penalized solution to the original one is provided. The accuracy in both strategies is almost analogous, provided the penalty parameter $\epsilon$ is $O(h^2)$ in the $H^1$ penalty approach and $O(h^4)$ in the $L^2$ penalty approach. The iterative methods developed for the proposed idea are highly efficient and furnish the theoretical outcomes. Keywords: Finite difference method, Elliptic PDEs, Penalty, Curved domain, Cartesian mesh. References: 1. S. Kale, and D. Pradhan, Error estimates of fictitious domain method with an $H^1$ penalty approach for elliptic problems, Comp. Appl. Math., Vol. 41, (2022), pp. 1-21. 2.B. Maury, Numerical Analysis of a finite element/volume penalty method, SIAM J. Numer Anal., Vol. 47(2), pp. 1126-1148, (2009). 3.N. Saito and G. Zhou, Analysis of the fictitious domain method with an $L^2$-penalty for elliptic problems, Numer. Funct. Anal. Optim. Vol. 36, (2015), pp. 501-527. 4.H. Suito, and H. Kawarada, Numerical simulation of spilled oil by fictitious domain method, Japan J. Indust. Appl. Math., Vol. 21, (2004), pp. 219-236.
• Classification : 65N85, 65N15
• Format : Talk at Waseda University
• Author(s) :
  • DEBASISH PRADHAN (Defence Institute of Advanced Technology, Pune - 411025, India)
  • Swapnil Kale (Defence Institute of Advanced Technology, Pune)

[00508] Imposing Neumann or Robin boundary conditions through a penalization method

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
• Type : Contributed Talk
• Abstract : We will present an n-dimensional extension of a penalization method previously suggested for Neumann or Robin boundary conditions. The existence and uniqueness are obtained using Droniou's approach for non-coercive linear elliptic problems, and we develop a boundary layer approach to establish the convergence of the penalization method. We present two-dimensional numerical examples using adequate schemes suitable for advection dominated problems, and outline the application of this method to population dynamics subject to climate change.
• Classification : 65N85, 65M85, 65N06, 65M06, 92D25
• Format : Talk at Waseda University
• Author(s) :
  • Bouchra Bensiali (École Centrale Casablanca)
  • Jacques Liandrat (École Centrale Marseille, I2M)

[01822] Domain decomposition for the Random Feature Method

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
• Type : Contributed Talk
• Abstract : The random feature method (RFM) is a framework for solving PDEs sharing the merits of both traditional and machine learning-based algorithms. The direct method for optimization shows a high accuracy but faces acute memory and time-consuming issues with the increase of the scale of the problem. We introduced the domain decomposition into RFM and build a distributed, low-communication, and high-parallelism framework which relieves the pressure of storage and improves solving efficiency significantly in RFM.
• Classification : 65N99, 65F20, 65-04, 65Y05
• Format : Talk at Waseda University
• Author(s) :
  • Yifei Sun (Soochow University)
  • Jingrun Chen (University of Science and Technology of China)
  • Weinan E (Peking University)

[00860] Probabilistic Domain Decomposition: Challenging Amdahl's curse on partial differential equations.

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
• Type : Contributed Talk
• Abstract : Probabilistic Domain Decomposition allows solving elliptic BVPs with remarkable scalability by taking advantage of probabilistic representations of BVPs. This representation is less convenient when dealing with non linear problems or even unknown in the case of the Helmholtz equation. However, these limitations can be circumvented by introducing some iterative schemes. In this presentation we aim to provide an insight on these algorithms alongside some proof of concept results obtained in FUGAKU and CINECA.
• Classification : 65N75, 68W10, 65N55
• Format : Online Talk on Zoom
• Author(s) :
  • Jorge Morón-Vidal (University Carlos III of Madrid)

[00547] Fictitious domain methods with finite elements and penalty over spread interface

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
• Type : Contributed Talk
• Abstract : We present a spread interface approach in fictitious domain methods to decipher the elliptic PDEs depicted over curved complex domains. In this approach, we employ the $L^2$ penalty for a small tubular neighborhood $\Omega_{\delta}$ near $\partial\Omega$ in $\mathrm{R}\backslash\Omega$ in place of the substantial penalty for the whole fictitious part $\mathrm{R}\backslash\Omega$. We achieve strong convergence results concerning the penalty parameter $\epsilon$ in addition to the a priori estimates and stability analysis. We implement the linear finite elements and acquire the expected error estimates. The comprehensive numerical investigations support the mathematical findings, which also anticipate optimal convergence regardless of the convexity and shape of the domain. Keywords: Fictitious domain methods, Elliptic problems, Curved domain, Error estimates, Uniform mesh. References: 1. S. Kale, and D. Pradhan, An augmented interface approach in fictitious domain methods, Comput. Math. with Appl., Vol. 125, pp. 238-247, (2022). 2. B. Maury, Numerical Analysis of a finite element/volume penalty method, SIAM J. Numer Anal., Vol. 47(2), (2009), pp. 1126-1148. 3. N. Saito and G. Zhou, Analysis of the fictitious domain method with an $L^2$-penalty for elliptic problems, Numer. Funct. Anal. Optim., Vol. 36, (2015), pp. 501-527. 4. S. Zhang, Analysis of finite element domain embedding methods for curved domains using uniform grids, SIAM J. Numer. Anal., Vol. 46(6), (2008), pp. 2843-2866.
• Classification : 65N85, 65N15, Numerical solutions to partial differential equations
• Format : Online Talk on Zoom
• Author(s) :
  • Swapnil Kale (Defence Institute of Advanced Technology, Pune)
  • Debasish Pradhan (Defence Institute of Advanced Technology, Pune)

MS [01170] High Performance Multigrid Methods for Large-Scale Applications

room : E708

• [03020] Improving AMG Strength of Connection
  • Format : Talk at Waseda University
  • Author(s) :
    • Wayne Mitchell (Lawrence Livermore National Laboratory)
  • Abstract : A crucial concept for algbraic multigrid (AMG) coarsening and interpolation is that of strength of connection (SoC) between degrees of freedom. The classical SoC measure is based on the relative sizes of entries in each row of the matrix and relies on heuristics that assume an M-matrix structure. This simple measure is cheap to evaluate and successful for many problems, but also relies on a user-defined strength threshold, which may need to be tuned for specific problems. In addition, the classical SoC measure can have difficulty identifying the proper strong connections for operators that are not M-matrices, particularly when there are both positive and negative off-diagonal entries in the same row. In this work, we examine low-cost techniques for building an auxiliary strength matrix that shares important properties with the original matrix operator while also being more amenable to the classical SoC measure. Applying classical SoC to this auxiliary strength matrix improves robustness of the SoC measure for a wider class of problems and across a wider range of strength thresholds.
• [03867] Performance improvements of algebraic multigrid algorithms on modern system architectures
  • Format : Talk at Waseda University
  • Author(s) :
    • Luc Berger-Vergiat (Sandia National Laboratories)
    • Jonathan Hu (Sandia National Laboratories)
    • Christian Glusa (Sandia National Laboratories)
    • Chris Siefert (Sandia National Laboratories)
  • Abstract : Multigrid methods are an important class of linear solvers and preconditioners for their high scalability on large computing systems. Implementing these algorithms on GPU based platforms remains a challenging task. In this talk we will discuss the current state of the MueLu package of Trilinos which provides algebraic multigrid methods on CPUs and GPUs and present results gathered on recent architectures.
• [05263] Monolithic Multigrid and Block Preconditioning for Magnetic Confinement Fusion Relevant Resistive MHD Simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Ohm (RIKEN Center for Computational Science)
    • John Shadid (Sandia National Laboratories)
    • Jesus Bonilla (Los Alamos National Lab)
    • Edward Phillips (Sandia National Laboratories)
    • Raymond Tuminaro (Sandia National Laboratories)
    • Jonathan Hu (Sandia National Laboratories)
    • Xian-Zhu Tang (Los Alamos National Lab)
    • Michael Crockatt (Sandia National Laboratories)
  • Abstract : A base-level mathematical basis for the continuum fluid modeling of dissipative plasma system is the resistive magnetohydrodynamic model. This model requires the solution of the governing partial differential equations (PDEs) describing conservation of mass, momentum, and thermal energy, along with various reduced forms of Maxwell’s equations for the electromagnetic fields. The resulting systems are characterized by strong nonlinear and nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that these interactions produce. These characteristics make scalable and efficient iterative solution, of the resulting poorly-conditioned discrete systems, extremely difficult. In this talk we utilize Drekar, a multi-physics simulation code built on top of the Trilinos framework, for the simulation of various resistive MHD problems. We consider the use of block preconditioners as well as monolithic multigrid for solving coupled physics block systems.
• [03865] Combined On/Off Node Performance Model for SPMV in Multigrid
  • Format : Talk at Waseda University
  • Author(s) :
    • Chris Siefert (Sandia National Laboratories)
  • Abstract : We propose combining traditional on-node memory-bandwidth based performance models (i.e., roofline) with inter-node performance models (i.e., ping-pong) to build a combined performance model to predict the performance of sparse matrix-vector products in the context of the Trilinos/MueLu algebraic multigrid software. We demonstrate the combined model on both CPU and GPU platforms and compare against actual Trilinos sparse matrix-vector product (SPMV) performance using Trilinos/MueLu.

MS [01077] Recent Advances on Spectral Methods and Applications

room : E709

• [03896] Barycentric Interpolation Based on Equilibrium Potential
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuhuang Xiang (Central South University )
    • Kelong Zhao (Central South University)
  • Abstract : A novel barycentric interpolation algorithm with specific exponential convergence rate is designed for analytic functions defined on the complex plane, with singularities located near the interpolation region, where the region is compact and can be disconnected or multiconnected. The core of the method is the efficient computation of the interpolation nodes and poles using discrete distributions that approximate the equilibrium logarithmic potential, achieved by solving a Symm's integral equation. It takes different strategies to distribute the poles for isolated singularities and branch points, respectively. In particular, if poles are not considered, it derives a polynomial interpolation with exponential convergence. Numerical experiments illustrate the superior performance of the proposed method.
• [04757] Log orthogonal functions in semi-infinite intervals: approximation results and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Sheng Chen (Beijing Normal University at Zhuhai)
  • Abstract : We construct two new classes of log orthogonal functions in semi-infinite intervals, log orthogonal functions (LOFs-II) and generalized log orthogonal functions (GLOFs-II), by applying a suitable log mapping to Laguerre polynomials. We develop a basic approximation theory for these new orthogonal functions and show that they can provide uniformly good exponential convergence rates for problems in semi-infinite intervals with slow decay at infinity. We apply them to solve several linear and nonlinear differential equations whose solutions decay algebraically or exponentially with very slow rates and present ample numerical results to show the effectiveness of the approximations by LOFs-II and GLOFs-II.
• [05466] A class of efficient spectral methods and error analysis for nonlinear Hamiltonian systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Waixiang Cao (Beijing Normal University )
    • Jing An (Guizhou Normal university)
    • Zhimin Zhimin Zhang (Wayne state University )
  • Abstract : In this talk, we investigate efficient numerical methods for nonlinear Hamiltonian systems. Three polynomial spectral methods (including spectral Galerkin, Petrov-Galerkin, and collocation methods) coupled with domain decomposition are presented and analyzed. Our main results include the energy and symplectic structure-preserving properties and error estimates. We prove that the spectral Petrov-Galerkin method preserves the energy exactly while both the spectral Gauss collocation and spectral Galerkin methods are energy conserving up to spectral accuracy. While it is well known that collocation at Gauss points preserves symplectic structure, we prove that the Petrov-Galerkin method preserves the symplectic structure up to a Gauss numerical quadrature error and the spectral Galerkin method preserves the symplectic structure up to spectral accuracy error. Finally, we show that all three methods converge exponentially, which makes it possible to simulate the long time behavior of the system. Numerical experiments indicate that our algorithms are efficient.

MS [00239] Shape and Topology Optimizations

room : E710

• [00244] PDEs for topology optimization considering manufacturability
  • Format : Talk at Waseda University
  • Author(s) :
    • Takayuki Yamada (The University of Tokyo)
  • Abstract : The topology optimization framework is to have the PDEs of the physical field of interest as constraints. In this study, we propose PDEs that expresses target manufacturability in order to consider it in a topology optimization framework.
• [00368] Topology optimization of supports for additive manufacturing with accessibility constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Grégoire Allaire (Ecole Polytechnique)
    • Martin Bihr (Safran)
    • Beniamin Bogosel (Ecole Polytechnique)
  • Abstract : This talk is concerned with an accessibility constraint, for shape and topology optimization of structures built by metallic additive manufacturing. Sacrificial supports are used to maintain a structure, during its building process. Removing them at the end is required but can be very difficult. Our work gives a new mathematical way to evaluate such an accessibility constraint, which is based on distance functions, solutions of eikonal equations. The main advantage is the possibility of computing shape derivatives of such a criterion with respect to both the structure and the support. We implement this accessibility constraint with the level-set method for topology optimization of structures.
• [03408] Dehomogenization in stress minimization problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Ferrer (CIMNE)
    • Grégoire Allaire (Ecole Polytechnique)
    • Perle Geoffroy-Donders (Ecole Polytechnique)
  • Abstract : In the last years, additive manufacturing has allowed to build lattice structures with impressive small length scale. This breakthrough has forced the topology optimization community to propose fast multi-scale topology optimization techniques. The dehomogenization method has recently shown very promising results in terms of performance and computational cost for compliance examples. In this work, we extend it to stress minimization problems and by considering singularities in the orientation field.
• [03530] The topological ligament: an approach based on thin tubular inhomogeneities
  • Format : Talk at Waseda University
  • Author(s) :
    • Charles Dapogny (CNRS & Université Grenoble Alpes)
  • Abstract : We propose a novel framework to calculate an approximate sensitivity of a functional depending on the domain with respect to the graft of a thin ligament. The resulting formulas are applied to: • The addition of a thin ligament to a structure in the course of a classical shape optimization process; • The optimization of the scaffold structure of a 3d printed structure; • A ``clever'' initialization process for the optimization of a truss structure.

MS [01168] Network based reduced-order models for forward and inverse PDE problems

room : E711

• [05171] REDUCED ORDER MODELING INVERSION OF MONOSTATIC DATA IN A MULTI-SCATTERING ENVIRONMENT
  • Format : Talk at Waseda University
  • Author(s) :
    • Mikhail Zaslavskiy (Southern Methodist University)
  • Abstract : We consider the reduced order model approach for inversion in the monostatic formulation targeting the synthetic aperture radar (SAR) data in the time domain. The monostatic data is given as a series of single input/single output (SISO) responses due to moving collocated sources and receivers, that is, the diagonal of the matrix-valued MIMO transfer matrix. The ROMs are constructed to match the data for each source-receiver pair separately, and these are used to construct internal solutions for the corresponding source using only data-driven Gramian. The data from different locations is then coupled via the approximate Lippman-Schwinger integral equation. Numerical experiments illustrating the performance of our approach will be provided.
• [05531] Waveform Inversion via Reduced Order Modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Mamonov (University of Houston)
    • Liliana Borcea (University of Michigan)
    • Josselin Garnier (Ecole Polytechnique)
    • Jorn Zimmerling (Uppsala University)
  • Abstract : We propose a novel approach to full waveform inversion (FWI), based on a data driven reduced order model (ROM) of the wave equation operator. The unknown medium is probed with pulses and the time domain pressure waveform data is recorded on an active array of sensors. The ROM is a projection of the wave equation operator on a subspace of wave equation solution snapshots. It can be constructed from the measured data via a nonlinear process and subsequently used for efficient velocity estimation. While the conventional FWI via nonlinear least-squares data fitting is challenging without low frequency information, and prone to getting stuck in local minima (cycle skipping effect), minimization of ROM misfit is behaved much better, even for a poor initial guess. For low-dimensional parametrizations of the unknown velocity the ROM misfit function is demonstrably close to convex. The proposed approach consistently outperforms conventional FWI in standard synthetic tests, as shown in the numerical experiments.
• [05544] Correlation-informed dictionary learning for imaging in complex media
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexei Novikov (Penn State University)
  • Abstract : We propose an approach for imaging in strongly scattering media that uses dictionary learning and connectivity information to estimate the sensing matrices in these media. It has two steps. The first step estimates, with high accuracy, the true Green’s function vectors using array data from multiple sparse sets of sources, whose locations and amplitudes are not known to us. This step yields a dictionary for wave propagation whose columns are those of the sensing matrix up to permutations. The second step orders these columns using Multi-Dimensional Scaling (MDS) with connectivity information derived from cross-correlations of the estimated Green’s function vectors. For these two steps to work together, we must combine data from large and small arrays. Through simulation experiments, we show that the proposed approach is robust and is able to provide high-resolution images.

MS [01190] Recent Advances in Modeling Complex Systems and Multiscale Problems in Mathematical Biology

room : E802

• [04951] A Spatially Averaged Model for Platelet Cohesion by vWF
  • Format : Talk at Waseda University
  • Author(s) :
    • Keshav Bhavesh Patel (University of Utah)
    • Aaron Fogelson (University of Utah)
  • Abstract : Platelet aggregation in high shear rate environments, in both healthy and stenotic arterioles, is mediated by Von Willebrand Factor (vWF). Computational fluid dynamics (CFD) models can study this process but are time-intensive and unable to explore sets of physiologically relevant parameters. In this talk, we will discuss a spatially averaged dynamical systems model of platelet aggregation. We quantify how vWF reduces aggregation time at high shear rates and determine essential parameters involved in aggregate formation.
• [04400] Investigating traveling waves in biophysical models of cardiac dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Stephanie Dodson (Colby College)
    • Timothy Lewis (University of California Davis)
  • Abstract : Regular cardiac function is characterized by coherent traveling waves of electrical activity that drive heart beats. When this process goes awry, the ensuing irregular rhythms are known as arrhythmias, which can be life-threatening. Hence, it is crucial to understand conditions that influence arrhythmia onset. In previous work, these traveling waves have been mathematically investigated in qualitative models of excitable media. We investigate traveling wave properties and arrhythmia onset using biophysically realistic models of cardiac dynamics.
• [05165] Modeling and Simulation of Mucin-like Polyelectrolyte Gels
  • Format : Talk at Waseda University
  • Author(s) :
    • Owen Lewis (University of New Mexico)
    • Jian Du (Florida Institute of Technology)
    • Aaron L Fogelson (University of Utah)
    • James P Keener (University of Utah)
  • Abstract : Volume phase transitions in polyeletrolyte gels play important roles in many biophysical processes such as mucus secretion, DNA packaging, nerve excitation, and cellular secretion. The swelling and deswelling of these charged polymer gels depend strongly on their ionic environment. In this paper, we present an extension to our previous two-fluid model for ion-binding-mediated gel swelling. The model treats the polyeletrolyte gel as a mixture of two continuum materials, the network and the solvent. We use mean-field arguments to derive the force densities that nano-scale species (ions and individual solvent particles) exert on these two species. The resulting model is suitable for the investigation of a large family of biologically relevant problems.
• [04304] Adaptive IMEX method for fractional PDE in viscoelastic fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Dipa Ghosh (IIIT DELHI)
  • Abstract : Fractional PDEs have emerged as a powerful tool for modelling multiphysics and multiscale processes in numerical simulations ranging from physics and biology to quantitative finance. We propose a novel family of time-asymptotically stable, implicit-explicit, adaptive time integration methods for the solution of the fractional advection-diffusion-reaction equations. The fractional diffusion equation (2D) and the incompressible, subdiffusive dynamics of the Rouse chain melts (α = 1/2) and the Zimm chain solution (α = 2/3) are used to assess the method.

MS [01218] Challenges in single-cell data science: theory and application

room : E804

• [03515] Functional annotation-driven unsupervised clustering for single-cell data
  • Format : Talk at Waseda University
  • Author(s) :
    • Keita Iida (Osaka University)
  • Abstract : Single-cell and spatial transcriptomics have enhanced our knowledge of molecular complexity in terms of gene expression heterogeneity in cell populations. However, conventional gene-based approaches may be insufficient in capturing such complexity as genes can interact with each other to regulate a number of biological functions. Here, we introduce ASURAT, a computational tool for simultaneous clustering and functional annotation of single-cell and spatial transcriptomes in terms of cell type, disease, biological process, and signaling pathway activity.
• [03908] Modelling cell differentiation: from psuedo-time to energy landscape
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jifan Shi (Fudan University)
  • Abstract : Interactions between genes determine cell development and differentiation. We first introduce pseudo-time of cells, which is also known as pluripotency. Next, we will focus on models from the perspective of energy landscape. We propose an energy landscape decomposition theory for cell differentiation with proliferation effect. Two energy landscapes collectively contribute to the establishment of non-equilibrium steady differentiation. We will also demonstrate feasible numerical methods and several interesting applications.
• [03682] Integrating data and dynamics in scRNA-seq data analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiejun Li (Peking University)
  • Abstract : In this talk, I will review some research progress of my group on the scRNA-seq data analysis in recent years. I will mainly focus on the integration of data and dynamics approach in this area, which includes the theory and algorithms for the RNA velocity, dynamical approach for the scRNA-seq data with temporal information, and deep learning type methods. This is a series of joint works with Prof. Luonan Chen, Qing Nie, and Dr. Peijie Zhou, Jifan Shi, Yichong Wu, Qiangwei Peng, et al.

contributed talk: CT132

room : E812

[01027] A Discussion on Numerical Methods to Solve Structural Engineering Problems

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E812
• Type : Contributed Talk
• Abstract : A number of numerical methods are developed by researchers to solve the linear/nonlinear, ordinary differential equations (ODEs) / partial differential equations (PDEs) developed for structural analysis such as vibration/bending/buckling/wave-propagation analysis in plates. The present talk is focused on a discussion of numerical approaches and their accuracy and convergence for plate vibrations i.e., linear PDE which can be extended as semi-analytic approaches to solving the nonlinear PDE during critical vibration analysis of plates.
• Classification : 74H15, 74S25, 74G15
• Format : Talk at Waseda University
• Author(s) :
  • Rahul Saini (H N B Garhwal Central University, Srinagar, Uttarakhand, India )

[00751] Crack Loading and Growth Analyses with the Virtual Element Method

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E812
• Type : Contributed Talk
• Abstract : The virtual element method is a modern discretization scheme for solving boundary value problems on polytopal meshes, sparing the explicit knowledge of element shape functions. In the context of numerical fracture mechanics, crack tip loading analyses and in particular crack growth simulations benefit from its ability of handling arbitrary complex meshes straightforwardly. This work aims to discuss challenges and opportunities of implementing concepts of fracture mechanics in the context of the virtual element method.
• Classification : 74R10, 74S05, 74A45, Numerical Fracture Mechanics
• Format : Talk at Waseda University
• Author(s) :
  • Kevin Schmitz (University of Kassel)
  • Andreas Ricoeur (University of Kassel)

[01067] Stoneley wave propagation at the interface between two initially stressed medium with interface energy

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E812
• Type : Contributed Talk
• Abstract : The present study investigates the propagation of Stoneley waves at interface of two distinct imperfectly bonded solid half-spaces considering strain and kinetic energies localized at interface. Gurtin−Murdoch (1975) and Eremeyev (2016) approaches are used to derive interface strain energy density, stress tensor, kinetic energy density accounting for non-perfect interface. Comparative analysis of dispersion curves is done numerically and presented through graphs. The findings have applications in geosciences for non-destructive characterization of thin inter-phases between solids.
• Classification : 74H10, 74B05
• Format : Online Talk on Zoom
• Author(s) :
  • Arindam Nath (Department of Mathematics, School of Sciences, NIT Andhra Pradesh, India)
  • Sudarshan Dhua (Department of Mathematics, School of Sciences, NIT Andhra Pradesh, India)

[00026] STRESS ANALYSIS OF AN EDGE CRACK UNDER TIME-HARMONIC WAVE DISTURBANCE

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E812
• Type : Contributed Talk
• Abstract : This article determines a stress intensity factor (SIF) at the tip of an edge crack in two considered models. Problem-1 is an orthotropic strip of a finite thickness bonded by an orthotropic half-plane, and problem-2 is an orthotropic vertical semi-infinite strip. Edge cracks have been invaded perpendicularly by time-harmonic elastic waves. The system has been solved by using Fourier transform and Schmidt method to find the approximate analytical expression for the SIF. The variations of in plane normalized SIF for the different crack lengths and thickness were depicted graphically (2D) for different particular cases.
• Classification : 74R99, 42A38, 74J15
• Format : Online Talk on Zoom
• Author(s) :
  • Neha Trivedi (Indian Institute of Technology (BHU) Varanasi, India)
  • Neha Trivedi (Indian Institute of Technology (BHU) Varanasi, India)

contributed talk: CT134

room : E817

[02528] Propagation of Rayleigh-like surface waves in multilayered nonlocal elastic media

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E817
• Type : Contributed Talk
• Abstract : Haskell matrix method is employed to derive the dispersion relation of Rayleigh-like surface waves propagating through a multilayered nonlocal elastic solid half-space. This dispersion relation is reduced for a 2-layered model to discuss the characteristics of phase speed of Rayleigh-like wave. For specific model, the effect of nonlocality on Rayleigh-like waves for 2- and 3-layered models has been depicted graphically. The particle motion remains elliptical, and influenced by the presence of nonlocality for 2-layered model.
• Classification : 74J15
• Format : Talk at Waseda University
• Author(s) :
  • Aarti Khurana (Panjab University Chandigarh)

[00637] Wave Scattering from Layers of Random Particulate Materials

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E817
• Type : Contributed Talk
• Abstract : To characterise any material with sound waves, the wave will propagate through several layers before reaching the material. If that material is a random particulate material, then to date there is no simple model to deal with the layers. In this talk we show how extending the quasi-crystalline approximation (\text{(a technique from statistical physics)}) to layers leads to clear and simple models which separate the influence of the microstructure from the material geometry.
• Classification : 74J20, 82D30, 45B05
• Format : Talk at Waseda University
• Author(s) :
  • Paulo Sergio Piva (The University of Sheffield)
  • Kevish Napal (The University of Sheffield)
  • Artur Gower (The University of Sheffield)

[00844] Evidence of Multiple Effective Wavenumbers in Isotropic Random Particulate Materials

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E817
• Type : Contributed Talk
• Abstract : In random particulate materials, it is generally assumed that if we average over all particle configurations, the averaged wave field satisfies the wave equation with a unique effective wavenumber k∗. As the medium is homogeneous and isotropic - because the particles have no specific orientation or direction - it is reasonable to assume the presence of one effective wavenumber. However, recent work theoretically predicted the existence of at least two (complex) effective wavenumbers for one fixed frequency. A phenomenon normally observed only in anisotropic media. Our goal is to find clear evidence of these wavenumbers using the Monte-Carlo approach and show how they influence the total field.
• Classification : 74J20, 74A40, 78A48, 82D30, 82M31, wave scattering, multiple scattering, random media, ensemble averaging, Monte Carlo methods
• Format : Talk at Waseda University
• Author(s) :
  • Aristeidis Karnezis (The University of Sheffield)
  • Artur Lewis Gower (The University of Sheffield)

[02548] Rayleigh-like waves in coated elastic half-space containing voids

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E817
• Type : Contributed Talk
• Abstract : Secular equation for Rayleigh-like surface waves propagating through an isotropic elastic media containing voids coated with a thin isotropic elastic layer with voids is derived. The layer and the half-space are in welded contact. The effective boundary condition method has been employed to obtain an approximate secular equation of second order in terms of the dimensionless thickness of layer. An explicit formula for Rayleigh-like wave speed is derived and the results have been plotted graphically.
• Classification : 74J15
• Format : Online Talk on Zoom
• Author(s) :
  • Savkirat Kaur (Dev Samaj College for Women, Chandigarh)

[00855] Mathematical modelling of edge wave on a functionally graded thermo-poro-elastic plate

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @E817
• Type : Contributed Talk
• Abstract : An analysis of flexural edge waves propagating in a thermally affected poroelastic plate supported by a Pasternak foundation is presented. The Kirchhoff plate theory and Moore-Gibson-Thomson (MGT) thermos elasticity theory are applied to study the displacement field of the plate and temperature distribution on edge wave, respectively. There are seven different porosity models considered to compare the edge wave behavior in different porous structures. The grid dispersion is optimized by applying the FDM to the wave equation. The effects of porosity, temperature, elastic foundation, cutoff-frequency, and wave frequency are investigated numerically.
• Classification : 74J20, 35L05, 35L53, 86-10, 74S20
• Author(s) :
  • Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)
  • Rahul Som (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)
  • Tanisha Kumari (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)

MS [02515] Novel deep learning methodologies in Industrial and Applied Mathematics

room : E818

• [05354] AI Lifecycle Zero-touch Orchestration within the Edge-to-Cloud Continuum for Industry 5.0
  • Format : Talk at Waseda University
  • Author(s) :
    • Marta Barroso Barroso (Barcelona Supercomputing Center)
  • Abstract : AI is one of the biggest megatrends towards the 5th industrial revolution. Although these technologies promise business sustainability as well as product and process quality, it seems that the ever-changing market demands and the complexity of technologies, impede broad application and reuse of Artificial intelligence (AI) models across the industry. KnowlEdge is an European project funded by the Horizon 2020 (H2020) that aims to develop of a new gene-ration of AI methods, systems, and data management infrastructure in order to break the entry barriers for these tech-nologies and unleash its full potential. In particular, knowlEdge project converges techniques from multiple computing areas, including AI , distributed data analytics, IoT, software engineering, edge and Cloud technologi-es into a unified software architecture. The outcomes of the project not only enable the automated extraction and utilization of data co-ming from multiple and geographically dispersed sources, it also provides a way of reusing and sharing AI models in an (semi-)automated way in particular companies that are only able to perform the execution of models rather than the training themselves.

MS [02447] Advances in Diesel Engine Design and Control for Industry 4.0

room : E819

• [04704] An Intelligent Control System for a Diesel Engine l
  • Author(s) :
    • Amna Batool Syeda (Mphil scholar, Center For Advanced Studies in Pure and Applied Mathematics, BZU Multan, Pakistan)
    • Khalid Saifullah Syed (Director of Center for Advanced Studies in Pure and Applied Mathematics, BZU Multan, Pakistan )
  • Abstract : We consider the design of an intelligent, efficient, optimal, robust and hybrid control system based on the adaptive neuro-fuzzy inference system and PID controllers. The system will control air, fuel and EGR for optimal performance and minimum emissions. The system design may involve deep learning of recurrent neural network having several hidden layers with LSTM layer to make the system efficient and more accurate. Optimal control may be incorporated using quadratic programming / genetic algorithm.
• [04750] In-Cylinder Combustion Investigation Against Some Injection Characteristics
  • Author(s) :
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
    • Anam Ali (CASPAM BZU Pakistan)
  • Abstract : This study investigates the impact of fuel injection timing and spray angle on combustion characteristics of a heavy-duty diesel engine. CFD simulations are carried out by employing appropriate models to represent different physical and chemical processes. These parameters have significant role in engine design for enhanced combustion efficiency and engine performance. Late injection results into relatively smooth burning rates and considerably lower temperature and pressure peaks without significantly compromising the combustion quality and engine power.
• [04780] In-Cylinder Combustion Investigation Against Some Injection Characteristics
  • Author(s) :
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
    • Anam Ali (CASPAM BZU Pakistan)
  • Abstract : This study investigates the impact of fuel injection timing and spray angle on combustion characteristics of a heavy-duty diesel engine. CFD simulations are carried out by employing appropriate models to represent different physical and chemical processes. These parameters have significant role in engine design for enhanced combustion efficiency and engine performance. Late injection results into relatively smooth burning rates and considerably lower temperature and pressure peaks without significantly compromising the combustion quality and engine power.
• [04965] Intake Plenum Design Improvement for a 12-Cylinder Diesel Engine
  • Author(s) :
    • Ms Saima Zainab (The Women University, Multan )
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
  • Abstract : The air flow in engine plenum is complex due to multidimensionality and transient nature of engine operation. This study describes the design modification of intake plenum geometry of a V12 diesel engine and analyses the effects on flow parameters. The original design was found to have strict limits, making it difficult to enhance engine efficiency. However, the modified design is more energy efficient, with greater volumetric efficiency, increased mass flow rate, and turbulent kinetic energy.

contributed talk: CT143

room : D101

[02405] STABILITY OF NON-ISOTHERMAL POISEUILLE FLOW IN FLUID OVERLYING POROUS DOMAIN

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D101
• Type : Contributed Talk
• Abstract : The linear stability analysis of thermal convection of Poiseuille flow in an anisotropic and inhomogeneous porous domain underlying fluid domain is investigated. The impact of depth ratio, anisotropy, inhomogeneity, Darcy number, Reynolds number and Prandtl number is inspected. An increase((decrease)) in anisotropy((inhomogeneity)) parameter follows unimodal((porous)) to bimodal((fluid and porous)) characteristic of neutral curves. Energy budget analysis is carried out to classify type of instability. Secondary flow patterns are analysed to validate the least stable mode.
• Classification : 76E17, 76E06, 76T99, 80A19, 76S05
• Format : Talk at Waseda University
• Author(s) :
  • Anjali Anjali (Department of Mathematics, Indian Institute of Technology Roorkee)
  • Premananda Bera (Department of Mathematics, Indian Institute of Technology Roorkee)
  • Arshan Khan (Department of Mathematics, Indian Institute of Technology Roorkee)

[00826] Saffman-Taylor fingers selection mechanism in non-newtonian fluids

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D101
• Type : Contributed Talk
• Abstract : We present an analytical approach, based on the Wentzel-Kramers-Brillouin technique, to predict the finger width of a simple fluid driving a non-Newtonian, power-law fluid. We find that in the limit of small surface tension, (\nu), the relation between the dimensionless (\nu), viscosity and finger width, (\Lambda), has the form: (\Lambda \sim \frac{1}{2} - \mathrm{O}(\nu ^ {-1/2})) for shear thinning case, and (\Lambda \sim \frac{1}{2} + \mathrm{O}(\nu^{2/(4-n)})) for shear thickening case. A detailed comparison is provided.
• Classification : 76E17
• Format : Talk at Waseda University
• Author(s) :
  • Diksha Bansal (IIIT Delhi)

[02409] Effect of Permeability on Couette Flow in Fluid-Porous System

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D101
• Type : Contributed Talk
• Abstract : A horizontal fluid layer overlying a porous layer is considered in which the plane Couette flow is induced due to uniform movement of upper plate and convection arises due to maintenance of temperature difference between the upper and lower plate. Fluid considered is Newtonian and incompressible which satisfies Boussinesq approximation. The porous layer is modelled by Darcy's law. The classical linear stability analysis is implemented to study the impact of media permeability for heavy oils.
• Classification : 76E06, 76E17, 76T99, 76F10, 76S05
• Format : Talk at Waseda University
• Author(s) :
  • Nandita Barman (Department of Mathematics)
  • Premananda Bera (Department of Mathematics)

[01033] Convective instabilities in vertical porous media

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D101
• Type : Contributed Talk
• Abstract : Stability of natural convection in vertical porous slabs is of significant importance due to its applications in several natural and industrial settings – building insulation involving an unventilated air gap and for breathing walls is one of them. In this talk, we will discuss natural convection in a vertical porous slab with a differential temperature between the vertical walls. We show that a temperature-dependent thermal diffusivity/dynamic viscosity plays an important on the convective stability.
• Classification : 76E06, 76S99, 76R50
• Format : Talk at Waseda University
• Author(s) :
  • Satyajit Pramanik (Indian Institute of Technology Guwahati)

MS [02567] Data-driven Computational Mechanics for Structures, Structural Dynamics, and Materials

room : D102

• [03428] Machine learning-based methods for the nonlinear structural analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Sangmin Lee (Seoul National University)
    • SiHun Lee (Seoul National University)
    • Haeseong Cho (Jeonbuk National University)
    • SANGJOON SHIN (Seoul National University)
  • Abstract : Nonlinear structural analysis plays an important role in many fields of engineering, but it requires substantial computational resources to conduct repetitive high-fidelity simulation. In this study, a machine learning based non-intrusive model order reduction (MOR) is proposed for the parameterized structural analysis in which the geometric nonlinearities are involved. For this purpose, the proper orthogonal decomposition (POD) is carried out to gather the reduced bases from the full-order snapshot matrix. Then, the modified nouveau variational autoencoder (mNVAE) is conducted to interpolate such POD coefficients.
• [04471] Hypernetwork-based low-rank neural ordinary differential equations for solving parameterized partial differential equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kookjin Lee (Arizona State University)
    • Youngsoo Choi (Lawrence Livermore National Laboratory)
    • Guangting Yu (Arizona State University)
  • Abstract : In this work, we propose a hypernetwork-based reduced order modeling approach for solving parameterized partial differential equations. The hypernetwork is trained to produce model parameters of latent dynamics models, which governs the evolution of reduced states in a low-dimensional manifold. We parameterize the latent dynamics as neural ordinary differential equations (NODEs). To improve the hypernetwork’s inference capability, we develop a variant of NODEs, low-rank NODEs, where the model parameters are approximated in low-rank.
• [05408] An augmented Lagrangian method to accelerate constrained optimization using hyperreduction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tianshu Wen (University of Notre Dame)
    • Matthew Zahr (University of Notre Dame)
  • Abstract : We present a numerical method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems of equations using an augmented Lagrangian framework. A globally convergent, hyperreduced trust-region framework is embedded in the proposed framework to accelerate the optimization process in each major iteration. The trust-region framework constructs a hyperreduction model via empirical quadrature procedure on-the-fly, which completely avoids an offline training phase.

MS [02426] Mathematics of turbulent transport and coherent structures

room : D401

• [04552] Optimisation of horizontal periodicity in steady Rayleigh–Bénard convection
  • Format : Talk at Waseda University
  • Author(s) :
    • Shingo Motoki (Osaka University)
    • Genta Kawahara (Osaka University)
    • Masaki Shimizu (Osaka University)
  • Abstract : Using a Newton–Krylov iteration, we have investigated steady solutions to the Boussinesq equations for Rayleigh–Bénard convection in a square periodic domain between horizontal walls with a constant temperature difference. We have found that a family of three-dimensional steady solutions with an optimal horizontal periodicity achieves higher wall-to-wall heat flux than those of two-dimensional solutions and turbulent states and exhibits the classical scaling commonly observed in convective turbulence.
• [04406] Chaos and unstable periodic orbits in subcritical Taylor-Couette flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Baoying Wang (Universitat Politècnica de Catalunya)
    • Roger Ayats (Institute of Science and Technology Austria (ISTA))
    • Kengo Deguchi (Monash University)
    • Alvaro Meseguer (Universitat Politècnica de Catalunya)
    • Fernando Mellibovsky (Universitat Politècnica de Catalunya)
  • Abstract : Although spectral approximation of turbulence typically requires a large number of modes, for relatively low Reynolds numbers the turbulent attractor lies on a low-dimensional manifold in phase space. The most extreme case is when the main features of the chaotic attractor can be quantified by a one-dimensional map on Poincaré section. We find this can indeed happen in subcritical Taylor-Couette flow, which should offer an important test case for connecting turbulence and periodic orbit analysis.
• [03988] The state-space structure of wall turbulence at high Reynolds numbers: a reduced-order model perspective
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthew McCormack (University of Edinburgh)
    • André V. G. Cavalieri (Instituto Tecnológico de Aeronáutica)
    • Yongyun Hwang (Imperial College London)
  • Abstract : Invariant solutions to the Navier-Stokes equations have been viewed to form the state-space skeleton of turbulence at low Reynolds numbers. However, as Reynolds number is increased, most of these invariant solutions currently computable were recently shown to be able to depict only partial processes of turbulence, and they neither resemble full-scale turbulence statistically nor dynamically. In this talk, I will present our recent efforts to understand the state-space structure of turbulence at moderately high Reynolds numbers in terms of invariant solutions utilising a reliable and robust reduced-order model.
• [03140] Coherent structures and the direct cascade in two-dimensional turbulence
  • Format : Talk at Waseda University
  • Author(s) :
    • Roman O Grigoriev (Georgia Institute of Technology)
    • Mateo Reynoso (Georgia Institute of Technology)
    • Dmitriy Zhigunov (Georgia Institute of Technology)
  • Abstract : We describe a mechanism of the direct cascade in 2D turbulence which explains when the predictions of the classical Kraichnan-Leith-Batchelor theory hold, when deviations are found, and what causes these deviations. Coherent structures of two types play a key role in our theory: the first type describes the dynamics of the largest scales accessible to the flow, while the second type describes the dynamics of small-scale filamentary vorticity stretched and folded by the large-scale flow.

MS [01003] Mathematical Modeling and Simulation in Land-Ocean Transition Zones

room : D402

• [05525] Shape Optimization of Incompressible Navier-Stokes flows with Shape Gradients
  • Format : Talk at Waseda University
  • Author(s) :
    • Shengfeng Zhu (East China Normal University)
    • Jiajie Li (East China Normal University)
  • Abstract : Shape design of fluid flows has applications in engineering. We consider shape optimization of incompressible flows with shape gradients. Traditional boundary shape gradients have high smoothness requirement on the boundary and is less general than the distributed shape gradient. We consider numerically finite element approximations to the distributed and boundary corrected shape gradients. A prior error estimates are shown. Numerical results are reported to verify theory and show effectiveness of shape gradient algorithms.
• [05546] Causal AI Ocean Learning and Prediction
  • Author(s) :
    • X. San Liang (Fudan University)
  • Abstract : Ocean-atmosphere forecasting is faced with many challenges such as open boundary condition specification, unresolved process parameterization, unknown physics modeling, etc. Even if all these are fixed, a more challenging issue that ever exists is the unpredictability intrinsically embedded in chaotic systems. The recent fast development of AI seems to be promising for a partial solution to these problems. But AI is also faced with the problem of interpretability. Due to the black-box nature, it is difficult for one to decide whether a forecast is acceptable or not. In this presentation, I will show how interpretability will be enhanced for AI algorithms with the aid of a recently developed causality analysis which has been rigorously established from first principles during the past 18 years (e.g., Liang, Information flow and causality as rigorous physical notions ab initio. Phys Rev E 94:052201, 2016). In the oceanographic context, this is easily understood as the tracing of predictability sources to make the maximal usage of information. Also the quantitative nature of the causality analysis allows for an adjustment of the neural network to remove spurious correlations toward an optimal performance. Demonstrated here will be an operational forecast of the surface circulation of a region in the South China Sea, and a decadal forecast of the Central Pacific-type El Niño.
• [03963] Simulation of Droplet-laden Turbulent Channel flow by LBM and Phase field method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dingyi Pan (Zhejiang University)
    • Yuqing Lin (Zhejiang University)
  • Abstract : Direct numerical simulation of droplet-laden turbulent channel flow is studied by coupled lattice Boltzmann method and phase field modeling with Cahn-Hilliard (CH) equation. The weighted essentially non-oscillatory (WENO) scheme is applied for the discretization of CH equation. The simulated friction Reynolds number is up to 180, and the mass conservation of droplet phase is well fulfilled. The results show that the existence of droplets contribute to the drag reduction of the turbulent channel flow.

MS [00869] Theory, numerics and data driven methods for fluids

room : D403

• [01798] Wellposedness of stochastic PDEs arising in fluid dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Krutika Tawri (University of California Berkeley)
  • Abstract : Stochastic forcing terms are commonly added to the governing equations to account for numerical and physical uncertainties in applications. In this talk, we will discuss recent results and new techniques in the analysis of stochastic models, arising in fluid dynamics.
• [03526] Error estimates for deep learning methods in fluid dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Jing Tian (Towson university)
    • Animikh Biswas (University of Maryland, Baltimore County)
    • Suleyman Ulusoy (American University of Ras Al Khaimah)
  • Abstract : In this talk, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier–Stokes equations. In particular, we obtain explicit error estimates for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.
• [01243] Reconstructing external driving forces in incompressible flow via low-mode observation
  • Format : Talk at Waseda University
  • Author(s) :
    • Vincent R Martinez (CUNY Hunter College & Graduate Center)
  • Abstract : In this talk, we describe a "spectral filtering" algorithm that reconstructs an apriori unknown external force in the 2D Navier-Stokes equations. This approach was developed by Celik, Olson, and Titi (2019) in order to recover the unobserved high-mode motion of the flow provided that sufficiently many low-modes are observed and that the external force is known. It is shown how this idea can be used to simultaneously recover both the unobserved motion and unknown forcing.
• [04541] Analysis of a rotationally constrained convection model
  • Format : Talk at Waseda University
  • Author(s) :
    • Yanqiu Guo (Florida International University)
  • Abstract : This talk is about the analysis of an asymptotically reduced system for rotationally constrained convection. This reduced system was derived from the 3D Boussinesq equations using the asymptotic theory. On the one hand, the nonlinear convection term has a reduced complexity since it contains only the horizontal gradient. On the other hand, the regularizing viscosity acts in the horizontal direction only. I will present some of our results motivated by the global regularity problem.

MS [00932] Some recent advances on time-modulated metamaterials

room : D404

MS [00877] Mathematical and Computational Methods for Topological Materials

room : D405

• [05595] Unfitted Computation of edge modes in photonic graphene
  • Author(s) :
    • Hailong Guo (The University of Melbourne )
    • Yi Zhu (Tsinghua University)
    • Xu Yang (University of California Santa Barbara)
  • Abstract : Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. In this paper, we propose a new unfitted Nitsche's method of computing edge modes in photonic graphene with some defect. The unique feather of the methods is that they can arbitrary handle high contrast with geometric unfitted meshes. We establish the optimal convergence of methods.

MS [02570] Parameter Estimation, Targeted Observation, and Data Assimilation in Coupled Systems

room : D407

• [03616] A novel approach of data assimilation: application to ENSO diversity predictions
  • Author(s) :
    • Wansuo Duan (Institute of Atmospheric Physics, Chinese Academy of Sciences)
  • Abstract : The talk introduces an approach of data assimilation (DA) entitled nonlinear forcing singular vector (NFSV) to neutralize combined effect of initial and model errors. The approach is applied to an intermediate-complexity ENSO model and reproduces the conditions of the emergence of both EP- and CP-El Niño events, eventually distinguishing El Niño types at two-season lead time in predictions. The NFSV-DA is a useful DA approach for offsetting initial and model error effects for ENSO predictions.
• [04195] Exploring data-driven sparse sensor placement for determining rain gauge locations
  • Author(s) :
    • Daiya Shiojiri (Chiba University)
    • Eiryo Kawakami (Chiba University)
    • Shunji Kotsuki (Chiba University)
  • Abstract : This study explores the data-driven sparse sensor placement (SSP) to determine rain gauge locations for efficiently estimating the spatiotemporal interpolation of precipitation. The SSP determines the rain gauge locations using dominant modes extracted from spatiotemporal precipitation data over a training period. Through evaluations using radar-analyzed precipitation, we found that the SSP-based rain gauges enable to provide more accurate precipitation fields compared to the current operational rain gauge network in Japan.
• [04176] The Conditional Nonlinear Optimal Perturbation method and it's application to the targeting observation for tropical cyclones
  • Author(s) :
    • Xiaohao Qin (LASG, Institute of Atmospheric Physics, Chinese Academy of Science)
    • Mu Mu (Fudan University)
    • Feifan Zhou (LACS, Institute of Atmospheric Physics, Chinese Academy of Science)
    • Boyu Chen (Chinese Meteorology Administration)
    • Jie Feng (Fudan University)
  • Abstract : To augment the routine observational network for better forecasts of tropical cyclones (TCs), targeting observations (TOs) have developed rapidly during the past several decades over China. In consequence, TC forecasts have benefitted a lot from these field campaigns. In this talk, research work and field campaigns of TOs are briefly overviewed. After that, we introduce a method named the conditional nonlinear optimal perturbation (CNOP), which is utilized to identify those areas should be additionally observed with priority in TOs. Using some examples, we explain how to use the CNOP method in mathematics, its impacts on improving TC forecasts, and its latest application in real time operational forecasts.
• [04998] Towards targeted observations of meteorological state for improving PM2.5 forecasts
  • Author(s) :
    • Lichao Yang (Institute of Atmospheric Physics, Chinese Academy of Sciences)
    • Wansuo Duan (Institute of Atmospheric Physics, Chinese Academy of Sciences)
  • Abstract : An advanced approach of conditional non-linear optimal perturbation (CNOP) was introduced to identify the sensitive area for targeted observations of meteorological fields associated with PM2.5 concentration forecasts of a heavy haze event that occurred in the Beijing–Tianjin–Hebei (BTH) region, China. We show numerically and physically that preferentially deploying additional observations in the sensitive areas identified by the CNOP approach can greatly improve the forecasting skill of PM2.5 forecasts.

MS [00891] Derivative-Free Optimization Theory, Methods, and Software

room : D501

• [01570] PRIMA: Reference Implementation for Powell's methods with Modernization and Amelioration
  • Format : Talk at Waseda University
  • Author(s) :
    • Zaikun Zhang (The Hong Kong Polytechnic University)
  • Abstract : Powell developed five widely used DFO solvers, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. They were coded in Fortran 77 with a unique style, which poses a significant obstacle to maintaining, exploiting, or extending them. PRIMA is a project providing the reference implementation of these solvers in modern languages. We will present the current stage of PRIMA, including the bugs we have spotted in the Fortran 77 code and the improvements we have achieved.

MS [02376] Recent Advances in Dynamic Games and Control Theory and Their Connection to Data Science

room : D502

• [03245] Stabilizability of Nash equilibrium
  • Format : Talk at Waseda University
  • Author(s) :
    • Renren Zhang (Shandong University)
  • Abstract : We investigate the stabilizability of Nash equilibrium of the game-based control system (GBCS), which was first introduced to model control systems whose structures involve rational agents. The stabilizability problem is whether the regulator can stabilize the system by regulating the Nash equilibrium formed by the agents. Some explicit conditions on the stabilizability of GBCS are given, by investigating the solvability relationship between the associated algebraic Riccati equations (AREs) and the algebraic Riccati inequalities (ARIs).
• [04475] Cooperation and Cost Sharing Problems in Supply Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Sanjith Gopalakrishnan (McGill University)
    • Sriram Sankaranarayanan (Indian Institute of Management, Ahmedabad)
  • Abstract : Across several contexts such as supply chain security or traceability, costly actions by firms can yield payoffs to other firms in the network. Such positive externalities imply network-wide cooperative strategies can yield improvements over firms independently choosing individually-rational actions. However, cooperation can be hindered by disagreements over cost-sharing arrangements. In this talk, we review two recent applications and develop a general framework to identify implementable cost sharing mechanisms that can sustain network-wide cooperative actions.
• [03268] Hodge allocation for cooperative rewards
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tongseok Lim (Purdue University)
  • Abstract : Lloyd Shapley's cooperative value allocation theory is a central concept in game theory that is widely used in various fields to allocate resources and assess individual contributions. The Shapley formula and axioms that characterize it form the foundation of the theory. Shapley value can be assigned only when all players are assumed to eventually form the grand coalition. We discuss how to extend Shapley's theory to account for value allocation in every partial coalition state.

MS [01145] High dimensional recent computational approaches in finance and control

room : D505

• [03993] Statistical Learning with Sublinear Regret of Propagator Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Yufei Zhang (London School of Economics and Political Science)
    • Eyal Neuman (Imperial College London)
  • Abstract : We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We characterize the trader’s performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for non-parametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. These kernel estimation methods extend existing methods from the area of Tikhonov regularisation for inverse problems and are of independent interest. The bound on the regret in the exploitation phase is obtained by deriving stability results for the optimizer and value function of the associated class of infinite-dimensional stochastic control problems.
• [04781] ROBUST UTILITY OPTIMIZATION VIA A GAN APPROACH
  • Format : Talk at Waseda University
  • Author(s) :
    • Hanna Wutte (ETH Zurich)
    • Florian Krach (ETH Zurich)
    • Josef Teichmann (ETH Zurich)
  • Abstract : We study the robust expected utility maximization problem. In this problem, an agent wants to maximize the expected utility of final wealth $X_T^\pi$ under her trading strategy $\pi$ in an uncertain market environment that chooses the worst case market measure $P$ for the given trading strategy, i.e., $\sup_{\pi} \inf_{P} \mathbb{E}_{P}[U (X^\pi_T )]$. This problem can be understood as a two-player zero-sum game between the agent and the market. We restrict our attention to markets consisting of one risk-free and $d$ risky assets $S$. Risky assets $S$ are given by Itô processes, where the drift $\mu$ and diffusion $\sigma$ are chosen by the market player out of a set of admissible candidate functions. To make this tractable, we consider a penalized version of the robust utility optimization problem, where the market model can choose any such continuous functions, but is penalized for deviating from a reference market model via a penalty functional $F$ . We suggest an algorithm to solve this problem using two recurrent neural networks (RNNs) with parameters $\theta$ and $\omega$, one for the agent and one for the market, respectively. Those RNNs are trained iteratively by competing in the zero-sum game \begin{equation}\sup_{\theta}\inf_{\omega}\mathbb{E}[U(X^{\pi_\theta,\mu_\omega,\sigma_\omega}_T) + F (\mu_\omega,\sigma_\omega ,S)] .\end{equation} On a high level, this can be interpreted as a generative adversarial network (GAN) approach, where the generator produces a trading strategy $\pi_\theta$ and the adversarial discriminator tries to find the worst case market model $(\mu_\omega,\sigma_\omega)$. Importantly, the use of RNNs allows both players to learn non-Markovian strategies. The utility function $U$ as well as the penalty function $F$ can be chosen freely. We examine several set-ups to empirically show the quality of our proposed algorithm. At first, we consider log-utility in a friction-less market and instantaneous penalization of the market parameters. In this case, an analytic solution is known to exist which is replicated by our trained model. When introducing friction to the market, or when using other utility functions or path-dependent penalties, analytic solutions no longer exist. Therefore, we construct new evaluation metrics and we observe that our trained model achieves convincing results. This is joint work with Florian Krach and Josef Teichmann.
• [05102] Deep Learning in Portfolio Selection under Market Frictions
  • Format : Talk at Waseda University
  • Author(s) :
    • Chen Yang (The Chinese University of Hong Kong)
  • Abstract : Incorporating market frictions in portfolio selection problems often leads to high-dimensionality even when the number of stocks is low, which makes it challenging for traditional grid-based numerical method. In this talk, we explore the application of deep learning method in portfolio selection problems with market frictions such as price impact, transaction cost, and capital gain taxes, and discuss the potential challenges.
• [05342] Machine Learning Surrogates for Parametric and Adaptive Optimal Execution
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Ludkovski (U California at Santa Barbara)
    • Tao Chen (U of Michigan)
    • Moritz Voss (U California at Los Angeles)
  • Abstract : We investigate optimal order execution with dynamic parametric uncertainty. Our base model features discrete time, stochastic transient price impact generalizing Obizhaeva and Wang (2013). We first consider learning the optimal strategy across a multi-dimensional range of model configurations, including price impact and resilience parameters, as well as initial stochastic states. We develop a numerical algorithm based on dynamic programming and deep learning, utilizing an actor-critic framework to construct two neural-network (NN) surrogates for the value function and the feedback control. We then apply the lens of adaptive robust stochastic control to consider online statistical learning of model parameters along with a worst-case min-max optimization. Thus, the controller is dynamically learning model parameters based on her observations while explicitly accounting for Bayesian uncertainty of the learned parameter estimates. We propose a modeling framework which allows a time-consistent 3-way marriage between dynamic learning, dynamic robustness and dynamic control. We extend our NN approach to tackle the resulting 8-dimensional adaptive robust optimal order execution problem, and illustrate with comparisons to alternative frameworks, such as adaptive or static robust strategies.

MS [00589] Computational Biomedical Physics and Mechanics

room : D514

contributed talk: CT186

room : D515

[02667] Coupled Active Contour Segmentation of Clue Cells from Immunofluorescence Microscopy

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Presence of clue cells is a critical criterion for diagnosis of bacterial vaginosis. We propose a coupled active contour model for segmenting the clue cells from immunofluorescence microscope images of the samples. It enables jointly segmenting the boundaries of the epithelial cell, its nucleus, and distinct bacteria. Convexification is formulated on top of the levelset framework using characteristic functions. Our approach provides a global optimal solution. Efficacy of the method is demonstrated on clinical data.
• Classification : 92C55, 92C50, 49N99, 90C25
• Format : Talk at Waseda University
• Author(s) :
  • Yongjian Yu (Axon Connected, LLC)
  • Jue Wang (Union College)

[01762] Generalized proofs of positivity of the solutions to population models

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Dynamic models of many processes in the biological and physical sciences are governed by systems of ordinary differential equations called compartmental systems. Since the dependent variables in such models denote population size, the solutions that start from positive initial conditions remain positive for all time. In this study, two generalized proofs of positivity of the solutions to compartmental models are presented. These compartmental models can be used in many applications including epidemiology and population dynamics.
• Classification : 92D25, 92-10
• Format : Talk at Waseda University
• Author(s) :
  • AUNI ASLAH MAT DAUD (Universiti Malaysia Terengganu)

[00667] Effect of tumor-associated neutrophils on tumor growth : A mathematical model

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @D515
• Type : Contributed Talk
• Abstract : Tumor-associated neutrophils (TANs) have been under discussion for their dual role on tumor microenvironment, but they are emerging as important agents in tumor invasion. In this study, we divided TANs into two different phenotypes: N1 TANs, the anti-tumor neutrophils and N2 TANs, the tumorigenic neutrophils. We developed a mathematical model to investigate the dynamics of tumor growth between different TANs and responses to various stimuli, and finally to build simulations for brain tumor treatment.
• Classification : 92C99, 35Q92, 37N25, Mathematical oncology
• Format : Talk at Waseda University
• Author(s) :
  • Haneol Cho (Konkuk university)
  • Yangjin Kim (Konkuk university)
  • Junho Lee (Konkuk university)

contributed talk: CT188

room : A201

[02517] Flocking Dynamics of Agents with Nonidentical Intrinsic Accelerations

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A201
• Type : Contributed Talk
• Abstract : Collective dynamics has attracted much attention over the past decades. It depicts a group of agents represents the identical dynamics under the interaction. There have been several papers proposed to study these. In this talk, we set up a flocking model where agents in a flock can have different intrinsic accelerations. We give some theoretical results to ensure the occurrence of flocking dynamics and some numerical simulations are provided to support these.
• Classification : 92D50, 92D25, 34D05, 93D20
• Format : Talk at Waseda University
• Author(s) :
  • Yu-Hao Liang (National University of Kaohsiung)

[01741] A cannibalistic natural enemy pest model with different harvesting strategies

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A201
• Type : Contributed Talk
• Abstract : In the present work, we discuss the dynamics of a cannibalistic predator-prey model in the presence of different harvesting schemes for the pest population and the provision of additional food to natural enemies. We present a detailed mathematical analysis and numerical evaluations to discuss the pest-free state, coexistence of species, stability, occurrence of different bifurcations, and the impact of additional food and harvesting schemes on the system's dynamics.
• Classification : 92Dxx
• Format : Talk at Waseda University
• Author(s) :
  • Jai Prakash Prakash Tripathi (Central University of Rajasthan, India)

[02503] Modelling mosquito dynamics and novel malaria vector control interventions

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A201
• Type : Contributed Talk
• Abstract : We present mathematical and statistical models of mosquito behaviour and feeding cycle dynamics. We analytically derive estimates of vectorial capacity for malaria (the potential of the mosquito population to transmit malaria). We parameterise these models to data from semi-field and field studies and evaluate the impact of current and novel vector control interventions in reducing vectorial capacity. We connect these models to malaria transmission models in humans to investigate the impact of these interventions in reducing clinical malaria transmission.
• Classification : 92D30, 92D45, 92D50, 92C60, Malaria modelling, mosquito behaviour
• Author(s) :
  • Nakul Chitnis (Swiss Tropical and Public Health Institute)

[01749] Mean Field Game Partial Differential Inclusions: Analysis and Numerical Approximation

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A201
• Type : Contributed Talk
• Abstract : We generalize second-order Mean Field Game PDE systems with nondifferentiable Hamiltonians to Mean Field Game Partial Differential Inclusions $($MFG PDIs$)$ by interpreting the $p$-partial derivative of the Hamiltonian in terms of subdifferentials of convex functions. We present conditions for the existence of unique weak solutions to stationary second-order MFG PDIs where the Hamiltonian is convex, Lipschitz, but possibly nondifferentiable. Moreover, we propose a strongly convergent monotone finite element scheme for the approximation of weak solutions.
• Classification : 65N15, 65N30, PDIs in connection with mean field game theory
• Format : Talk at Waseda University
• Author(s) :
  • Yohance Osborne (University College London)
  • Iain Smears (University College London)

[02236] An hp-version discontinuous Galerkin method for the generalized Burgers-Huxley Equations with weakly singular kernel

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A201
• Type : Contributed Talk
• Abstract : We study the numerical approximation for the generalized Burgers-Huxley equations with a weakly singular kernel. Firstly, we derive an a priori error estimate for the hp-version of discontinuous Galerkin (DG) time stepping method. For the start-up singularities near t = 0, using geometrically refined time-steps and linearly increasing approximation orders, we get the exponential rates of convergence. For the fully discretized system we combine the DG time-stepping method and DG finite element discretization in space. Finally, the computational results are presented to validate our theoretical results.
• Classification : 65N15, 65N30
• Format : Talk at Waseda University
• Author(s) :
  • Sumit Mahajan (Indian Institute of Technology, Roorkee)
  • Arbaz Khan (IIT Roorkee)

MS [00977] Recent advances on sparse optimization: algorithms and applications

room : A206

• [02162] Asymptotically Consistent Linear Convergence Rate of the Randomized Sparse Kaczmarz Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Liang Chen (Hunan University)
  • Abstract : The sparse Kaczmarz method has drawn much attention from researchers in recent years. This is mainly due to its capability of producing sparse solutions to linear systems, which is a core problem of many applications in the big-data era, such as sparse signal recovery and image processing. This method was shown to be linearly convergent in 2019. However, the convergence rate is not consistent with the well-known convergence rate of the randomized Kaczmarz method. In this work, we try to fix this gap by proposing an asymptotically consistent linear convergence rate for the former.
• [02234] A difference-of-convex algorithm for sparse support vector machines in high dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Ning Zhang (Dongguan University of Technology)
  • Abstract : The support vector machine（SVM）is a popular and powerful technique for binary classification. We consider the penalized SVM with a class of difference-of-convex penalties. We show that the difference-of-convex algorithm is guaranteed to produce an oracle estimator in two iterations if the solution to L1-norm SVM is selected as the initial estimator. We further prove that the d.c. algorithm for SCAD/MCP penalized SVM converges to a d-stationary point with local linear convergence rate.
• [01567] Frank-Wolfe type methods for a class of nonconvex inequality-constrained problems
  • Author(s) :
    • Liaoyuan Zeng (Zhejiang University of Technology)
    • Yongle Zhang (Sichuan Normal University)
    • Guoyin Li (University of New South Wales )
    • Ting Kei Pong (The Hong Kong Polytechnic University)
  • Abstract : The Frank-Wolfe method and its variants, which implement efficient linear oracles for minimizing smooth functions over compact convex sets, form a prominent class of projection-free first-order methods. In this talk, we extend the Frank-Wolfe method and its away-step variant for minimizing a smooth function over a possibly nonconvex compact set, based on our new generalized linear oracles. We discuss convergence and present numerical performance of our nonconvex Frank-Wolfe type methods for solving matrix completion problems.

contributed talk: CT191

room : A207

[02358] Minimal time for boundary controllability of linear hyperbolic balance laws

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
• Type : Contributed Talk
• Abstract : The purpose of this talk is to present our recent results on minimal control time for null and exact boundary controllability of 1-D linear hyperbolic balance laws with arbitrary internal and boundary coupling. We will show explicit and easy-to-compute formulas to completely characterize such critical quantities, which can be strictly smaller than the classical uniform lower bound. The difference between these two kinds of controllability will also be discussed.
• Classification : 93B05, 35L04, Control of Partial Differential Equations; Boundary Controllability; Hyperbolic system involving balance laws (with source term (i.e. internal coupling)) and Conservation laws (without source term); Optimal control time
• Format : Talk at Waseda University
• Author(s) :
  • Long Hu (Shandong University)
  • Guillaume Olive (Jagiellonian University)

[00864] Stabilization of time-periodic flows

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
• Type : Contributed Talk
• Abstract : At first, I shall explain the stability and stabilizability of an ODE around a periodic trajectory. A characterization of the stability of ODEs around a periodic trajectory using the Poincare map and Floquet theory will be discussed. Then, I shall explain the extension of the idea to the parabolic type of PDEs. In particular, as an application, the stabilization of the incompressible Navier-Stokes equation around a time-periodic trajectory will be discussed.
• Classification : 93B52, 93D15, 35B10, 34H15, 76D55
• Format : Talk at Waseda University
• Author(s) :
  • Debanjana Mitra (Department of Mathematics, IIT Bombay )

[01061] Computation of control for fractional nonlinear systems using Tikhonov regularization

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
• Type : Contributed Talk
• Abstract : Determining the control steering the dynamical system is equally important as it is to examine the controllability of a control system. This study computes the control for the approximately controllable nonlinear system governed by Caputo derivatives. By using operator theoretic formulations, the problem of computing the control gets converted into an ill-posed problem which is solved for stable approximations using Tikhonov regularization. An example is presented demonstrating the error and truncated control graphs using MATHEMATICA.
• Classification : 93B05, 93C10, 47A52, 34K37
• Format : Talk at Waseda University
• Author(s) :
  • Lavina Sahijwani (Indian Institute of Technology Roorkee, India)
  • N. Sukavanam (Indian Institute of Technology Roorkee, India)
  • D. N. Pandey (Indian Institute of Technology Roorkee, India)

[01995] Theoretical and Numerical Study of Regional Boundary Observability for Linear Time-Fractional Systems.

• Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
• Type : Contributed Talk
• Abstract : The goal of this talk is to examine the regional boundary observability for time-fractional systems involving the Riemann-Liouville fractional derivative. The aim is to reconstruct the initial state of the system under considerations on a desired subregion of the evolution domains' boundary. The reconstruction problem is converted into a solvability problem with the form $AX=b$ using an adaptation of the Hilbert uniqueness method. Some successful numerical examples were simulated and provided at the end.
• Classification : 93B07, 93B28, 26A33, 46F12
• Format : Online Talk on Zoom
• Author(s) :
  • Khalid Zguaid (Higher School of Education and Training of Agadir (ESEFA), Ibn Zohr University)
  • Fatima Zharae El Alaoui (Moulay Ismail University)

MS [00029] New Trends in Structural and Engineering Optimization

room : A508

• [03346] Numerical and experimental investigation on process parameters optimization in rapid heat cycle molding
  • Format : Talk at Waseda University
  • Author(s) :
    • Satoshi Kitayama (Kanazawa University)
    • Yusuke Yamazaki (Sodick Co. Ltd.)
    • Yoshikazu Kubo (Sodick Co. Ltd.)
    • Shuji Aiba (Sodick Co. Ltd.)
  • Abstract : Weldline that is forms when two or more melt fronts meet is one of the major defects in plastic injection molding (PIM), and it is important to reduce the wedline as much as possible. Rapid heat cycle molding (RHCM) is one of the effective PIMs for weldline reduction, but the process parameters are determined by the trial and error method. This paper optimizes the process parameters in RHCM by CAE and design optimization technique. The experiment is also conducted to examine the validity of the proposed approach.
• [01219] Acoustic metamaterials design with non-gradient material-field series-expansion topology optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaopeng Zhang (Dalian Dalian University of TechnologyUniversity of Technology)
  • Abstract : Designing bandgap acoustic metamaterial has important application potential but is also challenging. This study proposes a systematic topology optimization method of acoustic metamaterial to open single and multiple low-frequency bandgaps. To describe the complicated topologies of the multi-material acoustic metamaterial with a lower number of design variables, the material-field series expansion (MFSE) technique is adopted. With the interpolated scheme and the multi-material field description model, a clear three-material topology can be determined by two independent material-field functions with only 100 independent design variables. This greatly reduces the design variables for the topological description of the microstructure, enabling the problem to be solved using non-gradient optimization algorithms. The self-adaptive strategy based sequential Kriging optimization algorithm is then introduced to solve the optimization problems. Numerical examples prove the proposed topology optimization method can effectively provide the acoustic metamaterial designs with ultra-wide low-frequency bandgaps.
• [04675] Multiscale topology optimization to maximize dissipated energy
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Yamamoto (Kogakuin University)
  • Abstract : In this study, a multiscale topology optimization method for micro structure is proposed utilizing the homogenization method based on the asymptotic expansion. Energy dissipated in macroscopic component is maximized at a prescribed frequency. Design sensitivities of the homogenized macroscopic properties are calculated by applying the adjoint variable method in the frame work of the homogenization method. Adjoint variable method is hierarchically applied to obtain design sensitivities of the macroscopic dissipated energy.
• [03135] Multiscale topology optimization of fiber reinforced composite using homogenization design method.
  • Format : Talk at Waseda University
  • Author(s) :
    • Jaewook Lee (Gwangju Institute of Science and Technology (GIST))
  • Abstract : This presentation shows topology optimization of fiber reinforced composite with spatially-varying fiber structure. The numerical homogenization of the microscale unit-cell is performed at various fiber sizes. Then, the effective elasticity tensor is represented as the function of fiber size and orientations, together with the density. Topology optimization is carried out at macroscale, and the microscale composite structure is restored using the de-homogenization method. Both 2D and 3D design examples will be provided.

MS [00033] Recent Advances on Quantitative Finance

room : A510

• [05335] Dynamic programming for mean-variance portfolio selection
  • Format : Talk at Waseda University
  • Author(s) :
    • Martin Schweizer (ETH Zurich)
  • Abstract : We present a dynamic programming approach to solving the mean-variance portfolio selection problem in finite discrete time. This bypasses issues of time-inconsistency and hence does not need the introduction of an equilibrium or game-theoretic approach. The talk is based on joint work with Zhouyi Tan.
• [05363] Non-Concave Utility Maximization with Transaction Costs
  • Format : Talk at Waseda University
  • Author(s) :
    • shuaijie qian (Hong Kong University of Science and Technology)
    • Chen Yang (The Chinese University of Hong Kong)
  • Abstract : We consider the non-concave utility maximization problem, which appears in plenty of areas in finance, with transaction costs. Technically, we propose a proper terminal condition and lay the corresponding theoretical foundation of viscosity solutions. This terminal condition implies that any transaction close to maturity provides a marginal contribution to the target. We find that the introduction of transaction costs into non-concave utility problems can prevent the portfolio from unbounded leverage and also result in richer action regions than classical transaction costs problems with concave utilities.
• [05320] Optimal stopping without time consistency
  • Format : Talk at Waseda University
  • Author(s) :
    • Hanqing Jin (University of Oxford)
    • Yanzhao Yang (University of Oxford)
  • Abstract : We study a continuous time dynamic optimal stopping problem with a flow of preferences, which can be in non-expectation form and can depend on both the current time and state of the system in general. We will define a solution to the problem by the rationality of the agent, and compare it with other solutions appeared in literature.
• [03404] Optimal dividend payout with non-decreasing constraint
  • Format : Talk at Waseda University
  • Author(s) :
    • Zuo Quan Xu (The Hong Kong Polytechnic University )
    • Chonghu Guan (Jiaying University)
  • Abstract : We study a dividend payout problem under the classical Cram ́er-Lundberg model. The dividend payout must be non-decreasing over time and is subject to an upper bound constraint. Finding the optimal dividend payout strategy in this model is a long-standing open problem in risk theory. To overcome the difficulty, we first introduce a regime-switching problem --- a sequence of single-obstacle problems in ODE --- to approximate the original two-dimensional HJB equation and then take limit. We find a smooth switching boundary and the optimal strategy is given by the boundary.

MS [00538] Mathematical modeling, analysis, and simulation for complex neural systems

room : A511

• [04042] Learning optimal models of statistical events in spontaneous neural activity
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshitake Asabuki (Imperial College London)
    • Tomoki Fukai (Okinawa Institute of Science and Technology)
  • Abstract : The brain is thought to learn an internal model of the statistical environment for improved cognitive performance. Evidence suggests that spontaneous cortical activity represents such a model, or prior distribution, by replaying stimulus-evoked activity patterns with the probabilities that these stimuli were experienced. Here, we present a principle to robustly learn replay activity patterns in spiking recurrent neural networks and demonstrate how such spontaneous replay biases animals' perceptual decision making.
• [03841] The hierarchical organization of the Drosophila connectome
  • Format : Talk at Waseda University
  • Author(s) :
    • Kresimir Josic (University of Houston)
    • Alexander B. Kunin (Creighton University)
    • Jiahao Guo (University of Houston)
    • Kevin E. Bassler (University of Houston)
    • Xaq Pitkow (Rice University)
  • Abstract : The Hemibrain is the largest published connectome to date. It is the result of a dense reconstruction of over twenty thousand neurons and ten million synapses spanning the fruit fly Drosophila central brain. I will describe a novel approach to uncovering the hierarchical community structure of this connectome. This approach allows us to recover previously known and reveal novel features of the organization within the fly brain. Methods such as these will be essential to interpret the forthcoming connectomics data due to its size and complexity.
• [01437] The mechanism of abnormal beta-oscillation generated in striatum
  • Format : Talk at Waseda University
  • Author(s) :
    • Douglas Zhou (Shanghai Jiao Tong University)
  • Abstract : combining simulations of a neural network model and the analysis of the corresponding reduced neural mass model, we demonstrate how the cellular architecture and network dynamics of the ChAT - iMSN close loop in the striatum efficiently yield exaggerated beta oscillations. We find that beta oscillations can emerge from inhibitory interactions among iMSNs. And a slow inhibitory dynamic in iMSNs could be the underpinning of beta oscillations.
• [03947] Maturation of neurons reconciles flexibility and stability of memory: dual structural plasticity in the olfactory system
  • Format : Talk at Waseda University
  • Author(s) :
    • Bennet Sakelaris (Northwestern University)
    • Hermann Riecke (Northwestern University)
  • Abstract : It is essential for the brain to flexibly form new memories without overwriting and jeopardizing the stability of existing ones. Using a computational model of the olfactory bulb (OB) that captures several experimental observations, we investigate how the characteristic structural plasticity of the OB addresses this flexibility-stability tradeoff. We demonstrate that the evolution of the timescales of synaptic plasticity associated with the aging of adult-born cells allows the OB to strike a harmonious balance between the competing demands of flexibility and stability.

MS [00216] Recent Advances on interfaces dynamics modeling and simulation

room : A601

• [01231] A phase-field model and an energy-law preserving method for vesicles
  • Format : Talk at Waseda University
  • Author(s) :
    • Ping Lin (University of Dundee)
  • Abstract : We will first show how to develop a thermodynamically consistent phase field model for the binary incompressible (quasi-incompressible) fluid. We then show how to apply the idea to model vesicle motions and deformations through a narrowed channel. We will also introduce a Lennard-Jones type of interaction potential for vesicle-vesicle and vesicle-channel wall interactions. An energy law preserving computational method is then developed for the model. A few computational examples including vesicle-wall and multi-vesicle interactions will be presented to demonstrate the model and the computational method.
• [01214] Free boundary problems in cardiovascular diseases
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenrui Hao (Penn State University)
  • Abstract : I will present several free boundary problems based on the pathophysiology of cardiovascular disease. As an example, a mathematical model of atherosclerosis, based on this modeling approach, provides a personalized cardiovascular risk by solving a free boundary problem. Some interesting mathematical problems are also introduced by this new model to help us understand cardiovascular risk.
• [05636] Buckling on Erythrocyte Membranes in Narrow Capillary Flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Deyun Liu (Shanghai Jiao Tong University)
    • Kazuyasu Sugiyama (Osaka University)
    • Xiaobo Gong (Shanghai Jiao Tong University)
  • Abstract : Experiments and numerical simulations are conducted to understand the non-axisymmetric deformation of a single RBC in narrow tubes and the hydrodynamics associated. With decreasing capillary numbers, the stable deformation shapes of RBCs change from axisymmetric bullet shape to asymmetric deformation with buckling under the major effect of the negative pressure difference across cell membrane at the rear part of the deformed RBCs.
• [01394] Machine Learning of Self Organization from Observation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ming Zhong (Illinois Institute of Technology)
  • Abstract : Self organization (also known as collective behaviors) can be found in studying crystal formation, aggregation of cells/animals, social behaviors of insects and humans, etc. It is a challenging task to understand such behaviors from the mathematical point of view. We offer a statistical/machine learning approach to understand these behaviors quantitatively from observation data; moreover, our learning approach can aid in validating and improving the modeling of collective behaviors. We develop a learning framework to derive physically meaningful models to explain self organization from observation. We also investigate the stead state properties of our learned models, and extend the learning framework to include more complicated structures. We extend the learning approach to infer dynamical models for agents constrained on Riemannian manifolds. We further improve our learning capability to infer interaction feature variables as well as interaction kernels. We even study the effectiveness of our learning method on the NASA Jet Propulsion Laboratory's modern Ephemerides. Upon careful inspection of our model, we discover that it even captures potion of the general relativity effects. A complete learning theory on second-order systems is presented, as well as two new models on emergence of social hierarchy and combination of flocking and synchronization.