MS and CT list / Aug. 25, 15:30-17:10.

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

room : G301

• [04021] A learning-based projection method for model order reduction of transport problems
  • Format : Talk at Waseda University
  • Author(s) :
    • ZHICHAO PENG (Hong Kong University of Science and Technology)
    • Fengyan Li (Rensselaer Polytechnic Institute)
    • Min Wang (University of Houston)
  • Abstract : Due to the slow decay of the Kolmogorov n-width for transport problems, classical linear reduced order model (ROM) may be inefficient. To address this issue we propose a learning-based projection method following an offline-online decomposition framework. A moving low dimensional subspace is learned offline, and in the online stage, the full order problem is projected onto the learned subspace to reduce computational cost. We also numerically demonstrate the performance of the proposed method.
• [04197] An iterative algorithm for POD basis adaptation
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhizhang Wu (The University of Hong Kong)
    • Zhiwen Zhang (The University of Hong Kong)
  • Abstract : To construct reduced-order models using POD for convection-diffusion equations, fine-grid solvers are needed to obtain accurate solution snapshots for small diffusivities, while coarse-grid solvers are sufficient for large diffusivities. We develop an iterative algorithm that adapts the POD basis functions extracted at large diffusivities for the construction of reduced-order models at small diffusivities without resorting to fine-grid solvers. Convergence analysis and numerical results are provided to confirm the effectiveness of our method.
• [04384] Heat on hypergraph and 
its application to network analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiro Ikeda (RIKEN)
  • Abstract : In this talk, I will introduce the joint works with Atsushi Miyauchi (Tokyo Univ.), Yuuki Takai(KIT) and Yuichi Yoshida (NII). They are about heat on hypergraph and its application to network analysis. I will introduce the background of their papers and the fundamental notions for community detection of networks. First I review the notion of Laplacian and Cheegerʼs inequality for the usual undirected graph. After that, I introduce the definition of the (submodular) Laplacian for hypergraphs and the heat on them. I also introduce several properties of the Laplacian and heat such as maximal monotonicity of the Laplacian. Especially I explain well-definedness of the heat and the Personalized PageRank for hypergraphs. Moreover, I introduce applications of their properties to the community detection on hypergraphs. If time permitted, I will introduce recent works about submodular Laplacian with Uchida (Oita Univ.).
• [04987] Convergence Rate Analysis for Deep Ritz Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Jerry Zhijian Yang (Wuhan University)
  • Abstract : We provide a rigorous numerical analysis on deep Ritz method (DRM) for second order elliptic equations with Neumann boundary conditions. We establish the first nonasymptotic convergence rate in H1 norm for DRM using deep networks with ReLU2 activation functions. Our study also shed light on how to set the hyperparameter of depth and width to achieve the desired convergence rate in terms of number of training samples.

MS [00110] Computation on Supersingular and Superspecial Curves and its Applications

room : G302

• [04024] Decomposed Richelot isogenies of Jacobian varieties of hyperelliptic curves and generalized Howe curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshiyuki Katsura (University of Tokyo)
    • Katsuyuki Takashima (Waseda University)
  • Abstract : We advance previous studies on decomposed Richelot isogenies (Katsura– Takashima (ANTS 2020) and Katsura (J. Algebra)) which are useful for analysing superspecial Richelot isogeny graphs in cryptography. We first give a characterization of decomposed Richelot isogenies between Jacobian varieties of hyperelliptic curves of any genus. We then define generalized Howe curves, and present two theorems on their relationships with decomposed Richelot isogenies. We also give new examples including a non-hyperelliptic (resp. hyperelliptic) generalized Howe curve of genus 5 (resp. of genus 4).
• [04668] Some explicit arithmetics on curves of genus three and their applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tomoki Moriya (University of Birmingham)
    • Momonari Kudo (Fukuoka Institute of Technology)
  • Abstract : A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the 2-torsion subgroup of the domain. In particular, a Richelot isogeny whose codomain is the product of two or more principally polarized abelian varieties is called a decomposed Richelot isogeny. In this talk, I provide some explicit arithmetics on curves of genus 3, including algorithms to compute the codomain of a decomposed Richelot isogeny. I also provide explicit formulae of defining equations for Howe curves of genus 3 as solutions to computing the domain of a decomposed Richelot isogeny. Finally, I give a construction of an algorithm with complexity O~(p^3) (resp. O~(p^4)) to enumerate all hyperelliptic (resp. non-hyperelliptic) superspecial Howe curves of genus 3.
• [05345] Construction of superspecial curves of higher genera with extra automorphisms
  • Format : Talk at Waseda University
  • Author(s) :
    • Momonari Kudo (Fukuoka Institute of Technology)
  • Abstract : Superspecial curves are one of the most important objects in algebraic geometry over fields of positive characteristic, with applications to coding theory and cryptography, but explicit constructions and enumerations of such curves of higher genera are known to be quite difficult in general. In this talk, we develop several algorithms to construct superspecial curves of higher genera, restricting ourselves to the case of curves with non-trivial automorphisms, e.g., genus-4 hyperelliptic curves with order-6 automorphisms.
• [04048] Several examples of curves whose superspeciality imply maximality or minimality
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryo Ohashi (University of Tokyo)
    • Shushi Harashita (Yokohama National University)
  • Abstract : A curve over the finite field $\mathbb{F}_q$ of characteristic $p > 0$ is called maximal (resp. minimal) if the number of its $\mathbb{F}_q$-rational points attains the Hasse-Weil upper (resp. lower) bound. Maximal curves have been investigated for their applications to cryptography and coding theory. It is known that maximal or minimal curves over $\mathbb{F}_{p^2}$ are all superspecial, while superspecial curves over $\mathbb{F}_{p^2}$ are not necessary maximal nor minimal. However in this lecture, we will present several examples of curves $C$ which have the following property: If $C$ is superspecial, then $C$ is maximal or minimal over $\mathbb{F}_{p^2}$.

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

room : G304

• [04614] Lattice rules for integration on $\mathbf{R}^d$
  • Format : Talk at Waseda University
  • Author(s) :
    • Dirk Nuyens (KU Leuven)
  • Abstract : For integration of periodic functions of mixed smoothness on the unit cube lattice rules are a very good choice. Their group theoretical structure allows for a convenient error analysis. When integrating functions on $\mathbb{R}^d$ there are multiple ways of still making use of lattice rules. We could truncate the integration region, and take into account the truncation error and the projection distance to the periodic subspace; or we could do a substitution and map the integrand to the unit cube. Depending on how we proceed it is possible to retain the smoothness and obtain higher order convergence with a lattice rule.
• [04320] SNPE-B Revisited: Rethinking of Data Efficiency and Variance Reduction
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhijian He (South China University of Technology)
    • Yifei Xiong (University of Chinese Academy of Sciences)
    • Xiliang Yang (South China University of Technology)
  • Abstract : Sequential neural posterior estimation (SNPE) techniques have recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators. This paper reclaims the efficiency of SNPE-B proposed by Lueckmann et al. (2017) through sophisticated sampling strategies. We firstly introduce a concentrated loss function based on an adaptive calibration kernel that reweights the simulated data appropriately to improve the data efficiency. We also provide a theoretical analysis of the variance of importance sampling-based estimators. We then propose several variance reduction techniques including quasi-Monte Carlo sampling to further accelerate the process of learning. Numerical experiments demonstrate that our method outperforms the original SNPE-B method together with other existing competitors on certain tasks.
• [04916] Variable importance measures in high dimensional data sets
  • Format : Talk at Waseda University
  • Author(s) :
    • Art B Owen (Stanford University)
  • Abstract : This talk connects some ideas from QMC sampling to new problems in explainable AI. Variable importance measures in global sensitivity analysis are commonly derived from the ANOVA decomposition. The ANOVA is problematic with dependent variables. Then Shapley values and related quantities are used to measure importance, and those can be studied through the anchored decomposition, also common in quasi-Monte Carlo sampling. Based on work with Ben Seiler, Christopher Hoyt, Masayoshi Mase and Naofumi Hama.
• [03703] Tuning QMC point sets using WAFOM-like value
  • Format : Talk at Waseda University
  • Author(s) :
    • Makoto Matsumoto (Hiroshima University)
  • Abstract : There are many figures of merit for QMC point set P. The star discrepancy D^*(P) is a famous one. We restrict ourself to the case of 2-adic digital nets. Then, P can be considered as an F2-vector space, where F2 is the two-element field. Let P' be the perpendicular space of P. Then, P' is considered as the space of linear relations satisfied by P. As a rough sketch, P is more uniform if any non-zero element A in P' is sufficiently complicated. One way to measure the complexity of A is Niederreiter-Rosenbloom-Tsfasman (NRT) weight; the smallest NRT weight among all possible non-zero weights gives the t-value. As other figures of merits, we may consider Dick weight mu_alpha(A) of A in P'. Summation of 2^{-mu_alpha(A)} over nonzero A in P' gives figures of merit studied by Dick, and by considering the limit where alpha goes to infinity, we obtain WAFOM. It is used by Harase that NRT weight is invariant by lower triangular trransformation, but WAFOM differs, and so one can obtain better performance for smooth integrand when WAFOM is optimized while t-value is fixed. We study a justification of this method, and variation where Dick weight is replaced with NRT weight.

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

room : G305

• [02170] A reduction algorithm for reconstructing periodic pseudo-Jacobi matrices
  • Format : Online Talk on Zoom
  • Author(s) :
    • Natalia Bebiano (Department of Mathematics, Coimbra University)
  • Abstract : For the given signature operator $\mathcal{H}=I_{r}\oplus-I_{n-r}$, a pseudo-Jacobi matrix is a self-adjoint matrix relatively to a symmetric bilinear form $\langle \cdot,\cdot\rangle_{\mathcal{H}}$. In this talk, we consider recent inverse eigenvalue problems for this class of matrices. Necessary and sufficient conditions under which the problems have solution are presented. Numerical algorithms are designed according to the obtained theoretical results. Illustrative numerical examples are given to test the reconstructive algorithms.
• [05469] A Low-Cost Algorithm to Determine Orbital Trajectories
  • Format : Talk at Waseda University
  • Author(s) :
    • Sirani M. Perera (Embry-Riddle Aeronautical University)
    • David Canales (Embry-Riddle Aeronautical University)
    • Atahan Kurttisi (Embry-Riddle Aeronautical University)
    • Brian Baker-McEvilly (Embry-Riddle Aeronautical University)
  • Abstract : The increasing demand for effective methods to propagate trajectories in the circular restricted three-body problem (CR3BP) is driven by heavy traffic in the region. This presentation introduces a novel approach that utilizes interpolation for determining orbital trajectories. We present a novel algorithm for determining orbital motion in the CR3BP, which is specifically applied to different Cislunar trajectories. Our findings demonstrate a 50% reduction in time complexity compared to the existing methods.

contributed talk: CT015

room : G306

[02687] Semi-Markov Compartment Models

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G306
• Type : Contributed Talk
• Abstract : Compartment models are a widely used class of models that are useful when considering the flow of objects or people or energy between different labelled states, referred to as compartments. Recently we have constructed a general framework for fractional order compartment models, where the governing equations involve fractional order derivatives, via the consideration of a semi-Markov stochastic process. Here we show extensions to this approach to obtain more general operators.
• Classification : 34A08, 60K40, 92C45
• Format : Talk at Waseda University
• Author(s) :
  • Christopher Angstmann (University of New South Wales)
  • Bruce Henry (University of New South Wales)

[00439] Successive Approximations for Fractional BVPs with Non-local Boundary Conditions

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G306
• Type : Contributed Talk
• Abstract : In joint work with Dr. Kateryna Marynets, we adapt a numerical-analytic technique for constructing approximations to a system of nonlinear fractional differential equations with integral boundary conditions. The boundary conditions are parametrized, and the parameter values, which govern the solution’s behavior, are calculated numerically. The convergence of the method is improved using a dichotomy-type approach, and its applicability is extended to a wider class of problems. Our results are confirmed by a model example.
• Classification : 34A08, 34B10, 37M99, Fractional boundary value problems
• Format : Talk at Waseda University
• Author(s) :
  • Dona Pantova (TU Delft)
  • Kateryna Marynets (TU Delft)

[02449] Recent Advances in Fast Finite Difference Schemes for PDE Problems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G306
• Type : Contributed Talk
• Abstract : In this talk, a fast finite difference scheme is discussed to a hidden-memory variable-order time-fractional diffusion equation. To reduce the computational cost and memory, a modified exponential-sum-approximation method is utilized to discretize the hidden-memory variable-order fractional derivative. We then develop different techniques from the analysis of L1 methods to prove the convergence for the corresponding fast fully discrete scheme. Numerical experiments are presented to substantiate the theoretical results.
• Classification : 34A08, 26A33, 65D15, 65D40
• Format : Talk at Waseda University
• Author(s) :
  • Lu-Yao Sun (University of Macau)

[00847] Acute Lymphoblastic Leukemia diagnosis and treatment: a mathematical analysis

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G306
• Type : Contributed Talk
• Abstract : Despite the recent medical advances, treatments are unsuccessful in 15-20% of cases in Acute Lymphoblastic Leukemia ( ALL ) patients. The main aim of our study is to analyse data from bone marrow samples and to use artificial intelligence to improve current techniques of diagnosis in ALL protocols. Using machine learning techniques, our results predict bone marrow behavior and allow us to classify patients depending on their relapse risk.
• Classification : 34A12, 92-10
• Format : Online Talk on Zoom
• Author(s) :
  • Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
  • Salvador Chulián (University of Cádiz)
  • Álvaro Martínez-Rubio (Department of Mathematics, Universidad de Cádiz)
  • María Rosa (Department of Mathematics, Universidad de Cádiz)

contributed talk: CT023

room : G401

[00565] Resonance with a Delay Differential Equation

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G401
• Type : Contributed Talk
• Abstract : We propose here a delay differential equation with a linear time coefficient that produces transient resonant behavior. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. Also, for an appropriately tuned value of the delay, the height of the power spectrum goes through the maximum. This resonant behavior contrasts itself against the general behaviors observed with the constant coefficient delay differential equations.
• Classification : 34K23, 93C43
• Format : Talk at Waseda University
• Author(s) :
  • Kenta Ohira (Nagoya University)
  • Toru Ohira (Graduate School of Mathematics, Nagoya University)

[02400] A generalized structural bifurcation analysis of chemical reaction networks

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G401
• Type : Contributed Talk
• Abstract : Chemical reactions link metabolites and form complex networks in living cells. We have previously developed “structural bifurcation analysis,” by which bifurcation properties of reaction systems are determined solely from network topologies. In this work, we establish a precise formalization connecting our analysis to conventional methods based on Jacobian matrices. The formalization increases applicability of the analysis, e.g. determining multistationarity, without assuming the full-rankedness of stoichiometric matrices or eliminations of equations/chemicals.
• Classification : 34Hxx, 92Bxx, 34D10
• Format : Talk at Waseda University
• Author(s) :
  • Yong-Jin Huang (Division of Biological Sciences, Graduate School of Science, Kyoto University)
  • Takashi Okada (Division of Biological Sciences, Graduate School of Science, Kyoto University)
  • Atsushi Mochizuki (Institute for Life and Medical Sciences, Kyoto University)

[02688] Analytical Solutions of Delay Differential Equations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G401
• Type : Contributed Talk
• Abstract : Delay differential equations are an interesting class of non-local equations that involve a function and its derivatives evaluated at different points in time. By introducing a new class of functions, we have been able to provide fundamental solutions for autonomous linear delay differential equations. These functions, referred to as delay functions, relate the power series solutions of ordinary differential and delay differential equations and can be easily extended to more generalised series solutions.
• Classification : 34Kxx, 34K06, 44A10
• Format : Talk at Waseda University
• Author(s) :
  • Stuart-James Malouf Burney (University of New South Wales)
  • Christopher Angstmann (University of New South Wales)
  • Bruce Henry (University of New South Wales)
  • Byron Jacobs (University of Johannesburg)
  • Zhuang Xu (University of New South Wales)

[00776] Towards a modeling class for port-Hamiltonian systems with time-delay

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G401
• Type : Contributed Talk
• Abstract : The framework of port-Hamiltonian (pH) systems is a broadly applicable modeling paradigm. In this talk, we extend the scope of pH systems to time-delay systems. Our definition of a delay pH system is motivated by investigating the Kalman-Yakubovich-Popov inequality on the corresponding infinite-dimensional operator equation. Moreover, we show that delay pH systems are passive and closed under interconnection. We describe an explicit way to construct a Lyapunov-Krasovskii functional and discuss implications for delayed feedback.
• Classification : 34K06, 37J06, 93C05, 34A09
• Format : Talk at Waseda University
• Author(s) :
  • Dorothea Hinsen (TU Berlin)
  • Tobias Breiten (TU Berlin)
  • Benjamin Unger (University of Stuttgart)

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

room : G402

• [03942] “Mild solutions” for hereditary linear differential systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Junya Nishiguchi (Tohoku University)
  • Abstract : In this talk, we discuss the variation of constants formula for delay differential equations by introducing the notion of a mild solution, which is a solution under an initial condition having a discontinuous history function. Then the principal fundamental matrix solution is defined as a matrix-valued mild solution, and we obtain the variation of constants formula with this function.
• [04145] Linearized instability for neutral functional differential equations with state-dependent delays
  • Format : Talk at Waseda University
  • Author(s) :
    • Jaqueline Godoy Mesquita (Universidade de Brasília)
    • Bernhard Lani-Wayda (Justus-Liebig University)
  • Abstract : In this talk, I will present a linearized instability principle for neutral functional differential equations with state-dependent delays. Also, I will discuss open and developing problems in this field. This is a joint work with Professor Bernhard Lani-Wayda from Justus-Liebig University, in Giessen, Germany.
• [03765] Morse decomposition of the global attractor for delay differential equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Abel Garab (University of Szeged)
  • Abstract : We consider unidirectional cyclic systems of delay differential equations of the form \begin{equation*} \dot{x}^{i}(t)=g^i(x^i(t),x^{i+1}(t-\tau^{i})), \qquad 0\leq i\leq N, \end{equation*} where the indices are understood modulo $N+1$. We show that if the global attractor exists, then it does not contain any superexponential solution (i.e. that converges to $0$ faster than any exponential function). This allows us to construct a Morse decomposition of the global attractor of such equations, which is based on an integer valued Lyapunov function.

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

room : G404

• [04773] Electro-chemical based modelling of battery cells for automotive applications.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Edwin Knobbe (BMW AG)
  • Abstract : This contribution presents challenges with respect to modelling and (numerical) simulations of the interaction of mechanics and electro-chemistry for applications in battery cell development. Some of the challenges will be explained by examples relevant for automotive applications. For instance: solid mechanics to model the swelling behavior of battery cells during cycling, fluid mechanics with detailed chemistry during a thermal event and modelling electro-chemical phenomena at the interface between an electrode and a solid electrolyte.
• [02597] Analytical solution to a multilayer particle model for Li-ion cells under generic high current profiles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Javid Piruzjam (Mercedes-Benz AG)
    • Lukas Rubacek (Mercedes-Benz AG)
    • Thomas Carraro (Helmut Schmidt University / UniBw Hamburg)
  • Abstract : Reduced order Li-ion battery models are widely used in applications such as state of charge estimation by electric vehicles’ battery management systems, or cell characterization. Among those models, Single Particle Model is a computationally inexpensive physics-based solution. However, neglecting the effect of the electrolyte dynamics on the cell performance, SPM can lead to large errors especially at high current applications. In this work, we propose an analytical solution to a single particle model including electrolyte dynamics (SPMe) which is applicable for a wide range of currents. The boundary conditions and source terms in all differential equations are time-varying, and a spherical multilayer diffusion scenario is also considered which allows modelling particles coating and degradation effect.
• [05025] Microstructural resolved simulations of NVP-C electrodes for Sodium-ion batteries
  • Format : Talk at Waseda University
  • Author(s) :
    • Paul Maidl (German Aerospace Center)
    • Simon Hein (German Aerospace Center)
    • Timo Danner (German Aerospace Center)
    • Matthias Neumann (University Ulm)
    • Marcel Häringer (Karlsruher Institue of Technology )
    • Luca Schneider (Karlsruher Institue of Technology )
    • Werner Bauer (Karlsruher Institue of Technology )
    • Ingo Manke (Helmholtz-Zentrum Berlin)
    • Volker Schmidt (University Ulm)
    • Joachim R. Binder (Karlsruher Institue of Technology )
    • Arnulf Latz (German Aerospace Center)
  • Abstract : Sodium-ion batteries are a promising candidate for sustainable future energy storage technologies. Although they have some similarities with Lithium ion batteries, today's modelling and simulation techniques for Sodium-ion batteries is lacking behind their Lithium counterpart. One interesting material for both anode and cathode is NVP-C ($Na_3V_2(PO_4)_3$ with added carbon). In our contribution we show simulation approaches for virtual material characterization of its complex three-dimensional microstructure and its influence on cell performance.
• [05164] Improving Lithium-ion Battery Models for Porous Secondary Particles: A Comparison of Homogenized and Microscopic 3D Models
  • Format : Talk at Waseda University
  • Author(s) :
    • Javid Piruzjam (Mercedes-Benz AG)
    • Phillip Gräfensteiner (Ulm University)
    • Matthias Neumann (Ulm University)
    • Lukas Rubacek (Mercedes-Benz AG)
    • Volker Schmidt (Ulm University)
    • Thomas Carraro (Helmut Schmidt University / UniBw Hamburg)
  • Abstract : We present a study on a homogenized model for porous secondary particles of lithium-ion batteries in comparison with microscopic 3D models. The 3D microstructures are based on FIB-SEM tomography, which provides high-resolution images of the secondary particles. Homogenized electrode-level models are widely used in battery applications due to their computational efficiency, e.g., in the electric vehicle industry. However, the accuracy of these models can be improved if the transport processes within the porous particles are considered, especially when complex microstructures are involved. Our investigation aims to improve the quantitative prediction of multiscale models. To perform a comprehensive study, we use digital twins to obtain adequate stochastic representations of the microstructure.

MS [00545] Waves in complex and multiscale media

room : G406

• [05192] Water wave resonances between floating vessels: fundamentals to applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Hugh Wolgamot (University of Western Australia)
    • Wenhua Zhao (University of Western Australia)
  • Abstract : The narrow gap formed between floating vessels in close proximity supports resonances. This leads to a variety of problems of both theoretical and practical interest. In this talk the resonant structure of the coupled motion of the vessels and fluid is first investigated using linear potential flow theory for simple geometries. The interaction of prismatic vessels spanning a channel (a common experimental set-up) is then considered. Interaction with practical mechanical constraints (mooring) is discussed.
• [03152] Broadband energy capture by an array of heaving buoys
  • Format : Talk at Waseda University
  • Author(s) :
    • Amy-Rose Westcott (The University of Adelaide)
    • Luke Bennetts (The University of Adelaide)
    • Benjamin Cazzolato (The University of Adelaide)
    • Nataliia Sergiienko (The University of Adelaide)
  • Abstract : Broadband energy capture is sought by grading the resonant properties of an array of heaving buoy-type wave energy converters (WECs) in 2D. Linear potential-flow theory is applied and WEC interactions are modelled using multiple-wave scattering theory. The resonant properties of WECs are tuned via a linear spring-damper power take-off mechanism to manipulate the complex-frequency zeros. The resulting graded array captures near-perfect absorption (>97% of incident energy) from a targeted band of wavelengths spanning 1.5 times the array's length.
• [04111] Graded arrays for spatial frequency separation and amplification of water waves
  • Format : Talk at Waseda University
  • Author(s) :
    • Malte A Peter (University of Augsburg)
    • Luke G Bennetts (University of Adelaide)
    • Richard V Craster (Imperial College London)
  • Abstract : Wave-energy converters extracting energy from ocean waves are known to suffer from poor efficiency. We propose structures substantially amplifying water waves over a broad range of frequencies at selected locations, with the idea of enhanced energy extraction. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified locations. Transfer-matrix analysis is used for the analysis and results from wave-flume experiments confirm the amplification in practice.
• [05656] Unstable Wave Dynamics in Sea Ice
  • Author(s) :
    • Amin Chabchoub (Kyoto University )
    • Alberto Alberello (University of East Anglia)
    • Emilian Parau (University of East Anglia)
  • Abstract : Wave and sea ice properties in the Arctic and Southern Oceans are linked by feedback mechanisms. Therefore, the understanding of wave propagation in these regions is essential to model this key component of the Earth climate system. The most-striking effect of sea ice is the attenuation of waves at a rate proportional to their frequency. The nonlinear Schrödinger equation (NLS), a fundamental model for unidirectional and narrowband ocean waves, describes the full growth-decay cycles of unstable modes, a mechanism also known as modulational instability (MI). Here, a dissipative NLS (d-NLS) with characteristic sea ice attenuation is used to model the evolution of unstable waves. The MI in sea ice is preserved, however, in its phase-shifted form. Moreover, the frequency-dependent dissipation breaks the symmetry between the dominant left and right sideband.

MS [00552] Homogenization theory and applications

room : G501

• [01750] On the rate of convergence in homogenization of time fractional Hamilton-Jacobi equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyoshi Mitake (University of Tokyo)
  • Abstract : In this talk, we consider periodic homogenization for time fractional Hamilton-Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estimates on the rate of convergence. A main difficulty is the incompatibility between the function used in the doubling variable method, and the non-locality of the Caputo derivative. Our approach is to provide a lemma to prove the rate of convergence without the doubling variable method with respect to the time variable, which is a key ingredient. This is a joint work with Shoichi Sato (U. Tokyo).
• [01811] Discrete approximation of higher degree Laplacians
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Masamune (Tohoku University)
    • Hiroki Fukagawa (DeepFlow Inc)
  • Abstract : In this talk, we review some basic ideas in the theory of homogenization and discuss recent progress in the theory and applications of discrete approximation of equations involving, possibly higher degree, Laplacian. The talk is based on a collaborative effort with Hiroki Fukagawa from DeepFlow Inc.
• [03559] Homogenization of the rate-independent evolution of a random heterogeneous, elasto-plastic spring network
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefan Neukamm (TU Dresden)
  • Abstract : We consider a periodic network composed of elasto-plastic spring with stationary and ergodic coefficients, described as a evolutionary rate independent system (ERIS) and derive a homogenized, continuum model as evolutionary Gamma-limit. The limit can be described as a generalized Prandtl-Ishlinskii hysteresis model and we analyse a corresponding RVE approximation.

contributed talk: CT036

room : G502

[00820] Chemotaxis system with signal-dependent motility and the singular limit problem

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G502
• Type : Contributed Talk
• Abstract : We study the reaction-diffusion model that consists of equations that govern the evolution of bio-cells in a chemotactic environment. In our modeling framework, we assume that if the chemical concentration is low, then the cells move actively, whereas if the chemical concentration is high, they become less active. As we take a limit of conversion process, we formally obtain the singular limit problem of Fokker-Planck type diffusion. The aim of this study is to prove the global well-posedness of the singular limit problem and its convergence rigorously.
• Classification : 35K51, 35K57, 92C17
• Format : Talk at Waseda University
• Author(s) :
  • Changwook Yoon (Chungnam National University)
  • Yong-Jung Kim (KAIST)

[00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G502
• Type : Contributed Talk
• Abstract : We study the shape of bifurcation curve of positive solutions for the semipositone Minkowski-curvature problem $-\left( u^{\prime }/\sqrt{1-{u^{\prime }}^{2}}\right) ^{\prime }=\lambda f(u),$ in $\left( -L,L\right) $, and $u(-L)=u(L)=0,$ where $\lambda ,L>0$ and $\left( \beta -u\right) f(u)<0$ for $u>0$. We prove that if $f$ is either convex or concave, then the bifurcation curve is C-shaped.
• Classification : 34B15, 34B18, 34C23, 74G35
• Format : Talk at Waseda University
• Author(s) :
  • Shao-Yuan Huang (National Taipei University of Education)

[00519] Non-Newtonian fluids with discontinuous-in-time stress tensor.

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G502
• Type : Contributed Talk
• Abstract : We consider the system of equations describing the flow of incompressible fluids in bounded domain. Here, the Cauchy stress tensor has asymptotically $(s-1)$-growth with the parameter $s$ depending on the spatial and time variable. We do not assume any smoothness of $s$ with respect to time variable. Such a setting is a natural choice if the material properties are instantaneous. We establish the existence of weak solution provided that $s\ge\frac{3d+2}{d+2}$.
• Classification : 35K51, 35Q30, 76D05
• Format : Talk at Waseda University
• Author(s) :
  • Miroslav Bulicek (Charles University)
  • Piotr Gwiazda (Polish Academy of Sciences)
  • Jakub Skrzeczkowski (University of Warsaw)
  • Jakub Woźnicki (University of Warsaw)

[00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G502
• Type : Contributed Talk
• Abstract : An improvised collocation technique has been proposed to discretize multi-parameter fourth order non-linear extended Fisher Kolmogorov equation. The spatial direction has been discretized with quintic Hermite splines whereas temporal direction has been discretized with weighted finite difference scheme. The fourth order equation in space direction has been decomposed into second order using space splitting by introducing a new variable. The space splitting has been proposed to improvise the convergence of approximate solution. The proposed equation has been analyzed on uniform grid in both space and time directions. Error bounds for general order Hermite splines are established. $\epsilon$- uniform rate of convergence for the proposed scheme has also been discussed elaborately. The technique is illustrated by various numerical examples and error growth has been discussed by computing $L_2$ and $L_\infty$ norms.
• Classification : 35K41, 35K55, 65M70, 65N35
• Format : Online Talk on Zoom
• Author(s) :
  • Shelly Arora (Punjabi University, Patiala)
  • Priyanka Bhardwaj (Punjabi University, Patiala)
  • Saroj Kumar Sahani (South Asian University, New Delhi)

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

room : G601

• [05208] Basic Propagation Number
  • Format : Talk at Waseda University
  • Author(s) :
    • Juan B Gutierrez (University of Texas at San Antonio)
  • Abstract : In this talk, I present a framework that describes the necessary and sufficient conditions for propagation of one or more undesirable species, named here the nonconformist species, in a given environment when there is an intervention trying to counter their propagation. We assume that the dispersal of the nonconformist could be characterized by a reaction-diffusion process, whereas there is no spatial dependence for the action of the countermeasures. I present a generalized method that can analyze an arbitrary number of nonconformist species and countermeasures.

contributed talk: CT038

room : G602

[02692] Discovering extremal domains via shape optimization for passive tracers

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : Work in passive tracers investigates how properties of a tracer distribution depend on boundary conditions and properties of the underlying fluid flow. We apply shape optimization to discover extremal domains for Poiseuille flow informed by analytic predictions of spatial moments - such as mean, effective diffusivity, skewness - derived in prior work. With this combination of asymptotic formulas and numerical study, we find and report on surprising nonlinear behavior depending on shape parameters.
• Classification : 35Kxx, 90C90
• Format : Talk at Waseda University
• Author(s) :
  • Manuchehr Aminian (California State Polytechnic University Pomona)

[02566] A spherically symmetric and steady flow describing the motion of a viscous gaseous star

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : We consider a system of equations describing a spherically symmetric $n$-dimensional motion of a gaseous star, whose gas is viscous, heat-conducting, self-gravitating and bounded by the free-surface, and flows around a central rigid sphere. We discuss first unique existence of the solution to the corresponding stationary problem, and next do a large-time behaviour of the flow, under a certain restricted but physically plausible condition on parameters and initial data.
• Classification : 35M33, 35Q30, 35R35, 35Q85, 76N10
• Format : Talk at Waseda University
• Author(s) :
  • Morimichi Umehara (University of Miyazaki)

[02581] Well-Posedness and smoothness of geometric flows with nonlinear boundary conditions

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : Geometric flows are geometric evolution equations often depicting physical phenomena. We consider a class of geometric flows of order $2m \in 2\mathbb{N}$ describing evolving $n$-manifolds attached to fixed hypersurfaces with some nonlinear boundary conditions. We modify the theory of Maximal Regularity to accommodate quasilinear parabolic PDEs with such boundary conditions. For initial conditions in $W_p^{2m – \frac{2m}{p}}, p\geq \max\{2m, \frac{n}{2m}\}$) we show well-posedness and instantaneous smoothing of the solution on a maximal interval of existence.
• Classification : 35Kxx, 35Qxx
• Format : Talk at Waseda University
• Author(s) :
  • Daniel Goldberg (Technion-Israel Institute of Technology)

[01080] About Thermistor Problem: numerical study using Discrete Duality Finite Volume

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G602
• Type : Contributed Talk
• Abstract : We propose a DDFV for a coupled nonlinear parabolic-elliptic equations. The system is known as a generalization of the Thermistor problem which models a temperature dependent electrical resistor. We first establish some a prior estimates satisfied by the sequences of approximate solutions. Then, it yields the compactness of these sequences. Passing to the limit in the numerical scheme, we finally obtain that the limit of the sequence of approximate solutions is a weak solution to the problem under study.
• Classification : 35M30, 35K92, 35J46, 65N08
• Author(s) :
  • Manar Lahrache (Moulay Ismail University, Faculty of Science, Meknes, Morocco)

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

room : G605

• [04448] On the Riccati dynamics of 2D Euler-Poisson equations with attractive forcing
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yongki Lee (Georgia Southern University)
  • Abstract : The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows. In this talk, a Riccati system that governs pressureless two-dimensional EP equations is discussed. The evolution of divergence is governed by the Riccati type equation with several nonlinear/nonlocal terms. Among these, the vorticity accelerates divergence while others further amplify the blow-up behavior of a flow. The growth of these blow-up amplifying terms are related to the Riesz transform of density, which lacks a uniform bound makes it difficult to study global solutions of the multi-dimensional EP system. We show that the Riccati system can afford to have global solutions, as long as the growth rate of blow-up amplifying terms is not higher than exponential, and admits global smooth solutions for a large set of initial configurations. Several recent works in a similar vein will be reviewed.
• [04918] Critical thresholds in spherically symmetric Euler-Poisson systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Manas Bhatnagar (University of Massachusetts Amherst)
  • Abstract : We will see an introduction to the concept of Critical Threshold Phenomena (CTP) and how it plays a role in the Euler-Poisson systems. We will go over some of the existing results in this area and how the techniques have developed over time. In the end, we will see some new results on the multidimensional spherically symmetric Euler-Poisson systems.
• [04518] On multi-dimensional rarefaction waves
  • Format : Talk at Waseda University
  • Author(s) :
    • Tianwen Luo (Tsinghua University)
    • Pin Yu (Tsinghua University)
  • Abstract : We study the two-dimensional acoustical rarefaction waves under the irrotational assumptions. We provide a new energy estimates without loss of derivatives. We also give a detailed geometric description of the rarefaction wave fronts. As an application, we show that the Riemann problem is structurally stable in the regime of two families of rarefaction waves. This is a joint work with Prof. Pin Yu in Tsinghua Univerisity.
• [04947] Nonlocal traffic flow models
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Hamori (University of South Carolina)
    • Yongki Lee (Georgia Southern University)
    • Yi Sun (University of South Carolina)
    • Changhui Tan (University of South Carolina)
  • Abstract : In this talk, I will discuss a family of traffic flow models. The conventional Lighthill-Whitham-Richards model is notorious for exhibiting finite-time shock formation for all generic initial data. To address this issue, I will introduce a family of nonlocal traffic flow models, which incorporate look-ahead interactions. These models can be derived from discrete cellular automata models. Interestingly, we will explore how the nonlocal slowdown interactions prevent the shock formation, under certain suitable settings. Furthermore, I will also discuss the extension of these nonlocal models to second-order traffic flow models.

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

room : G606

• [03234] Duality Arguments in Analysis of Viscoelastic Contact Problem
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anna Ochal (Jagiellonian University in Krakow)
  • Abstract : We consider a mathematical model which describes the quasistatic frictionless contact of a viscoelastic body with a rigid-plastic foundation. We provide three different variational formulation of the model in which the unknowns are the displacement, the stress and the strain, respectively. We prove that they are pairwise dual of each other and they are well-posedness. The proofs are based on recent results on history-dependent variational inequalities and inclusions.
• [03636] Frictional contact problem for electrorheological fluid flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dariusz Pączka ( Warsaw University of Technology)
  • Abstract : We study the stationary flow of an isothermal, homogeneous and incompressible electrorheological fluid with slip boundary conditions of frictional type. The variational formulation of the flow problem has the form of a hemivariational inequality. Existence and uniqueness of a weak solution to the hemivariational inequality is proved for a material function $p(\cdot)$ of an electric field without any condition of monotonicity type on the extra stress tensor. This result is established by abstract theorems on existence and uniqueness of a solution to a subdifferential operator inclusion and a hemivariational inequality in the variable exponent Sobolev space.
• [03327] Numerical analysis of history-dependent variational-hemivariational inequality by virtual element method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wenqiang Xiao (School of Mathematical Sciences, Peking University)
  • Abstract : In this talk, we mainly introduce the virtual element method for solving two types of history-dependent variational-hemivariational inequalities arising in contact problems. In the first model, we consider an elastic material. The contact is modelled with a total slip-dependent version of Coulomb’s law of dry friction. In the second model, we consider viscoelastic material. We introduce fully discrete schemes for the above two problems, where the temporal integration is approximated by trapezoidal rule and the spatial variable is approximated by the virtual element methods. An optimal order error estimates is derived under appropriate solution regularity assumptions. Finally, numerical examples are reported, providing numerical evidence of the optimal convergence order theoretically predicted.
• [03250] Stability analysis for nonstationary Stokes hemivariational inequality
  • Format : Online Talk on Zoom
  • Author(s) :
    • Changjie Fang (Chongqing University of Posts and Telecommunications)
  • Abstract : In this talk, we consider hemivariational inequality problem for the evolutionary Stokes equations with a nonlinear slip boundary condition. We assume the slip boundary condition together with a Clarke subdifferential relation between the stress tensor and velocity. The existence of weak solutions is obtained by Galerkin method. In addition, stability is analyzed for a perturbed hemivariational inequality. We also present a result on the existence of a solution to an optimal control problem for the nonstationary Stokes hemivariational inequality

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

room : G701

• [04536] On stability of KdV solitons
  • Format : Talk at Waseda University
  • Author(s) :
    • Derchyi Wu (Institute of Mathematics, Academia Sinica,)
  • Abstract : Applying the inverse scattering theory, we present an orbital stability theorem of KdV $n$-solitons with explicit phase shifts.
• [05530] Rogue waves in the massive Thirring model
  • Format : Online Talk on Zoom
  • Author(s) :
    • Junchao Chen (Lishui University)
  • Abstract : In this talk, I will talk about general rogue wave solutions in the massive Thirring (MT) model. These rational solutions are derived by using the KP hierarchy reduction method and presented explicitly in terms of determinants whose matrix elements are elementary Schur polynomials. In the reduction process, three reduction conditions including one index- and two dimension-ones are proved to be consistent by only one constraint relation on parameters of tau-functions of the KP-Toda hierarchy. It is found that the rogue wave solutions in the MT model depend on two background parameters, which influence their orientation and duration. Differing from many other coupled integrable systems, the MT model only admits the rogue waves of bright-type, and the higher-order rogue waves represent the superposition of fundamental ones in which the non-reducible parameters determine the arrangement patterns of fundamental rogue waves. Particularly, the super rogue wave at each order can be achieved simply by setting all internal parameters to be zero, resulting in the amplitude of the sole huge peak of order N being 2N + 1 times the background. Finally, rogue wave patterns are discussed when one of the internal parameters is large. Similar to other integrable equations, the patterns are shown to be associated with the root structures of the Yablonskii-Vorob’ev polynomial hierarchy through a linear transformation. This work is joint with Bo Yang and Bao-Feng Feng.
• [03606] Resonant breather and rogue wave solutions to a coupled Sasa-Satsuma equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Baofeng Feng (University of Texas Rio Grande Valley )
    • Chengfa Wu (Shenzhen University)
  • Abstract : We firstly derive a set of 7 bilinear equations for a coupled Sasa-Sastsuma (CSSI) equation under nonzero boundary conditions and show that they can be reduced from the discrete and continuous KP-Toda hierarchy through a series of reductions such as the CKP-, dimension- and complex conjugate reductions. Then, we derive breather and rogue wave solutions in determinant form. In the last, we show the dynamical behavior of these solutions especially resonant breather solutions.
• [03607] Resonant breather and rogue wave solutions to a coupled Sasa-Satsuma equation
  • Author(s) :
    • Baofeng Feng (University of Texas Rio Grande Valley )
    • Chengfa Wu (Shenzhen University)
  • Abstract : We firstly derive a set of 7 bilinear equations for a coupled Sasa-Sastsuma (CSSI) equation under nonzero boundary conditions and and show they can be reduced from the discrete and continuous KP-Toda hierarchy through a series of reductions such as CKP-, dimension- and complex conjugate reductions. Then, we derive breather and rogue wave solutions in determinant form. In the last, we show the dynamical behavior of these solutions especially resonant breather solutions.

contributed talk: CT051

room : G702

[00579] Explosion times and its bounds for a system of semilinear SPDEs

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
• Type : Contributed Talk
• Abstract : In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, the bounds of the explosion times are obtained by using explicit solutions of an associated system of random PDEs and a formula due to Yor. We provide an estimate for the probability of the finite-time blow-up and the impact of the noise on the solution is investigated.
• Classification : 35R60, 60H15, 74H35
• Format : Talk at Waseda University
• Author(s) :
  • Karthikeyan Shanmugasundaram (Periyar University)

[01389] Exponential Behavior of Nonlinear Stochastic Partial Functional Equations Driven by Poisson Jumps and Rosenblatt Process

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
• Type : Contributed Talk
• Abstract : In this paper, we discuss the asymptotic behavior of mild solutions of nonlinear stochastic partial functional equations driven by Poisson jumps and the Rosenblatt process in a Hilbert space. The Rosenblatt process is the simplest non-Gaussian Hermite process. It has continuous non-differentiable paths and is self-similar with stationary increments. It is Murray Rosenblatt who first conceived of it. The results are obtained by using the Banach fixed point theorem and the theory of resolvent operator developed by Grimmer. Finally, an example is provided to illustrate the effectiveness of the obtained results.
• Classification : 35R60, 60H15, Stochastic Differential Equations
• Format : Talk at Waseda University
• Author(s) :
  • Anguraj Annamalai (PSG College of Arts & Science, Coimbatore, Tamil Nadu, India)

[01069] Global existence and stability of three species predator-prey system with prey-taxis

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
• Type : Contributed Talk
• Abstract : In this paper, we study the initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator in a bounded domain $\Omega \subset \mathbb{R}^n (n\geq 1)$with smooth boundary and homogeneous Neumann boundary conditions. The model parameters are assumed to be positive constants. We first prove the global existence of classical solutions under suitable assumptions on the prey-taxis coefficients $\chi_1,\chi_2$ and $d$. Moreover, we establish the global stability of the prey-only state and coexistence steady states by using Lyapunov functionals and LaSalle's invariance principle.
• Classification : 35A01, 35B35, Partial differential equations and Mathematical Biology ( To prove Global existence and stability for chemotaxis systems and predator-prey systems )
• Format : Talk at Waseda University
• Author(s) :
  • GURUSAMY ARUMUGAM (The Hong Kong Polytechnic University )

[02026] Variants of the penalty method for contact problems - Formulations unifying Nitsche and penalty methods

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
• Type : Contributed Talk
• Abstract : The penalty method is a simple yet effective computational technique of handling unilateral contact problems. In addition to its inconsistent, this method is often criticized of ill-conditioning when the penalty parameter goes to zero. We propose here new penalty methods overcoming the conditioning issue. We also established that some of our penalty formulations are equivalent of variants of Nitsche’s method, meaning that the inconsistent of these penalty methods is insignificant.
• Classification : 35A35, 65J15, 74M15, 74B05
• Format : Online Talk on Zoom
• Author(s) :
  • Ibrahima Dione (Professor at Moncton university)

[02641] Reconstructing electron backscatter diffraction data using vectorized total variation flow

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
• Type : Contributed Talk
• Abstract : Polycrystalline materials consist of crystal grains with distinct grain orientations and crystal structure. Electron backscatter diffraction is used to record the grain orientation. This orientation data might contain noise as well as the missing regions. We propose reconstructing the orientation data using weighted total variation flow, which is a pde obtained from solving the minimization problem. We then fill the missing region using the TV flow. This talk discusses the application of this reconstruction technique.
• Classification : 35A15
• Author(s) :
  • Emmanuel Atoleya Atindama (Clarkson University)
  • Prashant Athavale (Clarkson University)
  • Gunay Dogan (National Institute of Standards and Technology)

MS [00975] Data-driven methods for learning mathematical models

room : G703

• [05503] Recent Advances in Weak Form-Based System Identification
  • Format : Online Talk on Zoom
  • Author(s) :
    • David Bortz (University of Colorado - Boulder)
    • Daniel Messenger (University of Colorado - Boulder)
  • Abstract : Recent advances in data-driven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will present our weak form methodology which has proven to have surprising performance properties. After describing our equation learning (WSINDy) and parameter estimation (WENDy) algorithms, I will discuss applications to several benchmark problems to illustrate the computational efficiency, noise robustness, and modest data needs.
• [05502] Identification of variable coefficient PDEs using group projected subspace pursuit
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yuchen He (Shanghai Jiao Tong University)
    • Sung Ha Kang (Georgia Institute of Techonology)
    • Wenjing Liao (Georgia Institute of Technology)
    • Hao Liu (Hong Kong Baptist University)
    • Yingjie Liu (Georgia Institute of Technology)
  • Abstract : We propose a novel scheme, GP-IDENT, for identifying variable coefficient PDEs from noisy observations of single solution trajectories. To effectively solve the associated feature selection problems, we designed a group projected subspace pursuit (GPSP) algorithm, which is also suitable for general feature selection problems with group structure. We will provide examples to show that GP-IDENT can successively identify many non-linear high-order PDEs, and its effectiveness is also justified via comparisons with state-of-the-art methods.
• [05509] How much can one learn a PDE from its solution?
  • Format : Talk at Waseda University
  • Author(s) :
    • Yimin Zhong (Auburn University )
    • Hongkai Zhao (Duke University)
    • Yuchen He (Shanghai Jiao Tong University)
  • Abstract : In this work we study a few basic questions for PDE learning from observed solution data. Using various types of PDEs, we show 1) how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and 2) identifiability of a differential operator from solution data on local patches. Then we propose a consistent and sparse local regression method (CaSLR) for general PDE identification. Our method is data driven and requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.
• [05246] Learning Koopman Operators that Generalize Well
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bethany Lusch (Argonne National Laboratory)
  • Abstract : The Koopman operator is a way to represent a nonlinear dynamical system as a globally linear system. However, the linear system is infinite-dimensional, and the representation is difficult to find. Much recent research is on data-driven methods to approximate the Koopman operator. However, finding an approximation that generalizes well for a large region without finely sampling the space can be challenging. We explore learning a Koopman operator that can generalize well given limited data.

MS [01174] Hypernetworks and their dynamics in theory and applications

room : G704

• [04246] Bridging between higher-order mechanisms and phenomena
  • Format : Talk at Waseda University
  • Author(s) :
    • Giovanni Petri (CENTAI)
  • Abstract : Complex networks have become the main paradigm for modelling the dynamics of complex interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the multilayered real organization of many social, biological and man-made systems. At the same time, higher-order observables, typically topological or information-theoretic in nature and often sharing the same simplicial language, have been gathering attention for their capacity to capture properties of complex systems that are invisible to standard statistical descriptions. This had led to a certain confusion between these two facets, mechanisms on one side, phenomena on the other. Here, using recent examples from both dynamical models and neuroimaging analysis, I highlight collective behaviours induced by higher-order interactions, the difficulty in linking data and models through recent advances in topological data analysis and higher-order information theory, and finally outline key open questions for the physics of higher-order complex systems.
• [03667] Emergent hypernetworks in weakly coupled oscillators
  • Format : Talk at Waseda University
  • Author(s) :
    • Eddie Nijholt (Imperial College London)
    • Jorge Luis Ocampo-Espindola (Saint Louis University)
    • Deniz Eroglu (Kadir Has University)
    • István Kiss (Saint Louis University)
    • Tiago Pereira (Universidade de São Paulo)
  • Abstract : Networks of weakly coupled oscillators play a profound role in our understanding of complex systems. Studies on model reconstruction from data show the emergence of hyper-connections corresponding to triplet and higher-order interactions among oscillators, even though such models were originally defined as networks with only pairwise interactions. We show that hypernetworks can spontaneously appear in the presence of pairwise, albeit nonlinear, coupling given certain frequency resonance conditions. The conceptual explanation is that model reconstruction finds the so-called normal form of the system instead, which allows us to predict the emergent hypernetwork in terms of appearing and forbidden motifs. These results are moreover demonstrated in experiments with electrochemical oscillators. This is joint work with Jorge Luis Ocampo-Espindola, Deniz Eroglu, István Z. Kiss and Tiago Pereira.
• [04161] Do higher-order interactions promote coexistence in diverse ecological communities?
  • Format : Talk at Waseda University
  • Author(s) :
    • Theo L Gibbs (Princeton University)
    • Gabriel Gellner (University of Guelph)
    • Simon Levin (Princeton University)
    • Kevin McCann (University of Guelph)
    • Alan Hastings (UC Davis)
    • Jonathan Levine (Princeton University)
  • Abstract : Most ecological models assume that species interactions operate only between pairs of species. In a diverse community, however, higher-order interactions can emerge, in which two or more species jointly impact the growth of a focal species. In this talk, I will discuss two ways that higher-order interactions affect species coexistence. Randomly-sampled higher-order interactions do not promote coexistence, but additional constraints on the higher-order interactions can reverse exclusions caused by pairwise interactions.
• [04389] Hypernetworks: cluster synchronization is a higher order effect
  • Format : Talk at Waseda University
  • Author(s) :
    • Bob Rink (Vrije Universiteit Amsterdam)
    • Eddie Nijholt (Imperial College London)
    • Sören von der Gracht (Paderborn University)
  • Abstract : Many networked systems are governed by non-pairwise interactions that can be encoded by means of a hypernetwork. Here, we define dynamical systems on hypernetworks, and we explain how to classify robust cluster synchronization patterns by finding balanced partitions. We show that synchronization is determined by polynomial systems of high order. Hence, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, nonlinear effect. We show how this generates remarkable synchrony breaking bifurcations.

contributed talk: CT054

room : G709

[00996] A Decentralized Approach for Dynamic Graph Clustering

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G709
• Type : Contributed Talk
• Abstract : Interconnected networks characterized by interacting agents can be represented by weighted graphs, with the weight indicating their connection strength. Graph clustering arises naturally in these networks to assist decision making and co-ordination. Among the clustering methods, spectral clustering has emerged as a powerful tool but suffers from slow convergence for large dynamic graphs. Thus, we propose a fast incremental approach for dynamic graphs as an extension of its equivalent decentralized approach based on wave propagation.
• Classification : 37Mxx, 05Cxx, 65Fxx
• Format : Talk at Waseda University
• Author(s) :
  • Hongyu Zhu (Raytheon Technologies Research Center)
  • Hongyu Zhu (Raytheon Technologies Research Center)
  • Tuhin Sahai (SRI International)

[02220] Analytical approximation of phase dynamics for oscillators without polar symmetry

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G709
• Type : Contributed Talk
• Abstract : Predicting and controlling oscillatory systems, despite its relevance, is still an unachieved goal. A simplification method to ease this task is phase reduction, a dimensional reduction scheme that capture the dynamics of each oscillator in just one variable -the phase-. Despite phase reduction importance, analytical results are only available for systems with polar symmetry. In this talk we show how to perform analytical phase reduction on non-symmetric oscillators.
• Classification : 37Mxx, 37Nxx
• Format : Talk at Waseda University
• Author(s) :
  • Ivan Leon (Tokyo Tech Institute of Technology)
  • Hiroya Nakao (Tokyo Tech Institute of Technology)

[00204] Periodicity and Symmetry on a Class of Integral Equations with Weakly Singular Kernels

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G709
• Type : Contributed Talk
• Abstract : In this study, we introduce the periodic and symmetric properties of the states in a class of weakly singular integral equations. Motivation of this paper is based on the main results of previous paper: bounded forces produce bounded states in the infinite field. We furthermore observed that in finite times, steady states show. For each periodicity, two kinds of initial conditions apply: one is same as the original one, the other is the steady state from previous period. For symmetry, we apply same magnitudes of forces but opposite directions.
• Classification : 37Mxx, 31Axx, 33Exx
• Format : Talk at Waseda University
• Author(s) :
  • Shihchung Chiang (Chung Hua University)

[00939] Learning Dynamical Systems from Invariant Measures

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G709
• Type : Contributed Talk
• Abstract : Standard data-driven techniques for learning dynamical systems struggle when observational data has been sampled slowly and state derivatives cannot be accurately estimated. To address this challenge, we assume that the available measurements reliably describe the asymptotic statistics of the dynamical process in question, and we instead treat invariant measures as inference data. We reformulate the velocity learning as a PDE constrained optimization and present several numerical examples to demonstrate the effectiveness of the proposed approach.
• Classification : 37Mxx, 37Axx
• Format : Online Talk on Zoom
• Author(s) :
  • Jonah Botvinick-Greenhouse (Cornell University)
  • Yunan Yang (ETH Zürich)

contributed talk: CT052

room : G710

[02027] Understanding Difference Equation System Models using Telescoping Sums Method

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710
• Type : Contributed Talk
• Abstract : Difference equations frequently appear as discrete mathematical models of various biological and environmental phenomena. In this paper, the authors study the following systems: \begin{equation*} x_{n+1} = \dfrac{x_{n-3}}{\pm 1 \pm y_n x_{n-1} y_{n-2} x_{n-3}},\ \ y_{n+1} = \dfrac{y_{n-3}}{\pm 1 \pm x_n y_{n-1} x_{n-2} y_{n-3}}, \end{equation*} which were first considered by Elsayed in 2015, and results were proven using mathematical induction. This time, the authors present the solution forms of each system using telescoping sums technique. The advantages and disadvantages of the two methods are discussed. Boundedness and convergence of solutions shall be presented.
• Classification : 39A05, 39A22, 65Q10
• Format : Talk at Waseda University
• Author(s) :
  • Jerico Bravo Bacani (University of the Philippines Baguio)
  • Julius Fergy Tiongson Rabago (Kanazawa University)

[01893] Existence and blow-up solutions of fractional reaction-diffusion system of SPDEs

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710
• Type : Contributed Talk
• Abstract : In this talk, we investigate the existence and finite-time blowup solution of a reaction-diffusion system of stochastic partial differential equations (SPDEs) driven by two dimensional fractional Brownian motion. We provide sufficient conditions for the existence of a global solution. Moreover, we provide lower and upper bounds for the finite-time blowup solution of the system of SPDEs and obtain the lower and upper bounds for the probability of non-explosive solutions to our considered system
• Classification : 35R60, 60H15, 74H35
• Format : Online Talk on Zoom
• Author(s) :
  • Sankar Subramani (Periyar University, Salem, Tamilnadu.)
  • Manil T Mohan (Indian Institute Of Technology, Roorkee)
  • Karthikeyan Shanmugasundaram (Periyar University, Salem, Tamilnadu.)

[00504] Solar Influence on Earth's Seismicity and Applications in Earthquake Forecasting

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710
• Type : Contributed Talk
• Abstract : The scientific community is yet to find an effective method to forecast and avoid earthquake hazards, due to the problem complexity. After decades of debate, the Sun has again been recently brought forth as a potential precursor to earthquakes. This study aims to investigate the existence of such relationship from a dynamical systems perspective. Having confirmed the existence, we also show that Sun data can be included in forecasting models to improve forecasting accuracy.
• Classification : 37N05, 86A15, 60G55, 37Hxx
• Format : Talk at Waseda University
• Author(s) :
  • Matheus Henrique Junqueira Saldanha (University of Tsukuba)
  • Matheus Henrique Junqueira Saldanha (University of Tsukuba)
  • Yoshito Hirata (Faculty of Engineering, Information and Systems, University of Tsukuba)

[00628] Resource Dependent Competition and Extinction

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710
• Type : Contributed Talk
• Abstract : The classical theory of competitive exclusion does not consider the type of interaction between species. We create a new competition model in which the maximum population of a species is dependent on the availability of resources, or food supply, and competition is in the form of competition for these resources. We find this model always leads to stable coexistence and we investigate ways to bring about extinction.
• Classification : 37N25, 92D25, 92-10
• Format : Talk at Waseda University
• Author(s) :
  • Robert Garvey (University of Limerick)
  • Andrew Fowler (University of Limerick)

[00525] Global effect of COVID-19 disease dynamics on tertiary education system in developing countries

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710
• Type : Contributed Talk
• Abstract : A mathematical model that describes the effect of COVID-19 dynamics on the student population of higher learning institutions was studied. Qualitative analyses were done on the model, and numerical simulations were used to evaluate the effects of personal protective, quarantine, treatment, and management measures to mitigate the community spread of COVID-19. Finally, a cost-effectiveness analysis was used to ascertain the most-effective and least expensive strategy required for preventing and controlling the spread of the pandemic.
• Classification : 37N25, 37N35, 37N40, 37D10, 34C40
• Format : Online Talk on Zoom
• Author(s) :
  • John Olajide Akanni (Koladaisi University Ibadan, Oyo State, Nigeria)
  • Afeeze Abidemi (Federal University of Technology, Akure, Ondo State, Nigeria)
  • Oluwole Daniel Makinde (Faculty of Military Science, Stellenbosch University, South Africa)

MS [00595] Combinatorial topological dynamics

room : G802

• [03335] Morse-Smale quadrangulations and persistence of vector fields
  • Format : Talk at Waseda University
  • Author(s) :
    • Claudia Landi (Università di Modena e Reggio Emilia)
    • Clemens Luc Bannwart (Università di Modena e Reggio Emilia)
  • Abstract : The goal of this talk is to introduce a persistence barcode for discrete gradient vector fields defined on a combinatorial 2-manifold. The main ingredient is a decomposition of the manifold into quadrangle regions with vertices ordinately given by sinks, saddles, sources, and saddles. We will consider a bottleneck distance and an interleaving distance for such barcodes and we will present results about their stability.
• [04607] On the dynamics of the combinatorial model of the real line
  • Format : Online Talk on Zoom
  • Author(s) :
    • Pedro J. Chocano (Rey Juan Carlos University)
  • Abstract : In this talk, we describe the dynamics that appear when we consider a discrete dynamical system defined on the combinatorial model of the real line. Particularly, we show that there are no periodic points of period greater than or equal to 3, which contrasts with the classical setting (Sharkovski theorem). This fact motivates us to introduce multivalued maps to get richer dynamics than the ones obtained from single valued maps. To conclude we provide some examples.
• [04886] Topological Inference of the Conley Index
  • Format : Online Talk on Zoom
  • Author(s) :
    • Vidit Nanda (University of Oxford)
    • Ka Man Yim (University of Oxford)
  • Abstract : The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.
• [05010] Analysis of solids regarded as compositions of discrete entities
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andrey Jivkov (The University of Manchester)
  • Abstract : In contrast with the idealisation of materials as continua, their internal structures are regarded here as polyhedral complexes. One approach to formulate conservation laws of scalar (mass, energy, charge) and vector (linear and angular momentum) quantities on such complexes is presented. It uses combi-natorial differential forms, representing physical quantities, and operations with such forms (exterior derivatives, exterior products, and codifferentials), describing processes and conservations. The derived conservation laws are background independent.

MS [00766] Deep learning techniques for inverse problems and imaging

room : G808

• [03603] Deep learning-based medical image reconstruction from incomplete data
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qiaoqiao Ding (Shanghai Jiao Tong University)
  • Abstract : Image reconstruction from down-sampled and corrupted measurements, such as fast MRI and sparse-view/low-dose CT, is mathematically ill-posed inverse problem. Deep neural network (DNN) has been becoming a prominent tool in the recent development of medical image reconstruction methods. In this talk, I will introduce our work on incorporating classical image reconstruction method and deep learning methods. The experiments on both sparse-view CT and low-dose CT problem show that the proposed method provided state-of-the-art performance.
• [05360] Deep Unrolling Networks with Recurrent Momentum Acceleration
  • Format : Talk at Waseda University
  • Author(s) :
    • Qingping Zhou (School of Mathematics and Statistics, Central South University)
    • Junqi Tang (School of Mathematics, University of Birmingham)
    • Jinglai Li (School of Mathematics, University of Birmingham)
  • Abstract : Leveraging model-based iterative algorithms and deep learning, deep unrolling networks (DuNets) address inverse imaging problems. However, nonlinear problems hinder their efficacy. Our proposed recurrent momentum acceleration (RMA) framework employs a LSTM-RNN to simulate momentum acceleration, enhancing DuNets' performance. Applied to the learned proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods, it results in LPGD-RMA and LPD-RMA, respectively. Experimental results on nonlinear deconvolution and electrical impedance tomography indicate significant improvements, particularly for strongly ill-posed problems.
• [05368] Spatiotemoral Imaging with Diffeomorphic Optimal Transportation
  • Format : Talk at Waseda University
  • Author(s) :
    • Chong Chen (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : This talk introduces a concept called diffeomorphic optimal transportation (DOT), which combines the Wasserstein distance with Benamou--Brenier formula in optimal transportation and the flow of diffeomorphisms in large deformation diffeomorphic metric mapping. Using DOT, a new variational model for joint image reconstruction and motion estimation is proposed, which is suitable for spatiotemporal imaging involving mass-preserving large diffeomorphic deformations. The performance is validated by several numerical experiments in spatiotemporal tomography.
• [05387] Self-supervised deep learning for imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Ji (National University of Singapore)
  • Abstract : Deep learning has proved to be a powerful tool in many domains, including inverse imaging problems. However, most existing successful deep learning solutions to these inverse problems are based on supervised learning, which requires many ground-truth images for training a deep neural network (DNN). This prerequisite on training datasets limits their applicability in data-limited domains, such as medicine and science. In this talk, we will introduce a series of works on self-supervised learning for solving inverse imaging problems. Our approach teaches a DNN to predict images from their noisy and partial measurements without seeing any related truth image, which is achieved by neuralization of Bayesian inference with DNN-based over-parametrization of images. Surprisingly, our proposed self-supervised method can compete well against supervised learning methods in many real-world imaging tasks..

contributed talk: CT050

room : G809

[00909] Lipschitz stability of an inverse problem for Tumor Growth Model

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
• Type : Contributed Talk
• Abstract : We address an inverse problem of recovering a space-dependent semilinear coefficient in the Cahn–Hilliard type system modeling tumor growth described by a system of partial differential equations with Dirichlet boundary condition using boundary-type measurement. First, we establish a new higher-order weighted Carleman estimate for the given system and then a suitable regularity of solutions for this nonlinear system is derived. Finally, we prove Lipschitz type stability for the tumor growth model.
• Classification : 35R30, 35K15
• Format : Talk at Waseda University
• Author(s) :
  • Barani Balan Natesan (Central University of Tamil Nadu)

[02665] Modelling metal biosorption on algae-bacteria granular biofilms

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
• Type : Contributed Talk
• Abstract : A multiscale mathematical model describing the metals biosorption on algal-bacterial photogranules within a sequencing batch reactor is presented. The model is based on systems of mixed PDEs on a spherical free boundary domain and IDEs derived from mass conservation principles. The model is integrated numerically to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and biofilm adsorption properties on metal removal.
• Classification : 35R35, 35L45, 92-10, 92B05
• Format : Talk at Waseda University
• Author(s) :
  • Fabiana Russo (Temple University)
  • Alberto Tenore (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)
  • Maria Rosaria Mattei (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)
  • Luigi Frunzo (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)

[02666] Dynamics of biofouling in microfiltration systems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
• Type : Contributed Talk
• Abstract : Membrane technology is one of the most promising engineering strategies for freshwater production and wastewater treatment. The major concern results in the formation of a fouling layer leading to increasing hydraulic resistance and flux decline during membrane operations. A one-dimensional continuous model has been developed by considering a free boundary value problem describing biofouling dynamics in membrane bioreactors. Numerical results demonstrated the model accuracy in predicting biofouling effects and the implications on process management.
• Classification : 35R35, 35L45, 92-10, 92B05
• Format : Talk at Waseda University
• Author(s) :
  • Vincenzo Luongo (University of Naples Federico II)
  • Nicholas Cogan (Florida State University)

[02311] Lipschitz Stability of Recovering the Conductivity from Internal Current Densities

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
• Type : Contributed Talk
• Abstract : Hybrid imaging techniques have been developed recently to produce clearer images than those produced by electrical impedance tomography. We focus on the inverse problem arising in the quantitative step of many hybrid imaging methods, formulated as recovering the isotropic conductivity of an object given internal current densities generated by applying different boundary conditions to the electrostatic equation. We provide a local Lipschitz stability for the general inverse problem in both full and partial data cases.
• Classification : 35R30, 65N21, 92C55
• Format : Talk at Waseda University
• Author(s) :
  • Lingyun Qiu (Yau Mathematical Sciences Center, Tsinghua University; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
  • Siqin Zheng (Yau Mathematical Sciences Center, Tsinghua University)

[00973] Inverse source problem for a seventh-order Korteweg–de Vries equation

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
• Type : Contributed Talk
• Abstract : In this talk, we establish the boundary stability result concerning the inverse source problem for a seventh-order Korteweg–de Vries (KdV) equation. Initially, we derive a new boundary Carleman estimate for the given system using the Dirichlet–Neumann type boundary conditions. We finally obtain a Lipschitz-type boundary stability estimate of a seventh-order KdV equation using the regularity results of the nonlinear KdV equation and the Bukhgeim-Klibanov method.
• Classification : 35R30, 35Q53
• Format : Online Talk on Zoom
• Author(s) :
  • Arivazhagan Anbu (SRM Institute of Science and Technology, Tiruchirappalli )
  • Arivazhagan Anbu (Indian Institute of Technology Gandhinagar)

MS [00787] Space Weather: Modeling, Surrogates and Uncertainty Quantification

room : F308

• [02020] Model Calibration for Ensemble CME Simulation with the SWMF
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongfan Chen (University of Michigan)
    • Yang Chen (University of Michigan)
    • Xun Huan (University of Michigan)
    • Bartholomeus van der Holst (University of Michigan)
    • Shasha Zou (University of Michigan)
    • Zhenguang Huang (University of Michigan)
    • Nishtha Sachdeva (University of Michigan)
    • Aniket Jivani (University of Michigan)
    • Daniel Iong (University of Michigan)
    • Ward Manchester (University of Michigan)
    • Gabor Toth (University of Michigan)
    • Yifu An (University of Michigan)
  • Abstract : The Space Weather Modeling Framework $\left(SWMF\right)$ enables ensemble coronal mass ejection $\left(CME\right)$ simulation based on coupled first principles and/or empirical models. The main challenge of calibrating unknown parameters of such physics-based models lies in high computational complexity and potential model inadequacy. In this talk, we present model calibration for the parameters of Gibson-Low flux-rope-based CMEs. Leveraging machine learning tools, we quantify the uncertainty in flux-rope parameters by assimilating in-situ and remote observations.
• [02101] Model reduction with data assimilation for thermospheric mass density forecasting
  • Format : Talk at Waseda University
  • Author(s) :
    • Peng Mun Siew (Massachusetts Institute of Technology)
    • Richard Linares (Massachusetts Institute of Technology)
  • Abstract : Earth atmospheric drag remains one of the main sources of uncertainties for orbit prediction of space objects residing in the Low Earth Orbit. In this work, we explore the usage of machine learning-based techniques to develop a data-driven dynamic reduced-order model for real-time forecasting of the thermospheric density field. The high-dimensional thermospheric density field is projected onto a lower-dimensional latent space using nonlinear embedding via the deep encoder network.
• [01696] Bayesian Parameter Estimation for Ambient Solar Wind Models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Opal Issan (University of California San Diego)
    • Boris Kramer (University of California San Diego)
    • Enrico Camporeale (National Oceanic and Atmospheric Administration)
  • Abstract : The solar wind is an essential driver of space weather geomagnetic storms. A significant challenge in using first-principle solar wind models is estimating input parameters that can not be directly measured. Thus, we need to quantify the uncertainty of such input parameters on the solar wind. We perform global sensitivity analysis to understand which parameters influence the model output the most and learn the posterior distribution of the most influential input parameters via Bayesian inference.
• [02759] A multi-fidelity boosted method with built-in uncertainty quantification and its application to geomagnetic storms prediction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andong Hu (CIRES, CU Boulder)
    • Enrico camporeale (CIRES, CU Boulder)
    • Brian swiger (CIRES, CU Boulder)
  • Abstract : An multi-fidelity based Gated Recurrent Unit (GRU) method is developed to assist ensemble technique to forecast extreme space weather events and their reliability. We have implemented this method on two space weather applications, i.e., 1) a one-to-six-hour lead-time model that predicts the value of Disturbance storm time (Dst) using solar wind (SW) data; and 2) an geoelectric field model with multi-hour leading time using SW and SuperMag data.

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

room : F309

• [05386] Inverse problems for nonlocal PDEs with applications to quantum optics
  • Author(s) :
    • John Schotland (Yale University)
  • Abstract : I will discuss recent work with Jeremy Hoskins and Howard Levinson on reconstruction methods for inverse problems for nonlocal PDEs. Applications to quantum optics will be discussed.
• [05472] Implicit Ensemble Tangent Linear Models (IETLMs) for model differentiation
  • Author(s) :
    • Craig H Bishop (University of Melbourne)
    • Nathan W Eizenberg (University of Melbourne)
  • Abstract : Ideally, Tangent Linear Models (TLMs) predict the difference between perturbed and unperturbed non-linear forecasts of interest. The adjoint of a TLM gives the gradient of the non-linear model and is used in 4DVar data assimilation and in adjoint-based Forecast Sensitivity to Observation Impact (FSOI). The Local Ensemble Tangent Linear Model’s (LETLM) accuracy has been shown to be limited by its inability to account for implicit time stepping. Here we derive Implicit Ensemble TLMs (IETLMs) that, at most, require the number of independent ensemble members to be equal to the number of variables in the implicit computational stencil. The accuracy of the IETLM in the linear regime is confirmed using an implicitly time stepped Lorenz 96 model and a 9-member ensemble. IETLMs feature two sparse matrices: matrix N that operates on an initially unknown future time perturbation, and matrix L that operates on the current time perturbation. For ensemble perturbations in the non-linear regime, we develop a Diagonally Robust (DR) IETLM that reduces the chances of N becoming ill-conditioned. The performance of the DR IETLM was compared with traditional TLM performance using IETLM ensemble perturbations whose “Gilmour et al., 2001” measure of non-linearity ranged up to the non-linearity of operational 32 hr ensemble forecast perturbations. Over a wide range of non-linearity, the DR IETLM performance was found to match that of the traditional TLM provided the initial standard deviation of the ensemble perturbations was times the standard deviation of the test perturbations. Ideal FSOI requires the adjoint of a TLM that accurately predicts the known difference between corrected and uncorrected non-linear forecasts. The DR IETLM was found to meet this FSOI accuracy requirement much more closely than the traditional TLM when the ensemble perturbations were created by subtracting the corrected forecast from ensemble members that were centred on the uncorrected forecast. Finally, if time permits, a method for reducing the size of the ensemble required to produce accurate TLMs will be described.
• [05482] Advances in Integrating AI and Machine Learning with Data Assimilation for Weather Prediction
  • Author(s) :
    • Stephen G Penny (Sofar Ocean)
  • Abstract : Capabilities of AI/ML methods necessary for online data assimilation (DA), such as accounting for accurate model response to perturbations in initial conditions, will be discussed in the context of a variety of increasing complexity dynamical systems ranging from Lorenz-96, to quasi-geostrophic (QG) dynamics, to surface QG turbulence. In this context, the success of recurrent neural networks for achieving this goal will be demonstrated by integrating with conventional DA methods such as the Ensemble Kalman Filter (EnKF) and 4D-Var. Dynamical invariants such as the Lyapunov spectrum will also be explored both as a useful diagnostic and as tool to accelerate the training of ML models. Caveats regarding training on simulated datasets and reanalysis datasets will also be discussed.
• [05497] Learned weakly convex regularisers in inverse problems
  • Author(s) :
    • Zakhar Shumaylov (University of Cambridge)
    • Jeremy Budd (University of Bonn)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : In this talk, we consider the problem of learned regularisation in the area of imaging inverse problems. By showing limitations of existing methods arising in adversarial regularisation, we propose usage of weakly convex regularisers to address the problems. We provide a construction of weakly convex input neural networks and discuss convergence guarantees for the variational problem. We provide numerical evidence to exemplify their usage in the settings of sparse and limited angle computed tomography reconstruction.

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

room : F310

• [05085] Optimal scaling of radial basis function approximations
  • Format : Talk at Waseda University
  • Author(s) :
    • Elisabeth Larsson (Uppsala University)
    • Boštjan Mavrič (Institute of Metals and Technology)
    • Andreas Michael (Uppsala University)
    • Ulrika Sundin (Uppsala University)
  • Abstract : We revisit the question about which shape parameter to use in radial basis function approximations. We compute the flat shape parameter limit of a Gaussian interpolant as an expansion in even powers of the shape parameter and illustrate how the correction terms cancel the dominant part of the error for smooth solution functions. We also provide a closed form expression that explains the shape of the error curves in terms of the shape parameter.
• [04984] Interpolation on the sphere using series kernels
  • Format : Online Talk on Zoom
  • Author(s) :
    • Janin Jäger (KU Eichstätt-Ingolstadt)
    • Simon Hubbert (Birkbeck University of London)
  • Abstract : We study the use of series kernels for interpolation and approximation of data on a d- dimensional sphere. Kernels in series representation allow us to easily deduce geometric properties of the kernel, strict positive definiteness of the kernel, smoothness of the approximant and approximation error estimates. We will show how series representations can be derived for restrictions of radial basis functions from the surrounding Euclidean space to the sphere and state the explicit expansion for the generalised Wendland functions.
• [05064] (β,γ)-Chebyshev functions and points
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Marchetti (University of Padova)
  • Abstract : $(\beta,\gamma)$-Chebyshev functions are a generalization of classical Chebyshev polynomials of the first kind. They consist of a family of orthogonal functions on a subset of $[-1,1]$, which indeed satisfies a three-term recurrence formula and complies with various properties of classical families of orthogonal polynomials. Moreover, for certain configurations of parameters $\beta$ and $\gamma$, the roots of $(\beta,\gamma)$-Chebyshev functions contained in the corresponding orthogonality interval lead to a stable polynomial interpolation process.

contributed talk: CT067

room : F312

[00790] Machine learning methods with error analysis for optimal control problems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F312
• Type : Contributed Talk
• Abstract : We consider optimal control with partial differential equations (()PDE()) and present a numerical method based on machine learning including control error analysis. Physics-Informed Neural Networks (()PINN()) are used with the cost and penalty terms for the PDE as loss function. The model size is iteratively increased until the a posteriori estimated control error satisfies a given accuracy. The method is illustrated with numerical examples for 1D heat transfer and 3D turbine activation.
• Classification : 49M41, 49M25, 68T05, 65G20
• Format : Talk at Waseda University
• Author(s) :
  • Georg Vossen (Kreleld University of Applied Sciences)
  • Semih Sirin (Kreleld University of Applied Sciences)
  • Nicolai Friedlich (Kreleld University of Applied Sciences)

[00091] An infeasible interior-point arc-search algorithm for nonlinear constrained optimization

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F312
• Type : Contributed Talk
• Abstract : Most algorithms based on interior-point methods are categorized as line search since they compute a search direction on a straight line. In this talk, we propose an interior-point method for nonlinear programming problems that computes the search direction along with an ellipsoidal arc. We discuss the convergence of the proposed method, and numerical experiments indicate it can solve the CUTEst benchmark problems in fewer iterations. A modified method can further reduce the computation time.
• Classification : 49M37, 65K05, 90C30, 90C51
• Format : Talk at Waseda University
• Author(s) :
  • Einosuke Iida (Tokyo Institute of Technology)
  • Makoto Yamashita (Tokyo Institute of Technology)
  • Yaguang Yang (US NRC)

[01133] Surface wave propagation in coated poro-elastic layer due to point source

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F312
• Type : Contributed Talk
• Abstract : The impact of an internal energy source on an anisotropic fluid-saturated poro-elastic layer over a non-homogeneous semi-infinite medium is presented. The poroelastic layer is coated with a thin elastic layer. The Fourier transform and Green’s function techniques are applied to analyse the velocity profile of Love-type wave propagation. Error analysis between phase velocity with and without damping has been shown. It is found that the dispersiveness is caused by the non-homogeneity of the semi-infinite medium.
• Classification : 74-10, 74B10, 74H05, 74H45, 74J15
• Format : Online Talk on Zoom
• Author(s) :
  • Dipendu Pramanik (Department of Mathematics, Indian Institute of Technology Indore)
  • Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore)

[01134] A propagating edge wave on a crack plate

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F312
• Type : Contributed Talk
• Abstract : The study analyzes the characteristics of the bending edge wave on a semi-infinite Kirchhoff plate having a stationary crack on the plate and supported by an elastic foundation. The non-local elasticity theory is used to investigate the effect of non-local stress on the propagation of edge waves on the crack plate. Due to the presence of the crack, the stress intensity factor related to the edge wave propagation will be discussed via numerical analysis.
• Classification : 74-10, 74J15, 74K20, Surface waves in elastic plate
• Format : Online Talk on Zoom
• Author(s) :
  • Rahul Som (Department of Mathematics, Indian Institute of Technology Indore, India )
  • Santanu Manna (Assistant Professor, Indian Institute of Technology Indore)

[01038] Study of transitional stresses in rotating disc of materials with different Poisson Ratio under varying temperature

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F312
• Type : Contributed Talk
• Abstract : The present paper is devoted to a study of stress distribution in rotating disc of different materials with variable Poisson ratio. Seth’s transition theory is applied to the problems of elastic-plastic stresses in a rotating disc.Yield criteria and the associated flow rule are not taken into consideration for this study that forms the bases for the development of many researchers investigation. The obtained results allied in the direction of rotating disc made of an incompressible materials required higher angular speed for initial yielding as compared to disc made of gold, nickel and cast iron. At the internal surface of the compressible materials however, the circumferential stresses are showing higher values as compared to incompressible materials i.e. gold, nickel and cast iron required maximum circumferential stresses as compared to rubber material (incompressible). Also rotating disc required maximum stresses for the fully plastic state as compared to the initial yielding state.
• Classification : 74A10, 74B05, 74B10, 74B15, 74C05
• Format : Online Talk on Zoom
• Author(s) :
  • Jatinder Kaur (Chandigarh University Mohali , Chandigarh )
  • Sonia - (Chandigarh University Mohali , Chandigarh )
  • Nikita Madaan (Chandigarh University)

MS [00731] Optimal control: methods and applications

room : F401

• [04787] Curvature related properties of Finsler manifolds and applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Sorin Sabau (Tokai University)
  • Abstract : Finsler manifolds are important generalizations of Euclidean and Riemannian ones with applications in different domains of mathematics, physics and engineering. In the present talk we are going to present some recent results concerning Finsler connections, curvature and relation with statistical models in the real world. We suggest possible development of information geometry on Finsler manifolds that would allow a wide range of applications.
• [03504] Optimal microswimmer control and a microfluidic control example
  • Format : Talk at Waseda University
  • Author(s) :
    • Clement Moreau (RIMS, Kyoto University)
  • Abstract : Microscale swimmers are becoming increasingly prevalent. A natural question that arises from such swimmers, particularly those synthetic swimmers with targeted applications, is that of guidance and control. The purpose of this presentation is to give an overview of the results of optimal control theory in the study of micro-swimming organisms and devices. As an illustrative example, I will present time-optimal trajectories for a model of microfluidic control representing a swimmer guided through the external flow generated by a neighboring wall.
• [04894] Control Problems inspired by Biological Phenomena
  • Format : Talk at Waseda University
  • Author(s) :
    • Tetsuya J. Kobayashi (Institute of Industrial Science, UTokyo)
    • Takehiro Tottori (The University of Tokyo)
    • Shuhei A Horiguchi (The University of Tokyo)
  • Abstract : In order to understand the design principles of biological systems, which sometimes demonstrate more efficient and sophisticated behaviors than engineering systems, the notion of control is indispensable. However, the control theories developed in the engineering domain under their standard assumptions can not necessarily be appropriately applied to biological phenomena, resulting in limited applicability to biological systems. In this presentation, we will discuss several extended control theories inspired by biological phenomena and their potential applications.
• [04045] Control in biology: topics in bacterial growth
  • Format : Talk at Waseda University
  • Author(s) :
    • Jean-Baptiste Caillau (Université Côte d’Azur, CNRS, Inria, LJAD)
  • Abstract : We consider bacteria whose internal dynamics is modelled by the so-called self-replicator equations. This low dimensional ODE system accounts for the behaviour of the cell. The control mimics the allocation process of the cell that decides to use substrate either for gene expression or for its metabolism. Another control can be added to model an external action on a the bio-engineered cell; thanks to optogenetics, one can for instance use light to trigger the production by the cell of a metabolite of interest. Several criteria are of interest here, particularly growth maximisation, or metabolite production. Pontrjagin maximum principle allows to analyse these problems, revealing two characteristic features of these optimal control problems: Fuller phenomenon and turnpike behaviour. Some symbolic-numeric results are given to illustrate these. Joint work with colleagues from Biocore, McTAO and MICROCOSM Inria teams. Support from the ANR is acknowledged (Maximic project).

contributed talk: CT071

room : F402

[00489] Curvature related properties of Finsler manifolds and applications

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
• Type : Contributed Talk
• Abstract : Finsler manifolds are important generalizations of Euclidean and Riemannian ones with applications in different domains of mathematics, physics and engineering. In the present talk we are going to present some recent results concerning Finsler connections, curvature and relation with statistical models in the real world. We suggest possible development of information geometry on Finsler manifolds that would allow a wide range of applications.
• Classification : 53C60
• Format : Talk at Waseda University
• Author(s) :
  • Sorin Sabau (Tokai University)

[02394] Gaussian distributions on Riemannian symmetric spaces of non-positive curvature

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
• Type : Contributed Talk
• Abstract : Learning from data that live in Riemannian manifolds has become central to many applications, ranging from radar signal processing to neuroscience. In this talk, we present a generalisation of Gaussian distributions to Riemannian symmetric spaces of non-positive curvature, which include hyperbolic spaces, as well as spaces of real, complex and quaternion positive definite matrices, and spaces of structured Toeplitz or block-Toeplitz positive definite matrices and discuss applications to geometric statistics on such spaces.
• Classification : 53C22, 53B20, 53B50, 53C80, 53C35, Geometric statistics, probability on manifolds
• Format : Talk at Waseda University
• Author(s) :
  • Cyrus Mostajeran (Nanyang Technological University)
  • Salem Said (Université Grenoble-Alpes)

[02647] Poincaré operators for BGG complexes

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
• Type : Contributed Talk
• Abstract : Poincaré integral operators give explicit potential and provide an inverse of differential operators in the sense of null-homotopy. These operators play a key role in the mathematical and numerical analysis of fluid and electromagnetic problems. Consequences include the well-posedness of the Stokes problem and the p-robustness of high-order finite element methods. In this talk, we derive such operators for the Bernstein-Gelfand-Gelfand (BGG) complexes with potential applications in elasticity and relativity. The idea is to carry over the results for the de-Rham complex by Costabel and McIntosh to these cases by homological algebra.
• Classification : 58J10, 35N05, 58A12, 58A14, 65N30, finite element methods, Hilbert complexes, Bernstein-Gelfand-Gelfand construction, applied analysis
• Format : Talk at Waseda University
• Author(s) :
  • Andreas Čap (University of Vienna)
  • Kaibo Hu (University of Oxford)

[02312] Fractional controllability problem of semilinear hyperbolic systems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
• Type : Contributed Talk
• Abstract : In this communication, we talk about the fractional controllability problem of internally controlled semilinear hyperbolic systems. in the first method, we show the controllability of the linear system using Hilbert uniqueness method HUM, and the fractional controllability problem is solved applying Schauder’s fixed point theorem. Secondly, the analytics study is then attempted by employing generalized inverse methods and changed also into a fixed point problem. Hence, we give an approximate approach to find a control that brings the Riemann-Liouville fractional attained position (resp. speed) to the required position yd1 (resp. speed yd2). Finally, computing simulations are used to confirm the obtained results.
• Classification : 57-XX, 26-XX, 53-XX
• Format : Online Talk on Zoom
• Author(s) :
  • Mustapha Benoudi (Moulay Ismail University)

MS [00882] Geometric Shape Generation II: Design

room : F403

• [01764] Generation of Aesthetic Shape by Integrable Geometry
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenji Kajiwara (Institute of Mathematics for Industry, Kyushu University)
  • Abstract : We consider log-aesthetic curves (LAC), a family of planar curves developed in industrial design, as curves that car designers regard as “aesthetic.” We present a new mathematical framework of LAC on the theory of integrable systems and similarity geometry. Using this framework, LAC is shown to be a similarity geometry analogue of Euler’s Elastica. Based on this, we present generalizations of LAC to space curves and surfaces, which may be useful for generating aesthetic shapes.
• [01613] On the relationship between mimetic discretization and discrete exterior calculus
  • Format : Talk at Waseda University
  • Author(s) :
    • Sampei Hirose (Shibaura Institute of Technology)
  • Abstract : The mimetic discretization is a general framework for the discretization of differential operators using differential forms, including finite element and finite volume methods. On the other hand, the discrete exterior calculus is a method for dealing with differential forms on discrete spaces and is used in computer graphics and other applications. In this talk, the relationship between the mimetic discretization and the discrete exterior calculus developed by Anil Hirani and others will be discussed.
• [01640] Quantifying the shape of data using Topological Data Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • R U Gobithaasan (University Malaysia Terengganu)
    • Kenjiro Takai Miura (Shizuoka University)
    • Pawel Dlotko (Dioscuri Centre in Topological Data Analysis, Mathematical Institute, Polish Academy.)
  • Abstract : Topological Data Analysis (TDA) encodes the global structure and overall connectivity of high dimensional dataset, hence revealing the linearity, distribution, clusters and groups abnormality. TDA has two methodologies namely Persistent homology which produces Persistence Diagram and, TDA Mapper which is a graph representing the structure of the data. In this talk, we will discuss both the methodologies with numerical examples for efficient implementation.
• [01713] Biangular coordinates: moving forward
  • Format : Talk at Waseda University
  • Author(s) :
    • Rushan Ziatdinov (Keimyung University)
  • Abstract : A bipolar coordinate system, known as biangular coordinates, uses two angles rather than one to describe the location of a point in a plane. Most common curves' equations in biangular coordinates are still unknown, and little research has been done on the features of this coordinate system and its potential uses. This work aims to advance our understanding of biangular coordinates.

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

room : F412

• [03355] Martingale solutions to the stochastic thin-film equation in two dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Max Sauerbrey (TU Delft)
  • Abstract : We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension $d=2$ and allow in particular for solutions with non-full support. The construction relies on a Trotter-Kato time-splitting scheme, which was recently employed in $d=1$. The additional analytical challenges due to the higher spatial dimension are overcome using $\alpha$-entropy estimates and corresponding tightness arguments.
• [04416] SOLUTIONS TO THE STOCHASTIC THIN-FILM EQUATION FOR INITIAL VALUES WITH NON-FULL SUPPORT
  • Format : Online Talk on Zoom
  • Author(s) :
    • Manuel Victor Gnann (Delft University of Technology)
    • Konstantinos Dareiotis (University of Leeds)
    • Benjamin Gess (Bielefeld University and Max Planck Institute for Mathematics in the Sciences, Leipzig)
    • Günther Grün (University of Erlangen-Nuremberg)
    • Max Sauerbrey (TU Delft)
  • Abstract : We prove existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilities including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone, and by Gruen, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise. The construction of solutions with non-full support for the initial data using alpha-entropies shall be discussed.
• [04240] Existence of positive solutions to stochastic thin-film equations in the case of weak slippage
  • Format : Talk at Waseda University
  • Author(s) :
    • Lorenz Klein (FAU Erlangen-Nürnberg)
    • Günther Grün (FAU Erlangen-Nürnberg)
  • Abstract : We study stochastic thin-film equations for flow governed by surface tension and conjoining/disjoining interface potentials. For mobility exponents $n \in (2,3)$, we construct martingale solutions via spatial discretization, energy-entropy estimates based on stopping time arguments, and stochastic compactness methods. A crucial ingredient to extend methods used in the case $n=2$ are new discrete formulas for integration by parts which allow to treat nonlinearities related to Stratonovich correction terms. This is joint work with G. Grün.
• [04442] On finite speed of propagation for stochastic thin-film equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Günther Grün (FAU Erlangen-Nürnberg)
    • Lorenz Klein (FAU Erlangen-Nürnberg)
  • Abstract : In this talk, we present an energy method which allows to prove finite speed of propagation for sufficiently regular solutions to a class of stochastic thin-film equations with conservative multiplicative noise under periodic boundary conditions. Analytically, our approach is based on novel integral estimates combined with appropriate modifications of the technique previously used for stochastic porous-media and stochastic parabolic $p$-Laplace equations.

MS [00323] Integrating rough paths into domain applications

room : E501

• [01359] Addressing bias adversarially in online learning.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Elena Gal (University of Oxford)
  • Abstract : We consider a class of online problems where the true label is only observed when a data point is assigned a positive label by a learner, eg for bank loans. In this setting the labelled training set suffers from accumulating bias since it is created by learners past decisions. We propose to address the bias in the training set using adversarial domain adaptation. Our approach significantly exceeds SOTA on a set of challenging benchmark problems.
• [01353] Improving Training of Neural CDEs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jason Michael Rader (University of Oxford)
  • Abstract : Neural CDEs are continuous-time analogues of recurrent neural networks which are effective at handling irregular time steps, densely sampled data, and long time series. We present recent advances in training neural CDEs in a memory efficient manner for large-scale problems.
• [03470] From MMD-Regime detection to MMD-Generative Models with Applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Blanka Horvath (Universiry of Oxford)
    • Zacharia Issa (King's College London)
  • Abstract : Time series data derived from asset returns are known to exhibit certain properties, termed stylised facts, that are consistently prevalent across asset classes and markets. For example, to name a few, asset price returns are widely accepted to be non-stationary, non-auto correlative, and to exhibit volatility clustering. We refer the reader to \cite{cont2001empirical} for a thorough discussion of such properties. In this article we will turn our attention to one property in particular, the heteroscedastic nature of financial time series, since it is of imminent practical relevance to financial analysts and quants for a multitude of practical applications. In this context, one may be interested in whether a given asset returns series---or a set of series, in case of multiple assets---can be divided into periods in which the (random) asset price dynamics can be attributed to the same underlying distribution (up to, perhaps, a small estimation error). Such periods are often referred to as market regimes, and we call the task of finding an effective way of grouping these regimes the market regime clustering problem (MRCP). This article is devoted to the online detection of such regimes, i.e. to developing tools that help us recognise in real time (as data comes in) if a shift in the underlying regime is happening.
• [01236] Capturing Graphs with Hypo-Elliptic Diffusions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Csaba Toth (University of Oxford)
    • Darrick Lee (University of Oxford)
    • Celia Hacker (MPI for Mathematics in the Sciences)
    • Harald Oberhauser (University of Oxford)
  • Abstract : Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves according to a diffusion equation defined using the graph Laplacian. We extend this approach by leveraging classic mathematical results about hypo-elliptic diffusions. This results in a novel tensor-valued graph operator, which we call the hypo-elliptic graph Laplacian. We provide theoretical guarantees and efficient low-rank approximation algorithms.

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

room : E502

• [01940] Statistical inference for rough volatility: minimax theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Grégoire Szymanski (Ecole Polytechnique, CMAP)
    • Carsten Chong (Columbia University, 1Department of Statistics)
    • Marc Hoffmann (Université Paris Dauphine-PSL, Ceremade)
    • Yanghui Liu (Baruch College CUNY, 3Department of Mathematics)
    • Mathieu Rosenbaum (Ecole Polytechnique, CMAP)
  • Abstract : Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous statistical analysis of these models. To do so, we establish minimax lower bounds for parameter estimation and design procedures based on wavelets attaining them. We notably obtain an optimal speed of convergence of $n^{-1/(4H+2)}$ for estimating $H$ based on $n$ sampled data, extending results known only for the easier case $H>1/2$ so far. We therefore establish that the parameters of rough volatility models can be inferred with optimal accuracy in all regimes.
• [01388] Statistical inference for rough volatility: Central limit theorems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carsten H. Chong (HKUST)
    • Marc Hoffmann (Université Paris Dauphine-PSL)
    • Yanghui Liu (Baruch College CUNY)
    • Mathieu Rosenbaum (Ecole Polytechnique)
    • Grégoire Szymanski (Ecole Polytechnique)
  • Abstract : In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter $H<0.5$. In this paper, we derive a consistent and asymptotically mixed normal estimator of $H$ based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a priori relationship between volatility estimators and true volatility. Furthermore, our estimator attains a rate of convergence that is known to be optimal in a minimax sense in parametric rough volatility models.
• [02004] A GMM approach to estimate the roughness of stochastic volatility
  • Format : Online Talk on Zoom
  • Author(s) :
    • Anine Bolko (Aarhus University)
    • Kim Christensen (Aarhus University)
    • Mikko Pakkanen (University of Waterloo)
    • Bezirgen Veliyev (Aarhus University)
  • Abstract : I will present an approach to estimate log normal stochastic volatility models, including rough volatility models, using the generalised method of moments, GMM. In this GMM approach, estimation is done directly using realised measures, e.g., realised variance, avoiding the biases that arise from using a proxy of spot volatility. I will also present asymptotic theory for the GMM estimator, lending itself to inference, and apply the methodology to Oxford-Man realised volatility data.
• [01999] Asymptotically Efficient Estimation for Fractional Brownian Motion with Additive Noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Tetsuya Takabatake (Hiroshima University)
    • Grégoire Szymanski (Ecole Polytechnique, CMAP)
  • Abstract : We will talk about an asymptotically efficient estimation of the Hurst index and the volatility parameter for a fractional Brownian motion with additive noise based on discrete observations. We will propose an asymptotically efficient estimator combining the ideas of the one-step method and a quadratic variation-type estimator using pre-averaged data.

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

room : E503

• [00330] Adversarial flows
  • Format : Talk at Waseda University
  • Author(s) :
    • Lukas Weigand (Friedrich-Alexander-Universität Erlangen-Nürnberg )
    • Tim Roith (Friedrich-Alexander-Universität Erlangen-Nürnberg)
    • Martin Burger (Friedrich-Alexander-Universität Erlangen-Nürnberg)
  • Abstract : The fast gradient method and the fast gradient sign method are two popular methods to generate adversaries of neural networks. Iterative applications of those methods yield differential equations, corresponding to $p$-curves of maximum slope in $\mathbb{R}^d$ for the limit case $p=\infty$. We extend current analysis to this limit case, which allow us to generate distributional adversaries by corresponding $\infty$-curves of maximum slope in the $\infty$-Wasserstein space.
• [02000] Distributionally Robust Linear Predictors using the Max-Sliced Wasserstein Metric
  • Format : Talk at Waseda University
  • Author(s) :
    • Cynthia Rush (Columbia University)
  • Abstract : We study the classical problem of predicting an outcome variable, Y, using a linear combination of a d-dimensional covariate vector, X. We provide conditions under which linear predictors that minimize the worst-case prediction error over a ball of distributions determined by a type of max-sliced Wasserstein metric are equivalent to linear predictors whose coefficients solve: inf_β (E[(Y - < β, X >)^r])^(1/r) + 𝛿 || β ||, where r >1 and 𝛿 > 0 is a regularization parameter. A detailed analysis of the statistical properties of this metric yields a simple recommendation for the choice of regularization parameter. The suggested order of 𝛿, after a suitable normalization of the covariates, is typically d/n, up to logarithmic factors. Our recommendation is computationally straightforward to implement, pivotal, has provable out-of-sample performance guarantees, and does not rely on sparsity assumptions about the true data generating process. This is joint work with Jose Montiel Olea, Amilcar Velez and Johannes Wiesel.
• [00352] Minimax results for Surrogate risks in Adversarial Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Natalie Frank (NYU)
  • Abstract : Robustness to adversarial perturbations is of paramount concern in modern machine learning. One of the state-of-the-art methods for training robust classifiers is adversarial training, which involves minimizing a supremum-based surrogate risk. We prove a minimax theorem for this adversarial surrogate risk and discuss some of the algorithmic implications. Specifically, we use this minimax result to characterize the statistical consistency of surrogate risks in the adversarial setting.
• [00349] Robust second-order estimation algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Po-Ling Loh (University of Cambridge)
  • Abstract : We provide a new computationally-efficient algorithm that finds estimators for the empirical risk minimization problem. We show that these estimators are robust for general statistical models. Our workhorse is a novel robust variant of Newton’s method, and we provide conditions under which our version of Newton’s method variant provides accurate estimators for general convex objectives.

contributed talk: CT112

room : E504

[00394] Numerical methods for option pricing: need and challenges

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : The stability analysis of numerical methods is often challenging. In this talk, compact schemes are considered for the variable coefficient PDEs arising in option pricing. A sufficient condition for stability of the schemes has been derived using novel difference equation based approach. The condition number of amplification matrix is also analyzed, and an estimate for the same is derived. An example is provided using MATLAB to support the assumption taken to assure stability.
• Classification : 65N12, 65N06, 65N15
• Format : Talk at Waseda University
• Author(s) :
  • KULDIP SINGH PATEL (Indian Institute of Technology Patna)

[02118] The finite volume method for solving the oblique derivative BVP in geodesy

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : We formulate the oblique derivative boundary value problem applied in gravity field and present two approaches to its solution by the finite volume method. In the first approach, the oblique derivative in the boundary condition is decomposed into normal and two tangential components and approximated by the central scheme. In the second approach, the oblique derivative in the boundary condition is treated by the first order upwind scheme. Both approaches are tested by various experiments.
• Classification : 65N08
• Author(s) :
  • Zuzana Minarechová (Slovak University of Technology)
  • Marek Macák (Slovak University of Technology)
  • Karol Mikula (Slovak University of Technology)
  • Róbert Čunderlík (Slovak University of Technology)

[00156] Convergence of adaptive algorithms for parametric PDEs with lognormal coefficients

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin methods with residual based error estimation. In this talk we derive an adaptive refinement algorithm for an elliptic parametric PDE with unbounded lognormal diffusion coefficient steered by a reliable error estimator for both the spacial mesh and the stochastic space. Moreover, we will prove the convergence of the derived adaptive algorithm.
• Classification : 65N12, 65N50, 65F10, 65F55, 65D40
• Author(s) :
  • Nando Hegemann (Physikalisch-Technische Bundesanstalt)
  • Nando Farchmin (Physikalisch-Technische Bundesanstalt)

[02417] State equation for oscillator chains

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : We present a linear state equation between kinetic temperature and mass density that has been widely verified in boundary-driven one-dimensional nonequilibrium systems. We show that this relation holds even more universally and in particular when standard relations between purely mechanical and thermodynamic quantities do not apply. We investigate special situations in which phase transitions occur and the relation fails, as common in statistical mechanics. We also provide a theoretical explanation of how this happens.
• Classification : 82C05, 70-10
• Format : Talk at Waseda University
• Author(s) :
  • Vincenzo Di Florio (Politecnico di Torino)
  • Lamberto Rondoni (Politecnico di Torino)
  • Claudio Giberti ( University of Modena and Reggio Emilia)
  • Hong Zhao (Xiamen University)

[01929] Colored noise driven autonomous stochastic resonance

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : A one-dimensional linear autonomous system coupled to a generic stationary nonequilibrium fluctuating bath can exhibit a resonant response when its damped oscillation period matches some characteristic bath’s relaxation time. This condition justifies invoking the stochastic resonance paradigm, even if it can be achieved more easily by tuning the system to the bath and not vice versa, as is usually the case. The simple nature of the mechanism numerically investigated here suggests number of exciting applications
• Classification : 82C31
• Format : Online Talk on Zoom
• Author(s) :
  • SHRABANI MONDAL (Jadavpur University)
  • SHRABANI MONDAL (Jadavpur University)

MS [00949] Optimal and Efficient Algorithms for Inverse Problems

room : E505

• [03055] Conditional sampling via block-triangular transport maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Ricardo Baptista (California Institute of Technology)
    • Nikola Kovachki (NVIDIA)
    • Bamdad Hosseini (University of Washington)
    • Youssef Marzouk (MIT)
  • Abstract : We present an optimal transport framework for conditional sampling of probability measures. Conditional sampling is a fundamental task of solving Bayesian inverse problems and generative modeling. Optimal transport provides a flexible methodology to sample target distributions appearing in these problems by constructing a deterministic coupling that maps samples from a reference distribution (e.g., a standard Gaussian) to the desired target. To extend these tools for conditional sampling, we first develop the theoretical foundations of block triangular transport in a Banach space setting by drawing connections between monotone triangular maps and optimal transport. To learn these block triangular maps, we will then present a computational approach, called monotone generative adversarial networks (MGANs). Our algorithm uses only samples from the underlying joint probability measure and is hence likelihood-free, making it applicable to inverse problems where likelihood evaluations are inaccessible or computationally prohibitive. We will demonstrate the accuracy of MGAN for sampling the posterior distribution in Bayesian inverse problems involving ordinary and partial differential equations, and probabilistic image in-painting.
• [02631] Efficient importance sampling for Bayesian inverse problems using tensor-trains
  • Format : Talk at Waseda University
  • Author(s) :
    • Tiangang Cui (Monash University)
    • Sergey Dolgov (University of Bath)
    • Robert Scheichl (Heidelberg University)
  • Abstract : We propose an efficient importance sampling method for rare events in high-dimensional problems, by approximating the optimal importance distribution in a scalable way as the pushforward of a reference distribution under composition of order-preserving transformations based on tensor-train decompositions. By designing a ratio estimator that estimates the normalizing constant using a separate importance distribution, it applies also to Bayesian inverse problems. The efficiency and robustness are demonstrated numerically on high-dimensional problems constrained by differential equations.
• [02317] On structured linear measurements for tensor data recovery
  • Format : Talk at Waseda University
  • Author(s) :
    • Elizaveta Rebrova (Princeton University)
  • Abstract : Data-oblivious measurements present an important branch of low-rank data compression and recovery techniques, frequently used in streaming settings and within iterative algorithms. Typically, linear data-oblivious measurements involve some version of a random sketch that preserves the geometric properties of the data. When data is tensorial, a special challenge is to create a sketch with a structure that reflects tensor structure: this way, it can work similarly to a dense random sketch matrix but require much less memory to store and can be applied more efficiently. I will talk about our and others -- including Tropp, Udell et al, De Lathauwer et al -- recently proposed streaming sketch-based approaches for computing low-rank Tucker approximations of large tensors. I will discuss our new generalized theoretical guarantees for proving their accuracy on full-rank and noisy data with high probability from a wide range of measurements.

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

room : E507

• [03614] A Deep Conjugate Direction Method for Iteratively Solving Linear Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • ayano kaneda (waseda university)
    • David Hyde (Vanderbilt University)
    • Osman Aker (University of California)
    • Joseph Teran Michael ( University of California, Davis)
  • Abstract : We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search direction at each iteration. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We demonstrate the efficacy of our approach on spatially discretized Poisson equations, which arise in computational fluid dynamics applications, with millions of degrees of freedom. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.
• [03251] Wasserstein GAN and Transfer Learning in physics-informed neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Yihang Gao (The University of Hong Kong)
    • Michael Kwok-Po Ng (The University of Hong Kong)
  • Abstract : We study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of PDEs. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of PDEs observed from initial/boundary data. Under mild assumptions, we show the convergence of the obtained model. Moreover, we also study a SVD-based transfer learning method which stabilize the training and reduce the storage for PINNs.

contributed talk: CT103

room : E508

[00738] Proper Orthogonal Decomposition methods for the Navier Stokes equations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : In this talk we study numerical approximations to the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods. Several questions are considered: the influence of including snapshots that approach the velocity time derivative and the influence of considering different discretizations for the nonlinear term in the full order model and the reduced order model. Error bounds with constants independent of the Reynolds numbers are obtained in the numerical analysis.
• Classification : 65M12, 65M15, 65M60
• Format : Talk at Waseda University
• Author(s) :
  • Julia Novo (Universidad Autónoma de Madrid)

[00743] Recent Advances on POD methods for the Navier-Stokes equations.

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : We present some recent advances on proper orthogonal decomposition (POD) methods for the Navier-Stokes equations. Among them, recovering the pressure in a robust manner when the snapshots are discretely divergence-free. We analyze the different sources of error and how they affect the pressure recovery. We also study how to adapt the POD method for varying values of the Reynolds number.
• Classification : 65M12, 65M15, 65M60
• Format : Talk at Waseda University
• Author(s) :
  • Bosco García-Archilla (Universidad de Sevilla)

[01847] Non-reflective boundary conditions for the piston problem of gas dynamics

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E508
• Type : Contributed Talk
• Abstract : We consider the piston problem of gas dynamics, described by the Lagrangian formulation of the Euler equations for an ideal compressible gas. While a highly accurate numerical solution can be obtained in the interior of the domain through state-of-the-art techniques like WENO reconstruction and SSP-RK time-stepping, boundary discretization can lead to unphysical reflections. We investigate and implement several efficient boundary conditions to deal with this problem without significantly increasing the size of the computational domain.
• Classification : 65M08, 65M22, 76N30, 35L04, 35L65
• Format : Talk at Waseda University
• Author(s) :
  • Carlos Muñoz (KAUST)

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

room : E603

• [04088] DeePN2: A Deep Learning-Based Non-Newtonian Hydrodynamic Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Lidong Fang (Michigan State University)
    • Pei Ge (Michigan State University)
    • Lei Zhang (Shanghai Jiao Tong University)
    • Weinan E (Peking University)
    • Huan Lei (Michigan State University)
  • Abstract : A longstanding problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying microscale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure, and the heterogeneous interaction. DeePN2, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN2 using more complex micro-structural models. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.
• [04357] Numerical Analysis of Structural Green's Function in Multiple Scattering Theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoxu Li (Beijing Normal University)
    • Huajie Chen (Beijing Normal University)
  • Abstract : This work studies the multiple scattering theory, also called Green's function method, in the electronic structure calculations of disordered systems from a mathematical perspective. By analyzing the structural Green's function, which can be viewed as the representation of Green's function in some basis, we will (a) improve the space truncation way to accelerate model convergence; (b) establish a mathematical analysis framework for Green's function and provide a prior error estimate; (c) design two linear-scaling algorithms with systematically controllable error.
• [04087] Variational Monte Carlo from a Continuous Viewpoint
  • Format : Talk at Waseda University
  • Author(s) :
    • Juerong Feng (Beijing Normal University)
    • Huajie Chen (Beijing Normal University)
  • Abstract : We study the variational Monte Carlo (VMC) method for quantum many-body problems based on data-driven wavefunction ansatz. We present a continuous stochastic gradient flow formulation for the VMC algorithm and show the large-time asymptotics with an explicit decay bound in terms of the many-body Hamiltonian and the wavefunction parameterization. In particular, we perform a careful analysis of the interactions between the approximation error of the ground state wavefunction and the generalization error of the sampling.

MS [00295] Estimation problems over groups

room : E604

• [03118] Optimal Spectral Methods for Synchronization Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Anderson Ye Zhang (University of Pennsylvania)
  • Abstract : We study the performance of spectral methods for synchronization problems with additive Gaussian noises and incomplete data. Spectral methods refer to algorithms that use the leading eigenvectors of the data matrix followed by a normalization step. (1) For phase synchronization and orthogonal group synchronization, we prove that they achieve the minimax lower bound of the problem with a matching leading constant under a squared $\ell_2$ loss. This shows that the spectral method has the same performance as more sophisticated procedures including MLE, generalized power method, and SDP when consistent parameter estimation is possible. (2) For permutation synchronization, we propose a novel spectral method that overcomes a crucial limitation of existing ones and has improved numerical performance. We further show the proposed method is statistically optimal with an exponentially small error that matches the minimax rate.
• [05181] Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuai Huang (Emory University)
    • Mona Zehni (University of Illinois at Urbana-Champaign)
    • Ivan Dokmanic (University of Basel)
    • Zhizhen Zhao (University of Illinois at Urbana Champaign)
  • Abstract : A line of work starting with Kam (1980) employs the method of moments (MoM) with rotation-invariant features to reconstruct a 3D density map from its 2D tomographic projections at unknown, random orientations, assuming that the orientations are uniformly distributed. This line of work includes the recent orthogonal matrix retrieval approaches. In this talk, we extend the previous approaches and propose to jointly recover the density map and the orthogonal matrices by imposing spatial nonnegativity constraint.

contributed talk: CT106

room : E605

[00568] PRIMAL HYBRID METHOD FOR QUASILINEAR PARABOLIC PROBLEMS

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E605
• Type : Contributed Talk
• Abstract : A second-order quasi-linear parabolic initial-boundary value problem is approximated by using primal hybrid finite element method and Lagrange multipliers. Semidiscrete 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 quasilinear case using primal hybrid method. Finally, the results on numerical experiments confirm our theoretical findings.
• Classification : 65M60
• Format : Talk at Waseda University
• Author(s) :
  • Ajit Patel (The LNM Institute of Information Technology)
  • Ravina Shokeen (The LNM Institute of Information Technology)
  • Amiya Kumar Pani (Birla Institute of Technology & Science, Pilani)

[01135] Computational framework for design, optimization, and control of sintering process

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E605
• Type : Contributed Talk
• Abstract : Optimization and control of sintering, which is governed by macroscopic coupled electro-thermo-mechanical model, is critical for additive manufacturing. To reduce time in making process design decisions, we present a hybridized model-based and data-driven computational framework. In particular, we demonstrate an inverse estimation strategy combining offline-online efficient data assimilation and surrogate modeling. We test the performance of the proposed method in accelerating the estimation of sintering process parameters and hard-to-measure material properties like viscosity.
• Classification : 65M32, 65F55, 74H15, 60-08, 74D99
• Author(s) :
  • Rahul Dhopeshwar (TU Eindhoven)
  • Harshit Bansal (TU Eindhoven)
  • Karen Veroy (TU Eindhoven)

[00494] A two-grid discontinuous Galerkin method to nonlinear time-fractional diffusion equations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E605
• Type : Contributed Talk
• Abstract : A two-grid algorithm for discontinuous Galerkin method is proposed for nonlinear time-fractional diffusion initial-boundary-value problems. The numerical scheme consists of DG method for the spatial derivatives and L1-scheme for time stepping. Error estimate for the proposed scheme is obtained. The numerical experiments are presented to prove the efficiency of our algorithm.
• Classification : 65M60, 65M15
• Author(s) :
  • SANDIP MAJI (Indian Institute of Technology Guwahati)
  • Natesan Srinivasan (Indian Institute of Technology Guwahati)

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

room : E606

• [04627] Implementation of a finite element PDE solver in AMReX
  • Format : Online Talk on Zoom
  • Author(s) :
    • Karthikeyan Chockalingam (UKRI STFC Hartree Centre)
    • Alex Grant (UKRI STFC Hartree Centre)
    • Xiaohu Guo (UKRI STFC Hartree Centre)
  • Abstract : The scope of the current work is to embed a finite element implementation in AMReX. One of the advantages of using block-structured meshes is that each element does not require a unique isoparametric mapping. Initial testing of the implementation on the Poisson problem shows considerable performance gain compared to an unstructured finite element framework. The framework allows for the ease of implementing different types of higher-order elements. It has also been extended for solving Navier-Strokes.
• [04466] Cheap training sets of gyrokinetic surrogate models with active learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaohu Guo (UKRI STFC Hartree Centre)
    • Lorenzo Zanisi (UKAEA)
  • Abstract : Surrogate models of gyrokinetic turbulence play critical role in accelerating integrated models thus leading to faster post-discharge analysis, operations optimisation and flight simulator applications. Training sets for surrogates are obtained by brute-force approaches which may cause unnecessary, expensive oversampling, which limits the dimensionality of the input space and applications to high fidelity codes. We develop two-stage Active Learning pipeline to efficiently sample the input parameter space of gyrokinetic models, benchmark applications in multichannel integrated models.
• [05659] Cheap training sets of gyrokinetic surrogate models with active learning
  • Author(s) :
    • Lorenzo Zanisi (UK Atomic Energy Authority)
  • Abstract : Surrogate models of gyrokinetic turbulence play critical role in accelerating integrated models thus leading to faster post-discharge analysis, operations optimisation and flight simulator applications. Training sets for surrogates are obtained by brute-force approaches which may cause unnecessary, expensive oversampling, which limits the dimensionality of the input space and applications to high fidelity codes. We develop two-stage Active Learning pipeline to efficiently sample the input parameter space of gyrokinetic models, benchmark applications in multichannel integrated models.

contributed talk: CT105

room : E702

[02604] Particle dynamics in the KP approximation

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : The Kadomtsev-Petviashvili (KP) equation is a model equation describing weakly nonlinear dispersive and small amplitude waves propagating in a quasi-two-dimensional situation. Encoded in the KP model are relations that may be used to reconstruct the velocity fields in the fluid below a given surface wave. In this talk, velocity fields associated to exact solutions of the KP equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the one line-soliton solution and two-soliton solutions.
• Classification : 65M25, 37M05
• Format : Talk at Waseda University
• Author(s) :
  • Juan-Ming Yuan (Providence University)
  • Jen-Hsu Chang (National Yang Ming Chiao Tung University )
  • Henrik Kalisch (University of Bergen)
  • Yusuke Shimabukuro (Math. Inst.)

[00477] Relaxation process of Cahn–Hilliard equations with dynamic boundary conditions

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : This talk is concerned with a numerical analysis of the initial value problem for the Cahn–Hilliard equation with dynamic boundary conditions in one-dimensional space, using a structure preserving scheme based on the discrete variational derivative method. We discuss the relationship between the parameter related to the time evolution on the boundary and the time it takes for the numerical solution to approach a stationary solution.
• Classification : 65M22, 82C26, 65M06
• Format : Talk at Waseda University
• Author(s) :
  • Keiichiro Kagawa (RIES, Hokkaido University)
  • Yoshihiro Yamazaki (Waseda University)

[01384] Adaptive coupling method for multi-domain time integration for lithium-ion battery simulations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E702
• Type : Contributed Talk
• Abstract : The multiphysics and multiscale problem of simulating lithium-ion batteries at microscale is approached with a multi-domain time integration technique. The sub-domains of the electrolyte and the solid phase are simulated independently and coupled at certain interval. We obtain the adaptive coupling interval based on the error estimate evaluated on the Bulter-Volmer current density flux at the interface between the electrolyte and solid domains. The results are presented to discuss the computational benefits of such schemes.
• Classification : 65M22, 65M12, 65Y99, 65Z05
• Format : Online Talk on Zoom
• Author(s) :
  • Ali ASAD (CMAP, Ecole Polytechnique)
  • Romain de Loubens (TotalEnergies One Tech)
  • Laurent François (ONERA, DMPE)
  • Laurent Séries (CMAP, Ecole Polytechnique)
  • Marc Massot (CMAP, Ecole Polytechnique)

contributed talk: CT109

room : E703

[02218] Self-gravitational force calculation of infinitesimally thin gaseous disks based on adaptive mesh refinement accelerated by sparse fast Fourier transform

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E703
• Type : Contributed Talk
• Abstract : The central region of galaxies can be infinitesimally thin gaseous disks due to the angular moment conservation. Dynamic of gaseous disks is significant for probing the gas flows inward/outward to the origin of galaxies. Moreover, self-gravitational force calculation should be concerned during the evolution of galaxies. We can use the sparse fast Fourier transform (sFFT) to preserve the nearly linear complexity $O(N\log N)$ for numerical calculation based on adaptive mesh refinement (AMR) in this presentation.
• Classification : 65M80, 42A16, 42A38
• Format : Talk at Waseda University
• Author(s) :
  • Chien-Chang Yen (Fu Jen Catholic University)

[02300] Stability of Euler implicit/explicit-SAV schemes for the Navier-Stokes equations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E703
• Type : Contributed Talk
• Abstract : In this talk, the $H^2$ stability of two types of the first order Euler implicit/explicit-SAV schemes for the Navier-Stokes equations with finite element discretization is studied with smooth or non-smooth initial data. In the literature, the first order Euler implicit/explicit scheme for the Navier-Stokes for the initial data $u_0$ in $H^{\alpha}$ with $\alpha =1,2$ and the Euler semi-implicit/explicit scheme for the initial data $u_0$ in $H^0$ have been proven to have $H^2-$ almost unconditional stability. In this talk, with the help of scalar auxiliary variable approach, the $H^2$ unconditional stability of two types of the first order Euler implicit/explicit-SAV schemes for the Navier-Stokes equations for the initial data $u_0$ in $H^{\alpha}$ with $\alpha =0, 1,2$ are established, which improve the classical one. Numerical experiments are presented to support the stability results. This is joint work with Teng-Yuan Chang.
• Classification : 65Mxx, 86-08, 76Bxx
• Format : Talk at Waseda University
• Author(s) :
  • Ming-Cheng Shiue (National Yang Ming Chiao Tung University)
  • TENG-YUAN Chang (National Yang Ming Chiao Tung University)

[01288] A WENO-Based Scheme for Simulating Miscible Viscous-Fingering Instability in Highly Convection-Dominated Regimes

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E703
• Type : Contributed Talk
• Abstract : We develop a Diffuse interface numerical method that simulates the miscible Viscous-Fingering instability in highly convection-dominated regimes (Péclet number > 10000). The developed finite volume scheme uses a two-point flux approximation (TPFA) for Darcy law and a fifth-order Weighted Essentially Non-Oscillatory(WENO) approximation for the convection term of the transport equation. The details of the numerical scheme and simulation results that agree excellently with existing numerical or experimental data will be discussed in this talk.
• Classification : 65Mxx, 35Qxx, 76Dxx, 76Sxx, 76Rxx
• Author(s) :
  • Surya Narayan Maharana (Indian Institute of Technology Ropar)
  • Manoranjan Mishra (Indian Institute of Technology Ropar, India)

MS [00866] BEM and related methods for advanced applications

room : E704

• [04974] Time domain boundary elements and mesh refinements
  • Format : Online Talk on Zoom
  • Author(s) :
    • Heiko Gimperlein (University of Innsbruck)
  • Abstract : We discuss recent and on-going progress for time-domain boundary element methods for wave and elastodynamic problems, with a focus on locally refined meshes. Solutions of the time-dependent equations exhibit singularities due to geometry (corners), mixed or nonlinear (contact) boundary conditions. We discuss well-posed formulations for such problems as well as their approximation on locally refined meshes by h- and hp-versions. A priori and a posteriori esti- mates for the approximation error are presented for both the weakly singular and the hypersingular integral equations. The a posteriori estimates lead to an adaptive mesh refinement procedure. Numerical experiments illustrate the theoretical results. (joint with A. Aimi, G. Di Credico, C. Oezdemir and E. P. Stephan)
• [05091] On improving the flexibility of an IgA-BEM multi-patch code
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alessandra Sestini (Università di Firenze)
  • Abstract : Two flexibility improvements are introduced of a 3D multi-patch IgA-BEM approach for Helmholtz based on B-spline tailored numerical integration. The first concerns the possibility of developing the discretization in non-conforming C^0 multi-patch spline spaces, thus ensuring adaptivity at the patch level. The second consists in the capability of using non uniform tensor product formulations of the adopted quadrature rules which are based on quasi-interpolation. This allows us to deal with non-smooth inter-patch junctions.
• [04013] Solving 2D linear elastic wave equations by scalar potentials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Silvia Falletta (Polytechnic University of Turin)
  • Abstract : This talk focuses on the simulation of 2D soft scattering elastic wave propagation in isotropic homogeneous media, using the scalar potential decomposition in the time-harmonic regime. For problems defined in bounded domains, a Virtual Element Method (VEM) with varying mesh sizes and degrees of accuracy is proposed to approximate the two scalar potentials. For unbounded domains, a boundary element method is coupled with the VEM.
• [04853] Time-Domain BEM for the resolution of Elastodynamic Contact Problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Giulia Di Credico (University of Parma)
    • Alessandra Aimi (University of Parma)
    • Heiko Gimperlein (University of Innsbruck)
  • Abstract : We investigate a boundary element method (BEM) for the dynamic contact between a linearly elastic body and a rigid obstacle. The so-called Signorini problem is formulated on the boundary as a variational inequality for the elastodynamic equations, for which we consider a mixed formulation solvable by time-domain BEM coupled with Uzawa algorithm. Both theoretical and algorithmic aspects are discussed and numerical experiments, presented for different 2D geometries, show the optimal performance of the proposed approach.

contributed talk: CT117

room : E705

[02610] Discrete Tensor Product BGG Sequences: Splines and Finite Elements

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
• Type : Contributed Talk
• Abstract : In this talk, we present a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and div-div complexes as examples for our construction.
• Classification : 65N99, 41A15, 41A63, 65N30
• Format : Talk at Waseda University
• Author(s) :
  • Duygu Sap (University of Oxford)
  • Kaibo Hu (University of Oxford)
  • Guido Kanschat (Heidelberg University)
  • Francesca Bonizzoni (Politecnico di Milano)

[00748] New probabilistic algorithms for scientific supercomputing

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
• Type : Contributed Talk
• Abstract : Sustained strong scalability is hard to sustain beyond 10K processors due to the communication and synchronisation involved in domain decomposition for PDEs. Seeking to overcome them, Spigler and Acebrón introduced probabilistic domain decomposition, which inserts stochastic calculus in the formulation---however with slow error convergence. I will present a hybrid idea, SpAc, which retains most of the scope for embarrassing parallelism, while being orders of magnitude faster. Proof of concept supercomputing simulations will be discussed.
• Classification : 65Nxx
• Format : Talk at Waseda University
• Author(s) :
  • Francisco Bernal (Carlos III University of Madrid)

[02003] VEM approximation for the Stokes eigenvalue problem: a priori and a posteriori error analysis

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
• Type : Contributed Talk
• Abstract : We present a priori and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem. For the a priori analysis, we take advantage of the compactness of the solution operator to prove convergence of the eigenfunctions and eigenvalues. Additionally we propose a reliable and efficient a posteriori estimator in order to perform adaptive refinements that allow to recover the optimal order of convergence for non smooth eigenfunctions. We report some numerical tests
• Classification : 65Nxx
• Format : Talk at Waseda University
• Author(s) :
  • Felipe Lepe (Universidad del Bío Bío)

[02552] The inverse elastography problem

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
• Type : Contributed Talk
• Abstract : Optical coherence elastography (OCE) is an imaging modality that maps mechanical properties by using optical coherence tomography (OCT) to measure tissue displacement after mechanical excitation. From OCE elastograms, quantified elasticity mapping can be accomplished using an appropriate mathematical model of the tissue. In this talk we present a mathematical model to reconstruct the mechanical properties of an elastic medium, in the OCE imaging technique. We formulate the inverse model problem as a PDE-constrained optimization problem, where the objective function measures the discrepancy between observations and predictions. We will discuss different strategies for learning the space varying elasticity coefficients.
• Classification : 65Nxx, 65N21
• Format : Talk at Waseda University
• Author(s) :
  • Silvia Barbeiro (University of Coimbra)
  • Rafael Henriques (University of Coimbra)

[02175] Learning Interaction laws in particle- and agent-based systems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E705
• Type : Contributed Talk
• Abstract : We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances, or other variables. We discuss when this problem is well-posed, construct estimators for the interaction kernels with provably good statistically and computational properties, and discuss extensions to second-order systems, more general interaction kernels, and stochastic systems. We measure empirically the performance of our techniques on various examples, including families of systems with parametric interaction kernels, and settings where the interaction kernels depend on unknown variables. We also conduct numerical experiments to study the emergent behavior of these systems. This is joint work with F. Lu, J. Feng, P. Martin, J.Miller, S. Tang and M. Zhong.
• Classification : 70F17, 62M20, 34A55
• Format : Talk at Waseda University
• Author(s) :
  • Mauro Maggioni (Johns Hopkins University)

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

room : E708

• [03275] Block-structured and hierarchical hybrid grid matrix-free multigrid solvers for CFD applications at scale
  • Format : Talk at Waseda University
  • Author(s) :
    • Harald Koestler (Friedrich-Alexander Universität Erlangen-Nürnberg)
  • Abstract : In this talk an overview of applications and performance for matrix-free multigrid solvers implemented in the HPC software frameworks HyTeG and ExaStencils is provided. This includes scaling and efficiency results on CPU and GPU clusters and sample applications from geophysics, charged particle and ocean simulations.
• [05232] Recent Advances in Linear Solvers for Ice Sheet Modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Jonathan Hu (Sandia National Laboratories)
    • Jerry Watkins (Sandia National Laboratories)
    • Max Carlson (Sandia National Laboratories)
    • Mauro Perego (Sandia National Laboratories)
    • Kim Liegeois (Sandia National Laboratories)
    • Oscar Antepara (Lawrence Berkeley National Laboratory)
    • Samuel Williams (Lawrence Berkeley National Laboratories)
  • Abstract : We present recent ongoing work performed under the SciDAC FAnSSIE project to improve linear solver performance within land-ice simulations on GPU-based architectures. We'll review the current algorithmic approach that relies on specialized semicoarsening algebraic multigrid, challenges in adapting this approach to GPU architectures, and progress in improving performance and scaling. Finally, we'll present numerical results from the Albany simulation code on the HPE Cray Ex supercomputer Perlmutter.
• [05118] A Matrix-Free Approach for Algebraic Multigrid for High-Order Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Graham Harper (Sandia National Laboratories)
  • Abstract : We present a matrix-free approach for algebraic multigrid (AMG) for high-order systems. In particular, we focus on the case where an application may have a mix of domains with geometric structure and regions without geometric structure. We mix geometric multigrid (GMG) and AMG, but we approach the overall problem from a matrix-free AMG perspective on the finer levels. We present numerical results using Trilinos and MueLu to verify our methods.
• [03319] Mixed formulations and monolithic multigrid methods for smectic-A liquid crystals
  • Format : Online Talk on Zoom
  • Author(s) :
    • Abdalaziz Hamdan (Imperial College London)
    • Patrick Farrell (University of Oxford)
    • Scott MacLachlan (Memorial University of Newfoundland)
  • Abstract : Xia et al. recently proposed a new continuum model for smectic A liquid crystals. Here, we present a mixed finite-element formulation of that model and discuss the construction of solvers for the resulting nonlinear systems. We consider Newton-Krylov-Multigrid approaches, using Newton’s method to linearize and develop monolithic geometric multigrid preconditioners for the resulting saddle-point systems. We demonstrate this is an effective solver strategy when using a coupled “star” relaxation scheme and nested iteration.

contributed talk: CT115

room : E709

[02434] Multiobjective Mesh Optimization Algorithms for Quadrilateral Meshes

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : Accurate numerical PDE solutions require good quality computational meshes on the corresponding geometric domains. Both explicitly and implicitly tangled meshes are problematic for finite element simulations as are meshes with low quality elements. In this talk, we will present our multiobjective optimization methods for mesh untangling and quality improvement of quadrilateral meshes. The objective functions are developed by combining separate objective functions using ``no articulation of preferences”. Encouraging results from numerical experiments will be presented.
• Classification : 65N50, 65N30, 65K10
• Format : Talk at Waseda University
• Author(s) :
  • Moein Moradi (University of Kansas)
  • Suzanne Michelle Shontz (University of Kansas)

[00676] Recent Advances in 2-Lagrange Multiplier Method for Multiscale PDEs

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : The heterogeneous 2LM method, introduced in Loisel et al., SIAM J. Sci. Comput., 37, 2015, is a domain decomposition method where the coarse space is built using eigenvectors associated with subdomain eigenproblems. In this talk, we provide a new a-priori estimate for the norm of the coarse problem to guarantee further that the method is robust w.r.t the changes in the contrast of the diffusion coefficient. Numerical results are provided to support the theoretical findings.
• Classification : 65N55, 65F10, 65N30, 65N22
• Format : Talk at Waseda University
• Author(s) :
  • Hieu Nguyen (Fulbright University Vietnam)
  • Sébastien Loisel (Heriot-Watt University)

[02620] Power contraction of RAS with local impedance problems for the Helmholtz equation

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : The Helmholtz equation is notoriously difficult to solve, especially for the case of high wavenumber. The Restricted Additive Schwarz preconditioner with local impedance problems, often called the ORAS method, is arguably the most successful one-level parallel method for Helmholtz problems. This preconditioner can be applied on very general geometries, does not require parameter-tuning, and can even be robust to increasing wavenumber. To date, there is relatively little convergence analysis for this method. In the talk, I will present a novel analysis of the ORAS method.
• Classification : 65N55
• Format : Talk at Waseda University
• Author(s) :
  • Shihua Gong (The Chinese University of Hong Kong, Shenzhen)

[00461] hp/Spectral Element Methods for Elliptic Boundary Layer Problems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
• Type : Contributed Talk
• Abstract : Elliptic boundary layer problems arise in many applications including fluid dynamics, gas dynamics, plate and shell problems in structural mechanics, modeling of semiconductor devices and many more. We propose a least-squares hp-spectral element method for 1D elliptic boundary layer problems. The regularity estimates are stated and the main stability theorem is obtained using non-conforming spectral element functions. For the hp-version we use a 3 element mesh which allows us to resolve the boundary layers completely by placing very thin needle like elements near the boundary layer and a coarse mesh away from the layer. Numerical scheme and error estimates are obtained which are robust i.e. independent of the boundary layer parameter and decay exponentially in terms of the degree of the approximating polynomials. Numerical results confirm convergence results with various combinations of the boundary layer thickness, degrees of the approximating polynomials, and layers in the mesh.
• Classification : 65N35, 65N20, 65N50
• Author(s) :
  • Akhlaq Husain (Jamia Millia Islamia New Delhi)
  • Akhlaq Husain (BML Munjal University Gurgaon)

MS [00239] Shape and Topology Optimizations

room : E710

• [00419] Level set-based topology optimization method with nonlinear diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoyuki Oka (The University of Tokyo)
    • Takayuki Yamada (The University of Tokyo)
  • Abstract : In this talk, we shall consider a level set-based topology optimization method with nonlinear diffusion. Main results consist of the generalization of the method using reaction-diffusion equations, which improves convergence to optimized designs with the aid of singularity and degeneracy of diffusion coefficients, and therefore, a more practical method can be obtained.

contributed talk: CT122

room : E711

[00020] Image Functions Approximated by CNN

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : Convolutional Neural Networks (CNN) have been widely used to image understanding. However it remains an open problem to prove the approximation of image functions via CNN. In this work, it is proved that an image function can be approximated by CNN on the basis of the axiom of choice in set theory and an uncountable number of training data from the viewpoint of image decomposition.
• Classification : Artificial neural networks and deep learning
• Format : Talk at Waseda University
• Author(s) :
  • Jian-Zhou Zhang (Sichuan University)

[00141] Multiscale Perturbed Gradient Descent: Chaotic Regularization and Heavy-Tailed Limits

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this talk, we introduce multiscale perturbed GD (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed Lévy-stable process. (ii) By making connections to recently developed generalization bounds for heavy-tailed processes, we derive a generalization bound for the limiting SDE and relate the worst-case generalization error over the trajectories of the process to the parameters of MPGD. (iii) We analyze the implicit regularization effect brought by the dynamical regularization and show that, in the weak perturbation regime, MPGD introduces terms that penalize the Hessian of the loss function. Empirical results are provided to demonstrate the advantages of MPGD.
• Classification : 68T07, Machine learning, optimization, stochastic differential equations
• Format : Talk at Waseda University
• Author(s) :
  • Soon Hoe Lim (Nordita, KTH Royal Institute of Technology and Stockholm University)

[00541] Reinforcement Learning-based Data Collection and Energy Replenishment in SDIoT

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : In software-defined internet of things (SDIoT) with wireless rechargeable sensor networks, a novel reinforcement learning-based method is proposed for collecting data and scheduling mobile sinks to recharge the sensor nodes. The suggested technique extends the network lifetime while ensuring the QoS of the SDIoT. Finally, the results show that the suggested approach significantly increases the energy efficiency and also increases the network's lifetime.
• Classification : 68T05, 68T40, 68T20, 68Q06, Internet of Things; Machine learning; Reinforcement learning
• Format : Talk at Waseda University
• Author(s) :
  • Vishnuvarthan Rajagopal (Research scholar, Department of Electronics and Communication Engineering, Anna University Regional Campus, Coimbatore.)
  • Bhanumathi V (Assistant Professor, Department of Electronics and Communication Engineering,Anna University Regional Campus, Coimbatore.)

[00535] Reinforcement Learning with Variable Exploration

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E711
• Type : Contributed Talk
• Abstract : Reinforcement learning is a powerful machine learning technique, but unreliable when multiple agents learn simultaneously. Our work applies Q learning to the Iterated Prisoner's Dilemma, an ideal setting to study AI cooperation. We investigate how different frameworks for variable exploration rates effect performance by escaping local optima. One result finds shorter learning periods produce more cooperation, potentially indicating incentive alignment. This furthers previous studies by carefully considering the ways exploration rate might vary over time.
• Classification : 68T05, 91A26, 37N40, 91A05
• Format : Talk at Waseda University
• Author(s) :
  • Brian Mintz (Dartmouth College)
  • Feng Fu (Dartmouth College)

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

room : E802

• [04322] A mathematical model of microtubule assembly and polarity in dendrites
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Nelson (Duke University)
    • Veronica Ciocanel (Duke University)
    • Scott McKinley (Tulane University)
  • Abstract : The microtubule cytoskeleton is responsible for sustained transport of cellular cargo inside neurons. However, microtubules must also be dynamic and rearrange their orientation in response to injuries. We introduce a spatially-explicit mathematical model of dendritic microtubule growth dynamics using parameters informed by experimental data. We explore several hypotheses of microtubule growth using both a stochastic model and a continuum model, and use fluorescence microscopy experiments to validate mechanisms such as limited tubulin and length-dependent catastrophe.
• [04441] Parameter Estimation for Mechanistic Models of Tear Film Breakup
  • Format : Talk at Waseda University
  • Author(s) :
    • Rayanne A Luke (George Mason University)
    • Richard J Braun (University of Delaware)
    • Tobin A Driscoll (University of Delaware)
    • Deborah Awisi-Gyau (Alcon Research LLC)
    • Carolyn G Begley (Indiana University)
  • Abstract : Tear film breakup is related to dry eye disease. Breakup causes include evaporation and divergent flow; related quantities cannot be directly measured during breakup. We determine such variables by fitting thin film fluid dynamics models for breakup to experimental data. Our results suggest that evaporation and divergent flow cooperate to drive faster breakup; purely evaporative cases exhibit slower thinning. These results are the first to make a tight comparison between such models and experimental data.
• [05183] Modelling Glucose Regulation: Lipotoxicity and the Progression to Type 2 Diabetes
  • Format : Talk at Waseda University
  • Author(s) :
    • Katharine R Faulkner (University of British Columbia)
  • Abstract : As an individual moves from healthy to pre-diabetic to diabetic, there are many physiological changes that occur, but it is not known which of these changes are the main drivers of the progression to type II diabetes. In this talk, I will describe a simple model for glucose regulation and how modeling can help determine which of these physiological changes are capable of pushing an individual from healthy to diseased. By framing this problem in terms of bifurcations, we can find models that create qualitative changes to the system that allow for movement between healthy and diseased states. We will examine a model that includes the toxicity of lipids in the pancreas, and find a bifurcation that describes the progression to type II diabetes.
• [04351] PIEZO1 regulates cellular coordination during collective cell migration
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinghao Chen (University of California, Irvine)
    • Jesse Holt (University of California, Irvine)
    • Beth Evans (University of California, Irvine)
    • John Lowengrub (University of California, Irvine)
    • Medha Pathak (University of California, Irvine)
  • Abstract : The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during wound healing. Through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1’s contributions to keratinocyte collective migration, an essential component of the healing process. Here, through a 2D-multiscale model of wound closure which links observations at both the single and multicell scales, and subsequent experimental validation, we identify cell directionality as being impacted by PIEZO1 activity during wound closure.

contributed talk: CT124

room : E803

[02091] Stock Data has Shape: Managing Stock Portfolio via Topology-informed Machine Learning

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E803
• Type : Contributed Talk
• Abstract : Given time-series data of a stocks portfolio, we generate sequences of point-cloud embeddings and use topology-based features to train a classifier on a binary classification task: determine whether or not a stock performs well on day-to-day trading. Using the trained classifier, we predict which stocks in our portfolio are projected to earn on a future trading day. We evaluate our topology-informed classifier via standard metrics and projected cumulative earnings based on a tier-structured investment scheme.
• Classification : 68Txx, 68Uxx, Machine Learning
• Format : Talk at Waseda University
• Author(s) :
  • Paul Samuel Ignacio (University of the Philippines Baguio)

[00031] Stoneley wave in the transversely isotropic thermoelastic diffusion materials

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E803
• Type : Contributed Talk
• Abstract : This paper investigate the secular equations of Stoneley wave propagating through bonded and unbonded interfaces between two dissimilar transversely isotropic thermoelastic diffusion half-spaces. These equations are solved numerically by modelling two distinct crustal rocks and the resultant phase velocities and attenuations are plotted graphically. This analysis explicates the position and permeability of fractures and also helps in the assessment of valuable materials under earth’s crust. Some particular cases are also deduced from the present formulation.
• Classification : Continuum Mechanics
• Format : Talk at Waseda University
• Author(s) :
  • Sanjay Debnath (Mizoram University)

[01045] Advances on intimate partner femicide applying machine learning techniques and algorithms

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E803
• Type : Contributed Talk
• Abstract : Intimate partner femicide (IPF) is female’s leading cause of violent death worldwide. The accuracy of existing risk assessment instruments for IPF developed by conventional statistics is not completely competitive. In this study, machine learning techniques and algorithms for classification were used to discriminate between lethal or non-lethal violence against women by intimate partners and to detect which variables discern them the most. The obtained evidenced-based knowledge could assist professionals in predicting and preventing lethality.
• Classification : 68Txx
• Author(s) :
  • Esperanza Garcia-Vergara (Universidad Loyola Andalucia)
  • Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain))

[02472] Geometry and mechanics of shape-programmable systems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E803
• Type : Contributed Talk
• Abstract : Modern responsive materials such as liquid crystal elastomers (LCEs) can be pre-programmed to undergo spatially inhomogeneous deformations in response to external stimuli such as heat and light. Shape-programming of LCEs has been the subject of intense research in recent years, resulting in the discovery of patterning designs and techniques that allow flat 2D sheets to assume target geometries upon activation. In this talk, we present recent mathematical, computational and experimental advances in shape-programming of LCEs.
• Classification : 74-04, 74-10, 74S05, 74M05, 74G65
• Format : Talk at Waseda University
• Author(s) :
  • Daniel Duffy (University of Cambridge)
  • Cyrus Mostajeran (Nanyang Technological University)
  • John Simeon Biggins (University of Cambridge)
  • Timothy J White (University of Colorado Boulder)
  • Mark Warner (University of Cambridge)

[00397] A continuum model for the bulldozing of an immersed granular material in a confined geometry

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E803
• Type : Contributed Talk
• Abstract : We present a reduced-order continuum model for the bulldozing of an immersed, sedimented granular material by a rigid piston in a fluid filled gap between two parallel plates. In our model, the granular pile and the overlying fluid layer evolves as coupled thin-films. We solve our model numerically for a variety of different scenarios to develop insight into the interactions between wall friction, internal viscous-like stresses, and fluid flow both above and through the pile.
• Classification : 74-10, 76-10
• Format : Talk at Waseda University
• Author(s) :
  • Liam Morrow (University of Oxford)
  • Chris MacMinn (University of Oxford)

MS [03056] Data-driven methods to discover within-host biological dynamics

room : E804

• [03279] How to find a pertinent research question: the identification and exploration of known unknowns
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mayla R Boguslav (Colorado State University)
    • Nourah M Salem (University of Colorado Anschutz Medical Campus)
    • Elizabeth White (University of Colorado Anschutz Medical Campus)
    • Katherine J Sullivan (University of Colorado Anschutz Medical Campus)
    • Michael Bada (University of Colorado Anschutz Medical Campus)
    • Teri L Hernandez (University of Colorado Anschutz Medical Campus)
    • Sonia M Leach (National Jewish Health)
    • Lawrence E Hunter (University of Colorado Anschutz Medical Campus)
    • Michael Kirby (Colorado State University)
  • Abstract : Scientific discovery progresses by exploring new and uncharted territory. More specifically, it advances by a process of transforming unknown unknowns first into known unknowns, and then into knowns. Over the last few decades, researchers have developed many knowledge bases to capture and connect the knowns, which has enabled topic exploration and contextualization of experimental results. But recognizing the unknowns is also critical for finding the most pertinent questions and their answers. Little work has focused on how scientists might use them to trace a given topic or experimental result in search of open questions and new avenues for exploration. We present methods and tools to help researchers automatically uncover these unknowns through the illumination of specific goals for scientific knowledge.
• [05174] A summary of algorithms for sparse feature selection for Biological Data
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michael Kirby (Colorado State University)
  • Abstract : Biological data sets such as transcriptomics, proteomics or metabolomics are characterised by their high dimension n and small sample size p. Realistically, it is a daunting challenge to deduce meaningful biological mechanisms when p<
• [03409] Improving decoy detection for protein-protein interaction models
  • Format : Online Talk on Zoom
  • Author(s) :
    • Corey OHern (Yale University)
  • Abstract : Computational prediction and design of proteins is a difficult task that results in models with a wide variation in quality. Decoy detection algorithms seek to classify computational models as high-quality or low-quality without knowledge of the experimental structures. Recently, dramatic improvements have been made in decoy detection of models for single proteins, but decoy detection of protein-protein interface (PPI) models is still challenging. To assess the current state-of-the-art for PPI decoy detection, we scored computational models generated using rigid-body docking software, ZDOCK, from a dataset of 33 heterodimeric high-resolution x-ray crystal structures against a standard measure of similarity to the x-ray crystal structures. We found that for some targets there is a strong correlation between the docking and ground truth scores (i.e. easy targets), whereas for other targets there are only weak correlations (i.e. difficult targets). We show that a metric that characterizes the “flatness” of the target interfaces can distinguish easy from difficult targets, where flat targets possess only weak correlations between the docking and ground truth scores. In addition, most rigid docking software methods generate highly imbalanced datasets containing mostly low-quality computational models. Balanced datasets of PPI models reduce sampling bias, which makes it easier to identify the physical features that can classify PPI computational models.
• [05206] Early Detection of Disease: An intersection between artificial intelligence and biomathematics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Juan B Gutierrez (University of Texas at San Antonio)
  • Abstract : Many states of disease are progressive, having a silent phase in which pathogenesis advances without the manifestation of any symptoms. However, small perturbations can be detected by a complex signal such as electrocardiography. In this talk, I will present how to approach the detection of subtle physiological signals through the systematic design of the architecture of an artificial neural network capable of detecting liver-stage malaria with an accuracy of +90%.

contributed talk: CT133

room : E812

[00208] Love wave along the interface with triangular irregularity

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
• Type : Contributed Talk
• Abstract : Propagation of the love wave is studied along the irregular interface between the porous layer and the elastic half-space. The porous layer is assumed to be saturated by two immiscible fluids. The irregularity at the interface is considered in the form of a triangular pit embedded in the half-space. The elastic half-space is considered to be initially stressed under the effect of gravity. A complex transcendental and implicit relation between the frequency and the phase speed of the Love wave is derived in the form of a dispersion relation. A numerical study is conducted to observe the effect of material parameters and irregularity on the behavior of the Love wave. A significant impact of the triangular pit, porosity, and frequency is observed on the phase speed of the propagating Love wave and depicted graphically.
• Classification : 74J15
• Format : Talk at Waseda University
• Author(s) :
  • Ashish Arora (I. K. Gujral Punjab Technical University)

[00861] Using elastic waves to measure mechanical stress

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
• Type : Contributed Talk
• Abstract : In principle, elastic waves could be used to assess the stress in a material, as the higher the stress, the faster the wave will propagate. However, the speed also depends on material parameters, which is why there are no robust (non-invasive) measurement techniques. In this talk we show how to overcome these challenges by using universal relationships between stress and wave speeds. This has led to robust measurements with either bulk waves [2] or surface waves [3]. Universal relationships in continuum mechanics are those that hold for any type of material, or constitutive choice [1]. To measure stress, it would be ideal to have a relationship between the wave speed and the stress that holds for any elastic material. However, there is only one such universal relationship: $\rho v_{12}^2 - \rho v_{21}^2 = \sigma_{11} - \sigma_{22}$, where $\sigma_{ij}$ are the components of the Cauchy stress tensor, and $v_{12} (v_{21})$ is the speed of a shear wave propagating in the $x_1 (x_2)$ direction that is polarised in the $x_2 (x_1)$ direction. Inspired by this identity we propose, and experimentally validate, several new ultrasonic methods. [1] Truesdell, Clifford, and Walter Noll. "The non-linear field theories of mechanics." The non-linear field theories of mechanics. Springer, Berlin, Heidelberg, 1992. 1-579. [2] Li, Guo-Yang, Artur L. Gower, and Michel Destrade. "An ultrasonic method to measure stress without calibration: The angled shear wave method." The Journal of the Acoustical Society of America 148.6 (2020): 3963-3970. [3] Li, Guo-Yang, et al. "Non-destructive mapping of stress and strain in soft thin films through sound waves." Communications Physics 5.1 (2022): 1-7.
• Classification : 74J05, 74B10, 74B15, 74J25
• Format : Talk at Waseda University
• Author(s) :
  • Art Gower (University of Sheffield)
  • Michel Destrade (University of Galway)
  • Guo-yang Li (Harvard Medical School and Wellman Center for Photomedicine)

[00002] Propagation of Lamb wave in the plate of microstretch thermoelastic diffusion materials

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
• Type : Contributed Talk
• Abstract : The present study investigates the effect of three thermoelastic theories on the propagation of Lamb wave in a linearly isotropic microstretch diffusion plate subject to stress free thermally insulated/impermeable and isothermal/isoconcentrated boundary conditions. The secular equations of the Lamb wave are obtained for both symmetric and anti-symmetric modes of vibration. The phase velocities and attenuation coefficients are computed numerically for a particular model and these results are compared for the three theories: Coupled Thermoelasticity theory, Lord-Shulman theory and Green-Lindsay theory. The velocity curves and the attenuation coefficients are illustrated graphically. It is observed that there are three modes of velocity and attenuation for each symmetric and anti-symmetric vibration. We have noticed that the velocity of the corresponding Lamb wave increases from first to third mode of symmetric vibration in both thermally insulated/impermeable and isothermal/isoconcentrated plates. At short wavelength, the secular equation of symmetric mode of vibration reduces to that of Rayleigh surface wave for both the plates. Some special cases are also deduced from the present formulation.
• Classification : 74J15, 74B15, 80A17, 80A10
• Format : Online Talk on Zoom
• Author(s) :
  • Sarat Singh Sanasam (Mizoram University)
  • Sanjay Debnath (Mizoram University)

[00613] Phase-field systems coupled with large deformations

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
• Type : Contributed Talk
• Abstract : Multiphase dynamical systems coupled with finite strain are used for the mathematical description of many phenomena in soft matter physics and biology, such as swelling and wetting processes of gels. We derive a thermodynamically consistent framework to couple phase fields and mechanics in a gradient flow structure allowing for various dissipation mechanisms. Combining modeling tools, rigorous analytical considerations, and the construction of numerical implementations allows us to understand practical and technical details from different perspectives.
• Classification : 74Fxx
• Format : Talk at Waseda University
• Author(s) :
  • Leonie Schmeller (Weierstrass Institute)
  • Barbara Wagner (Weierstrass Institute)
  • Dirk Peschka (Weierstrass Institute)

[00865] A novel hybrid microphysical–rheological multiscale constitutive model of ferroelectrics

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
• Type : Contributed Talk
• Abstract : For describing mutually coupled dissipative processes in ferroelectrics, in particular ferroelectric domain switching and viscoelasticity, a hybrid micromechanical - rheological constitutive model is developed and embedded in the framework of a multiscale modeling approach. The mathematical theory is consistent against the background of rational thermodynamics and deals with two types of internal variables. The advanced modeling approach is applied to identify novel energy harvesting cycles exploiting dissipative effects, resulting in a major electric work output.
• Classification : 74M25, 74F05, 74M05, 74N30, 74Q15
• Format : Talk at Waseda University
• Author(s) :
  • Andreas Warkentin (University of Kassel)
  • Andreas Ricoeur (University of Kassel)

contributed talk: CT135

room : E817

[02054] Low regularity ill-posedness for elastic waves and ideal compressible MHD in 3D and 2D

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817
• Type : Contributed Talk
• Abstract : We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. If time permits, we will also present the corresponding results in 2D. This talk is based on joint works with Haoyang Chen and Silu Yin.
• Classification : 76N15, 76N30, 35L60, 35L67, 35Q35
• Format : Talk at Waseda University
• Author(s) :
  • Xinliang An (National University of Singapore)
  • Haoyang Chen (National University of Singapore)
  • Silu Yin (Hangzhou Normal University)

[01096] Stability modulation by a reaction in Navier-Stokes flow

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817
• Type : Contributed Talk
• Abstract : Channel/pipe flows mathematically modeled by the Navier-Stokes equation can be stabilized or destabilized by a slight viscosity stratification. We perform linear stability analysis (LSA) and non-linear simulation (NLS) for such flow, where a reaction changes the viscosity. The analysis involves a WENO-based diffuse-interface method for NLS and the Chebyshev spectral method for LSA. This talk will discuss how varying parameters representing the physical forces present in the system can control flow instabilities.
• Classification : 76Vxx, 80Axx, 35Qxx, 65Mxx, Navier-stokes equation, Reaction effects in flows, Chemically reacting flows, Finite volume methods for initial value and initial-boundary value problems involving PDEs
• Format : Talk at Waseda University
• Author(s) :
  • Manoranjan Mishra (Indian Institute of Technology Ropar, India)
  • Surya Narayan Maharana (Indian Institute of Technology Ropar)

[02142] Self-similar hierarchy of vortices in turbulence

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817
• Type : Contributed Talk
• Abstract : By direct numerical simulations, we show that there exists the hierarchy of vortex axes in turbulence, which is self-similar in a wide range of scales, i.e., in the inertial range and a lower part of the dissipation range. This result means that the volume fraction occupied by the tubular vortices at each scale is independent of the scale.
• Classification : 76F65, 65Z05
• Format : Talk at Waseda University
• Author(s) :
  • Tomonori Tsuruhashi (The University of Tokyo)
  • Susumu Goto (Osaka University)
  • Sunao Oka (Osaka University)
  • Tsuyoshi Yoneda (Hitotsubashi University)

[01101] Supersonic Pre-Transitional Disturbances in Boundary Layers on Porous Surfaces

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817
• Type : Contributed Talk
• Abstract : The effect of wall permeability on the response of pre-transitional supersonic boundary layers subject to low-amplitude, free-stream vortical disturbances is investigated via asymptotic methods and numerically. Equally-spaced cylindrical pores couple the pressure and wall-normal velocity fluctuations when the spanwise diffusion is negligible, thereby reducing the growth of low-frequency laminar streaks and Görtler vortices on concave porous walls. Highly-oblique Tollmien-Schlichting waves that develop further downstream are instead enhanced. This finding is confirmed by a triple-deck analysis.
• Classification : 76N20, 76N25, 35C20
• Format : Talk at Waseda University
• Author(s) :
  • Ludovico Fossà (The University of Sheffield)
  • Pierre Ricco (The University of Sheffield)

[01861] Scattering of an Ostrovsky wave packet in a layered waveguide

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817
• Type : Contributed Talk
• Abstract : In this talk I will discuss the scattering of an Ostrovsky wave packet in a two layered waveguide with a delamination sandwiched between imperfect bonding. When the layers have different densities, the strains are described by a system of coupled Boussinesq equations. Asymptotic solutions are constructed, complemented by numerical simulations, and are used to analyse the scattering of the strain waves. These results can provide a tool to control the integrity of layered structures.
• Classification : 74J30, 76B15, 35G25, 35G30
• Format : Online Talk on Zoom
• Author(s) :
  • Jagdeep Tamber (Nottingham Trent University)

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

room : E819

• [05053] Numerical Investigation of HCCI Combustion in the High Pressure Engine
  • Author(s) :
    • Rafia Waqar (Bahauddin Zakariya University, Multan)
    • Khalid Saifullah Syed (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan)
  • Abstract : This study numerically investigates Homogeneous Charge Compression Ignition (HCCI) combustion in a heavy duty engine operating at 4 MPa boosted intake pressure. Effect of variations in charge composition and temperature on combustion performance parameters such as indicated mean effective pressure, indicated torque, indicated power, indicated specific fuel consumption and fuel efficiency are analyzed. Maximum fuel efficiency (~ 47%) is obtained for equivalence ratios between 0.09 − 0.2 for initial temperatures 350 K and 400 K.

contributed talk: CT145

room : D101

[00705] A boundary integral method for slow free surface flows

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D101
• Type : Contributed Talk
• Abstract : In this talk we will present a boundary integral method suitable for the solution of creeping flow boundary value problems where the boundary presents singularities in the stresses. We use the method to solve the problem of the planar extrusion of a Newtonian fluid at zero Reynolds number and, in particular, to determine the shape of the free surface in the immediate neighbourhood of the separation point for a range of capillary numbers.
• Classification : 76M15, 76D05, 76D07, Free-surface fluid flows, singularities
• Format : Talk at Waseda University
• Author(s) :
  • Loïc Gobet (University of Montreal)
  • Robert Gwyn Owens (University of Montreal)

[02583] Novel shock-capturing procedure for discontinuous Galerkin method for compressible flows

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D101
• Type : Contributed Talk
• Abstract : In this work we develop a novel shock capturing procedure based on adaptive reformation of finite volume sub-cells for higher order discontinuous Galerkin method. For this we developed a sub-cell shock indicator based on Harten’s strategy to provide enhanced shock detection using just the degrees of freedom in respective mesh element. We apply this new procedure in the current state-of-the-art entropy stable discontinuous Galerkin method and demonstrate some numerical results for 1D compressible Euler equations.
• Classification : 76M10, 76M12, 76-10, 35L65
• Format : Online Talk on Zoom
• Author(s) :
  • Kedar Shridhar Wagh (Indian Institute of Science)
  • S. V. Raghurama Rao (Indian Institute of Science)
  • Sashikumaar Ganesan (Indian Institute of Science)

[02372] Stokes flow past circular cylinders in slip-patterned microchannel using BEM

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D101
• Type : Contributed Talk
• Abstract : We present Stokes flow past staggered circular cylinders in microchannel with an alternating slip and no-slip on the channel walls. We utilize Boundary Element Method (BEM) to numerically solve Stokes equation. In order to gain a deep insight of flow mechanics, we investigate the streamlines, velocity profiles, and pressure drops with varying slip-length, radius of the cylinder, and spacing between the cylinder. The findings of this study might be helpful for mixing enhancement in microchannel.
• Classification : 76M15, 35Q30, 76B15, 65N38, 76M10
• Author(s) :
  • Chandra Shekhar Nishad (Pandit Deendayal Energy University Gandhinagar )

[00878] Large-amplitude problem of BGK model

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D101
• Type : Contributed Talk
• Abstract : BGK equation is a relaxation model of the Boltzmann equation for simulation of various kinetic flow problems. In this work, we study asymptotic stability of the BGK model when the initial data is not necessarily close to global equilibrium pointwisely. Main difficulty of the BGK equation comes from the highly nonlinear structure of the relaxation operator. To overcomes this issue, we derive refined control of macroscopic fields to guarantee the system enters quadratic nonlinear regime.
• Classification : 76P05, 35B35, 35B40, 82C40
• Format : Talk at Waseda University
• Author(s) :
  • Gichan Bae (Seoul National University)
  • Gyounghun Ko (POSTECH)
  • donghyun lee (POSTECH)
  • Seokbae Yun (Sungkyunkwan University)

[00096] Multi-scale analysis of concentration distribution inside porous medium channel configuration

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D101
• Type : Contributed Talk
• Abstract : A multiple-scale perturbation analysis is presented for the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid channel filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation and the periodic pressure gradient. Homogenization technique is used to find the concentration distribution up to third order. For a fixed amplitude of oscillation and pulsation, frequency of pressure pulsation has stronger effect on the dispersion.
• Classification : 76M50, 76R99, 76S99
• Format : Online Talk on Zoom
• Author(s) :
  • Timir Karmakar (Department of Mathematics, National Institute of Technology Meghalaya, Shillong, Meghalaya 793003)
  • Swarup Barik (2Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203)
  • Raja Sekhar G P (Indian Institute of Technology Kharagpur India)

contributed talk: CT128

room : D102

[00531] Calibration of hardening parameters for the absence of hysteresis test-data

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D102
• Type : Contributed Talk
• Abstract : A mathematical model is developed to estimate combined nonlinear isotropic-kinematic hardening parameters of ductile materials using Ramberg-Osgood constants for monotonic and cyclic stress-strain curves. This compact model can be performed even if the hysteresis curves test results are unavailable for the specimens subjected to high amplitude cyclic loading. The model is applied for AW6082 and HX220-BD, Finite Element simulation results are compared with test results, and very good agreements are obtained.
• Classification : 74C15, 74-10
• Format : Talk at Waseda University
• Author(s) :
  • Eray Arslan (TU Wien)
  • Milan Zigo (MAGNA STEYR Fahrzeugtechnik GmbH & Co KG)

[00423] Understanding elastic-plastic stress distributions during cold rolling of sheet metal

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D102
• Type : Contributed Talk
• Abstract : In cold rolling, a metal sheet is passed between two rotating rollers which reduce the thickness of the sheet. In this talk, we present our new elastic-plastic mathematical model for describing the stress distribution during cold rolling, which is an extension of some existing asymptotic models, where elastic effects are neglected. At leading order, our model returns the popular slab-type analysis, but at higher orders, through-thickness variations can be predicted accurately.
• Classification : 74C05, 74M10, 41A60, 35C20, 35Q74
• Format : Talk at Waseda University
• Author(s) :
  • Francis Flanagan (Department of Mathematics and Statistics, University of Limerick)
  • Doireann O'Kiely (Department of Mathematics and Statistics, University of Limerick)
  • Alison O'Connor (School of Engineering, Bernal Institute, University of Limerick)
  • Mozhdeh Erfanian (School of Mathematics, University of Warwick)
  • Ed Brambley (School of Mathematics, University of Warwick)

[01137] Stability and Dispersion analysis for Rayleigh-type waves in non-local media

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D102
• Type : Contributed Talk
• Abstract : We present the non-local elastic behavior of Rayleigh-type surface waves in a layered media comprising an inhomogeneous medium and a fiber-reinforced layer. The dispersion equation is derived using an approximate asymptotic displacement solution of the governing wave equation. Using the Finite Difference Scheme, the stability conditions are determined for the equations of group velocity and phase velocity.The effects of various defining parameters on propagation are discussed and graphically depicted.
• Classification : 74-10, 74B10, 74H05, 74H45, 74J15
• Format : Online Talk on Zoom
• Author(s) :
  • Manasa Bhat (Department of Mathematics, Indian Institute of Technology Indore.)
  • Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore)

[00003] Reflection of plane waves in a rotating transversely isotropic thermoelastic diffusion solid half-space from impedance boundary in a fractional-order thermo-elasticity

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D102
• Type : Contributed Talk
• Abstract : The governing equations of a rotating transversely isotropic thermoelastic medium with diffusion in a fractional-order derivative thermo-elasticity are formulated. The velocity equation is obtained, which indicates the existence of four quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface with impedance boundary is studied. The effects of anisotropy, rotation and impedance parameters on reflection coefficients are shown graphically.
• Classification : 74-Mechanics of deformable solids
• Author(s) :
  • Dr. Anand Kumar Yadav (Shishu Niketan Sr. Sec School Sector 22D Chandigarh, India)

[00414] Asymptotically Modelling Plastic Deformation during Cold Rolling of Sheet Metal

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D102
• Type : Contributed Talk
• Abstract : Cold rolling is a metal forming process where strip of metal passes between two rollers and comes out thinner. We present a multiple-scale asymptotic model of cold rolling. Assuming rigid perfectly-plastic material and large rolls, we explain how to rederive and go beyond existing theories. Results agree well with FE simulations, and suggest the origin of residual stress in the resulting strip. This modelling approach has potential applications in many metal forming processes.
• Classification : 74C05, 74M10, 41A60, 35C20, 35Q74
• Author(s) :
  • Mozhdeh Erfanian (School of Mathematics, University of Warwick)
  • Ed Brambley (School of Mathematics, University of Warwick)
  • Francis Flanagan (Department of Mathematics and Statistics, University of Limerick)
  • Doireann O'Kiely (Department of Mathematics and Statistics, University of Limerick)

contributed talk: CT149

room : D402

[00362] Nonlinear biphasic mixture model: existence and uniqueness results

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D402
• Type : Contributed Talk
• Abstract : The purpose of this study is to develop a multiphase mathematical model based on interstitial hydrodynamics and tissue deformation mechanics within an in vitro solid tumor. We use classical mixture theory to derive the balance equations for mass and momentum. The study makes a significant contribution by treating hydraulic resistivity as anisotropic and heterogeneous, which leads to strongly coupled and nonlinear PDEs. We further establish existence and uniqueness result in a weak sense.
• Classification : 76Txx, 76Zxx, 35Q74, 35D30, Analysis of nonlinear partial differential equations
• Format : Talk at Waseda University
• Author(s) :
  • Meraj Alam (Mahindra University, Hyderabad)
  • Adrian Muntean (University of Karlstad)
  • Raja Sekhar G P (Indian Institute of Technology Kharagpur India)

[01579] Boltzmann equation with generalized collisional invariants

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D402
• Type : Contributed Talk
• Abstract : I demonstrate the Boltzmann equation with the generalized collision invariants. We investigate the dissipation process and transport characteristics obtained by such Boltzmann equation with the generalized collision invariants. Such results also imply the characteristics of fluids with anomalous diffusion.
• Classification : 82Bxx, 93A16
• Format : Talk at Waseda University
• Author(s) :
  • Ryosuke Yano (Tokio Marine dR. Co., Ltd.)

[02585] Structured Dissipative mappings with their applications in Control Systems

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D402
• Type : Contributed Talk
• Abstract : In this paper, we find necessary and sufficient conditions to identify pairs of matrices $X$ and $Y$ for which there exists $\Delta \in \mathbb C^{n,n}$ such that $\Delta+\Delta^*$ is positive semidefinite and $\Delta X=Y$. Such a $\Delta$ is called a dissipative mapping taking $X$ to $Y$. The minimal-norm dissipative mapping is then used to determine the distance to asymptotic instability for dissipative-Hamiltonian systems under general structure-preserving perturbations.
• Classification : 93Dxx, 65Fxx, 34Axx
• Format : Talk at Waseda University
• Author(s) :
  • Mohit Kumar Baghel (Indian Institute of Technology Delhi)
  • Nicolas Gillis (Université de Mons)
  • Punit Sharma (Indian Institute of Technology Delhi)

[00327] COBIT As An Information Governance Framework

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D402
• Type : Contributed Talk
• Abstract : This contributed talk aimed to present the information governance frameworks , In order to answer to the problem of the study, first we will present the information governance definition and importance, the information governance frameworks, then we'll show the COBIT as one of the important frameworks, its benefits and its principles, finally the study concluded that COBIT is a framework that ensure an optimum information technology.
• Classification : 93Dxx, 93Axx, 93-00
• Format : Online Talk on Zoom
• Author(s) :
  • Amina Feddaoui (Chadli Bendjedid university el tarf)

[02049] A Hybrid AMR Low-Rank Tensor Approach for Solving the Boltzmann Equation

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D402
• Type : Contributed Talk
• Abstract : Computational complexity grows exponentially in a grid-based approach to modeling the Boltzmann equation as dimensionality increases. Scalable low-rank tensor decomposition techniques have been developed to mitigate such issues, but challenges remain when applying real-world boundary conditions in engineering systems with complex geometries. To address these challenges, we propose a novel hybrid algorithm where quad-tree adaptive mesh refinement (AMR) is applied in real space while a low-rank approximation is used in velocity space.
• Classification : 76P05, 35Q83, 65M50
• Author(s) :
  • Samuel Jun Araki (Jacobs Technology Inc. / Air Force Research Laboratory)

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

room : D403

• [04953] Estimation of parameters on the fly via nudging methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Jared P Whitehead (Brigham Young University)
  • Abstract : We demonstrate the utility of an algorithm that allows for the estimation and recovery of parameters in a dissipative dynamical system. Rigorous justification of the algorithm is established for specific settings, and numerical simulations are used to demonstrate that it works in various settings and for different circumstances including the estimation of a full forcing function and additive and multiplicative parameters.
• [04093] Uniform Boundedness of Entropy to Compressible Navier-Stokes Equations with Vacuum
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinkai Li (South China Normal University)
  • Abstract : In the presence of vacuum, the physical entropy for polytropic gases behave singularly and it is thus hard to study its dynamics. In this talk, we present some recent studies on the uniform boundedness of the entropy to the viscous compressible ideal gas in the presence of vacuum either at the far field or on the gas-vacuum interface. It will be shown in this talk that, in the case that the vacuum presents at the far fields only, the uniform boundedness of the entropy can be propagated locally or globally if the initial density decays slowly, while if the initial density decays sufficiently fast, the entropy becomes unbounded immediately after the initial time, in particular, the entropy tends to infinity at the far field.
• [05089] A unified framework for the analysis of accuracy and stability of a class of data assimilation methods for the Navier-Stokes equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Michal Branicki (University of Edinburgh)
    • Animikh Biswas (University of Maryland Baltimore County)
  • Abstract : Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications, where nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation techniques. We develop a unified framework for the analysis of several well-known and empirically efficient data assimilation techniques derived from various Gaussian approximations of the Bayesian filtering problem for geophysical-type dissipative dynamics with quadratic nonlinearities. Our approach also elucidates the links between the approximate-Bayesian and control-theoretic approaches to data assimilation. We consider the `model' dynamics governed by the two-dimensional incompressible Navier–Stokes equations and observations given by noisy measurements of finite volume elements, modal or nodal points of the velocity field. In this setup the continuous-time data assimilation techniques, the so-called 3DVar and EnKF (Ensemble Kalman filter), are given by stochastically forced Navier–Stokes equations. We derive rigorous conditions for the (time-asymptotic) accuracy and stability of these algorithms and show the relevance of the so-called covariance inflation and localisation for assuring the necessary bounds. These conditions involve an interplay between the resolution of the observations associated with the covariance operator underlying the data assimilation algorithms and, for the first time, elucidate the properties of the EnKF as well as of the 3DVar for a general covariance operator which is common and relevant for volume and nodal observations.

contributed talk: CT153

room : D404

[01362] Nanoparticle Shape Effect On a Sodium–Alginate Based Cu–nanofluid Under a Transverse Magnetic Field

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : Sodium-alginate based nanofluids represent a new generation of fluids with improved performances in terms of heat transfer. This work examines the influence of the nanoparticle shape on a non–Newtonian viscoplastic Cu–nanofluid pertaining to this category. In particular, a stretching/shrinking sheet subjected to a transverse magnetic field is considered. The proposed Cu–nanofluid consists of four different nanoparticles having different shapes, namely bricks, cylinders, platelets, and blades dispersed in a mixture of sodium alginate with Prandtl number Pr  =  6.45. Suitable similarity transformations are employed to reduce non–linear PDEs into a system of ODEs and these equations and related boundary conditions are solved numerically by means of a Runge–Kutta–Fehlberg method. Moreover, analytical solutions are obtained through the application of a MAPLE built–in differential equation solver "Dsolve". The behavior of prominent parameters against velocity and temperature is analyzed. It is found that the temperature increases for all shapes of nanoparticles with the viscoplastic parameter and the Eckert number.
• Classification : 80A05, Nanofluid
• Format : Talk at Waseda University
• Author(s) :
  • ABID HUSSANAN (University of Education, Lahore, Pakistan)

[00971] Quantify the classicality of quantum states

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : In this talk, I will first introduce classicality and quantumness in a given quantum state. As quantumness speeds up quantum algorithms, gauging the "non-quantumness" or so-called "classicality" becomes an important task. Next, I will demonstrate using descent flow on smooth manifolds to resolve the issue. Finally, I will exhibit several numerical experiments to clarify whether our proposed method is reliable and applicable.
• Classification : 81P50, 15B10, 53Z99
• Format : Talk at Waseda University
• Author(s) :
  • BingZe Lu (Mathematics, National Cheng Kung University)
  • YuChen Shu (Mathematics, National Cheng Kung University)
  • Matthew M. Lin (National Cheng Kung University)

[00321] Modeling of hydromagnetic unsteady flow over a upright plate using Pseudospectral method

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : This study looks at the effects of a crosswise magnetic field along with thermal radiation proceeding the unsteady two-dimensional magneto hydrodynamic viscous flow, electrically insulating, and Newtonian fluid across an upright plate next to a Darcian rule. For governing equations, Pseudospectral Method is used. In this inquiry, the governing non-linear, coupled partial differential equations are decoded using Pseudospectral scheme that is reliable, effective, and has undergone substantial validation. The technique's precision and efficacy are proven.
• Classification : 80Axx, 80Mxx, 80M22
• Format : Online Talk on Zoom
• Author(s) :
  • Anju Saini (Graphic Era (Deemed to be University) Dehradun)

[00993] The effect of extended coupling in transport system

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : Totally Asymmetric Simple Exclusion Process is a stochastic model to recognize the nature of non-equilibrium transport systems. Inspired by the vehicular traffic phenomena, we have actuated a new kind of coupling rule on transport dynamics. The impact of the designed dynamics on system properties has been analyzed over phase diagrams, phase transitions, finite size effect, and shock position. The calculated numerical results from mean-field theory are verified through the ground of Monte Carlo simulation.
• Classification : 82C26, 82C70, 65C05, 60G10
• Format : Talk at Waseda University
• Author(s) :
  • Tamizhazhagan S (National Institute of Technology Tiruchirappalli.)
  • Atul Kumar Verma (NIT Trichy, India )

[02430] Hessian geometric derivation of macroscopic thermodynamic uncertainty relations (TUR)

• Session Time & Room : 5D (Aug.25, 15:30-17:10) @D404
• Type : Contributed Talk
• Abstract : The recently developed Hessian geometry of force and flux spaces in chemical reaction networks provides a geometric derivation of TUR. The relations are obtained from a comparison of two Riemannian metric tensors - one characterizes the pseudo entropy production and the other the current fluctuations. This geometry yields a characterization of the error term as the norm of a linear subspace component of the flux vector and thus characterizes the fluxes where TUR become equalities.
• Classification : 82Cxx, 53Zxx, 80Axx
• Format : Talk at Waseda University
• Author(s) :
  • Dimitri Loutchko (The University of Tokyo)
  • Tetsuya J Kobayashi (The University of Tokyo)

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

room : D407

• [03679] A case study of a dust event using the RAMS-MLEF atmosphere-aerosol coupled data assimilation system
  • Author(s) :
    • Ting-Chi Wu (Central Weather Bureau/International Integrated Systems, Inc.)
    • Milija Zupanski (Colorado State University/Cooperative Institute for Research in the Atmosphere)
  • Abstract : This study demonstrates the capability of an atmosphere-aerosol coupled data assimilation RAMS-MLEF (Regional Atmospheric Modeling System - Maximum Likelihood Ensemble Filter) using a dust event over the Arabian Peninsula, which is an area known to be severely under-sampled. One important lesson learned is that the location and timing of observations largely determines the improvements achieved by data assimilation. The lack of observations also makes it very challenging to perform a quantitative verification of results.
• [04249] Impact of Soil Moisture Observation in the Coupled Atmosphere-Land Data Assimilation System
  • Format : Talk at Waseda University
  • Author(s) :
    • Sujeong Lim (Ewha Womans University)
    • Seon Ki Park (Ewha Womans University)
    • Milija Zupanski (Colorado State University/Cooperative Institute for Research in the Atmosphere)
  • Abstract : Soil moisture is important in a coupled atmosphere-land surface model because it propagates to atmospheric variables in the planetary boundary layer through the latent and sensible heat fluxes. In this study, we introduce the results of the assimilation of both atmospheric and soil moisture observations within a strongly coupled data assimilation system, taking into account the cross-covariance between the atmosphere and land.
• [04599] Application and improvement of Land Data Assimilation System at CWB
  • Author(s) :
    • PO-HSUN LIN (CWB / International Integrated Systems, Inc. (IISI))
  • Abstract : Interactions between land and atmospheric components are critical for coupled model forecasting. Improved accuracy of soil initial conditions has been shown to enhance land-atmosphere interactions in coupled processes. The Central Weather Bureau of Taiwan has collaborated with the National Center for Atmospheric Research to optimize the use of the High-Resolution Land Data Assimilation System in order to improve the deterministic forecast over Taiwan. The results of this collaboration will be presented in this summary.

MS [00143] Recent advances in stochastic optimal control and contract theory

room : D505

• Author(s) :
  • Mehdi Christian Talbi (ETH Zurich)
  • Thibaut Mastrolia (UC Berkeley)
• Abstract : Mean field optimal stopping problems correspond to optimization problems where a central planner controls a distribution of interacting agents by assigning each of them a stopping time. After explaining how these problems can be studied through dynamic programming, we propose an application to contract theory: one Principal proposes contracts to interacting Agents, and each contract includes a continuous payment and a retirement time, which leads the Principal to solve a mixed control-and-stopping mean field problem.