MS and CT list / Aug. 23, 15:30-17:10.

MS [00604] Frontiers of Collaboration with Industry: Towards International Mathematical Commons

room : G301

• [01944] European Consortium for Mathematics in Industry - research and education
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessandra Micheletti (Università degli Studi di Milano)
  • Abstract : The European Consortium for Mathematics in Industry (ECMI) is a consortium of academic institutions and industrial companies that acts co-operatively to promote and support the use of mathematical modelling, simulation, and optimization in any activity of social or economic importance. ECMI is devoted to research motivated by industrial problems and education of Industrial Mathematicians to meet the growing demand for such experts. In this talk we will present an overview of ECMI activities in research, education and international cooperation.
• [01965] EU-MATHS-IN OpenDesk. Un infrastructure to boost industry's competitiveness.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Manuel Cruz (EU-MATHS-IN OpenDesk; LEMA-ISEP | Instituto Superior de Engenharia do Porto)
    • Véronique Maume-Deschamps (EU-MATHS-IN OpenDesk; Université Claude Bernard Lyon 1 | Institut Camille Jordan)
    • Peregrina Quintela Estévez (EU-MATHS-IN OpenDesk; CITMAga)
    • Alexander Scherrer (EU-MATHS-IN OpenDesk; Fraunhofer Institute for Industrial Mathematics ITWM)
    • Antonino Sgalambro (EU-MATHS-IN OpenDesk; Sheffield University Management School; National Research Centre of Italy)
    • Janusz Szwabinski (EU-MATHS-IN OpenDesk; Wrocław University of Science and Technology)
  • Abstract : The EU-MATHS-IN OpenDesk is a one-stop-shop aimed to make companies more competitive through mathematical technologies (MSODE). It facilitates the access to the best European technology transfer centres and coordinates the looking for the most appropriate partners to solve the current challenges. In this talk, the main points of interest of the OpenDesk will be introduced as well as its main services and procedures.
• [02986] mathematics in the society: rethinking its role, one graduate student at a time.
  • Format : Online Talk on Zoom
  • Author(s) :
    • yuliy baryshnikov (UIUC)
  • Abstract : Each year, a wave of new PhD in mathematics graduate. Statistically just about half of them will find a position in academia. How are we preparing the rest to the increasingly important role the mathematicians play in the modern society? In this talk I will present some observations and experiences from perspectives of both academic and industrial research departments.
• [05594] A Knowledge Exchange Hub for the Mathematical Sciences
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ulrike Tillmann (Isaac Newton Institute)
  • Abstract : An influential 2018 review of knowledge exchange (KE) in the mathematical sciences in the UK called for an improved infrastructure at national level. Five years later, we report on the journey towards a KE-Hub, its vision and ambitions. An important part of the journey was the award winning Virtual Forum for KE in the Mathematical Sciences (V-KEMS) set-up during the pandemic.

MS [00710] Gender Equality in Mathematics: A Global Perspective

room : G302

• [02658] Women in mathematics: an experience report and some facts about the European situation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : In this talk I will discuss some facts about the situation of female mathematicians in Europe, provide an introduction to the European Women in Mathematics (EWM) association, and give a personal account on women and mathematics in our society.
• [03111] Challenges for US Women in Math and the Activities of the AWM
  • Format : Online Talk on Zoom
  • Author(s) :
    • Talitha Washington (Association for Women in Mathematics)
  • Abstract : While there have been many strides in getting more women into the mathematical sciences, the percentage of women receiving doctorates in mathematics has been decreasing. The complexities of the intersectionality of gender, race, and ethnicity warrant more diverse approaches. The purpose of the Association for Women in Mathematics (AWM) is to create a community where women can thrive. This presentation will share how AWM’s activities promote equitable opportunity for women and others of marginalized genders.
• [01795] The Standing Committee for Gender Equality in Science
  • Format : Talk at Waseda University
  • Author(s) :
    • Carol Woodward (Lawrence Livermore National Laboratory)
  • Abstract : Several unions in the International Science Council formed the Standing Committee for Gender Equality in Science (SCGES) in 2020 with the goal of promoting gender equality across all science disciplines. This talk will introduce the SCGES and discuss its activities, including delivery of a webinar series, an annual reporting activity to help share activities among participants, participation in the Global Women’s Breakfast, and the release of a statement on gender equality in times of COVID-19. LLNL-ABS-844495.
• [02912] Panel Discussion on Gender Equality
  • Format : Talk at Waseda University
  • Author(s) :
    • Carol Woodward (Lawrence Livermore National Laboratory)
    • Maria J. Esteban (CNRS and University Paris-Dauphine)
    • GuiYing Yan (Shandong University)
  • Abstract : In this session, we will have a panel discussion with speakers from our minisymposium discussing the state of gender equality in science and mathematics specifically.

MS [01834] Structure analysis and dynamics modelling in graphs and networks

room : G304

• [01988] information-opinion dynamics on social multilayer networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fei Jing (City University of Hong Kong)
  • Abstract : Here we model these two phenomena as a co-evolution dynamics of information and public opinion on heterogeneous multiplex networks, including a few extreme individuals with constant opinions and a vast majority of general individuals with vacillating views.
• [04619] Characterizing Cycle Structure in Complex Networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tianlong Fan (University of Fribourg)
  • Abstract : A cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. In this work, we define the cycle number matrix, and the cycle ratio, an index that quantifies node importance. Numerical experiments on identifying vital nodes for network connectivity and synchronization and maximizing the early reach of spreading show that the cycle ratio performs overall better than other benchmarks.
• [03130] Collaborative deep learning framework for network inference and dynamical prediction
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiao Ding (Anhui University)
  • Abstract : How to use incomplete data to infer network structure as well as predict the dynamics simultaneously is a meaningful and challenging question. To this end, we develop a COllaborative deep learning framework for Network inference and Dynamical prediction (CoND). Extensive experiments demonstrate that COND outperforms the baseline methods regarding both tasks for different networks and dynamical models. To further validate the effectiveness of COND, we demonstrate the superior performance of CoND on two real datasets.
• [05541] Multichannel game on structured populations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Fanpeng Song (Shandong University)
  • Abstract : In this talk, we introduce a framework of multichannel game on structured populations and explore the effect of topological properties to the evolutionary dynamics. Significantly, we find that the heterogeneity of populations is detrimental to the dynamics, especially in BA networks. In addition, modest population size and high interaction are in favor of the dynamics. These results are meaningful for the research on cooperation and human development.

MS [02154] Hypergeometric functions in statistics and particle physics

room : G305

• [04146] Twisted cohomology and likelihood ideals
  • Author(s) :
    • Simon Telen (MPI MiS Leipzig)
    • Saiei-Jaeyeong Matsubara-Heo (Kumamoto University)
  • Abstract : A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We obtain a basis for cohomology from a basis of this coordinate ring. We investigate the dual picture, where twisted cycles correspond to critical points. We show how to expand a twisted cocycle in terms of a basis, and apply our methods to Feynman integrals from physics.
• [04152] Algebraic A-hypergeometric Laurent series and residues
  • Author(s) :
    • Alicia Dickenstein (University of Buenos Aires)
  • Abstract : A-hypergeometric systems of partial differential equations (introduced by Gelfand, Kapranov and Zelevinsky) have natural geometric solutions, with singularities on the associated discriminant. We describe A-hypergeometric algebraic Laurent series associated with Cayley configurations of n lattice configurations in n space. These algebraic series are generated by certain combinatorially defined sums of point residues, whose computation can be interpreted in terms of a toric degeneration. Joint work with E. Cattani and F. Martinez.
• [04334] Sampling from toric models and hypergeometric functions
  • Author(s) :
    • Shuhei Mano (The Institute of Statistical Mathematics)
  • Abstract : The toric model is an important class of stochastic models, and sampling from toric models has various applications including statistics. The sampling problem is related with hypergeometric functions, because the normalizing constant of the probability function is a multi-variable polynomial and satisfies a GKZ-hypergeometric system. In this talk, I will review several problems in which the relationship works effectively.

MS [00353] Interpretable constrained tensor decompositions: models, algorithms, efficient implementations and applications

room : G306

• [04776] A quadratically convergent proximal algorithm for nonnegative tensor decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Nico Vervliet (KU Leuven)
    • Andreas Themelis (Kyushu University)
    • Panagiotis Patrinos (KU Leuven)
    • Lieven De Lathauwer (KU Leuven)
  • Abstract : The canonical polyadic decomposition is key in a variety of applications in signal processing and data analysis. While this decomposition is unique under mild conditions, including prior knowledge such as nonnegativity often helps to interpret the components. We derive a proximal Gauss-Newton-type algorithm for nonnegative tensor factorization. We show global convergence to local minima, as well as a $Q$-quadratic convergence rate to global optima in the exact case.
• [03079] PARAFAC2-based coupled matrix and tensor factorizations with constraints
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carla Schenker
    • Xiulin Wang (Dalian University of Technology)
    • Evrim Acar (Simula Metropolitan Center for Digital Engineering)
  • Abstract : There is an emerging need to jointly analyze time-evolving data sets together with static data in many areas such as social networks and omics data analysis. PARAFAC2-based coupled matrix and tensor factorizations are a promising approach in that direction, since PARAFAC2 is capable of capturing time-evolving patterns. We present a flexible algorithmic framework for such factorizations which facilitates linear couplings and various constraints on all modes, including the evolving mode in the PARAFAC2 model.
• [03791] Constrained Tucker Decompositions and Conservation Principles for Direct Numerical Simulation Data Compression
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Dunlavy (Sandia National Laboratories)
  • Abstract : Low-rank tensor decompositions applied to numerical simulation data for compression and reduced-order modeling often focus only on minimizing global error norms between data and the low-rank model. We present an approach for computing goal-oriented low-rank tensor decompositions that incorporates problem-specific quantities of interest (QoIs) through general nonlinear constraints added to the tensor model loss function. Results for compression of direct numerical simulation data from multiple applications are presented to demonstrate the utility of this approach.
• [03819] Incremental Nonnegative Tucker Decomposition with Block-coordinate Descent and Recursive Approaches
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rafal Zdunek (Wroclaw University of Science and Technology)
    • Krzysztof Fonal (Wroclaw University of Science and Technology)
  • Abstract : We extend the standard model of Nonnegative Tucker decomposition (NTD) to an incremental or online version, assuming volatility of observed multi-way data along one mode. Two computational approaches are proposed: one is based on the recursive update model, and the other uses the concept of the block-Kaczmarz method. The experimental results performed on various datasets and streaming data demonstrate high efficiently of both algorithmic approaches with respect to the baseline NTD methods.

contributed talk: CT012

room : G401

• Session Time & Room : 3E (Aug.23, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Various studies present mathematical models of ordinary and fractional differential equations to reduce delinquent behavior and encourage prosocial growth. However, these models do not include the fear effect of the judiciary and of other gangs on one criminal gang, which is necessary to depict the behavioral changes of criminals. Hence, this talk will discuss a fractional-order of crime transmission model with the fear effect of the judiciary on offenders with competition effect in different gangs.
• Classification : 26A33, 00A71, 34A08
• Format : Talk at Waseda University
• Author(s) :
  • Trilok Mathur (Birla Institute of Technology and Science, Pilani)
  • Shivi Agarwal (Birla Institute of Technology and Science, Pilani)
  • Komal Bansal (Birla Institute of Technology and Science, Pilani)

• Session Time & Room : 3E (Aug.23, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : The universally prestarlike functions of order α ≤ 1 in the slit domain Λ = C [1;∞) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk Δ (and other circular domains in C). In this paper, we obtain the Fekete-Szegö inequality for such functions by using Variational Method. We conclude that this paper presents a new class of functions analytic in the slit domain, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well-known classes. The paper deals with several ideas and techniques used in geometric function theory.
• Classification : 30C45
• Format : Talk at Waseda University
• Author(s) :
  • Lourthu Mary Joseph (Yuvabharathi International School)

• Session Time & Room : 3E (Aug.23, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : A thermostat is a device that detects the temperature of a physical system and takes the requisite actions to maintain the system's temperature at a predetermined set point. This paper deals with a fully fractional thermostat model involving Riemann-Liouville fractional derivatives. By choosing an appropriate weighted Banach space of continuous functions, we employ the Banach contraction principle to establish the existence and uniqueness result. An example is presented to validate our theoretical finding.
• Classification : 26A33, 34A08, 34K10, 34K37, 65L10, Fractional differential equations, Riemann-Liouville fractional derivative, Thermostat model, Banach contraction principle, Product rectangle rule, Numerical simulation.
• Format : Online Talk on Zoom
• Author(s) :
  • KIRAN KUMAR SAHA (Indian Institute of Technology Roorkee)
  • NAGARAJAN SUKAVANAM (Indian Institute of Technology Roorkee)

• Session Time & Room : 3E (Aug.23, 17:40-19:20) @G401
• Type : Industrial Contributed Talk
• Abstract : In this talk , we found the analytical solution of unsteady free convective flow of an electrically conducting and viscous incompressible fluid between two infinite parallel plates when one plate moves with a ramped velocity. An applied Magnetic field has been taken into consideration. Laplace transform techniques were used to find the non-dimensional governing equations analytically. The effect of various values for magnetic field magnetic parameter, Grashof number and time parameter are demonstrated graphically.
• Classification : 26A33, 33C65, 33C20
• Format : Online Talk on Zoom
• Author(s) :
  • Sangeeta Kumari (Chandigarh University)
  • Vanita Vatsa (Depaertment of Mathematics, DCRUST, Murthal, INDIA)

contributed talk: CT017

room : G402

[01974] Solving fractional Hantavirus model: A new approach

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
• Type : Contributed Talk
• Abstract : In the present work, fractional order Hantavirus epidemic model introduced by \cite{peixoto2006effect,hantavirus2010modeling} is integrated using new iterative method (NIM) and implicit $\theta-$ method ($\theta=1$). New iterative method has been developed by Daftardar-Gejji and H. Jafari \cite{daftardar2006iterative}. Using new iterative method and $ \theta-$ method \cite{yakit2018explicit}, we have developed a new numerical algorithm to solve fractional differential equations (FDEs) in the Hantavirus model. Dynamics of the hanta virus model is studied. Hantavirus model of fractional order represents mouse population before and after getting influenced by Hantavirus under various conditions and its effect on birth rate and death rate of mice is studied. This model represents a Hantavirus infection in rodents and alien population. It has been observed that solution obtained by new algorithm is accurate and in good agreement when compared with solution obtained by other established algorithms. Further, effects of harvesting efforts $E(t)$ as an optimal control on spread of Hantavirus infection is studied. It has been observed that, population of both susceptible and infected rodents minimizes when we apply optimal control.
• Classification : 34AXX, 03-XX, 26AXX
• Format : Talk at Waseda University
• Author(s) :
  • Yogita Mahesh Mahatekar (COEP Technological University)
  • Amey Deshpande (MIT World peace University)

[01748] Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
• Type : Contributed Talk
• Abstract : We develop a mathematical network model based on balance non-linear first order ordinary differential equations to study large-scale simultaneous mRNA translation in the cell. The central feature of the model is that it is a cooperative system and this property guarantees the monotonicity of the flow. We derive that trajectories within each level set of the first integral globally converge to the fixed point. One of our findings is that raising the drop-off rate in an mRNA that is "jammed" by ribosomes can increase the network's overall protein synthesis rate.
• Classification : 34E10, 37N25, 92-10, 93D20
• Format : Talk at Waseda University
• Author(s) :
  • Aditi Jain (IIT Ropar)
  • Michael Margaliot (Tel Aviv University)
  • Arvind Kumar Gupta (IIT Ropar)

[01668] Order Reconstruction in Microfluidic Channels

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
• Type : Contributed Talk
• Abstract : We analytically and numerically study Order reconstruction (OR) solutions within the Landau-de Gennes theory for nematic liquid crystals in long shallow channel geometries. OR solutions describe liquid crystal polydomains, i.e., subdomains of distinct director orientation separated by domain walls. Such solutions are of interest due to their potential applications in drug delivery technologies and optical devices for instance. We investigate OR solutions in different physical settings: nematic liquid crystals, passive and active nematodynamics, and ferronematics.
• Classification : 34E10, 76A15, 34A99
• Format : Online Talk on Zoom
• Author(s) :
  • James Dalby (University of Strathclyde)

[02390] Discontinuous Galerkin method for time-fractional delay differential equation

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
• Type : Contributed Talk
• Abstract : In this article, we analyze the discontinuous Galerkin method for time-fractional partial differential equation with delay term $u(\theta(t))$, where $\theta(t)=t-\tau(t)< t$. The well-posedness of the fully discrete scheme for a fractional delay system is investigated. Also, we show the optimal order of convergence in the energy norm. Some numerical results are provided to support theoretical results.
• Classification : 26A33, 35D30, 65M60, 34K37
• Format : Talk at Waseda University
• Author(s) :
  • Raksha Devi (Department of Mathematics, Indian Institute of Technology, Roorkee )
  • Dwijendra N. Pandey (Department of Mathematics, Indian Institute of Technology, Roorkee )

[01090] A high order approximation scheme for non-linear time fractional reaction-diffusion equation

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G402
• Type : Contributed Talk
• Abstract : We discuss a high order numerical scheme for the non-linear time fractional reaction-diffusion equation of order $\alpha\in (0, 1)$. A cubic approximation and compact finite difference schemes are used to approximate the time-fractional and spatial derivatives respectively. The numerical scheme achieves convergence rate of order $4-\alpha$ in the temporal direction and $4$ in the spatial direction. Further, numerical experimentation is performed to demonstrate the authenticity of the proposed numerical scheme.
• Classification : 26A33, 35R11, 35A35
• Format : Online Talk on Zoom
• Author(s) :
  • Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)
  • Deeksha Singh (Indian Institute of Technology (BHU) Varanasi)

MS [02600] Applied and computational discrete algorithms

room : G404

• [04306] Parallel Batch-Dynamic Graph Algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Julian Shun (MIT)
  • Abstract : There has been significant interest in graph analytics due to their applications in many domains, including social network and Web analytics, machine learning, biology, and physical simulations. Real-world graphs today are massive and also dynamic. As many real-world graphs change rapidly, it is crucial to design dynamic algorithms that efficiently maintain graph statistics upon updates, since the cost of re-computation from scratch can be prohibitive. Furthermore, due to the high frequency of updates, we can improve performance by using parallelism to process batches of updates at a time. This talk presents new graph algorithms in this parallel batch-dynamic setting. Specifically, we present the first parallel batch-dynamic algorithm for approximate k-core decomposition that is efficient in both theory and practice. Our algorithm is based on our novel parallel level data structure, inspired by the sequential level data structures of Bhattacharya et al. and Henzinger et al. Given a graph with n vertices and a batch of B updates, our algorithm maintains a (2 + epsilon)-approximation of the coreness values of all vertices (for any constant epsilon > 0) in O(B log^2(n)) amortized work and O(log^2(n) loglog(n)) span (parallel time) with high probability. We implement and experimentally evaluate our algorithm, and demonstrate significant speedups over state-of-the-art serial and parallel implementations for dynamic k-core decomposition. We have also designed new parallel batch-dynamic algorithms for low out-degree orientation, maximal matching, clique counting, graph coloring, minimum spanning forest, single-linkage clustering, some of which use our parallel level data structure.
• [03109] Approximation: a Paradigm for Designing Parallel Graph Algorithms
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alex Pothen (Purdue University )
    • S M Ferdous (Pacific Northwest National Lab )
  • Abstract : We describe a paradigm for designing parallel algorithms by approximation techniques. Instead of solving a problem exactly, for which parallel algorithms may not exist, we seek a solution with provable approximation guarantees. Furthermore, we design these algorithms to be concurrent. We discuss linear and submodular matching and edge cover problems for which such algorithms have been designed, and describe their use in solving problems in sparse matrix computations and load balancing problems in quantum chemistry.
• [02991] Nested dissection ordering on GPUs
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoye Sherry Li (Lawrence Berkeley National Lab)
  • Abstract : Nested dissection ordering is an important preprocessing step in sparse matrix factorizations. It is effective in reducing the amount of fill in the factored matrices. As of now, there is no good algorithm nor software to compute such an ordreing on GPUs. We have made some progress in this direction. We will present our new algorithms designed for GPUs, including multilevel graph coarsening and finding small separators at each level, and the results of parallel runtime and ordering quality.
• [05454] Accelerating AI using Fast and Feasible Matrix Multiplication
  • Format : Online Talk on Zoom
  • Author(s) :
    • Oded Schwartz (The Hebrew University)
  • Abstract : AI requires large resources, both for training and for inference. It involves significant time spent on matrix multiplication, typically between 45%-95%. Most current math libraries (for CPU and GPU) and all state-of-the-art hardware accelerators (such as Google’s TPU and Intel’s / Habana Lab’s Gaudi) are based on the cubic-time classic matrix multiplication algorithm, despite more than five decades of research on sub-cubic time algorithms. In this talk I will review several of the challenges in utilizing fast matrix multiplication algorithms, and recent solutions that can allow faster application in practice.

MS [01768] Computer-assisted proofs in differential equations

room : G405

• [05182] Smooth imploding solutions for 3D compressible fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Javier Gomez Serrano (Brown University)
  • Abstract : In this talk I will present results on singularity formation for the 3D isentropic compressible Euler and Navier-Stokes equations for ideal gases. These equations describe the motion of a compressible ideal gas, which is characterized by a parameter called the adiabatic constant. Finite time singularities for generic adiabatic constants were found in the recent breakthrough of Merle, Raphaël, Rodnianski and Szeftel. Our results allow us to drop the genericity assumption and construct smooth self-similar profiles for all values of the adiabatic constant. In particular, we will construct the first smooth self-similar profile for a monoatomic gas. Part of the proof is very delicate and requires a computer-assisted analysis. Joint work with Tristan Buckmaster and Gonzalo Cao-Labora.
• [02910] Computer-assisted proofs of localized patterns in the planar Swift-Hohenberg equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthieu Cadiot (McGill University)
    • Jean-Philippe Lessard (McGill University)
    • Jean-Christophe Nave (McGill University)
  • Abstract : In this talk, I will present computer-assisted proofs of stationary localized patterns in the planar Swift-Hohenberg equation. Using a Newton-Kantorovich approach, we develop a numerical method to prove local existence and uniqueness of strong solutions in $\mathbb{R}^m$. In particular, I will explain how we manage to approximate the inverse of the linearization of the PDE around some approximated solution. Finally, I will expose the numerical details of some specific computer-assisted proofs.
• [05035] Rigorous computation of Poincare maps
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Wilczak (Jagiellonian University)
    • Tomasz Kapela (Jagiellonian University)
    • Piotr Zgliczyński (Jagiellonian University)
  • Abstract : We present recent advances on interval methods for rigorous computation of Poincare maps. We also discuss the impact of choice of Poincare section and coordinate system on obtained bounds for computing Poincare map nearby fixed points.
• [02908] Validation of Elliptic Invariant Tori in Hamiltonian Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Chiara Caracciolo (Uppsala University)
  • Abstract : The applicability of KAM theorem to realistic physical problems can be significantly improved by CAPs. These proofs exploit the explicit computation of approximately invariant solutions by the mean of normal forms or parametrization methods. I will discuss the extension of these techniques to lower-dimensional elliptic tori and present an algorithm based on a parametrization method. I will discuss the main benefits of this technique and how it can be made completely rigorous. Based on joint works with J-Ll. Figueras, A. Haro, U. Locatelli.

MS [00621] Frontiers of Collaboration with Industry: Succeeding through Failure

room : G406

• [01441] Mobility Optimization Engine and its Real-world Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Katsuki Fujisawa (Kyushu University)
  • Abstract : Various efforts have been made to realize a so-called super-smart society recently. Our project team builds services to create new industries and other services through corporate collaboration. We have utilized large-scale computing infrastructures and developed the Cyber-Physical System Mobility Optimization Engine (CPS-MOE) that provides various functions, including creating new industries. It can reduce cost and industrial waste and constructing services to calculate the optimum control schedule of transportation agencies. The latest research results and industry-academia collaborative projects using CPS-MOE will be presented in this talk.
• [02078] Mathematical modeling with industry in the water sector: what makes good practice
  • Format : Talk at Waseda University
  • Author(s) :
    • Anthony John Jakeman (Australian National University)
  • Abstract : We emphasize the role of good practices in conducting an integrated assessment exercise in water availability settings, underlining attention throughout the framing, assessment and engagement steps. We stress the notion of reflexivity on pathway decisions at each decision fork in the exercise and a holistic attention to uncertainty sources throughout the process, not just in the formulated models. These aspects will be illustrated with a case study in a catchment of the Murray-Darling Basin.
• [01474] An international research program on industrial problems for math students.
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Suito (Tohoku University)
  • Abstract : In this talk, a student research program with industrial projects in mathematics, called “g-RIPS-Sendai”, which has been held in Japan since 2018 is introduced. This program offers graduate students in mathematics stimulating opportunities to work on realistic research projects provided by industries. For industrial partners, this program provides chances to try new mathematical approaches with fresh ideas from young students. Our experiences including several difficulties will be shared and discussed.
• [02098] Collaboration with early graduate researchers, and improvements on simulated annealing
  • Format : Talk at Waseda University
  • Author(s) :
    • Joseph David (University of Washington)
    • Kemal Aziez Rachmansyah (Tohoku University)
    • Rikuto Shigemi (University of Tsukuba)
    • Zachary Brennan (Iowa State University)
  • Abstract : Students with a pure mathematics background can struggle to find early opportunities in industry without the correct guidance. As opposed to traditional graduate internships which may expect certain familiarity with industry-related problems, a hybrid academic-industry approach with both academic and industry mentors can provide a bridge for early graduate students wishing to transition to industry. This talk discusses the pros and cons of one such program from the perspective of a mid-career graduate student.

MS [00571] Mathematics in biological pattern formation: modeling, analysis, and applications

room : G501

• [04548] Patterning conditions in bilayer reaction-cross-diffusion systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Antoine Diez (Kyoto University Institute for the Avanced Study of Human Biology (ASHBi))
    • Andrew L. Krause (Durham University)
    • Philip K. Maini (University of Oxford)
    • Eamonn A. Gaffney (University of Oxford)
    • Sungrim Seirin-Lee (Kyoto University)
  • Abstract : Various biological systems such as the skin can be modelled by reaction-cross-diffusion networks in a so-called bilayer geometry where two independent reaction-cross-diffusion systems are coupled by a linear transport law. This work considers an arbitrary number of reacting species and gives quantitative theoretical asymptotic conditions, supported by numerical simulations, under which the coupling itself triggers patterning or stabilizes a homogeneous equilibrium.
• [04979] Multilevel mathematical modeling methods for morphogenesis of bacterial cell populations
  • Format : Talk at Waseda University
  • Author(s) :
    • Sohei Tasaki (Hokkaido University)
    • Madoka Nakayama (Hokkaido University)
    • Masaharu Nagayama (Hokkaido University)
    • Izumi Takagi (Tohoku University)
  • Abstract : Bacterial cell populations exhibit diverse growth morphologies and collectively form a robust system that can withstand environmental fluctuations. The diversity of macroscopic spatiotemporal patterns and flexible environmental responses in morphogenesis are supported by a variety of cellular states. Therefore, to understand the morphogenesis of bacterial populations, it is necessary to construct and analyze multilevel mathematical models that connect the cellular and tissue levels. Here we propose two multilevel modeling methods.
• [04657] A continuous model for bacteria growth with short range interactions, growth and interaction: derivation and analysis of pattern formation
  • Format : Talk at Waseda University
  • Author(s) :
    • Sophie Hecht (CNRS, LJLL, Sorbonne Université)
  • Abstract : We study a mathematical model to describe the spatial evolution of micro-colony growth with bacteria of variable size. This PDE model describes the dynamics of the density of bacteria due to short-range interaction, growth, and division. We first derive the model from a many particles system by performing a large number limit followed by a localization limit. The difficulty in these limits resides in the lack of compactness according to the size variable. We then investigate the process of pattern formation in a two-dimensional domain. We analyse how the cross-diffusion inherent to the model linked to the size variable can impact the formation of spatial patterns such as size sorting.
• [03139] Approximation for nonlocal Fokker-Planck equations by a Keller–Segel system
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshitaro Tanaka (Future University Hakodate)
    • Hideki Murakawa (Ryukoku University)
  • Abstract : To describe biological phenomena such as cell migration and cell adhesion many models with advective nonlocal interaction have been proposed. As an attempt to construct an analysis method for these equations, we approximate the nonlocal Fokker-Planck equation by the combination of a Keller-Segel system. We show that the solution of the nonlocal Fokker-Planck equation with any even continuous integral kernel can be approximated as a singular limit of the Keller-Segel system by controlling parameters.

MS [00072] Evolution equations in materials science: Multiscale modeling, analysis, and simulation

room : G502

• [04230] A two-scale model describing swelling phenomenon in porous materials
  • Format : Talk at Waseda University
  • Author(s) :
    • Kota Kumazaki (Kyoto University of Education)
    • Adrian Muntean (Karlstad University)
  • Abstract : In this talk, we propose a two-scale model describing the swelling phenomenon in porous materials. This model consists of a diffusion equation for the relative humidity distributed in materials and a free boundary problem describing the swelling process in microscopic pores. We consider each microscopic pore as a one-dimensional interval and correspond the interval to each point of materials. In this talk, we discuss the global solvability of this model.
• [04483] Improved corrector regularity in homogenization with non-smooth coefficients
  • Format : Talk at Waseda University
  • Author(s) :
    • Grigor Nika (Karlstad University)
  • Abstract : We propose an advanced model of microscopic heat conduction, capable of addressing size effects in heterogeneous media. By leveraging sound scaling arguments, we enhance the differentiability of the corrector in the classical problem of periodic homogenization of linear elliptic equations in three dimensions. This enables us to elucidate the crucial role that correctors play in quantifying the differences between the microscopic and macroscopic solutions in heterogeneous media. Furthermore, if the data are of the form $f={\rm div}~{\rm \bf F}$ with ${\rm \bf F} \in {\rm L}^{3}(\Omega, \mathbb{R}^3)$, then we recover a stronger version of the classical corrector convergence theorem.
• [03965] Solvability of a dynamical model for the elastic curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Chiharu Kosugi (Yamaguchi University)
    • Toyohiko Aiki (Japan Women's Univeristy)
  • Abstract : To establish a mathematical model for stretching and shrinking motions of the compressible elastic curves like rubber bands, we discuss problems whose feature is that the strain function is nonlinear and non-smooth, and the stress function has singularity. For the problem, thanks to a priori estimates for the strain from below and center of mass globally in time we can show results on existence, uniqueness, and large time behavior of solutions.
• [04592] Numerical simulations and analysis for mathematical modeling of adsorption phenomena
  • Format : Talk at Waseda University
  • Author(s) :
    • Yusuke Murase (Meijo University)
  • Abstract : In this talk, we discuss numerical simulations ans mathematical properties of mathematical modeling for adsorption phenomena and modeling for moisture transport in concrete material. The adsorption model is a free boundary problem composed by heat equation and free boundary equation, and the moisture transport model is combined with adsorption model and diffusion equations. Which is proposed by T. Aiki, K. Kumazaki, N. Sato, and Y. Murase.

contributed talk: CT040

room : G601

[02384] An Energy Stable Semi-implicit Scheme for the Euler System under Diffusive Scaling

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G601
• Type : Contributed Talk
• Abstract : An asymptotic preserving (AP) and energy stable scheme for the barotropic Euler system under a diffusive scaling is designed and analysed. A semi-implicit upwind finite volume on a staggered grid which dissipates the mechanical energy is introduced. The proposed scheme preserves the positivity of density and is consistent with weak solutions. The results of extensive case studies are presented to substantiate the robustness and efficacy of the proposed scheme as well as the theoretical claims.
• Classification : 35L45, 35L65, 35L67, 35L60
• Format : Talk at Waseda University
• Author(s) :
  • Arun Koottungal Revi (Indian Institute of Science Education and Research Thiruvananthapuram)
  • Mainak Kar (Indian Institute of Science Education and Research Thiruvananthapuram)

[00103] Two-dimensional Riemann problem for a new hyperbolic model for thin film flow of a perfectly soluble anti-surfactant solution

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G601
• Type : Contributed Talk
• Abstract : This work is concerned with formulation of three-dimensional thin film model for an anti-surfactant solution and hence constructing unique global solution for a two-dimensional Riemann problem for the corresponding reduced hyperbolic form. We analyze the interactions of classical and non-classical waves in detail to construct the global solution of the corresponding 2-D Riemann problem. Further, we provide the expressions for strength, location and propagation speed of delta shock wave at each interaction point.
• Classification : 35L65, 76L05, 35F55
• Format : Talk at Waseda University
• Author(s) :
  • RAJA SEKHAR TUNGALA (Department of Mathematics, Indian Institute of Technology Kharagpur)

[00943] Similarity solutions for cylindrical shock wave in self-gravitating non-ideal gas with axial magnetic field: Isothermal flow

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G601
• Type : Contributed Talk
• Abstract : The solution using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the axial magnetic field for isothermal flow. Numerical computations were performed for power law and exponential law shock paths, to see the behaviour of flow variables. The study provides how the variations in the various parameter taken in this study affect the propagation of shock and the flow behind it.
• Classification : 35L45, 58J45, 35L67, 35Q35, 76L05, Fluid Mechanics
• Format : Talk at Waseda University
• Author(s) :
  • Nandita . (Dept. of Applied Mathematics & Scientific Computing, IIT Roorkee, Roorkee,India 247667)

[00025] Riemann problem and limiting behaviour of a macroscopic production model

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G601
• Type : Contributed Talk
• Abstract : We are concerned with a macroscopic production model which is a hyperbolic system of conservation laws with the equation of state for a Van der Waals gas. Solution to the Riemann problem for the system for all types of initial data is constructed, which contains a vacuum state for certain initial data. Delta shock wave solution and vacuum state is observed in limiting cases.
• Classification : 35L65, 35L67
• Format : Talk at Waseda University
• Author(s) :
  • Balakrishna Chhatria (Indian Institute of Technology Kharagpur)

[00021] Study of sonic-supersonic patch arising in axisymmetric relativistic transonic flow

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @G601
• Type : Contributed Talk
• Abstract : In this work, we study a sonic-supersonic patch arising in 3-D axisymmetric relativistic transonic flows. The main difficulty here is the coupling of nonhomogeneous terms due to axisymmetry and the sonic degeneracy for the relativistic flow. However, using the characteristic decompositions of angle variables, we prove the existence and regularity of solutions in partial hodograph plane first and then by using an inverse transformation, we construct a smooth solution in the physical plane.
• Classification : 35L65, 35M10, 35M33, 35Q75, 35A01
• Author(s) :
  • RAHUL BARTHWAL (Indian Institute of Technology Kharagpur)
  • RAHUL BARTHWAL (Indian Institute of Technology Kharagpur)
  • T Raja Sekhar (Indian Institute of Technology Kharagpur)

MS [00061] Reaction-Diffusion models in Ecology and Evolution

room : G602

• [00120] Front Propagation in the Shadow Wave-Pinning Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Gomez (University of Pennsylvania)
    • King-Yeung Lam (The Ohio State University)
    • Yoichiro Mori (University of Pennsylvania)
  • Abstract : In this paper we consider a non-local bistable reaction-diffusion equation arising from cell polarization. A typical solution of this model exhibits an interface with velocity regulated by the total mass. The feedback between mass-conservation and bistablity causes the interface to approach a fixed limit. In the limit of a small diffusivity $\varepsilon^2\ll 1$, we prove that for any $0<\gamma<1/2$ the interface can be estimated within $O(\varepsilon^\gamma)$ of the location as predicted using formal asymptotics.
• [00109] Propagation speeds in a shifting environment
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Giletti (University of Lorraine)
  • Abstract : I will discuss the asymptotic behavior of solutions of reaction-diffusion equations with shifting heterogeneity. Such a situation arises in the modeling of population dynamics under an environmental change, due to global warming or the invasion by competing species. Two situations will be considered, depending on whether the reaction or the diffusion is heterogeneous. We will see that the heterogeneity may modify the nature of the propagation by inducing some unexpected threshold or acceleration phenomena.
• [00067] Lotka-Volterra competition-diffusion system: the critical competition case
  • Format : Talk at Waseda University
  • Author(s) :
    • Dongyuan XIAO (Meiji University)
    • Matthieu Alfaro (Universite de Rouen Normandie)
  • Abstract : We consider the competition system in the so-called critical competition case. The associated ODE system then admits infinitely many equilibria. We first show the non-existence of ultimately monotone traveling waves. Next, we study the large-time behavior of the solution of the Cauchy problem with a compactly supported initial datum and provide a sharp description of the profile of the solution.
• [00080] Coexistence of strains in some reaction-diffusion systems for infectious disease
  • Format : Talk at Waseda University
  • Author(s) :
    • Lou Yuan (Shanghai Jiao Tong University)
    • Rachidi Salako (University of Nevada at Las vegas)
  • Abstract : We study the global dynamics of some reaction-diffusion systems for multiple strains and investigate how the coexistence of strains is impacted by the movement of populations and spatial heterogeneity of the environment. For the case of two strains, general conditions for the existence, uniqueness and stability of coexistence steady states are found. Surprisingly, when there is no coexistence of strains, it is possible for the weak strain to be dominant for intermediate diffusion rates, in strong contrast to small and large diffusion cases where the weak strain goes extinct.

MS [01043] Applications of applied mathematics towards ocean engineering and related technologies

room : G605

• [01761] AuX (X = Cu, Ag) monolayers promising Thermoelectric materials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Kulwinder Kaur (Mehr Chand Mahajan DAV College for Women, Chandigarh)
  • Abstract : Under the application of strain, the electronic and thermoelectric properties of AuX (X = Cu, Ag) monolayers are investigated using density functional theory with the help of Boltzmann transport equations. At 6% strain, ultralow lattice thermal conductivity is observed. The maximum value of ZT is 2.20 and 1.40 for unstrained case and enhances to 3.61 and 2.91 at 6% strain for AuCu and AuAg monolayers, respectively, which compare favorably to several promising thermoelectric materials.
• [01770] One-Dimensional Hetero-Nanothread Fibres for high mechanical energy storage Applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marutheeswaran Srinivasan (Amrita Vishwa Vidyapeetham)
    • Ramesh Sivasamy (Amrita Vishwa Vidyapeetham)
  • Abstract : Searching for high density energy materials is a key challenge for the engineering sciences. Recently discovered carbon nanothread bundles (CNB) exhibit higher mechanical strengths than carbon nanotube bundles. MD simulation and continuum elastic theory show that CNB exhibits a high mechanical energy storage density of up to 1.76 MJ kg−1. The results suggest CNB is an ideal candidate for fiber applications. We look at how mechanical behavior changes with heteroatom doping in the pristine state.
• [01763] The Li-based quaternary Heusler compound LiYPdSn: A promising thermoelectric material
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jaspal Singh Dhillon (Mata Sundri University Girls College)
  • Abstract : A newly discovered Li-based quaternary Heusler compound LiYPdSn is investigated which is the 18 Valence Electron Count (VEC) rule follower, non-magnetic, stabilized in FCC cubic structure of F-43m space group, possessing a melting point of 1700K. The Boltzmann transport equations and the Density Functional Theory is employed to investigate its dynamic stability, electronic band structure, thermodynamic response, motivating mechanical and elastic properties, thermodynamic response, which finally results in favorable thermoelectric performances and safe environmental opportunities.
• [02187] Mathematical modeling and Environmental Impact of COVID 19 pandemic
  • Format : Online Talk on Zoom
  • Author(s) :
    • Satarupa Dey (Shyampur Siddheswari Mahavidyalaya)
  • Abstract : The corona virus disease was declared as a global pandemic on the year 2020 due to its rapid spread and complex impact on human health. By the end of the pandemic in 2021, there has been numerous impacts on environment. The prolonged lockdown enhanced the quality of air and water in urban areas on the other hand use of personal protective equipment and mask have increased plastic pollution in water bodies due to its improper disposal. In this study the positive as well as negative impact of corona virus pandemic on environment is discussed.

MS [00733] Compressible fluid dynamics and related PDE topics

room : G606

• [01614] Convergence Rate Estimates for the Low Mach and Alfven Number Three-Scale Singular Limit of Compressible Ideal Magnetohydrodynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Qiangchang JU (Institute of Applied Physics and Computational Mathematics, Beijing)
  • Abstract : Convergence rate estimates are obtained for singular limits of the compressible ideal magnetohydrodynamics equations, in which the Mach and Alfven numbers tend to zero at different rates. The proofs use a detailed analysis of exact and approximate fast, intermediate, and slow modes together with improved estimates for the solutions and their time derivatives, and the time-integration method. This is a joint work with Bin Cheng and Steve Schochet
• [01617] Nonlinear asymptotic stability of vortex sheets with viscosity effects
  • Format : Talk at Waseda University
  • Author(s) :
    • Qian Yuan (Chinese Academy of Sciences)
  • Abstract : In this talk, we can see that although a vortex sheet is not an asymptotic attractor for the compressible Navier-Stokes equations, a viscous profile that approximates the vortex sheet can be computed explicitly. It is shown that if the strength of vortex sheet is weak, then its associated viscous profile is asymptotically stable in the $ L^\infty $-norm with small initial perturbations for the compressible Navier-Stokes equations.
• [01660] Time-asymptotic expansion with pointwise remainder estimates for 1D viscous compressible flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Kai Koike (Tokyo Institute of Technology)
  • Abstract : We consider solutions to 1D compressible Naiver−Stokes equations around a constant steady state. We construct a time-asymptotic expansion with pointwise remainder estimates. The leading-order term of the expansion is the well-known diffusion wave and the higher-order terms are newly introduced family of waves which we call higher-order diffusion waves. Thanks to the pointwise remainder estimates, we can show that the expansion is valid for a fixed point $x$ and also in any $L^p(\mathbb{R})$-norm including the case of $1\leq p<2$. The proof is based on pointwise estimates of Green’s function.
• [01694] Asymptotic stability for the two-phase Navier-Stokes equations with surface tension and gravity
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirokazu Saito (The University of Electro-Communications)
  • Abstract : We consider the motion of two immiscible, viscous, incompressible capillary fluids, fluid$_+$ and fluid$_-$, in the presence of a uniform gravitational field acting vertically downward in $\mathbf{R}^N$ for $N \geq 3$. At the initial time, fluid$_-$ occupies a half-space-like domain such as oceans of infinite depth, while the complement of its closure is filled with fluid$_+$. The asymptotic stability of the trivial steady state is proved if fluid$_-$ is heavier than fluid$_+$.

MS [00783] PDE Eigenvalue Problems: Computational Modeling and Numerical Analysis

room : G701

• [01877] LOWER EIGENVALUE BOUNDS FOR THE HARMONIC AND BI-HARMONIC OPERATOR
  • Format : Talk at Waseda University
  • Author(s) :
    • Carsten Carstensen (Humboldt-Universitaet zu Berlin umboldt-Universitaet zu Berlin)
    • Sophie Puttkammer (Humboldt-Universitaet zu Berlin umboldt-Universitaet zu Berlin)
  • Abstract : Like guaranteed upper eigenvalue bounds with conforming finite element methods, guaranteed lower eigenvalue bounds (GLB) follow from min-max principles. Part 1 recalls GLB for the simplest second-order and fourth-order eigenvalue problems from a simple post-processing. The maximal mesh-size therein destroys nive adaptive mesh-refining and motivates a new methodology. Prt 2 present a new method with fine-tuned stabilization for the direct computation of GLB. Part 3 studies an optimal adaptive mesh-refining algorithm.
• [01904] Reduced order models for parametric PDE eigenvalue problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniele Boffi (KAUST)
  • Abstract : It is well known that the approximation of parametric eigenvalue problems offer much more challenges than the the corresponding source problems. This is due in particular to the lack of smoothness of the solutions with respect to the parameters. Multiplicities, clusters, and crossing of eigenvalues must be dealt with in an appropriate way in order achieve meaningful and accurate solutions. We discuss how to track the eigensolutions in presence of multidimensional parameters and we propose new ideas for the model order reduction of eigenvalues problems.
• [01686] Verification of guaranteed lower eigenvalue bounds form a hybrid-high order method
  • Format : Talk at Waseda University
  • Author(s) :
    • Carsten Carstensen (Humboldt-Universität zu Berlin)
    • Benedikt Gräßle (Humboldt-Universität zu Berlin)
    • Ngoc Tien Tran (Friedrich-Schiller-Universität Jena)
  • Abstract : A new class of skeletal methods provides direct guaranteed lower eigenvalue bounds $($GLB$)$ under verifiable assumptions on the maximal mesh-size and discretisation parameters. The verification of the GLB condition requires the knowledge of some stability constants and its validity implies that the computed discrete eigenvalue is already a GLB. This talk discusses the explicit estimation of the stability constants for the hybrid-high order $($HHO$)$ eigenvalue solver of Carstensen-Ern-Puttkammer $[$Numer.Math. 149, 2021$]$ and its recent modification with an even simpler p-robust parameter selection. We prove an a priori quasi-best approximation property and establish stabilization-free reliable and efficient a posteriori error control. Computer benchmarks provide striking numerical evidence for optimal high-order convergence rates of the associated adaptive mesh-refining algorithm.
• [01859] Poisson solvers for the biharmonic eigenvalue problem with the Navier boundary condition
  • Format : Talk at Waseda University
  • Author(s) :
    • Baiju Zhang (Beijing Computational Science Research Center )
    • Hengguang Li (Wayne State University)
    • Zhimin Zhang (Wayne State University)
  • Abstract : Consider the biharmonic eigenvalue problem with the Navier boundary condition. The Ciarlet-Raviart mixed method solves this problem by decomposing the 4th-order operator into two Laplacians but can produce spurious eigenvalues in non-convex domains. To overcome this difficulty, we adopt a recently developed mixed method, which decomposes the biharmonic equation into three Poisson equations and still recovers the original solution. Using this idea, we design an efficient biharmonic eigenvalue algorithm, which contains only Poisson solvers. With this approach, eigenfunctions can be confined in the correct space and thereby spurious modes in non-convex domains are avoided. Numerical results will be reported to validate the algorithm.

MS [00049] Interfaces between kinetic equations and many-agent social systems. Part II

room : G702

• [04945] Sticky-particle Cucker-Smale dynamics and the entropic selection principle for the Euler-alignment system
  • Format : Talk at Waseda University
  • Author(s) :
    • Trevor Leslie (University of Southern California)
    • Changhui Tan (University of South Carolina)
  • Abstract : In this talk, I will discuss weak solutions to the Euler-alignment system for collective behaviors. I will introduce an entropic selection principle that serves to isolate a unique weak solution. Notably, the solution can be constructed and approximated using Cucker-Smale dynamics, with sticky particle collision rules. I will present an analytical convergence result, as well as the formation of finite and infinite time clusters.
• [04190] Structure-preserving particle method for the Vlasov-Landau-Maxwell system
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rafa Bailo (University of Oxford)
    • Jose Carrillo (University of Oxford)
    • Jingwei Hu (University of Washington)
  • Abstract : Vlasov-Landau-Maxwell equation is often considered as the first-principle physics model for plasmas. We introduce a novel particle method for this equation which preserves the basic physical properties such as conservation of mass, momentum, and energy, and even decay of entropy. The method is based on a proper regularization of the Landau collision operator so that it can be naturally coupled with the classical particle-in-cell (PIC) method to preserve the structure. Various plasma benchmark tests such as collisional Landau damping and two-stream instability will be presented.
• [03372] On solutions to the kinetic Cucker-Smale model with singular communication weights
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinwook Jung (Jeonbuk National University)
    • Young-Pil Choi (Yonsei University)
  • Abstract : In this talk, we investigate the existence of solutions to the kinetic Cucker-Smale model with singular communication weights $\phi(r) = r^{-\gamma}$. First, we establish the local-in-time well-posedness of strong solutions to the equation in a weighted Sobolev space for $\gamma \in [d-1, d+1/4)\setminus \{d\}$. Secondly, we present the existence of weak solutions for $\gamma \in [d-1, d)$ and also the uniqueness result when $\gamma =d-1$. This talk is based on the collaboration with Y.-P. Choi.
• [03940] Interaction energy minimizers on bounded domains
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ruiwen Shu (University of Georgia)
    • José Carrillo (University of Oxford)
  • Abstract : I will discuss the behavior of interaction energy minimizers on bounded domains. When the interaction potential is more singular than Newtonian, then mass does not tend to concentrate on the boundary; when it is Newtonian or less singular, then mass necessarily concentrate on the boundary for purely repulsive potentials. We also draw a connection between bounded-domain minimizers and whole-space minimizers.

contributed talk: CT044

room : G703

[01047] Large Deviations for Two-Dimensional Stochastic Tidal Dynamics Equations driven by Levy Noise

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @G703
• Type : Contributed Talk
• Abstract : The objective is to establish a Wentzell-Freidlin type large deviation principle (LDP) for solution of stochastic tidal dynamics equations driven by Levy Noise. The LDP is equivalent to the Laplace principle in a Polish space. The solution space of the considered equation is Polish. Hence Laplace principle will be established for the stochastic tidal dynamics equations using weak convergence approach for non-negative functionals of a general Poisson random measure and Brownian motion.
• Classification : 35Q35, 60H15, 60G65, 60F10
• Format : Talk at Waseda University
• Author(s) :
  • HASEENA A (Assistant Professor, Government College Chittur)

[01641] Cut singularity of compressible Stokes flow

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @G703
• Type : Contributed Talk
• Abstract : In this talk we study the cut singularity governed by a compressible Stokes system. The cut is a non-Lipshitz boundary. The divergence of the leading corner singularity vector has different trace values on either sides of cut. In the consequence the pressure solution must have a jump across the streamline emanating from the cut tip. We establish a piecewise regularity of the solution by subtracting the related singular functions.
• Classification : 35Q35, 76N10, 76F50
• Format : Talk at Waseda University
• Author(s) :
  • Tae Yeob Lee (Pohang University of Science and Technology)
  • Jae Ryong Kweon (Pohang University of Science and Technology)

[01840] On the inviscid limit of the stochastic Navier-Stokes equation

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @G703
• Type : Contributed Talk
• Abstract : We study the asymptotic behavior of solutions to the two-dimensional stochasitc Navier-Stokes (SNS) equation in the small viscosity limit. The SNS equation is supplemented with no-slip boundary condition, in which a strong boundary layer shall appear in the limit. Several equivalent dissipation conditions are derived to ensure the convergence hold in the energy space. One novelty of this work is that we do not assume any smallness for the noise.
• Classification : 35Q35, 60H15, 76D10
• Format : Talk at Waseda University
• Author(s) :
  • Meng Zhao (Shanghai Jiao Tong University)
  • Ya-Guang Wang (Shanghai Jiao Tong University)

MS [00496] Recent development in Quantum Simulation and Stochastic Methods

room : G704

• [02819] Asymmetric transport and topological invariants
  • Format : Talk at Waseda University
  • Author(s) :
    • Guillaume Bal (University of Chicago)
  • Abstract : Transport asymmetries along interfaces separating insulating bulks have a topological origin. The talk proposes a classification of partial differential systems with topological invariant computed explicitly by a Fedosov-Hörmander formula. Asymmetric transport is associated to another topological invariant whose calculations is less direct. A bulk-edge correspondence states that the two invariants in fact agree. The theory is applied to graphene-based topological insulators. Time permitting, the above spectral analysis will be contrasted with a temporal picture.
• [02812] Asymmetric transport computations in Dirac models of topological insulators
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhongjian Wang (Nanyang Technological University)
    • Guillaume Bal (University of Chicago)
    • Jeremy Hoskins (University of Chicago)
  • Abstract : We will present a fast algorithm for computing transport properties of two-dimensional Dirac operators with linear domain walls, which model the macroscopic behavior of the robust and asymmetric transport observed at an interface separating two two-dimensional topological insulators. Our method is based on reformulating the partial differential equation as a corresponding volume integral equation, which we solve via a spectral discretization scheme. We demonstrate the accuracy of our method by confirming the quantization of an appropriate interface conductivity modeling transport asymmetry along the interface, and moreover, confirm that this quantity is immune to local perturbations. We also compute the far-field scattering matrix generated by such perturbations and verify that while asymmetric transport is topologically protected the absence of back-scattering is not.
• [01869] Quantum Orbital Minimization Method for Excited States Calculation on Quantum Computer
  • Format : Talk at Waseda University
  • Author(s) :
    • Yingzhou Li (Fudan University)
  • Abstract : We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H2, LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.
• [02283] Bloch decomposition based method for Schroedinger equation with random inputs
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhongyi Huang (Tsinghua University)
  • Abstract : In this talk, we focus on the analysis and numerical methods for the Schroedinger equation with lattice potential and random inputs. Here we recall the well-known Bloch decomposition-based split-step pseudo-spectral method where we diagonalize the periodic part of the Hamilton operator so that the effects from dispersion and periodic lattice potential are computed together. Meanwhile, for the random non-periodic external potential, we utilize the generalize polynomial chaos with Galerkin procedure to form an ODE system which can be solved analytically. Furthermore, we analyse the convergence theory of the stochastic collocation method for the linear Schroedinger equation with random inputs. We provide sufficient conditions on the random potential and initial data to ensure the spectral convergence.

MS [00563] PDE's on Mathematical Physics and Biology

room : G709

• [04143] The effect of diffusion on principal eigenvalues for Hamilton-Jacobi equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Cristina Brändle (U. Carlos III Madrid)
  • Abstract : We deal with the ergodic problem of viscous Hamilton–Jacobi equations with superlinear Hamiltonian, inward-pointing drift and a positive potential function that vanishes at infinity. We characterize the generalized principal eigenvalue with respect to diffusion and also specify the necessary and sufficient condition so that the spectral function contains a plateau.
• [03901] Population models with an interface region inside the domain
  • Format : Talk at Waseda University
  • Author(s) :
    • Pablo Alvarez-Caudevilla (Universidad Carlos III de Madrid)
    • Pablo Alvarez Caudevilla (Universidad Carlos III de Madrid)
  • Abstract : We will discuss several models that might be regarded as migration models of populations moving from one part of a domain to the other and becoming part of the population living on the other side. Different situations assuming symmetry of movement between both sides of the domain, following a logistic model in their own environment and assuming spatial heterogeneities, are going to be discussed. Through such a common boundary both populations are coupled, acting as a permeable membrane on which their flow moves in and out. We will describe the precise interplay between the stationary solutions with respect to the parameters involved in the problem, in particular the growth rate of the populations and the coupling parameter involved on the boundary where the interchange of flux is taking place.
• [04005] A bifurcation result for a fractional semilinear Neumann problem
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Vilasi (University of Messina)
  • Abstract : We will examine a parameterized elliptic problem governed by the Neumann fractional Laplacian on a bounded domain of $\mathbb R^N$, $N\geq 1$, with a general nonlinearity. This problem arises, in particular, when looking for steady state solutions to Keller-Segel systems in which the diffusion of the chemical is non-local. By variational arguments we will show the existence of non-trivial solutions, local minima of the corresponding energy functional, that branch off the null one for small values of the parameter. We will also derive some regularity results, as well as other qualitative properties of the solutions.
• [04254] Systems of coupled nonlinear Schrödinger equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Eduardo Colorado (Universidad Carlos III de Madrid)
  • Abstract : Along the talk we will see some results about existence of solutions to general coupled systems of nonlinear Schrödinger (NLS) equations (and systems of coupled NLS-nonlinear Korteweg-de Vries equations). To do so, we will use variational techniques once one pass to the elliptic system obtained by looking for standing solitary wave solutions (or standing-travelling wave solutions) for the NLS coupled system (or the NLS-NKdV coupled system).

MS [00196] Recent development of mathematical geophysics

room : G710

• [01262] Global solutions for rotating MHD equations in the critical space
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryo Takada (The University of Tokyo)
    • Keiji Yoneda (Kyushu University)
  • Abstract : We consider the initial value problem for the incompressible rotating magnetohydrodynamics equations in $\mathbb{R}^3$. We prove the unique existence of global solutions for large initial data in the scaling critical space $\dot{H}^{\frac{1}{2}}(\mathbb{R}^3)$ when the rotation speed is sufficiently high. In order to control large magnetic fields, we introduce a modified linear solution for the velocity, and show its smallness in a suitable space-time norm by means of the dispersive effect of the Coriolis force.
• [02684] Multi-scale interaction of tropical weather in a simplified three-dimensional model
  • Format : Talk at Waseda University
  • Author(s) :
    • Daisuke Takasuka (University of Tokyo)
  • Abstract : In the tropics, various kinds of weather systems are spontaneously realized, as represented by mesoscale convective systems, equatorial waves, the Madden–Julian oscillation ((\rm{MJO})). They interact with each other through moist processes, wave–mean-flow interaction, and so on. As an example of this, we will present a non-linear multi-scale process in the MJO initiation, which involves the mean tropical circulations and equatorial waves, using a simplified three-dimensional fluid dynamical model.
• [00606] Eigenvalue Problem for Perturbation Operator of Two-jet Kolmogorov Type Flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Tatsu-Hiko Miura (Hirosaki University)
  • Abstract : We consider the linear stability of the two-jet Kolmogorov type flow which is a stationary solution to the vorticity equation on the unit sphere given by the zonal spherical harmonic function of degree two. Using the mixing structure of the two-jet Kolmogorov type flow, we show that the perturbation operator does not have eigenvalues except for zero. As an application, we also prove the occurrence of the enhanced dissipation in the linearized setting.
• [00377] On the physics-informed neural networks approximating the primitive equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Quyuan Lin (University of California, Santa Barbara)
    • Ruimeng Hu (University of California, Santa Barbara)
    • Alan Raydan (University of California, Santa Barbara)
    • Sui Tang (University of California, Santa Barbara)
  • Abstract : Large scale dynamics of the oceans and the atmosphere are governed by the primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is in general a hard task. In this talk, I will introduce physics-informed neural networks (PINNs) to tackle this challenge, and show the theoretical error estimates and the results from numerical experiments that confirm the reliability of PINNs.

MS [00237] Recent progress in multiscale modeling and computational methods in material sciences

room : G801

• [05400] Numerical methods for topology optimization and applications
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xiaoping Wang (Hong Kong university of science and technology)
  • Abstract : n this talk, I will introduce some numerical methods for topology optimization based on threshold dynamics method. Applications to linear elasticity, fluid network and porous media problems will be discussed.
• [05389] Optimal error estimate for the Multiscale Finite Element Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Pingbing Ming (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
    • Siqi Song (Academy of Mathematics and Systems Science)
  • Abstract : We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic systems with rapidly oscillating periodic coefficients that are bounded and measurable, which may admit rough microstructures. As a by-product of the energy estimate, we derive the rate of convergence in L$^{d/(d-1)}-$norm with $d$ the dimensionality.
• [05618] On median filters for motion by mean curvature
  • Format : Talk at Waseda University
  • Author(s) :
    • Selim Esedoglu (University of Michigan)
  • Abstract : The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition by another class of methods known as threshold dynamics. Based on this connection, we revisit median filters in light of recent work on the threshold dynamics method.
• [02920] Structure-preserving methods based on minimizing movement scheme for gradient flows with respect to transport distances
  • Format : Talk at Waseda University
  • Author(s) :
    • Chaozhen Wei (University of Electronic Science and Technology of China)
  • Abstract : I will present a novel structure-preserving numerical method for gradient flows w.r.t Wasserstein-like transport distances induced by concentration-dependent mobilities, which arise widely in materials science and biology. Based upon the minimizing movement scheme and modern operator-splitting schemes, our method has built-in positivity or boundedness preserving, mass conservation, and energy-dissipative structures. I will show the flexibility and performance of our methods through simulation examples including different free energy functionals, general wetting boundary conditions and degenerate mobilities.

MS [00507] Stochastic Dynamical Systems and Applications

room : G802

• [04264] Three-dimensional numerical study on wrinkling of vesicles in elongation flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Wang Xiao (Huazhong University of Science and Technology)
  • Abstract : We study the wrinkling dynamics of three-dimensional vesicles in time-dependent elongation flow by utilizing an immersed boundary method. The numerical results well match the predictions of perturbation analysis for a quasi-spherical vesicle. The parallel simulation can compute 512^3 Eulerian fluid grids and save the computation cost by at least an order of magnitude compared with the CPU algorithm. In addition, the parallel simulation can be directly extended to study other initial vesicles and external flows.
• [04452] Energetic Variation associated with nonlinear Schrödinger equations with Anderson Hamiltonian
  • Format : Talk at Waseda University
  • Author(s) :
    • Qi Zhang (Yau Mathematical Sciences Center, Tsinghua University, China/Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, China)
  • Abstract : We study the variation problem associated with nonlinear Schrödinger equations with Anderson Hamiltonian in $2$-dimensional torus. Under the paracontrolled distribution framework from singular SPDEs theory, we obtain the existence of the ground state solution by considering the minimization problem of the corresponding energy functional with $L^2$ constraints. We also obtain the tail estimate on the distribution of the principal eigenvalue via the variational representation. This is joint work with Prof. Jinqiao Duan.
• [04457] Macroscopic approximation for stochastic N-particle system with small mass
  • Format : Online Talk on Zoom
  • Author(s) :
    • Wei Wang (Nanjing University)
  • Abstract : In this talk we present a small mass limit approximation on macroscopic scale for stochastic $N$-particle system. On macroscopic scale we have a slow-fast system and then by coupling the system on microscopic scale, an averaging approach is applied to derive the small mass limit. We also present this method to several different systems.
• [04557] Effective wave factorization for a stochastic Schrodinger equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Ao Zhang (Central South University)
  • Abstract : We study the homogenization of a stochastic Schrodinger equation with a large periodic potential in solid state physics. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of an effective equation. Our method is based on two-scale convergence and Bloch waves theory.

MS [00345] Recent Developments for High-frequency Waves and Tomography

room : G808

• [02057] Eulerian PDE methods for complex-valued eikonals in attenuating media
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jiangtao Hu (Chengdu University of Technology)
    • Jianliang Qian (Michigan State University)
    • Shingyu Leung (The Hong Kong University of Science and Technology)
  • Abstract : Seismic waves in earth media usually undergo attenuation. In the regime of high-frequency asymptotics, a complex-valued eikonal is essential for describing wave propagation in attenuating media. Conventionally, it is computed by ray-tracing methods defined by ODEs, but those irregularly distributed results hinder their applications. This talk proposes a unified eulerian PDE for several popular real ray-tracing methods. We also develop a highly accurate numerical scheme using factorization and LxF-WENO scheme.
• [01878] Uniformly convex neural networks and iterated network Tikhonov (iNETT) method
  • Format : Online Talk on Zoom
  • Author(s) :
    • Davide Bianchi (Harbin Institute of Technology, Shenzhen)
    • Guanghao Lai (Harbin Institute of Technology, Shenzhen)
    • Wenbin Li (Harbin Institute of Technology, Shenzhen)
  • Abstract : We propose a non-stationary iterated network Tikhonov (iNETT) method for the solution of ill-posed inverse problems. The iNETT employs deep neural networks to build a data-driven regularizer, and it avoids the difficult task of estimating the optimal regularization parameter. To achieve the theoretical convergence of iNETT, we introduce uniformly convex neural networks to build the data-driven regularizer. Rigorous theories and detailed algorithms are proposed for the construction of convex and uniformly convex neural networks. In particular, given a general neural network architecture, we prescribe sufficient conditions to achieve a trained neural network which is component-wise convex or uniformly convex; moreover, we provide concrete examples of realizing convexity and uniform convexity in the modern U-net architecture. With the tools of convex and uniformly convex neural networks, the iNETT algorithm is developed and a rigorous convergence analysis is provided. Lastly, we show applications of the iNETT algorithm in 2D computerized tomography, where numerical examples illustrate the efficacy of the proposed algorithm.
• [03580] Linearized Inverse Potential Problems at a High Frequency
  • Format : Talk at Waseda University
  • Author(s) :
    • Boxi XU (Shanghai University of Finance and Economics)
  • Abstract : We investigate the recovery of the potential function from many boundary measurements at a high frequency for linear or nonlinear equations. By considering such a linearized form, we obtain Hölder type stability which is a big improvement over logarithmic stability in low frequencies. Increasing stability bounds for these coefficients contain a Lipschitz term with a factor growing polynomially in terms of the frequency, a Hölder term, and a logarithmic term that decays with respect to the frequency as a power. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of sufficiently many Fourier modes of the potential function. By choosing the high frequency appropriately, the numerical evidence sheds light on the influence of the growing frequency and confirms the improved resolution. This is the joint work with Prof. Victor Isakov, Prof. Shuai Lu, Prof. Mikko Salo, and Mr. Sen Zou.
• [03600] An Embedding Method for Hyperbolic Conservation Laws on Implicit Surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Chun Kit Hung (The Hong Kong University of Science and Technology)
    • Shingyu Leung (The Hong Kong University of Science and Technology)
  • Abstract : In this talk, we will present a novel embedding method for solving scalar hyperbolic conservation laws on surfaces. The proposed method represents the interface implicitly through the zero-level set of its signed distance function and introduces a pushforward operator to extend the surface flux function to neighboring level surfaces. By solving an extended conservation law in a tubular neighborhood of the interface, it has been proven that the solution is the constant-normal extension of the surface conservation law. Numerical examples will be presented to demonstrate the accuracy and performance of the proposed method.

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

room : G809

• [05416] STABILITY ESTIMATES FOR AN INVERSE PROBLEM FOR SCHRODINGER OPERATORS AT HIGH FREQUENCIES FROM ARBITRARY PARTIAL BOUNDARY MEASUREMENTS
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ganghua Yuan
    • Xiaomeng Zhao (Northeast Normal University)
  • Abstract : In this talk, we consider the partial data inverse boundary value problem for the Schrodinger operator at a high frequency in a bounded domain in $\mathbb R^n$, $n\geq3$. Assuming that the potential is known in a neighborhood of the boundary, we obtain the logarithmic stability when both Dirichlet and Neumann data are taken on arbitrary open subsets of the boundary . We used a method combining the CGO solution, Runge approximation and Carleman estimate.
• [04623] Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Michel Cristofol (Aix-Marseille Université)
    • Shumin Li (University of Science and Technology of China)
    • Yunxia Shang (Shanghai Normal University)
  • Abstract : We consider the determination of a coefficient or the source term in a strong coupled quantitative thermoacoustic system of equations. For this purpose, we establish a Carleman estimate for the coupled quantitative thermoacoustic equations. Applying this Carleman estimate, we prove stability estimates of Hölder type for inverse problems involving the observation of only one component: the temperature or the pressure.
• [05434] Inverse problems for transport equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Giuseppe Floridia (Sapienza Università di Roma)
  • Abstract : In this talk we present several inverse problems, introduced in recent papers, for transport equations via Carleman estimates. We approach also the general case of first-order hyperbolic equations with time-dependent coefficients.
• [04572] Unique continuation for wave equations in asymptotically anti-de Sitter spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Takase (Kyushu University)
  • Abstract : An asymptotic anti-de Sitter space is a Lorentzian manifold with a Lorentz metric diverging at the boundary of the manifold. It is also used as a model of outer space, and in particular, the problem of determining the inner structure from the data at the boundary has attracted attention in theoretical physics as AdS/CFT correspondence. The wave equation in this space is a degenerate equation. In this talk, I will present results on the fundamental property of unique continuation for this wave equation.

MS [02499] Machine Learning for dynamics and its applications

room : F308

• [03000] Learning Strange Attractors with Reservoir Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Allen Hart (University of Bath)
  • Abstract : This talk is based on a preprint by myself, Juan-Pablo Ortega, and Lyudmila Grigoryeva, which shows that the celebrated Takens Embedding Theorem is a particular case of a much more general statement according to which, randomly generated Echo State Networks (with linear activations) trained on generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.
• [04147] Dynamical system properties of reservoir computing models
  • Format : Talk at Waseda University
  • Author(s) :
    • kengo nakai (Okayama University)
    • Miki U. Kobayashi ( Rissho University)
    • Yoshitaka Saiki (Hitotsubashi University)
    • Natsuki Tsutsumi (Tokyo University of Marine Science and Technology)
  • Abstract : It has been reported that reservoir computing is effective in the inference of time-series and some characteristics. We construct a model from training time-series of dynamical system with tangencies between stable and unstable manifolds or hetero-chaos, coexisting of invariant sets of different number of unstable dimensions. We confirm that these dynamical properties as well as fixed points and periodic orbits can be reconstructed by reservoir computing.
• [02889] Predicting tipping point with machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Ying-Cheng Lai (Arizona State University)
  • Abstract : Compared with the existing works on model-free prediction of chaotic systems, to predict a tipping point is significantly more challenging, because the training data are from the system when it is in a steady state. The speaker will describe the tipping-point mechanism, discuss how dynamical noise can be exploited in a machine learning scheme to predict the future occurrence of tipping points, and present benchmark examples as well as a real-world application.
• [02921] Machine Learning for Predicting Missing Dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Shixiao Willing Jiang (ShanghaiTech University)
  • Abstract : We present a framework for recovering missing dynamics using available data and machine learning techniques. The framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. The map for this non-Markovian transition kernel is represented by appropriate RKHS or LSTM formulation. Supporting numerical results include the Lorenz system, the Kuramoto-Sivashinsky equation, etc.

MS [01897] New Tools for Nonlinear Time Series Analysis

room : F309

• [05007] Pattern-based approaches to identifying coupling structures among multivariate time series
  • Format : Talk at Waseda University
  • Author(s) :
    • Reik V. Donner (Magdeburg-Stendal University of Applied Sciences)
  • Abstract : Nonlinear analysis methods based on the occurrences of patterns have recently proven valuable tools for time series analysis. In this talk, I will review some recently developed approaches based on co-occurrence statistics between ordinal patterns, graphlets, or extreme events in multivariate time series and their use for correctly distinguishing direct from indirect coupling in otherwise challenging situations, including examples of variables with poor observability characteristics.
• [03507] Transition network approaches for nonlinear time series analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Zou (East China Normal University)
  • Abstract : Complex networks are powerful tools for nonlinear time series analysis, which are undergoing fast development in the recent decade. Here we propose a novel way to construct multi-scale transition networks from time series, which are based on coarse-graining partitions of phase space. Using time series from both discrete Henon map and continuous Rössler systems, we demonstrate that the multi-scale transition entropy values of the resulting networks show the same power as the Lyapunov exponents, identifying chaotic transitions successfully. The advantage is that our method works successfully when only a small number of 3–5bins is used for the partition generation, while the traditional static node entropy measures work poorly. Further experimental examples in fMRI and ECG analysis show that these entropy measures are able to characterizing different rhythmic states of subjects, showing high potential for time series analysis from complex systems.
• [04058] Persistent homology induced by ordinal patterns for multivariate time series
  • Format : Talk at Waseda University
  • Author(s) :
    • Taichi Haruna (Tokyo Woman's Christian University)
  • Abstract : We present a method to construct a filtered simplicial complex from a given multivariate time series using the intersections of ordinal patterns. The filtered complex reflects information about couplings among individual time series. A measure of the complexity of couplings can be defined from its persistent homology groups. The behavior of the complexity measure is investigated in terms of its mathematical properties and applications to examples.
• [04580] Reconstruction of causal graphs with self loops
  • Format : Online Talk on Zoom
  • Author(s) :
    • X. San Liang (Fudan University)
  • Abstract : Causality analysis is an important problem lying at the heart of science. An endeavor during the past years viewing causality as a real physical notion so as to formulate it from first principles, however, seems to have gone unnoticed. This study introduces to the community this line of work. The resulting formula is transparent, and can be implemented as a computationally very efficient algorithm for application. Different from the previous work along this line, here an algorithm is also implemented to quantify the influence of a unit to itself. While this forms a challenge in some causal inferences, here it comes naturally, and hence the identification of self-loops in a causal graph is fulfilled automatically as the causalities along edges are inferred. To demonstrate the power of the approach, presented here are two applications in extreme situations. The first is a network of multivariate processes buried in heavy noises (with the noise-to-signal ratio exceeding 100), and the second a network with nearly synchronized chaotic oscillators. In both graphs, confounding processes exist. While it seems to be a challenge to reconstruct from given series these causal graphs, an easy application of the algorithm immediately reveals the desideratum. Particularly, the confounding processes have been accurately differentiated.

MS [02025] Recent Advances on the Analysis and Applications of Continuous and Discrete Integrable Systems

room : F310

• [03560] Rogue waves and their patterns in the vector nonlinear Schrödinger equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Baofeng Feng (University of Texas Rio Grande Valley )
    • Peng Huang (Shenzhen University)
    • Chengfa Wu (Shenzhen University)
    • Guangxiong Zhang (Shenzhen University)
  • Abstract : This talk presents the general rogue wave solutions and their patterns in the vector (or M-component) nonlinear Schrödinger (NLS) equation. We derived the explicit solution for the rogue wave expressed by tau-functions that are determinants of K×K block matrices with an index jump of M+1. Patterns of the rogue waves for M=3,4 and K=1 are thoroughly investigated.
• [03656] Whitham modulation theory of Riemann problem for nonlinear integrable equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yaqing Liu (Beijing Information Science and Technology University)
  • Abstract : The Riemann problem of the nonlinear integrable equation with step-like initial value is explored by Whitham modulation theory, which is a modified version of the well-known finite-gap integration method. Based on the reparameterization of the solution with the use of algebraic resolvent of the polynomial defining the solution, the periodic wave solutions of the nonlinear integrable equation are described by the elliptic function along with the Whitham modulation equations. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity initial value. The proposed analytic results are confirmed through direct numerical simulations.
• [03369] Quantum variational principle for Lagrangian 1-forms
  • Format : Talk at Waseda University
  • Author(s) :
    • Sikarin Yoo-Kong (Naresuan University)
  • Abstract : In this talk, we will present a new type of the propagator associated with the Lagrangian 1-forms called the (continuous) multi-time propagator. With this new type of the propagator, a new paradigm on summing over possible paths arises since one needs to take into account not only summing over possible spatial paths but also summing over possible temporal paths. The quantum intragrability (a.k.a multi-dimensional consistency), which mainly relies on the classical Lagrangian 1-form closure relation, will be captured in the language of Feynman path integration.
• [05098] Three-dimensional fundamental diagram of stochastic cellular automata
  • Format : Talk at Waseda University
  • Author(s) :
    • Kazushige Endo (Kindai University)
  • Abstract : Cellular automata including Burgers cellular automaton are not only examples of ultradiscrete analogue of integrable systems, but also mathematical models which show fundamental mechanisms of traffic flow. For example, a phase transition from free flow to congested flow in a traffic system is well-known and has been studied using fundamental diagram. Fundamental diagram is an object showing relation between the density of traffic (particles) and their mean momentum. However, the density of particles is not a unique parameter to determine the mean momentum. Several systems whose mean momentum is uniquely determined by a pair of the density and another conserved quantity have been discovered. In this talk, we show a three-dimensional framework of the fundamental diagram of stochastic cellular automata and its theoretical derivation.

MS [01197] Numerical linear algebra in convex and nonconvex optimization

room : F311

• [01875] Nonconvex accelerated gradient descent without parameter tuning
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoki Marumo (University of Tokyo)
    • Akiko Takeda (University of Tokyo)
  • Abstract : We propose a new first-order method for minimizing nonconvex functions with a Lipschitz continuous gradient and Hessian. The proposed algorithm is an accelerated gradient descent method with two restart mechanisms. It finds a solution where the gradient norm is less than $\varepsilon$ in $O(\varepsilon^{-7/4})$ function and gradient evaluations. Unlike existing algorithms with similar complexity bounds, our method requires no prior knowledge of problem-dependent parameters. Several numerical results illustrate that the proposed method is promising.
• [02180] Low Rank Tensor Decompositions and Approximations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jiawang Nie (University of California, San Diego)
    • Li Wang (University of Texas, Arlington)
    • Zequn Zheng (University of California, San Diego)
  • Abstract : There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.
• [05344] Efficient and numerically stable interior-point algorithms for convex optimization
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ming Gu (UC Berkeley)
  • Abstract : We present efficient and numerically stable interior-point algorithms for linear programs, quadratic programs, as well as second order cone programs (socp), with supporting numerical results. In particular, our stable algorithms for socp achieves full machine precision accuracy, whereas existing interior-point methods for socp are known to be highly unstable.

MS [01040] Optimization and its Applications

room : F312

• [01444] Non-Smooth Integrability Theory
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuhki Hosoya (Chuo University)
  • Abstract : We study a method of calculating the utility function from a candidate of a demand function that is not differentiable but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a demand function to be a demand function. The first is conditions for the Slutsky matrix, and the second is the existence of a concave solution to a partial differential equation. Moreover, we show that the upper semi-continuous weak order that corresponds to the demand function is unique, and this weak order is represented by our calculated utility function. We provide applications of these results to econometric theory. First, we show that, under several requirements, if a sequence of demand functions converges to some function with respect to the metric of compact convergence, then the limit is also a demand function. Second, the space of demand functions that have uniform Lipschitz constants on any compact set is complete under the above metric. Third, the mapping from a demand function to the calculated utility function becomes continuous. This implies that a consistent estimation method for the demand function immediately defines a consistent estimation method for the utility function using our calculation method.
• [01446] Theoretical analysis of two time-scale update rule for training GANs
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoki Sato
    • Hideaki Iiduka (Meiji University)
  • Abstract : A theoretical analysis of a two time-scale update rule $(\text{TTUR})$ for training generative adversarial networks $(\text{GANs})$ has been given using decaying learning rates. In this talk, we give a theoretical analysis of TTUR using constant learning rates and show that, for TTUR using constant learning rates, the number of steps needed to train GAN decreases as the batch size increases. We also provide numerical results to support our theoretical analyses.
• [01450] Production Prices and Walrasian Intertemporal Competitive Equilibrium Prices in a Generalized Neoclassical Production Economy
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoki Yoshihara (University of Massachusetts Amherst)
  • Abstract : We examine a general correspondence between production prices in classical and Marxian economics and the Walrasian competitive equilibrium prices in the standard general equilibrium theory by considering a standard intertemporal economy with a discounted lifetime utility function and a set of general neo-classical production technologies. This work resembles Duménil and Levy (1985) and Dana et. al (1989), but unlike these, a path of intertemporal Walrasian equilibrium prices is characterized by the Euler equation, derived from the economic model in this paper. In addition, equilibrium factor prices are endogenously determined and can vary across periods. Therefore, our intertemporal Walrasian equilibrium is much closer to the standard neoclassical type, compared to the intertemporal competitive equilibrium defined by Dana et. al (1989). However, we will show that any intertemporal Walrasian equilibrium prices converge to a system of production prices in the long term.
• [01982] Optimal Growth in the Two-Sector Robinson-Shinkai-Leontief Model
  • Format : Talk at Waseda University
  • Author(s) :
    • Minako Fujio (Yokohama National University)
    • Ali M. Khan (The Johns Hopkins University)
    • Liuchun Deng (Yale-NUS College)
  • Abstract : In this talk we synthesize the findings on the two-sector Robinson-Shinkai-Leontief model of optimal growth with and without discounting and demonstrate a variety of optimal dynamics. We provide a taxonomy of the optimal policy and the dynamics it yields for the entire parameter space of the model. At the same time, we shall focus on the two approaches we rely on to delineate those results, the value-loss minimization and the dynamic programming.

MS [00356] Recent progress in variational problems with nonlocality

room : F401

• [03830] The elastica functional as the critical Gamma-limit of the screened Gamow model
  • Format : Talk at Waseda University
  • Author(s) :
    • Theresa Simon (University of Münster)
    • Cyrill Muratov (University of Pisa)
    • Matteo Novaga (University of Pisa)
  • Abstract : I will consider the large mass limit of a nonlocal isoperimetric problem in two dimensions with screened Coulomb repulsion. In this regime, the nonlocal interaction localizes on the boundary of the sets. It turns out that in the case of exactly cancelled surface area, the problem changes from length to curvature minimization: The next-order Gamma limit is given by the elastica functional, i.e., the integral over the squared curvature over the boundary.
• [04447] Reduced energies for thin ferromagnetic films with perpendicular anisotropy
  • Format : Talk at Waseda University
  • Author(s) :
    • Cyrill Muratov (University of Pisa)
  • Abstract : We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction. Starting with a microscopic model that regularizes the stray field near the material’s lateral edges, we carry out an asymptotic analysis of the energy by means of Γ-convergence. Depending on the scaling assumptions on the size of the material domain vs. the strength of dipolar interaction, we obtain a hierarchy of the limit energies that exhibit progressively stronger stray field effects of the material edges. These limit energies feature, respectively, a renormalization of the out-of-plane anisotropy, an additional local boundary penalty term forcing out-of-plane alignment of the magnetization at the edge, a pinned magnetization at the edge, and, finally, a pinned magnetization and an additional field-like term that blows up at the edge, as the sample’s lateral size is increased. The pinning of the magnetization at the edge restores the topological protection and enables the existence of magnetic skyrmions in bounded samples.
• [03755] Minimal partitions for local and nonlocal energies
  • Format : Talk at Waseda University
  • Author(s) :
    • Annalisa Cesaroni (University of Padova)
  • Abstract : The Kelvin problem, posed by Lord Kelvin in 1887, is the problem of finding a partition of $\mathbb{R}^3$ into cells of equal volume, so that the total area of the surfaces separating them is as small as possible. I will discuss some related problems in $\mathbb{R}^n$, in particular the problem of finding the foam whose cell minimizes a general perimeter functional among all periodic partitions given by lattice tilings. Moreover I will present some qualitative results in low dimension.
• [03839] Asymptotics of phase field models for crystal defects
  • Format : Talk at Waseda University
  • Author(s) :
    • Adriana Garroni (Sapienza, University of Rome)
    • Sergio Conti (University of Bonn)
    • Stefan Mueller (University of Bonn)
  • Abstract : We consider Nabarro Peierls type model for line defects in crystals. We study the asymptotics in scaling regime which allows for the number of dislocations to diverge and results, in the limit as the lattice spacing tends to zero, in a macroscopic model for plasticity where the relevant variable is a diffuse quantity that represents the dislocation density.

MS [00941] Numerical methods for Hamilton-Jacobi equations and their applications

room : F402

• [01729] HJ equations in optimizing system-level performance objectives of Evolutionary Game Theory models
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Vladimirsky (Cornell University)
  • Abstract : Evolutionary Game Theory models time-dependent competitions of "types" or "strategies" in a population. EGT can be used to model the natural selection in biological systems or evolving behavioral patterns among humans. Controlling EGT-models to optimize some system-level performance measures can be accomplished through solving HJ equations. We illustrate this by optimizing drug therapies with an EGT-based model of cancer dynamics. Parts of this talk reflect joint work with Mark Gluzman, MingYi Wang, and Jake Scott.
• [02691] Maximizing the probability of desirable outcomes in Hamilton-Jacobi framework
  • Format : Talk at Waseda University
  • Author(s) :
    • MingYi Wang (Cornell University)
  • Abstract : We introduce new tools for robust stochastic control of indefinite-horizon processes. In particular, we maximize the probability of keeping the (random) cumulative cost under any specific threshold. Our approach yields a 2nd-order HJB equation and “threshold-aware” optimal policies recovered for all initial configurations and a range of threshold values. We illustrate this method using examples from drug therapy optimization and sailboat path-planning. Joint work with A. Vladimirsky, J. Scott, and REU students at Cornell University.
• [03127] Data assimilation for the eikonal equation on a manifold
  • Format : Talk at Waseda University
  • Author(s) :
    • Jerome Fehrenbach (Institut de Mathematiques de Toulouse)
    • Lisl Weynans (University of Bordeaux)
  • Abstract : We propose a method to determine the source(s) and principal direction of a front propagation on an anisotropic surface, from indirect nonlinear measurements. This model aims at describing the propagation of electrical waves at the surface of the heart. The framework of variational data assimilation leads to minimize a quadratic cost-function on a manifold. The Gauus-Newton algorithm is implemented using the Exp_x map on this manifold.
• [03171] Hamilton-Jacobi equations on graphs with applications to data depth and semi-supervised learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Jeff Calder (University of Minnesota)
    • Mahmood Ettehad (Institute for Mathematics and its Applications (IMA))
  • Abstract : Shortest path graph distances are widely used in data science and machine learning, however, they can be highly sensitive to corruption in graph structures. In this talk we study a family of Hamilton-Jacobi equations on graphs called the p-eikonal equation. We show that p=1 is a provably robust distance-type function on a graph and converges in the continuum limit to a geodesic density weighted distance function. We present applications to data depth and semi-supervised learning.

MS [00747] Analysis and Numerics on Deep Learning Based Methods for Solving PDEs

room : F403

• [04381] Learning Functional Priors and Posteriors from Data and Physics
  • Author(s) :
    • Xuhui Meng (Huazhong University of Science and Technology)
  • Abstract : We develop a new Bayesian framework based on deep generative models to quantify uncertainties arising from both noisy and gappy data in predictions of physics-informed neural networks (PINNs) as well as deep operator networks (DeepONets). We test the proposed method for (1) forward/inverse PDE problems; (2) PDE-agnostic physical problems, e.g., 100-dimensional Darcy problem. The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainties given limited and noisy data.
• [03134] AI for Combustion
  • Author(s) :
    • Zhiqin Xu (Shanghai Jiao Tong University)
  • Abstract : The development of detailed chemistry mechanisms of hydrocarbon fuels paves the way to realistic simulations of practical combustors. However, due to chemistry stiffness, the simulation of large-size detailed mechanisms become forbiddingly expensive, especially for very large-scale simulation. In this talk, I will introduce a deep learning based model reduction method for simplifying chemical kinetics. We also use a deep learning based method to overcome the limitation of using small step-size in simulating the combustion ODE systems.
• [03476] DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting
  • Author(s) :
    • Yuan Lan (Huawei Theory Lab)
    • Zhen Li (Huawei Theory Lab)
    • Jie Sun (Huawei Theory Lab)
    • Yang Xiang (Hong Kong University of Science and Technology)
  • Abstract : Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers utilize the representation power of DNNs to approximate the input-output relations in an automated manner. However, the lack of physics-in-the-loop often makes it difficult to construct a neural network solver that simultaneously achieves high accuracy, low computational burden, and interpretability. In this work, focusing on a class of evolutionary PDEs characterized by decomposable operators, we show that the classical ``operator splitting'' technique can be adapted to design neural network architectures. This gives rise to a learning-based PDE solver, which we name Deep Operator-Splitting Network (DOSnet). Such non-black-box network design is constructed from the physical rules and operators governing the underlying dynamics, and is more efficient and flexible than the classical numerical schemes and standard DNNs. To demonstrate the advantages of our new AI-enhanced PDE solver, we train and validate it on several types of operator-decomposable differential equations. We also apply DOSnet to nonlinear Schr\"odinger equations which have important applications in the signal processing for modern optical fiber transmission systems, and experimental results show that our model has better accuracy and lower computational complexity than numerical schemes and the baseline DNNs.
• [04359] Residual Minimization for PDEs: Failure of PINN and Implicit Bias
  • Author(s) :
    • Qixuan Zhou (Shanghai Jiao Tong University)
    • Tao Luo (Shanghai Jiao Tong University)
  • Abstract : In this talk, we discuss the performance of PINN methods for problems with discontinuities. For linear elliptic PDEs with discontinuous coefficients, we present by experiments that PINN cannot approximate the true solution. We then prove this by introducing a modified equation. And we point out there is still some pattern behind this failure, which is a type of implicit bias. Finally, we will extend some of these results to quasilinear elliptic equations and systems.

MS [00385] Origami Engineering (2/2)

room : F411

• [01402] Solitons in Origami / Kirigami Tessellations and Their Underlying Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Rinki Imada (The University of Tokyo)
    • Tomohiro Tachi (The University of Tokyo)
  • Abstract : The non-uniform folding of origami/kirigami tessellation, the folding where the configuration of their unit cell isn’t identical, is potentially a great source of nonlinear phenomena. We can mathematically understand these phenomena by the nature of the dynamical systems induced by their geometry. In this presentation, we report the “soliton-like” phenomenon with the propagation of localized deformation in origami/kirigami tessellations which comes from different mechanisms, i.e., the homoclinic/heteroclinic solutions of their dynamical systems.
• [01403] Macroscopic Behavior of Kirigami Tessellations with Contact Surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Akito Adachi (The University of Tokyo)
    • Tomohiro Tachi (The University of Tokyo)
  • Abstract : Origami and kirigami tessellations with contact surfaces have potential applications including flexible electronics and wearable devices. However, the manufacturing process requires a simultaneous folding of all creases, which makes the pattern difficult to be manufactured. In this study, we reveal the macroscopic behavior of kirigami variations with contact surfaces through singular value decomposition of the kinematic deformation of each module; through this study, we explore the possibility of manufacturing such tessellations by tension-induced buckling.
• [01432] Miura fold bending in two directions and their combination
  • Format : Talk at Waseda University
  • Author(s) :
    • Sora Moriyama (The University of Tokyo)
    • Tomohiro Tachi (The University of Tokyo)
    • Kuo-chih Chuang (Zhejiang University)
  • Abstract : For Miura folds, where the unit cell is usually composed of parallelograms, it is known that folds that are not parallel to the row’s direction can be deformed in-plane after folding. If the unit cell is constructed so that it has different angles in the column’s direction, it is deformable out-of-plane after folding. By understanding and combining these mathematically, we will present the Miura fold, which can be deformed in any direction.
• [01526] Development study of foldable and portable comfortable acoustic space
  • Format : Online Talk on Zoom
  • Author(s) :
    • Keiko Yamazaki (Meiji University)
    • Masanori Hashiguchi (KEISOKU ENGINEERING SYSTEM CO., LTD.)
    • Dahai Mi (KEISOKU ENGINEERING SYSTEM CO., LTD.)
    • Ichiro Hagiwara (Meiji University)
  • Abstract : The purpose of our research is to develop a simple sound-reducing shade to enjoy playing music at home. The requirements for the shade are relatively inexpensive, foldable, suitable size and acoustic environment for playing, and most importantly sound dampening ability. Normally, the development of such a product requires many prototypes and verifications, but in this research, by utilizing finite element analysis to find the optimum material and shape without producing a large number of prototypes.

MS [00686] Higher-order networks for complex systems

room : F412

• [02955] Clustering and trajectory classification via the Hodge Laplacian
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael Schaub (RWTH Aachen University)
  • Abstract : We present methods to cluster point cloud data and trajectories based on spectral properties of the Hodge Laplacian. Our approach relies on similar ideas as found in spectral embeddings such as Laplacian eigenmaps. However, rather than constructing a single graph to cluster the data, we consider appropriately constructed simplicial complexes, and (a set of) associated Hodge-Laplacians which allow us to leverage a rich set of topological features for classification.
• [02956] Kernel-based independence measures, hypergraphs, and higher-order interactions
  • Format : Talk at Waseda University
  • Author(s) :
    • Mauricio Barahona (Imperial College London)
  • Abstract : This talk will cover the use of kernel-based methods for the detection of higher order interactions and the relationships with formalizations using hypergraphs.
• [02966] Higher-Order Phase Oscillator Networks from Phase Reductions
  • Format : Talk at Waseda University
  • Author(s) :
    • Christian Bick (Vrije Universiteit Amsterdam)
  • Abstract : Synchronization is a fascinating effect of the interaction between coupled oscillatory units and is ubiquitous in biological systems. If the coupling between units is sufficiently weak, phase reductions provide an adequate description of the dynamics. We discuss phase reductions beyond first order that yield phase oscillator networks with higher-order interactions. Specifically, we discuss how the nonpairwise higher-order phase interactions depend on the shape of the limit cycles and the underlying network structure.
• [03193] When do two networks have the same steady state ideal?
  • Format : Talk at Waseda University
  • Author(s) :
    • Mark Curiel (University of Hawaii at Manoa)
    • Elizabeth Gross (University of Hawaii at Manoa)
    • Carlos Munoz (San Jose State University)
  • Abstract : Chemical reaction networks are often used to model biological processes, e.g. cell signaling. Assuming mass action kinetics, a reaction network gives rise to a polynomial system. We consider the ideal generated by these polynomials, called steady-state ideals. Our main results describe three combinatorial operations on the reaction graph that preserve the steady-state ideal. Furthermore, we give combinatorial conditions to identify monomials in a steady-state ideal.

contributed talk: CT074

room : E501

[00872] Stability Estimates in Bayesian D-Optimal Experimental Design

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E501
• Type : Contributed Talk
• Abstract : We studied stability properties of the expected utility function in Bayesian optimal experimental design. We proved a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space. As an example we have non-linear Bayesian inverse problems with Gaussian likelihood satisfying general assumptions. Theoretical convergence rates are demonstrated numerically in three different examples.
• Classification : 62K05, 62F15, 35R30, Bayesian Inverse Problems
• Format : Talk at Waseda University
• Author(s) :
  • Tapio Helin (Lappeenranta University of Technology)
  • Duc-Lam Duong (Lappeenranta University of Technology)
  • Jose Rodrigo Rojo Garcia (Lappeenranta University of Technology)

[01009] A phase transition of various retention rules from multivariate analysis for big datasets.

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E501
• Type : Industrial Contributed Talk
• Abstract : Estimating the number of significant components(factors, resp.) from principal component analysis(explanatory factor analysis, resp.) in datasets of finance/biology is essential. However, statistical software's default estimation method behaves pathologically for big datasets. We analyze the phase transition of the default rule as to the intra-class correlation of various data-generation models, and introduce a more acceptable estimation by random matrix theory for large sample correlation matrices. We also compare our rule to retention rules proposed to date.
• Classification : 60F15, 62H25
• Format : Online Talk on Zoom
• Author(s) :
  • Atina Husnaqilati (Mathematics Department, Universitas Gadjah Mada)
  • Yohji Akama (Mathematical Institute, Tohoku University)

[01051] Moderate Deviations for Shell Model of Turbulence

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E501
• Type : Contributed Talk
• Abstract : This work establishes the central limit theorem and moderate deviation principle for stochastic shell model of turbulence driven by multiplicative noise. The method of weak convergence introduced by Budhiraja and Dupuis has been followed in order to establish our results. The equivalence of Laplace principle and large deviation principle under Polish spaces contributes to reduce the complexity.
• Classification : 60F05, 60H15
• Format : Online Talk on Zoom
• Author(s) :
  • Sridevi C.S. (Bharathiar University, Coimbatore, Tamil nadu)

[02188] Rare events of weak noise-driven dynamical systems

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E501
• Type : Contributed Talk
• Abstract : Real-world dynamical systems can be susceptible to events with a low probability of occurrence but severe repercussions. The aim is to asymptotically quantify the likelihood of these events in dynamical systems represented by stochastic differential equations (SDEs). First, we will go through the mathematical framework for investigating such situations. Then, we will demonstrate a numerical obstacle when using a rare events method due to diverging the tilting factor, aka Radon-Nikodym derivative. A solution will be proposed and shown using multiple scenarios.
• Classification : 60F10, 65C20, 49M05, 49M29, 65C05
• Author(s) :
  • Mnerh Alqahtani (University of Hafr Al Batin)
  • Tobias Grafke (University of Warwick)

contributed talk: CT076

room : E502

[02343] Construction and analysis of splitting methods for Chemical Langevin Equations

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E502
• Type : Contributed Talk
• Abstract : Consider modeling the stochastic dynamics underlying different chemical systems, which is usually described by the Gillespie Stochastic Simulation Algorithm (SSA), i.e. the Markov process arising from taking into account every single chemical reaction event. While exact and easy to implement, this algorithm is computationally expensive for chemical reactions involving a large number of molecular species. As an approximation, Chemical Langevin Equations (CLEs) can work for large number of species or/and reactions. In this talk, we construct an explicit splitting method applied to the system of CLEs for a simple example of a reversible bimolecular reaction. The drift term of this stochastic differential equation system satisfies a local one-sided Lipschitz condition and the diffusion term involves square root terms. We then present the main ideas of a mean-square convergence proof, as well as numerical illustrations. The results are joint work with Youssra Souli, Johannes Kepler University, Linz.
• Classification : 60H10, 65C30, 60H35
• Format : Talk at Waseda University
• Author(s) :
  • Evelyn Buckwar (Johannes Kepler University)
  • Youssra Souli (Johannes Kepler University)

[02547] Split S-ROCK methods for stiff It\^{o} stochastic differential equations

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E502
• Type : Contributed Talk
• Abstract : We propose explicit stochastic Runge--Kutta methods for stiff It\^{o} stochastic differential equations. The family of the methods is constructed on the basis of the Runge--Kutta--Chebyshev methods, and we utilize a Strang splitting-type approach. The derived methods achieve weak order $2$, and have high computational accuracy for relatively large time-step size, as well as good stability properties. In numerical experiments, we confirm that our methods are superior to existing methods in computational accuracy.
• Classification : 60H10, 65L05, 65L06
• Format : Talk at Waseda University
• Author(s) :
  • Yoshio Komori (Kyushu Institute of Technology)
  • David Cohen (Chalmers University of Technology)
  • Kevin Burrage (Queensland University of Technology)

[01044] Nonlinear SPDE models of particle systems

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E502
• Type : Contributed Talk
• Abstract : Interacting particle systems provide flexible and powerful models that are useful in many application areas. However, particle systems with large numbers of particles are very complex. Therefore, a common strategy is to derive effective equations that describe the time evolution of the empirical particle density. Our aim is to consider non-Gaussian models that provide approximation of the Dean-Kawasaki equation. This is the joint work with Kremp and Perkowski.
• Classification : 60H15, 35Q83, 65M08
• Format : Talk at Waseda University
• Author(s) :
  • Ana Djurdjevac (Freie Universität Berlin)

[01806] Well-posedness of a class of SPDE with fully monotone coefficients perturbed by Levy noise

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E502
• Type : Contributed Talk
• Abstract : In this talk, we consider a class of stochastic partial differential equations with fully locally monotone coefficients in a Gelfand triplet. Under certain generic assumptions of the coefficients, we prove the existence of a probabilistic weak solution as well as the pathwise uniqueness of the solution, which implies the existence of a unique probabilistic strong solution. Finally, we allow both the diffusion and jump noise coefficients to depend on the gradient of the solution.
• Classification : 60H15, 35R60, 35Q35
• Format : Talk at Waseda University
• Author(s) :
  • Ankit Kumar (Indian Institute of Technology, Roorkee, Uttarakhand )
  • Manil T. Mohan (Indian Institute of Technology, Roorkee, Uttarakhand)

[01017] Feature Collisions in Neural Networks: Theory and Practice

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E502
• Type : Contributed Talk
• Abstract : Deep neural networks are behind many breakthroughs in the last decade, but much of their behavior remains poorly understood. In particular, under some conditions, neural networks can be insensitive to changes of large magnitude, in which case the features are said to collide. We will discuss necessary conditions for such feature collisions to occur, and we will introduce the null-space method, a numerical approach to create data points with colliding features for many vision tasks.
• Classification : 68-XX, 68Txx, 68T30, 68T07
• Author(s) :
  • Utku Ozbulak (Ghent University)
  • Joris Vankerschaver (Ghent University)

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

room : E503

• [02840] A Quantitative Central Limit Theorem arising from Time-Frequency Analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Gi-Ren Liu (National Cheng Kung University)
  • Abstract : In this talk, we will discuss the distribution distance between the output $F$ of the scattering transform (ST) of a Gaussian process and its scaling limit $G$. ST is a nonlinear transformation that involves a sequential interlacing convolution and nonlinear operators, which is motivated to model the convolutional neural network. We will show that the total variation distance between the distributions of the output of ST and a chi-square random variable with one degree of freedom converges to zero at an exponential rate. For achieving this goal, we derive a recursive formula to represent the nonlinearity of ST by a linear combination of Wiener chaos and then apply the Malliavin calculus and Stein's method to estimate the maximal difference between the expectation values of $h(F)$ and $h(G)$ over a specific set of test functions $h$. This talk is based on joint work with Yuan-Chung Sheu (National Yang Ming Chiao Tung University, Taiwan) and Hau-Tieng Wu (Duke University, USA).
• [02846] Market Price-Volatility Simulator
  • Format : Talk at Waseda University
  • Author(s) :
    • Riki Kitano (Ritsumeikan University)
  • Abstract : In this talk, a combination of the Fourier-Malliavin-Mancino method and the Lyons’s signature method under a stochastic volatility diffusion setting will be discussed.
• [02733] A graph discretized approximation of diffusions on Riemannian manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Kawabi (Keio University)
    • Satoshi Ishiwata (Yamagata University)
  • Abstract : In this talk, we discuss a graph discretized approximation for diffusions on a complete Riemannian manifold $M$. More precisely, for a given drifted Schrödinger operator ${\mathcal A}=-\Delta-b+V$ on $M$, we introduce a family of random walks in the flow generated by the drift $b$ with killing on a sequence of proximity graphs. The drifted Schrödinger semigroup $\{ {\rm e}^{t{\mathcal A}} \}_{t\geq 0}$ is approximated by discrete semigroups generated by the family of random walks.

contributed talk: CT084

room : E504

[02315] On Adaptive Kalman Filtration

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : We consider a linear partially observed system. The coefficients of this system depend on some finite - dimensional unknown parameter. We study the problems of the construction of adaptive Kalman filtration equations. The adaptive filter is constructed in two steps. First we propose a preliminary estimator using observations on a relatively small interval of observations. Then this estimator is used for construction of One-step MLE-process. Finally the last estimator allows us to construct an adaptive recurrent filter.
• Classification : 62M05, 62M20, 62F12, 62G20
• Format : Talk at Waseda University
• Author(s) :
  • Yury Kutoyants (Le Mans University )

[02316] Spatio-temporal modeling with SPDE based GMRF

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : Gaussian random fields (GRFs) are a type of geostatistical model used in spatial inference problems. In many such contexts data are available at a given spatial scale, whereas predictions are required at another scale that represents a different spatial configuration. The GRF model of interest and the accompanying Bayesian inferential procedure use the INLA-SPDE approach. In this talk I will describe the GRF model, the inference procedure and discuss challenges in this situation.
• Classification : 62M30, 62P12, 60G60, 60H15, 62F15, Infer spatio-temporal precipitation patter in Austria
• Format : Talk at Waseda University
• Author(s) :
  • Corinna Perchtold (Johannes Kepler University, Linz)
  • Evelyn Buckwar (Johannes Kepler University)
  • Johan Lindström (Lund University)

[02365] Fuzzy C-Medoids Clustering on the Foreign Currency Exchange Rate Against the Indonesian Rupiah

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E504
• Type : Industrial Contributed Talk
• Abstract : The exchange rate is always fluctuating, indicates the presence of heteroscedasticity. Forecasting currency exchange rate movements is necessary in order to make a correct decision. In this study, clustering was carried out using a fuzzy c-medoids algorithm with distances based on the estimated parameters of the GARCH model. The case study used is data on foreign exchange rates against the Indonesian Rupiah (IDR) for the monthly period of January 2018–October 2022.
• Classification : 62M10
• Format : Online Talk on Zoom
• Author(s) :
  • Vemmie Nastiti Lestari (Universitas Gadjah Mada)
  • Abdurakhman Abdurakhman (Universitas Gadjah Mada)
  • Dedi Rosadi (Universitas Gadjah Mada)

[00112] Vibration control on unplanned change in vehicle mass model

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E504
• Type : Contributed Talk
• Abstract : Prolonged vibration transfer to the human body during riding affects human health. In this work, we proposed a heuristic-based chaotic artificial bee colony (ABC) optimization technique to mitigate the vibration response of running vehicle with context to the safety and comfort of passengers during a ride. We have modeled the vehicle's six degrees of freedom dynamics as a half-car with passive suspension and passengers in a seated position. In the proposed work, two fundamental techniques are used in our analysis. Firstly, we estimate how changing the passenger mass in a vehicle affects the vibration behaviour of the entire system. This is done by simulating the dynamical model computationally and numerically over different bumpy roads. Thereby, distinguishing between the causal roles of mass, safety, and comfort, we formulate technologically constrained optimization problems and minimize the peak jerks of the vehicle and passengers. Further, implement techniques to optimize the vibration levels and design suspension parameters accordingly. The study also analyses the extreme range of vibration levels and comfort relationships for several road conditions to estimate the net effect of vehicle weight change during the ride.
• Classification : 68-XX, 68Txx, 68T20, 37Nxx, 37N40
• Format : Online Talk on Zoom
• Author(s) :
  • Darakhshan Jabeen Syeda (Birla Institute of Technology Mesra, Ranchi)

[02319] Parameter estimation of the Richards model in multi-wave epidemic cases

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E504
• Type : Industrial Contributed Talk
• Abstract : The Richards model with changepoint detection can model multi-wave infectious disease transmission. Next, choose the best parameter estimation method from non-linear least squares and genetic algorithm to accurately predict COVID-19 cases in Indonesia and Japan. Genetic algorithm predictions outperform non-linear least squares. A genetic algorithm only needs a range for the initial value, while non-linear least squares need an exact value. The government and health facilities can use prediction results to prevent infectious disease epidemics.
• Classification : 62P10, 92B15, 92B05
• Format : Talk at Waseda University
• Author(s) :
  • Faihatuz Zuhairoh (Universitas Gadjah Mada )
  • Dedi Rosadi (Universitas Gadjah Mada )
  • Adhitya Ronnie Effendie (Universitas Gadjah Mada )

contributed talk: CT086

room : E505

[02093] British Call Option On Stocks under Stochastic Interest Rate

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @E505
• Type : Contributed Talk
• Abstract : The closed form expression for the price of the British put and call options have long been established where both interest rate and volatility are assumed to be constant. In reality, these assumptions do not fully reflect the variable nature of the financial markets. In this paper, we derived a closed form expression for the arbitrage-free price of the British call option by assuming stochastic interest rate which follows the Cox-Ingersoll-Ross model and constant volatility.
• Classification : 62P05
• Format : Talk at Waseda University
• Author(s) :
  • Felipe Jr Raypan Sumalpong (Mindanao State University - Iligan Institute of Technology)
  • Kreanne Falcasantos (Mindanao State University - Iligan Institute of Technology)

[02348] Multi-day Value-at-Risk estimation by GARCH and Extreme Value Theory

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @E505
• Type : Contributed Talk
• Abstract : The conventional VaR models have been unable to predict huge losses by market prices because these underestimate the probability of extreme price fluctuations. To overcome this problem, McNeil and Frey introduced a two-step approach combining the GARCH model and EVT. In this study, we investigate the estimation of multi-day VaR based on a bootstrapping simulation approach with GARCH-EVT, as well as perform back-testing in order to evaluate its ability to provide appropriate multi-day VaR estimation.
• Classification : 62P05
• Format : Talk at Waseda University
• Author(s) :
  • Ichiro Nishi (Tokio Marine Holdings, Inc.)

[02034] Relation between transaction costs and search frictions in optimal maximization

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @E505
• Type : Contributed Talk
• Abstract : We consider an optimal investment problem to maximize expected power-utility of random terminal wealth in a market with two types of illiquidity: transaction costs and search frictions. We suppose an investor trades only at arrival times of Poisson process, and pays proportional transaction costs for purchasing or selling stocks. We characterize a unique optimal trading strategy and provide asymptotic expansions on small transaction costs and small search frictions for boundaries of no-trade region and value function.
• Classification : 62P05, 49N90, Financial mathematics, Stochastic analysis
• Format : Talk at Waseda University
• Author(s) :
  • Tae Ung Gang (KAIST Stochastic Analysis and Application Research Center)
  • Jin Hyuk Choi (UNIST)

[00250] Formation of delta shock waves and vacuum states in the vanishing pressure limit of the Riemann solution to the isentropic Euler system for logarithmic equation of state with the Coulomb-like friction term

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @E505
• Type : Contributed Talk
• Abstract : We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb-like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self-similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero-pressure gas dynamics system with a body force when the pressure vanishes.
• Classification : 35L65, 35L67, 35L45
• Format : Talk at Waseda University
• Author(s) :
  • Anupam Sen (Post Doctoral Fellow at Centre for Applicable Mathematics, Tata Institute of Fundamental Research)

MS [00960] Hierarchical Low Rank Tensors and DNNs for High-dimensional Approximation

room : E506

• [02980] Weighted sparse and low-rank least squares approximation
  • Format : Talk at Waseda University
  • Author(s) :
    • Philipp Trunschke (Nantes Université)
    • Martin Eigel (WIAS Berlin)
    • Anthony Nouy (Nantes Université)
  • Abstract : Many functions of interest exhibit weighted summability of their coefficients with respect to some dictionary of basis functions. The resulting best $n$-term approximations can be estimated efficiently from samples. We propose to encode the coefficients in a simultaneously sparse and low-rank tensor format to improve the efficiency of the algorithms performing this approximation. Based on a weighted Stechkin lemma and the restricted isometry property, we provide approximation error and sample complexity bounds.
• [04007] Iteratively Reweighted Least Squares Recovery on Tensor Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Sebastian Kraemer (RWTH Aachen University)
  • Abstract : A fundamental approach to tensor recovery traces back to affine rank minimization. We emphasize that the latter problem is always solved via asymptotic minimization of well-known log-det functions, in practice approachable through iteratively reweighted least squares. Additionally to local convergence properties, in numerical experiments, the theoretical phase transition for generic tensor recoverability becomes observable. Alternating optimization on tensor tree networks in turn allows to apply a relaxed method under minimal, polynomial complexity even in high dimensions.
• [04663] Empirical Tensor Train Approximation in Optimal Control
  • Format : Talk at Waseda University
  • Author(s) :
    • Mathias Oster (TU Berlin)
    • Reinhold Schneider (TU Berlin)
  • Abstract : We display two approaches to solve finite horizon optimal control problems. First we solve the Bellman equation numerically by employing the Policy Iteration algorithm. Second, we introduce a semiglobal optimal con- trol problem and use open loop methods on a feedback level. To overcome computational infeasability we use tensor trains and multi-polynomials, together with high-dimensional quadrature, e.g. Monte-Carlo. By controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term numerical evidence is given.
• [05144] Dynamical low-rank approximation of Vlasov-Poisson equations on polygonal spatial domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Andreas Zeiser (HTW Berlin)
    • André Uschmajew (University of Augsburg)
  • Abstract : We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov-Poisson equations based on separation of space and velocity variables, as proposed in several recent works. A less studied aspect is the incorporation of boundary conditions in the DLRA model. We use a variational formulation of the projector splitting which allows to handle inflow boundary conditions on piecewise polygonal spatial domains. Numerical experiments demonstrate the principle feasibility of this approach.

MS [00917] High-dimensional regression and sampling

room : E507

• [04266] Weighted least-squares approximation in expected $L^2$ norm
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthieu Dolbeault (Sorbonne Université)
    • Albert Cohen (Sorbonne Université)
    • Abdellah Chkifa (Mohammed VI Polytechnic University)
  • Abstract : We investigate the problem of approximating a function in $L^2$ with a linear space of functions of dimension $n$, using only evaluations at m chosen points. We improve on earlier results based on the solution to the Kadison-Singer problem, by using a randomized greedy strategy, which allows to reduce the oversampling ratio $m/n$ and provides an algorithm of polynomial complexity.
• [05485] On the relation between adaptive and non-adaptive randomized sampling
  • Format : Talk at Waseda University
  • Author(s) :
    • Stefan Heinrich (RPTU Kaiserslautern-Landau)
  • Abstract : Recently the author solved a long-standing problem of Information-Based Complexity: Is there a constant $c>0$ such that for all linear problems the randomized non-adaptive and adaptive $n$-th minimal errors can deviate at most by the factor $c$? The analysis of vector-valued mean computation showed that the answer is negative. In this talk we give a survey on this and related results concerning further aspects the problem.
• [05488] A multivariate Riesz basis of ReLU neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Cornelia Schneider (Friedrich-Alexander Universität Erlangen)
    • Jan Vybiral (CzechTechnical University)
  • Abstract : We consider the trigonometric-like system of piecewise linear functions introduced recently by Daubechies, DeVore, Foucart, Hanin, and Petrova. We provide an alternative proof that this system forms a Riesz basis of $L_2([0,1])$ based on the Gershgorin theorem. We also generalize this system to higher dimensions $d>1$ by a construction, which avoids using (tensor) products. As a consequence, the functions from the new Riesz basis of $L_2([0,1]^d)$ can be easily represented by neural networks. Moreover, the Riesz constants of this system are independent of $d$, making it an attractive building block regarding future multivariate analysis of neural networks.

MS [02181] Numerical methods and analysis for linear systems and eigenvalue problems

room : E508

• [04543] A variant algorithm of the IDR(s) method for solving linear systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Lei Du (Dalian University of Technology)
  • Abstract : The Induced Dimension Reduction method (IDR($s$) proposed by Sonneveld and van Gijzen is an efficient method for solving large, sparse and nonsymmetric linear systems, after then many variants have been proposed. The method has also been generalized to solve matrix equations and eigenvalue problems. In this talk, we consider using the Anderson acceleration technique and propose a new variant to accelerate the IDR($s$) method. Some numerical experiments are presented to show the efficiency of our proposed algorithm.
• [03550] Randomized block Kaczmarz methods with k-means clustering for solving linear systems
  • Author(s) :
    • Ke Zhang (Shanghai Maritime University)
    • Xiang-Long Jiang (Shanghai Maritime University)
    • Junfeng Yin (Tongji University)
  • Abstract : In this talk, by following the philosophy of the block Kaczmarz methods, we propose a randomized block Kaczmarz method with the blocks determined by the k-means clustering. It can be considered as an efficient variant of the relaxed greedy randomized Kaczmarz algorithm by using a practical probability criterion for selecting the working block submatrix per iteration. The new algorithm is proved to be convergent when the linear system is consistent. A practical variant of the new method is also given. Some numerical examples are given to verify the effectiveness of the proposed methods.

MS [00586] Challenges for Attaining High-performance in Numerical Software

room : E603

• [03413] Adaptation of XAI to Numerical Libraries: A Case Study for Automatic Performance Tuning
  • Format : Talk at Waseda University
  • Author(s) :
    • Takahiro Katagiri (Nagoya University)
  • Abstract : AI is one of crucial technologies. On the other hand, we have been adapting to auto-tuning (AT) for numerical software. By utilizing AI technology, it is expected to establish AT function for performance tuning on numerical libraries. However, it is difficult to verify correctness for obtained AI model. Adaptation of explainable AI (XAI) is one of solutions. In this presentation, several scenarios for adapted XAI to AT function will be demonstrated.
• [03472] Parallel Eigensolvers Based on Minimization Strategies
  • Format : Talk at Waseda University
  • Author(s) :
    • Doru Thom Popovici (Lawrence Berkeley National Lab)
    • Osni Marques (Lawrence Berkeley National Laboratory)
    • Mauro Del Ben (Lawrence Berkeley National Laboratory)
    • Andrew Canning (Lawrence Berkeley National Laboratory)
  • Abstract : This presentation will show recent developments in unconstrained minimization strategies for the solution of eigenvalue problems in electronic structure calculations. These schemes employ a preconditioned conjugate gradient approach that avoids an explicit reorthogonalization of the trial eigenvectors, in contrast to typical iterative eigensolvers, therefore reducing communications and becoming an attractive approach for the solution of very large problems on massively parallel computers. The presentation will also discuss the need to rearrange calculations (sometimes counteractively) to achieve performance, in particular on GPUs.
• [03700] Mixed-precision iterative refinement for real-symmetric eigenvalue decomposition with clustered eigenvalues
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Uchino (Shibaura Institute of Technology)
    • Katsuhisa Ozaki (Shibaura Institute of Technology)
    • Toshiyuki Imamura (RIKEN)
  • Abstract : Uchino et al. presented two mixed-precision iterative refinement algorithms (herein called Algorithm 1 and 2) for the real-symmetric eigendecomposition based on the algorithm proposed by Ogita and Aishima. Algorithm 2 offers the same convergence and advantages in terms of computational speed compared to Algorithm 1, as demonstrated through numerical experiments on the supercomputer Fugaku housed at RIKEN R-CCS. We will also show that Algorithm 2 is much faster than the eigensolver provided in ScaLAPACK.
• [04170] Mixed Precision Iterative Refinement with H-matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Spendlhofer (Tokyo Institute of Technology)
    • Rio Yokota (Tokyo Institute of Technology)
  • Abstract : It has been shown that the solution to a dense linear system can be accelerated by using mixed precision iterative refinement relying on approximate LU-factorization. We investigate the usage of both mixed precision and low-rank approximations for obtaining an approximate factorization. When employing the hierarchical matrix format, we are able to attain results accurate to a double precision solver at a lower complexity of $\order{n^2}$ for certain matrices.

contributed talk: CT104

room : E604

[00983] Effective time step analysis of numerical schemes for gradient flows

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E604
• Type : Contributed Talk
• Abstract : A gradient flow has an important role in PDEs and it has a variety of applications including biological fields. In this talk, we briefly introduce the unconditionally stable numerical schemes for type of gradient flows and analyze them by comparing the real and its rescaled time steps, which has been a critical issue in this field. Some numerical simulations are performed to confirm our result.
• Classification : 65M12
• Format : Talk at Waseda University
• Author(s) :
  • Seunggyu Lee (Korea University)
  • Woon-Jae Hwang (Korea University)

[01365] Non symmetric discontinuous Galerkin method for fractional differential equations

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E604
• Type : Contributed Talk
• Abstract : We study discontinuous Galerkin method for non-autonomous TF-ADR initial boundary value problems (IBVPs) with time fractional derivative of Caputo type. Recently, many efforts have been made to develop effective numerical methods for solving time-fractional problems. One of the typical direct numerical methods is the L1-Scheme, which can be viewed as a piecewise linear approximation to the fractional derivative. We used the classical L1-schemes for time discretization and discontinuous Galerkin method for space variable. Error bounds are established in the discrete energy norm. Finally, the convergence result is verified numerically.
• Classification : 65M12, 65M15, 65M60
• Format : Talk at Waseda University
• Author(s) :
  • GAUTAM SINGH (NIT TIRUCHIRAPPALLI)

[01006] VMS-based Stabilized FE Analysis of Time-dependent Coupled Unified Stokes-Brinkman-Transport Model

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E604
• Type : Contributed Talk
• Abstract : We present a Variational Multi-Scale (VMS)-based stabilized FE analysis for completely unified unsteady Stokes-Brinkman model with standard continuity and Beavers-Joseph-Saffman interface conditions, strongly coupled with transient transport equation. The fluids’ viscosities depend on the solute concentration. A simplified algebraic subgrid multiscale approach with time-dependent sub-scales is employed. A fully-implicit Euler scheme is used for time-discretization. We analyse the stability and convergence properties of the method. Appropriate numerical experiments are conducted to verify the method’s credibility.
• Classification : 65M12, 65M22, 65M60
• Format : Online Talk on Zoom
• Author(s) :
  • Manisha Chowdhury (Indian Institute of Technology Jodhpur)
  • B.V. Rathish Kumar (Indian Institute of Technology Kanpur)

[00962] Discontinuous Galerkin method for a high order nonlocal conservation law

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E604
• Type : Contributed Talk
• Abstract : We consider a Direct Discontinuous Galerkin (DDG) method for solving a time dependent partial differential equation with convection-diffusion terms and a fractional operator of order $\alpha \in (1,2)$. This equation was introduced to describe dunes morphodynamics and was then used for signal processing. For the DDG method, suitable numerical fluxes are introduced. We prove nonlinear stability estimates along with convergence results. Numerical experiments are given to illustrate behaviors of solutions and to verify convergence order.
• Classification : 65M12, 65M60, 26A33
• Author(s) :
  • Afaf Bouharguane (Université de Bordeaux/INRIA)
  • Afaf Bouharguane (University of Bordeaux)
  • Nour Seloula (University of Caen)

MS [01064] Recent Advances on Manifold Optimization

room : E605

• [04372] Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuya Yamakawa (Kyoto University)
    • Hiroyuki Sato (Kyoto University)
  • Abstract : Recently, the approximate Karush--Kuhn--Tucker (AKKT) conditions, also called the sequential optimality conditions, have been proposed for nonlinear optimization in Euclidean spaces, and several methods to find points satisfying such conditions have been developed by researchers. These conditions are known as genuine necessary optimality conditions because all local optima satisfy them with no constraint qualification (CQ). In this paper, we extend the AKKT conditions to nonlinear optimization on Riemannian manifolds and propose an augmented Lagrangian (AL) method that globally converges to points satisfying such conditions. In addition, we prove that the AKKT and KKT conditions are indeed equivalent under a certain CQ. Finally, we examine the effectiveness of the proposed AL method via several numerical experiments.
• [04682] Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Kangming Chen (Kyoto University)
    • Hiroyuki Sato (Kyoto University)
    • Ellen Hidemi Fukuda (Kyoto University)
  • Abstract : In this research, we propose a conjugate gradient descent algorithm for vector optimization on Riemannian manifolds. We extend the concepts of Wolfe conditions and Zoutendjik conditions to Riemannian manifolds. The convergence of the proposed method is proved for different choices of the parameter beta, including the Riemannian extension of Fletcher-Reeves, Conjugate Descent, and Dai-Yuan. Numerical experiments are conducted to validate the proposed method.
• [04852] Gauss-Southwell type descent methods for low-rank matrix optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • André Uschmajew (University of Augsburg)
    • Guillaume Olikier (Université Catholique de Louvain)
    • Bart Vandereycken (University of Geneva)
  • Abstract : We consider gradient-related methods for low-rank matrix optimization with a smooth strongly convex cost function. The methods operate on single factors and share aspects of both alternating and Riemannian optimization. We compare two possible choices for the search directions based on Gauss-Southwell type selection rules: one using the gradient of a factorized non-convex formulation, the other using the Riemannian gradient. Both methods provide convergence guarantees for the gradient that are analogous to the unconstrained case.
• [03269] Min-max optimization on manifolds
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bamdev Mishra (Microsoft )
  • Abstract : In this talk, we discuss some recent algorithms on min-max optimization problems over Riemannian manifolds.

contributed talk: CT101

room : E606

[00858] An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E606
• Type : Contributed Talk
• Abstract : I will introduce an efficient method for solving 2nd order, linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. Within a marching scheme, the solution is generated either via a nonoscillatory phase function (computed by defect correction), or spectral collocation, whichever is more efficient for the current timestep. With numerical experiments I will show that our algorithm outperforms other state-of-the-art oscillatory solvers and has a frequency-independent runtime.
• Classification : 65Lxx, 34E05, 65L60, 34-04, 65Gxx
• Format : Talk at Waseda University
• Author(s) :
  • Fruzsina Julia Agocs (Center for Computational Mathematics, Flatiron Institute)
  • Alex Harvey Barnett (Center for Computational Mathematics, Flatiron Institute)

[01151] Structure-Preserving Neural Networks for Hamiltonian Systems

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E606
• Type : Contributed Talk
• Abstract : When solving Hamiltonian systems using numerical integrators, preserving the symplectic structure is crucial. We analyze whether the same is true if neural networks (NN) are used. In order to include the symplectic structure in the NN's topology we formulate a generalized framework for two well-known NN topologies and discover a novel topology outperforming all others. We find that symplectic NNs generalize better and give more accurate long-term predictions than physics-unaware NNs.
• Classification : 65Lxx, 68T07, 85-08
• Format : Talk at Waseda University
• Author(s) :
  • Philipp Horn (Eindhoven University of Technology)
  • Barry Koren (Eindhoven University of Technology)
  • Veronica Saz Ulibarrena (Leiden University)
  • Simon Portegies Zwart (Leiden University)

[00013] Singularly perturbed problems on a graph

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E606
• Type : Contributed Talk
• Abstract : In this talk, a singularly perturbed convection diffusion problems on a graph domain will be discussed. Initially, the problem is designed on a simple graph i.e k-star graph. On the common vertex, the continuity and the Kirchhoff's conditions will be discussed along with their complexity. The problem may be extended to a general graph with many vertices and edges. Some tests problems will be discussed based on upwind finite difference methods using piece-wise Shishkin meshes. Error estimates and the order of convergence are to be discussed.
• Classification : 65Lxx, 65Mxx
• Format : Online Talk on Zoom
• Author(s) :
  • Vivek Kumar Aggarwal (Delhi Technological University)

[00460] A Multigrid Method for Many-Electron Schrodinger Equations with ACE

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E606
• Type : Contributed Talk
• Abstract : We parameterize the many-electron wave functions by atomic cluster expansion $($ACE$)$ approach and calculate ground-state energies and electron densities of some molecule systems within the variational Monte Carlo framework. Compared with the neural-network-based representations, the novelty of our method lies in $($i$)$ a convenient and accurate linear polynomial expansion; $($ii$)$ a hierarchical structure that applies naturally to a multigrid variation; and $($iii$)$ possibly revealing the correlation of the system by increasing the body-order.
• Classification : 35Q40, 65N25, 65N35, 81Q05
• Format : Talk at Waseda University
• Author(s) :
  • Dexuan Zhou (Beijing Normal University)

[02103] Global in Time Weak Solutions to Singular 3D Quasi-Geostrophic Systems

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E606
• Type : Contributed Talk
• Abstract : Geophysicists have studied 3D Quasi-Geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large time scale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in $\mathbb{R}_{+}\times\Omega$ with an equation on the boundary satisfied by the trace, where $\Omega$ is either $2D$ torus or a bounded convex domain in $\mathbb{R}^2$. In this talk, we show the existence of global in time weak solutions to a family of singular 3D quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The proof is based on the construction of approximated models which combine the Galerkin method at the boundary and regularization processes in the bulk of the domain. The main difficulty is handling the degeneration of the background density profile at the boundary.
• Classification : 35Q35, 76D03
• Format : Online Talk on Zoom
• Author(s) :
  • Yiran Hu (University of Texas at Austin)

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

room : E701

MS [00624] At the interface between neural networks and differential equations

room : E702

• [01535] Machine learning for/with Differential Equation Modeling: Statistics and Computation
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yiping Lu (Stanford University)
  • Abstract : Massive data collection and computational capabilities have enabled data-driven scientific discoveries and control of engineering systems. However, there are still several questions that should be answered to understand the fundamental limits of just how much can be discovered with data and what is the value of additional information. For example, 1) How can we learn a physics law or economic principle purely from data? 2) How hard is this task, both computationally and statistically? 3) What’s the impact on hardness when we add further information (e.g., adding data, model information)? I’ll answer these three questions in this talk in two learning tasks. A key insight in both two cases is that using direct plug-in estimators can result in statistically suboptimal inference. The first learning task I’ll discuss is linear operator learning/functional data analysis, which has wide applications in causal inference, time series modeling, and conditional probability learning. We build the first min-max lower bound for this problem. The min-max rate has a particular structure where the more challenging parts of the input and output spaces determine the hardness of learning a linear operator. Our analysis also shows that an intuitive discretization of the infinite-dimensional operator could lead to a sub-optimal statistical learning rate. Then, I’ll discuss how, by suitably trading-off bias and variance, we can construct an estimator with an optimal learning rate for learning a linear operator between infinite dimension spaces. We also illustrate how this theory can inspire a multilevel machine-learning algorithm of potential practical use.​ For the second learning task, we focus on variational formulations for differential equation models. We discuss a prototypical Poisson equation. We provide a minimax lower bound for this problem. Based on the lower bounds, we discover that the variance in the direct plug-in estimator makes sample complexity suboptimal. We also consider the optimization dynamic for different variational forms. Finally, based on our theory, we explain an implicit acceleration of using a Sobolev norm as the objective function for training
• [02223] Momentum Based Acceleration for Stochastic Gradient Descent
  • Format : Talk at Waseda University
  • Author(s) :
    • Kanan Gupta (Texas A&M University)
    • Stephan Wojtowytsch (Texas A&M University)
    • Jonathan Wolfram Siegel (Texas A&M University)
  • Abstract : We will discuss first order optimization algorithms based on discretizations of the heavy ball ODE. Particularly, we introduce a discretization that leads to an accelerated gradient descent algorithm, which provably achieves an accelerated rate of convergence for convex objective functions, even if the stochastic noise in the gradient estimates is significantly larger than the gradient. We compare the optimizer’s performance with other popular optimizers on the non-convex problem of training neural networks on some standard datasets.
• [03468] The Effects of Activation Functions on the Over-smoothing of GCNs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bao Wang (University of Utah)
  • Abstract : Smoothness has been shown to be crucial for the success of graph convolutional networks (GCNs); however, over-smoothing has become inevitable. In this talk, I will present a geometric characterization of how activation functions of a graph convolution layer affect the smoothness of their input leveraging the distance of graph node features to the eigenspace of the largest eigenvalue of the (augmented) normalized adjacency matrix, denoted as M. In particular, we show that 1) the input and output of ReLU or leaky ReLU activation function are related by a high-dimensional ball, 2) activation functions can increase, decrease, or preserve the smoothness of node features, and 3) adjusting the component of the input in the eigenspace M can control the smoothness of the output of activation functions. Informed by our theory, we propose a universal smooth control term to modulate the smoothness of learned node features and improve the performance of existing graph neural networks.
• [03523] On the generalization and training of Deep Operator Networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Yeonjong Shin (North Carolina State University)
    • Sanghyun Lee (Florida State University)
  • Abstract : We propose a novel training method for Deep Operator Networks (DeepONets). DeepONets are constructed by a sum of products of two sub-networks, namely, branch and trunk networks. The goal is to effectively learn DeepONets that accurately approximate nonlinear operators from data. The standard approaches train the two sub-networks simultaneously via first-order optimization methods. The proposed method, however, trains trunk networks first based on norm-minimization, and then trains branch networks in sequence. Furthermore, we estimate a generalization error of DeepONets in terms of the numbers of training data, sensors in inputs and outputs, and DeepONet size. Several numerical examples including Darcy flow in heterogeneous porous media are presented to illustrate the effectiveness of the proposed training method.

MS [00974] Finite element complexes and multivariate splines

room : E703

• [02331] A polytopal exterior calculus framework
  • Format : Online Talk on Zoom
  • Author(s) :
    • Francesco Bonaldi (University of Perpignan)
    • Daniele Antonio Di Pietro (University of Montpellier)
    • Jerome Droniou (Monash University)
    • Kaibo Hu (University of Oxford)
  • Abstract : For $\Omega\subset \mathbf{R}^n$, the de Rham complex of differential forms $$ 0\rightarrow H\Lambda^0(\Omega)\stackrel{d}{\rightarrow}H\Lambda^1(\Omega)\stackrel{d}{\rightarrow} \cdots \stackrel{d}{\rightarrow} H\Lambda^n(\Omega)\stackrel{d}{\rightarrow}0 $$ is essential to establish the well-posedness of certain PDE models; developing discrete versions of this complex is a key for designing robust schemes for these models. We will present two such discrete complexes, inspired by the DDR and VEM approaches, of arbitrary order, and applicable on generic meshes. Compared to FEEC, these complexes benefit from the flexibility and high-level construction of polytopal methods.
• [05349] Finite Element Complex
  • Format : Talk at Waseda University
  • Author(s) :
    • Long Chen (University of California at Irvine)
    • Xuehai Huang (Shanghai University of Finance and Economics)
  • Abstract : This presentation provides an overview of finite element complex construction, showcasing the finite element de Rham complex through a geometric decomposition method. The construction is extended to additional finite element complexes, such as the Hessian complex, elasticity complex, and divdiv complex, using the Bernstein-Gelfand-Gelfand (BGG) framework. The resulting finite element complexes hold potential applications in numerical simulations for the biharmonic equation, linear elasticity, general relativity, and other geometry-related PDEs.
• [05423] Diagram chases yielding discrete elasticity complexes
  • Format : Talk at Waseda University
  • Author(s) :
    • Jay Gopalakrishnan (Portland State University)
  • Abstract : Differential complexes have shed new insight into the finite elements in recent years. This talk is devoted to the elasticity complex, which provides an example of how complicated exact sequences of spaces can be built from simple ones. Lining up two simpler complexes, we start by performing a "diagram chase", which often goes by the name of Bernstein-Gelfand-Gelfand resolution. The purpose of this talk is to outline a few cases where this process can be perfectly mimicked at the discrete level. The earliest example in three-dimensions is on mesh of macroelements of Alfeld splits, facilitated by the understanding of supersmoothness from research into splines. Other emerging constructions will also be touched upon. (Parts of the talk contain results obtained jointly with S. Christiansen, S. Gong, J. Guzman, K. Hu, and M. Nielan.)
• [03116] Nonconforming finite element exterior calculus
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuo Zhang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : A family of nonconforming finite element complexes are presented for n-dimensional de Rham complexes, $n\geq 2$. Particularly, the n-dimensional Crouzeix-Raviart elements are used to discretize the space of 0 forms. These finite element spaces are generally not constructed by Ciarlet's triples, and can be viewed as nonconforming splines. New theories are presented so that many basic properties of the finite element spaces and complexes can be established.

MS [01672] High accuracy compact methods for partial differential equations

room : E704

MS [00262] numerical analysis, modeling and applications in phase-field its relevant methods

room : E705

• [02938] Multiscale topology optimization method for lattice materials
  • Author(s) :
    • Yibao Li (Xi'an Jiaotong University)
    • Qing Xia (Xi'an Jiaotong University)
    • Xin Song (Xi'an Jiaotong University)
    • Qian Yu (Xi'an Jiaotong University)
    • Binhu Xia (Xijing University )
  • Abstract : In this talk, we will introduce an efficient multiscale topology optimization method for lattice materials. In macro-scale, we present a second-order unconditionally energy stable schemes for the topology optimization problem. Using porous media approach, our objective functional composes of five terms including mechanical property, Ginzburg-Landau energy, two penalized terms for solid and the volume constraint. A Crank-Nicolson method is proposed to discrete the coupling system. We prove that our proposed scheme is unconditionally energy stable. In macro-scale, we propose a simple volume merging method for triply periodic minimal structure. A modified Allen–Cahn type equation with a correction term is proposed. The mean curvature on the surface will be constant everywhere at the equilibrium state. Computational experiments are presented to demonstrate the efficiency of the proposed method.
• [04437] An efficient nonsmooth global optimization-based bound-preserving approach for the Cahn-Hilliard equation
  • Author(s) :
    • Xiangxiong Zhang (Purdue University)
  • Abstract : It is quite difficult to construct bound-preserving schemes for many high order time-dependent PDEs. For instance, it is difficult to prove that the Cahn-Hilliard equation with polynomial potential admits a bound-preserving solution, yet a bound-preserving numerical solution is often preferred. Instead of directly constructing a bound-preserving scheme, we consider a global optimization based post processing in each time. Due to the nonsmooth terms in the cost function, such an optimization based approach has often been regarded as inefficient. However, it is possible to obtain an efficient solver by using optimal parameters obtained from asymptotic convergence rate formula. We demonstrate that the selection of optimization algorithm parameters from combing such an asymptotic convergence rate formula with time continuation in a time-dependent problem can give an efficient high order accurate bound-preserving post-processing solver, which costs O(n) per time step.
• [04079] New unconditionally stable higher-order consistent splitting schemes for the Navier-Stokes equations
  • Author(s) :
    • JIE SHEN (Purdue University)
    • Fukeng Huang (National University of Singapore)
  • Abstract : The consistent splitting schemes for the Navier-Stokes equations decouple the computation of pressure and velocity, and do not suffer from the splitting error. However, only the first-order version of the consistent splitting schemes is proven to be unconditionally stable for the time dependent Stokes equations. We construct a new class of consistent splitting schemes of orders two to four for Navier-Stokes equations based on Taylor expansions at time $t_{n+k}$ where $k\ge 1$ is a tunable parameter. We show that, for some suitable choices of $k$, they are unconditionally stable for the time dependent Stokes equations, and by combining them with the generalized scalar auxiliary variable (GSAV) approach, we construct, for the very first time, unconditionally stable (in H^1 norm) and totally decoupled schemes of orders two to four for the velocity and pressure, and provide rigorous optimal error estimates. We shall also present some numerical results to show the computational advantages of these schemes.
• [05375] Efficient decoupling energy stable approach for coupled type gradient flow systems with anisotropy for alloys
  • Author(s) :
    • Xiaofeng Yang (University of South Carolina)
  • Abstract : The multi-component alloy phase-field model is a highly complex coupled gradient-like flow model that involves the coupling of multiple Allen-Cahn/Cahn-Hilliard equations with different types of flow field equations. Our ultimate goal is to develop efficient numerical algorithms of the decoupling type for this model. In our initial attempt, we focus on designing a second-order linear unconditional energy stable scheme for the solidification of pure metal, which is further coupled with free flow incorporating Darcy's force. The numerical method is primarily based on the derivative class of the IEQ (Invariant Energy Quadratization) method, which has gained prominence in recent years. Specifically, we combine the so-called EIEQ method with the modified projection method and employ the novel ZEC (Zero-Energy-Contribution) decoupling method to obtain the desired numerical scheme. This approach is versatile and can be applied to a wide range of models involving flow, magnetic, and electric field coupling. To validate the effectiveness of the scheme, we conduct extensive 2D and 3D numerical simulations as well.

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

room : E708

• [02942] Optimal convergence of the arbitrary Lagrangian-Eulerian second-order projection method for the Navier-Stokes equations on an evolving domain
  • Author(s) :
    • Buyang Li (The Hong Kong Polytechnic University)
    • Qiqi Rao (The Hong Kong Polytechnic University)
    • Yupei Xie (The Hong Kong Polytechnic University)
  • Abstract : In this talk, we introduce how to prove the optimal convergence of the arbitrary Lagrangian-Eulerian second-order projection method for the Navier-Stokes equations on an evolving domain.
• [03545] Exponential Spactral Method for Semilinear Subdiffusion Equations with Rough Data
  • Author(s) :
    • Qiqi RAO (PolyU)
  • Abstract : A new spectral method is constructed for the linear and semilinear subdiffusion equations with possibly discontinuous rough initial data. The new method effectively combines several computational techniques, including the contour integral representation of the solutions, the quadrature approximation of contour integrals, the exponential integrator using the de la Vall ́ee Poussin means of the source function, and a decomposition of the time interval geometrically refined towards the singularity of the solution and the source function. Rigorous error analysis shows that the proposed method has spectral convergence for the linear and semilinear subdiffusion equations with bounded measurable initial data and possibly singular source functions under the natural regularity of the solutions.
• [05520] A convergent algorithm for the interaction of mean curvature flow and surface diffusion
  • Author(s) :
    • Charles M. Elliott (University of Warwick)
    • Harald Garcke (University of Regensburg)
    • Balázs Kovács (Paderborn University)
  • Abstract : In this talk we will discuss a numerical approach for the interaction of mean curvature flow and a diffusion process on the surface. The evolving surface finite element discretisation is analysed for a coupled geometric PDE system. We will present an algorithm based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface; give insight into the stability estimates; which lead to optimal-order $H^1$-norm error estimates. We will present numerical experiments reporting on: convergemce, preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections. Based on a joint work with C. M. Elliott (Warwick) and H. Garcke (Regensburg).

MS [00179] Advances in forward and inverse problems of wave equations

room : E709

• [03446] A high-accuracy boundary integral equation method for wave scattering by 3D analytic surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Wangtao Lu (Zhejiang University)
    • Jun Lai (Zhejiang University)
  • Abstract : In this talk, we present a high accuracy boundary integral equation method for wave scattering by a closed analytic surface. The surface is assumed to parameterize in earth-like latitude and longitude coordinates. Any analytic function on it can be firstly approximated by its Fourier series in the latitude variable, and then piecewise Legendre polynomials in the longitude variable. By doing so, we can accurately approximate the standard single-, double-, and adjoint double-layer integral operators in two stages. First, the integrals in the latitude direction are approximated by a nearly optimal algorithm for computing the Fourier transforms of the related kernel functions. Second, the resulting single-variable integrals in the latitude direction have weakly singular kernels, and can be spectrally discretized by pre-designed high-accuracy quadrature rules. We study exterior and interior boundary value problems to validate efficiency and accuracy of the proposed method.
• [03520] Fast algorithms for multiple elastic obstacles scattering and inverse scattering
  • Format : Talk at Waseda University
  • Author(s) :
    • Jun Lai (Zhejiang University)
  • Abstract : Elastic wave scattering and inverse scattering have been appeared in a lot of important applications, including non-destructive testing, seismic inversion, and medical imaging, etc. Integral equation method provides an effective tool for solving elastic wave scattering and inverse scattering problems. In this talk, fast and high order numerical methods based on integral equations will be presented for elastic wave equations in the presence of multiple obstacles. In particular, I will talk about the numerical algorithms using high order discretization of singular integrals and the fast multipole method for evaluating the multiple elastic scattering problem, as well as their applications in the inverse elastic wave scattering based on the time reversal method.
• [05069] Exploring inverse obstacle scattering with an impedance model
  • Format : Talk at Waseda University
  • Author(s) :
    • Travis Askham (New Jersey Institute of Technology)
    • Manas Rachh (Flatiron Institute)
    • Carlos Borges (University of Central Florida)
    • Jeremy Hoskins (University of Chicago)
  • Abstract : It is well known that in certain limits the impedance boundary condition can mimic the sound hard, sound soft, and transmission boundary conditions. Here we explore the performance of this approximation in inverse obstacle scattering problems. We find that for certain problems a relaxation of the usual measurement of scattering error improves the quality of obstacle recovery.
• [03858] Hybrid methods for the application of singular integral operators
  • Format : Talk at Waseda University
  • Author(s) :
    • Leslie Greengard (New York University and Flatiron Institute)
    • Shidong Jiang (Flatiron Institute)
    • Jun Wang (Tsinghua University)
    • Fredrik Fryklund (Courant Institute, NYU)
    • Samuel F Potter (Courant Institute, NYU)
  • Abstract : We present hybrid asymptotic/numerical methods for the accurate computation of elliptic and parabolic volume and layer potentials in two and three dimensions.

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

room : E710

• [05491] Machine-Learned Whitney Forms for Structure Preservation
  • Format : Talk at Waseda University
  • Author(s) :
    • Jonas Albert Actor (Sandia National Laboratories)
    • Nathaniel Trask (Sandia National Laboratories)
    • Andy Huang (Sandia National Laboratories)
  • Abstract : For many applications, scientific machine learning techniques provide few guarantees on structure preservation or convergence rates. Towards this limitation, we introduce a partition of unity architecture to parameterize data-driven Whitney forms, allowing discovery of mixed finite element spaces. The resulting geometric parameterization extracts reduced models from full-field data while exactly preserving physics and matching expected convergence rates. We provide examples for H(div) problems in two dimensions, highlighting the capabilities of the learned Whitney form architecture.
• [04438] Study of a structure preserving discretization framework for Maxwell-Klein-Gordon equations.
  • Format : Online Talk on Zoom
  • Author(s) :
    • Snorre Christiansen (University of Oslo)
    • Tore Halvorsen (University of Oslo)
    • Claire Scheid (Côte d'Azur University)
  • Abstract : We propose a numerical discretization framework for a general family of gauge invariant mechanical Lagrangian. Through the definition of a discrete gauge invariant Lagrangian, we study a fully discrete leap-frog time integration scheme based on conforming space discretizations. We prove the stability and convergence of the scheme without the a priori knowledge of the solution. We will then show how our general framework apply to the Maxwell-Klein-Gordon system.
• [05131] Compatible finite elements for terrain following meshes
  • Format : Talk at Waseda University
  • Author(s) :
    • Karina Kowalczyk (Imperial College London)
    • Colin J Cotter (Imperial College London)
  • Abstract : In this talk we are presenting a new approach for compatible finite element discretisations for atmospheric flows on a terrain following mesh. In classical compatible finite element discretisations, the H(div)-velocity space involves the application of Piola transforms when mapping from a reference element to the physical element in order to guarantee normal continuity. In the case of a terrain following mesh, this causes an undesired coupling of the horizontal and vertical velocity components. We are proposing a new finite element space, that drops the Piola transform. For solving the equations we introduce a hybridisable formulation with trace variables supported on horizontal cell faces in order to enforce the normal continuity of the velocity in the solution. Alongside the discrete formulation for various fluid equations we discuss solver and time-stepping approaches that are compatible with them and present our latest numerical results. In the case of the Helmholtz equations we give a proof of well-posedness of the arising discrete system.
• [04775] Structure-preserving discretization of momentum-based formulations of fluids using discrete exterior calculus
  • Format : Talk at Waseda University
  • Author(s) :
    • Christopher Eldred (Sandia National Laboratories)
  • Abstract : Representation of physical quantities as differential forms (using exterior calculus) has proved to be a powerful approach to formulating continuum mechanics. However, most prior work has focused on scalar-valued differential forms, and therefore electrodynamics and velocity-based formulations of fluids. This talk will present progress towards a discrete exterior calculus for (vector) bundle-valued differential forms, such as those needed to describe momentum, and illustrate its applicability for discretization of momentum-based formulations of (charged) fluid models.

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

room : E711

MS [00137] Mathematical Aspects of Multiscale Phenomena in Materials and Complex Fluids

room : E802

• [00202] Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Weizhu Bao (National University of Singapore)
    • Fukeng Huang (National University of Singapore)
    • Tiezheng Qian (Hong Kong University of Science and Technology)
  • Abstract : In this talk, we present numerical simulations for the pinch-off dynamics in the Stokes regime and the diffusion-dominated regime by adopting the Cahn-Hilliard-Navier-Stokes model derived by applying Onsager's variational principle. The Cahn-Hilliard-Navier-Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry. Ample numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime, respectively. In particular, the crossover between these two regimes is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is inevitably accessed by the pinching neck of the interface. Discussions are also provided for numerical examples that are performed for the breakup of long liquid filaments and show qualitatively different phenomena in different scaling regimes. This is a joint work with Fukeng Huang and Tiezheng Qian.
• [00195] Multiscale analysis of nonlinear material models with carrier kinetics
  • Format : Talk at Waseda University
  • Author(s) :
    • Qing Xia (KTH Royal Institute of Technology)
    • Ludmila Prokopeva (Purdue University)
    • William Henshaw (RPI)
    • Alexander Kildishev (Purdue University)
    • Gregor Kovacic (RPI)
    • Jeffrey Banks (RPI)
    • Donald Schwendeman (RPI)
  • Abstract : In this talk, we introduce Maxwell-Bloch equations for modeling interactions between light and nonlinear optics. The model is based on real-valued rate equations, which describe kinetics of electrons between the ground state and excited states in the multi-level atomic system. We will show the rate equation approach is connected to the complex-valued density matrix approach via the Schrödinger's equation. Different multi-level atomic systems will be shown and multi-scale analysis is performed.
• [00209] Energetic-variational particle-based method for Fokker-Planck Models.
  • Format : Talk at Waseda University
  • Author(s) :
    • Kaitlin O'Dell (University of Utah)
    • Yekaterina Epshteyn (University of Utah)
    • Chun Liu (Illinois Institute of Technology)
  • Abstract : Fokker-Planck models with energy-dissipation structures arise in many scientific and engineering applications. We present a novel energetic-variational particle-based approach for simulation of such nonlinear high-dimensional Fokker-Planck systems which cannot be solved using traditional numerical methods. First, we compare the performance of the proposed particle-based scheme with the finite-volume structure-preserving method on low-dimensional Fokker-Planck systems. Then, we apply new method for the analysis of the high-dimensional Fokker-Planck equations that describe grain boundaries dynamics in polycrystalline materials.
• [00214] Phase transitions in near-liquid solids
  • Format : Talk at Waseda University
  • Author(s) :
    • Yury Grabovsky (Temple University)
    • Lev Truskinovsky (ESPCI)
  • Abstract : We consider a class of two-dimensional compressible Hadamard materials with very small shear modulus and a double-well potential for the energy as a function of specific volume. Such energy is not rank one convex and is in need of relaxation. While computing energy relaxation seems hopeless, identifying its binodal - the boundary separating stable and unstable homogeneously deformed configurations seems more tractable. I will describe several necessary and sufficient conditions for stability and show how they allow us to bound hydrostatic strains on the binodal. Then, in a surprising twist, I will show how the optimality of our bound would generate an excellent approximation to the entire binodal. This is a joint work with Lev Truskinovsky.

MS [00704] Numerical Software Libraries Enabling Benefits to Scientific Applications

room : E803

• [01829] The Need of Ecosystems of Numerical Libraries for Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Ulrike Meier Yang (Lawrence Livermore National Laboratory)
  • Abstract : The emergence of heterogeneous computers with increasingly complex architectures necessitates continuous adaptation of software to take advantage of increased performance potential. Thus, the use of multiple mathematical libraries designed by expert mathematicians and software developers is crucial for application codes. Often, there exist interoperabilities between these libraries. So, as each library is ported to a new computer architecture, it is also important that these libraries continue to work together. This requires a healthy well-designed ecosystem. This talk will discuss the importance of a well-adjusted ecosystem of math libraries and its impact on applications.
• [01773] Factorization based sparse solvers and preconditioners for robust solutions
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoye Sherry Li (Lawrence Berkeley National Laboratory)
  • Abstract : Many high fidelity simulation and data analysis involve large-scale multiphysics and multiscale modeling problems that generate highly ill-conditioned and indefinite algebraic equations. The factorization based algorithms are indispensible building blocks in the solver stack to solve these numerically challenging problems. We will highlight how factorizations and low-rank approximate factorizations can be effectively used as standalone direct solvers or as preconditioners for iterative solvers. The focus will be on recent advances in SuperLU and STRUMPACK targeting at exascale machines and applications.
• [01874] Exploring the HPC Frontier with Ginkgo
  • Format : Talk at Waseda University
  • Author(s) :
    • Marcel Koch (KIT)
    • Hartwig Anzt (UTK)
    • Terry Cojean (KIT)
  • Abstract : This talk will give an overview of the Ginkgo library and highlight its features through several integrations. Ginkgo is a modern C++ library composed of numerical linear algebra algorithms which are optimized for multicore processors and Nvidia, AMD, and Intel GPUs. The use of sustainable software development principles allows the rapid development of cutting edge algorithms with high-quality interfaces. Among others, these are used in plasma simulation, cardiac electrophysiology, or CFD.
• [01866] Scalability Study for Planewave DFT Solvers
  • Format : Talk at Waseda University
  • Author(s) :
    • Doru Thom Popovici (LBNL)
    • Mauro del Ben (LBNL)
    • Andrew Canning (LBNL)
    • Osni Marques (LBNL)
  • Abstract : Modern supercomputers vary in compute power and network capabilities. For example, Summit and Frontier make use of GPUs for accelerating computation, while relying on either a fat-tree or dragonfly topology for transferring data between the nodes. On the other hand, Fugaku has thousands of CPUs and uses a six-dimensional torus for communication. In this work, we want to study these differences in the context of scaling the eigenvalue solvers used in planewave DFT calculations. More specifically, we will focus on four algorithms meant to solve a nonlinear eigenvalue problem, namely Conjugate Gradient, RMM-DIIS, Jacobi Davidson and Unconstrained. We will show that for each algorithm different considerations must be taken when parallelizing the computation. We will provide proxy applications for each algorithm, and we will provide a thorough analysis of each code on some of the state-of-the-art supercomputers. We will emphasize that systematic approaches can be derived to guide the parallelization such that the computation can effectively use the compute and network resources.

MS [00819] Secure Computing: Maintaining Personal Privacy while Analyzing Data

room : E804

• [04041] Construction of Differentially Private Summary with Homomorphic Encryption
  • Format : Talk at Waseda University
  • Author(s) :
    • HAYATO YAMANA (Waseda University)
    • Shojiro USHIYAMA (Waseda University)
    • Tsubasa TAKAHASHI (LINE Corp.)
  • Abstract : A differentially private summary for range queries is constructed using homomorphic encryption to hide the raw data from the computation server. To shorten the processing time, we proposed a new method to merge adjacent close values in the histogram if the difference between the adjacent data is small. Then, we confirmed that the accuracy of the proposed method was equivalent to a state-of-the-art algorithm and the processing time is O(n).
• [04961] Federated Learning with Differential Privacy and Secure Computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsubasa Takahashi (LINE Corporation)
  • Abstract : Improving user experience while respecting user privacy is important nowadays. Last year we released federated learning in LINE messenger’s keyboard area to make users sticker selection easier and more personalized while preserving user privacy. Our FL also employs Differential Privacy (DP) to make exploiting user privacy more difficult. This talk presents our FL+DP, and recent advancement of privacy amplification with secure computing.
• [05348] Network Security and Analytics for Reliability
  • Format : Talk at Waseda University
  • Author(s) :
    • Yukio Uematsu (Tokyo University of Science/Nokia)
  • Abstract : In recent years, a vast number of IoT devices have been connected to the cloud through mobile networks. This talk will address two fundamental issues, namely security and data reliability, in the context of mobile network data analytics. We will present some use cases for data management that combine edge and cloud computing while ensuring data reliability.

contributed talk: CT123

room : E811

[01196] Deep Solvers in Shape Optimization

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E811
• Type : Contributed Talk
• Abstract : We introduce a novel mesh-free method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic deep solver, which can be shown to converge for a wide class of seminilinear PDEs, and a suitable representation of the shape gradient. In contrast to finite element, volume and difference methods, our approach does not require a discretization of the domain’s interior. We also present examples for performance illustration.
• Classification : 68T07, 65N99
• Format : Talk at Waseda University
• Author(s) :
  • Maximilian Würschmidt (Trier University)
  • Frank Seifried (Trier University)
  • Luka Schlegel (Trier University)
  • Volker Schulz (Trier University)

[01477] Optimization of a submerged piezoelectric device using an ANN Model

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E811
• Type : Contributed Talk
• Abstract : The design of a submerged piezoelectric wave energy converter (PWEC) device has been analyzed to optimize the power generated by the PWEC device. An artificial neural network (ANN) is adopted to optimize the geometric parameters of the device. First, a numerical model is introduced using the boundary element methodology (BEM). The input database for the modeling of the ANN model is generated using the Latin Hypercube Sampling method, and the output database for the modeling of the ANN model is simulated using the numerical model based on BEM. Four hundred samples are used to model the ANN with data taken in a 70:30 ratio for training and validation of the model. The prediction of the optimal parameter values for the design of the PWEC device is carried out using a database containing 3000 sample points generated randomly using the LHS method. The developed ANN model shows a good agreement between the training accuracy and the validation accuracy. Also, the model forecast provides a range for the geometric parameters of the PWEC device to optimize power generation.
• Classification : 68T07, 68T20, 68V99
• Format : Talk at Waseda University
• Author(s) :
  • Vipin V (Birla Institute of Technology and Science Pilani, Hyderabad Campus)
  • SANTANU KOLEY (Dept.of Mathematics, Birla Institute of Technology and Science - Pilani, Hyderabad Campus)

[01817] Time-series medical data classification using echo state network

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E811
• Type : Contributed Talk
• Abstract : Most time-series medical data classification tasks are carried out using deep recurrent neural networks. However, deep neural networks tend to consume enormous computational power. Echo state network is an efficient model for processing temporal data due to its low training cost. The reservoir maps input signals into a high-dimensional dynamical system and the readout layer extracts patterns from it. Therefore, we developed a new methodology that can classify time-series data using echo state network.
• Classification : 68T07, 62R07, 62P10
• Format : Talk at Waseda University
• Author(s) :
  • Zonglun Li (University College London)

[02164] Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstruction

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E811
• Type : Contributed Talk
• Abstract : State-of-the-art reconstruction methods in inverse problems have been developed by incorporating latest advances in deep learning. Before learning approaches can be used in safety-critical areas like medical imaging, a model must not only provide a reconstruction, but also an estimate of its reliability. This study presents a cascaded architecture of null space networks and combines it with recent progress of uncertainty quantification in computer vision. This way, two key properties are met: data-consistency and uncertainty-awareness.
• Classification : 68T07, 68T37, 92C50, 92C55
• Format : Talk at Waseda University
• Author(s) :
  • Christoph Angermann (VASCage – Research Centre on Vascular Ageing and Stroke)
  • Simon Goeppel (Universität Innsbruck)
  • Markus Haltmeier (Universität Innsbruck)

MS [00632] From model-blind to model-aware learning of inverse problems in imaging

room : E812

• [03308] Beyond supervised learning in imaging: measurement-driven computational imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Julian Tachella (CNRS, ENSL)
  • Abstract : Most computational imaging algorithms rely either on hand-crafted prior models (total variation, wavelets) or on supervised learning with a ground truth dataset of references. The first approach generally obtains suboptimal reconstructions, whereas the latter is impractical in many scientific and medical imaging applications where ground-truth data is expensive or even impossible to obtain. In this talk, I will present recent algorithmic and theoretical advances in unsupervised learning for imaging inverse problems that overcome these limitations, by learning from noisy and incomplete measurement data alone and leveraging weak prior knowledge on the reconstructed image distribution, such as invariance to groups of transformations (rotations, translations, etc.) and low-dimensionality.
• [03519] Deep Learning for Reconstruction in Nano CT
  • Format : Talk at Waseda University
  • Author(s) :
    • Alice Oberacker (Saarland University)
    • Anne Wald (Georg-August-Universität Göttingen)
    • Bernadette Hahn-Rigaud (Universität Stuttgart)
    • Tobias Kluth (Universität Bremen)
    • Johannes Leuschner (Universität Bremen)
    • Maximilian Schmidt (Universität Bremen)
    • Thomas Schuster (Saarland University)
  • Abstract : Tomographic X-ray imaging at the nano-scale helps reveal the structures of materials like alloys and biological tissue. However, environmental perturbances during data acquisition can cause motion between the object and scanner. To reduce noise in the back-projection, a learned version of the RESESOP-Kaczmarz method was investigated. The deep network was trained with simulated imaging data to unroll the iterative reconstruction process, allowing the network to learn the back-projected image after a fixed number of iterations.
• [04062] Learning intrinsic shape representations via LBO spectra
  • Format : Talk at Waseda University
  • Author(s) :
    • serena morigi (University of Bologna)
  • Abstract : Neural fields are emerging as a new function representation paradigm for image processing, computer vision, computer graphics, and more. The intrinsic neural fields rely on a feature embedding based on the Laplace Beltrami Operator. We derive the embedding functions from the solution of graph Laplacian-based variational regularization problems. This allows to impose property which directly derived from the associated variational formulation. An efficient model-aware method as well as a model-blind neural network will be presented.
• [04272] Inexact Algorithms for Bilevel Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Mohammad Sadegh Salehi (University of Bath)
  • Abstract : We consider hyperparameter estimation for variational methods formulated as a bilevel learning problem. Due to the use of numerical solvers, one can only compute an inexact gradient with respect to the hyperparameters. We introduce and analyse a new framework that dynamically updates the accuracy in inexact algorithms and selects stepsizes based on linesearch. We compare the performance of our method with existing methods through numerical experiments.

MS [02342] On dataset sparsification and data reconstruction in deep learning

room : E817

• [03191] Data sampling for surrogate modeling and optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Tyler H Chang (Argonne National Laboratory)
  • Abstract : In surrogate modeling for nonconvex blackbox optimization, global convergence is driven by the global approximation error of an interpolatory model. For large complex problems, achieving global model accuracy can be prohibitively expensive, so model-based optimization techniques such as Bayesian optimization rely on adaptive sampling to tradeoff between exploration and exploitation. However, these techniques are known to scale poorly with dimension. Therefore, we analyze an alternative approach based on response surface methodology coupled with static design-of-experiments.
• [03317] Bayesian inference via dataset sparsification
  • Format : Online Talk on Zoom
  • Author(s) :
    • Trevor Campbell (UBC)
  • Abstract : A Bayesian coreset is a sparsified dataset that can be used to reduce the cost of inference. Constructing high-quality coresets remains a challenge. In this work we introduce a new method for coreset construction that involves subsampling the data, and then optimizing a variational flow parametrized by coreset weights. Theoretical results demonstrate that our method achieves exponential data compression in a representative model. Experiments demonstrate accurate inference with reduced runtime compared with standard inference methods.
• [03934] Foundations of Information Leakage in Machine Learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Reza Shokri (National University of Singapore)
  • Abstract : This talk will explore the foundations of data privacy in machine learning, with a specific focus on membership inference attacks.
• [04492] Understanding Reconstruction Attacks with Dataset Distillation
  • Format : Talk at Waseda University
  • Author(s) :
    • Noel Loo (Massachusetts Institute of Technology)
  • Abstract : Dataset reconstruction attacks are attacks which aim to recover portions of training data from a trained neural network with access to only the model parameters. In this talk, we study the efficacy of these attacks in both infinite and finite-width regimes, and show that these reconstruction attacks are closely related to dataset distillation. In doing so, we study the properties of recovered images, namely what makes images easy to reconstruct, and how they affect training.

MS [00793] SIAM Student Chapter Research Presentations

room : E818

• [04039] SPHERICAL FRAMELETS FROM SPHERICAL DESIGNS
  • Author(s) :
    • Yuchen XIAO (City University of Hong Kong)
  • Abstract : In this paper, we investigate in detail the structures of the variational characterization $A_{N,t}$ of the spherical $t$-design, its gradient $\nabla A_{N,t}$, and its Hessian $H(A_{N,t})$ in terms of fast spherical harmonic transforms. Moreover, we propose solving the minimization problem of $A_{N,t}$ using the trust-region method to provide spherical $t$-designs with large values of $t$. Based on the obtained spherical $t$-designs, we develop (semi-discrete) spherical tight framelets as well as their truncated systems and their fast spherical framelet transforms for the practical spherical signal/image processing. Thanks to the large spherical $t$-designs and localization property of our spherical framelets, we are able to provide signal/image denoising using local thresholding techniques based on a fine-tuned spherical cap restriction. Many numerical experiments are conducted to demonstrate the efficiency and effectiveness of our spherical framelets, including Wendland function approximation, ETOPO data processing, and spherical image denoising.
• [04179] Introducing Deep Unfolding: Incorporating Prior Knowledge into Deep Learning Models
  • Author(s) :
    • Yumeng REN (City University of Hong Kong)
  • Abstract : Deep unfolding (DU) methods accelerate iterations for inverse problems by incorporating prior knowledge into deep learning models, which can be based on backbone iterations such as the ADMM algorithm for reconstruction tasks and a PDE discretization scheme for learning PDEs from data. In this talk, I will introduce the basics of DU methods, ADMM-type backbone iterations and recent advances.
• [05002] Koopman analysis and Dynamic mode decomposition of Elementary Cellular Automata
  • Author(s) :
    • Keisuke Taga (Waseda University)
    • Yuzuru Kato (Future University Hakodate)
    • Yoshihiro Yamazaki (Waseda University)
    • Hiroya Nakao (Tokyo Institute of Technology)
  • Abstract : We perform Koopman spectral analysis and Dynamic mode decomposition (DMD) for Elementary Cellular Automata (ECA). Koopman operator is a linear operator describing the time evolution of observables of a dynamical system, and DMD is a data-driven approach to Koopman analysis. ECA is the simplest example of finite-state systems that describe spatiotemporal patterns and, thus, a good testbed for assessing the performance of DMD. We report the reproducibility of the dynamics and spectral properties of ECA by different DMD algorithms and explain the linear algebraic background.

MS [00255] Recent developments in fast algorithms for inverse problems and imaging

room : E819

• [03339] Streaming Methods for Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Eric de Sturler (Virginia Tech)
  • Abstract : We discuss Golub-Kahan type methods for streaming problems. As big data applications become ever more prominent, in many applications we can only solve problems such as linear or nonlinear regression problems in chunks. Data may come in over a larger span of time and we cannot (or prefer not) to wait until all data is available, the problem may be too large to fit in memory, or data is coming in at a rate that we can use only sampled data and use it in chunks. There is a need for methods that can work efficiently under such conditions. We discuss extensions for GKB-type methods that select and build effective search spaces over multiple subsets of data and/or matrix-blocks to compute accurate solutions with limited memory available. Apart from streaming applications this may also be useful for modern computing architectures that have highly non-uniform memory access. This is joint work with Julianne Chung, Jiahua Jiang, Misha Kilmer, and Mirjeta Pasha.
• [03433] Sequential model correction for nonlinear inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Arttu Arjas (University of Oulu)
    • Andreas Hauptmann (University of Oulu)
    • Mikko Sillanpää (University of Oulu)
  • Abstract : Linear inverse problems are usually solved with first-order gradient methods. For nonlinear problems one must resort to second-order methods that are computationally more expensive. In this work we approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error. We analyze the sequence theoretically and present numerical results.
• [02062] Plants, robots and dynamic tomography
  • Format : Talk at Waseda University
  • Author(s) :
    • Tommi Heikkilä (University of Helsinki)
  • Abstract : The need for dynamic tomography can arise from many applications, e.g. imaging nutrient perfusion in plant stems for carbon uptake and metabolism studies. While the measurements may be sparse, obtaining the reconstructions can be computationally intensive, since 3D volumes evolving over time leads to 4D tomography. Thus we need fast and efficient methods: our choice are sparse representation systems such as (complex) wavelets and (cylindrical) shearlets, tested on dynamic data from a motorized phantom.
• [04602] Deep learning methods for data-driven uncertainty quantification
  • Format : Talk at Waseda University
  • Author(s) :
    • Ling Guo (Shanghai Normal University )
  • Abstract : In this talk, we will present some recent developments on using Physics-informed neural networks (PINNs) to quantify uncertainty propagation in a unified framework forward, inverse and mixed stochastic problems based on scattered measurements. We will also present generative models for data-driven uncertainty quantification, including physics-informed generative adversarial networks and Normalizing field flows.

contributed talk: CT139

room : E820

[02040] Simulation of landslide-generated waves using non-hydrostatic numerical model

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E820
• Type : Contributed Talk
• Abstract : The reduced two-layer non-hydrostatic (NH-2LR) numerical model is developed and used to study landslide-generated waves. The NH-2LR model is validated using analytical solutions and laboratory experiments. Simulations involves landslide motions on a flat bottom as well as over a sloping beach. The effects of dispersion and non-linearity are then investigated; dispersion is important in the early generation and propagation of landslide-generated waves, whereas non-linearity has a significant influence on maximum run-up.
• Classification : 76B15, 76M12, 35L60
• Format : Talk at Waseda University
• Author(s) :
  • Sri Redjeki Pudjaprasetya (Institut Teknologi Bandung)
  • Dede Tarwidi (Telkom University)
  • Didit Adytia (Telkom University)

[00901] Effect of porous layer fitted on a floating bridge in mitigating waveload

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E820
• Type : Contributed Talk
• Abstract : Scattering of oblique water waves by a floating bridge with porous wall fitted on its vertical sides is studied. Significant changes are noticed in wave reflection due to changes in porosity. It is observed that as the porosity increases, the values of the reflection coefficient decrease. The behavior of various parameters, such as depth, porous wall width, porosity and angle of incidence, on the reflection coefficient are also carried out.
• Classification : 76B07, 76B15, 35P10, 76S05, 76B55
• Format : Online Talk on Zoom
• Author(s) :
  • Shilpi Jain (IIT Guwahati )
  • Swaroop Nandan Bora (Indian Institute of Technology Guwahati)

[02148] A comparative study on scattering of water waves by barriers of various kinds.

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E820
• Type : Contributed Talk
• Abstract : The present study outlines the mathematical and computational details needed to compute the solutions on the scattering of surface water waves by a finite dock, thin rectangular elastic plate and circular elastic plate in finite depth water. The boundary value problem is handled for solutions analytically using a matched eigenfunction expansion . Various physical quantities associated with the scattering problems are studied for various values of wave and structural parameters. A selection of results are given to illustrate the variations of scattering coefficients and to compare with existing solutions.
• Classification : 76B15
• Format : Online Talk on Zoom
• Author(s) :
  • SOFIA SINGLA (IIITUNA, UNA)

[00331] Mathematical modelling of fluid-particle interaction

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E820
• Type : Contributed Talk
• Abstract : Fluid-particle interactions are fundamental to many problems in industry and biology, for example aircraft icing, where ice adheres to aircraft, and the movement of drugs/thrombi in blood. Mathematical modelling and asymptotic methods can be used to reduce such problems to simple ODEs and PDEs which can be solved to reveal an intriguing variety of particle motions. Current work includes an ice particle submerged in water, and a particle in lubrication flow with application to blood.
• Classification : 76B10, 76D08, 76D09, 76M45
• Author(s) :
  • Ellen Mary Jolley (UCL)

[02695] The position of the axon initial segment assembly site can be predicted from the shape of the neuron

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @E820
• Type : Contributed Talk
• Abstract : A unique compartment called the axon initial segment (AIS) was found critical for the proper development of neuronal polarity. It is unclear how AIS is assembled near the proximal end of the axon during axon specification. In this study, we show that the position of the AIS assembly site is correlated with the zero set of the leading eigenfunction of the Laplace-Beltrami operator solved over the geometry of the neuron. We will then discuss the implications from this observation.
• Classification : 92C20, 92C15
• Format : Talk at Waseda University
• Author(s) :
  • Zhuang Xu (The University of New South Wales)
  • Paul Curmi (University of New South Wales)
  • Christopher Angstmann (University of New South Wales)

MS [02569] Quantification of Business Uncertainties through Industrial Mathematics

room : D101

• [04526] Topological methods for detection of uncertainties in Artificial Intelligence
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroaki Kurihara (Artificial Intelligence Laboratory, Fujitsu Research, Fujitsu)
  • Abstract : Recently, with the development of AI technology, AI has been increasingly used for decision-making in various domains where sophisticated knowledge is required. Although well-trained AI models are used in such situations, AI has a weakness in that its predictive ability is reduced for data that was not included during training. In this talk, we will introduce a method to verify the uncertainty of the output of AI by observing the topological information of trained models.
• [04919] Consecutive eigenvalues distribution of asymmetric quantum Rabi models
  • Format : Talk at Waseda University
  • Author(s) :
    • MASATO WAKAYAMA (NTT Institute for Fundamental Mathematics)
  • Abstract : We focus spectral structure of the asymmetric quantum Rabi models (AQRM), which are widely studied as one of the most fundamental models of light-matter interaction. Particularly, we will discuss the symmetric structure of the consecutive (i.e., nearest) eigenvalues of the AQRM when we vary the flip term, which is the symmetric-breaking parameter of the Hamiltonian.
• [05125] Changing the Misconception of Subsea Cable Laying Norm
  • Format : Talk at Waseda University
  • Author(s) :
    • Kamaudin Ismail (Ifactors Sdn Bhd)
  • Abstract : The world today is undeniably heavily reliant on technology. As a result of the continuous advancement in technology, the demand for data transmission services is at an all-time high. Subsea cables are one of the major foundation of global connectivity. It is responsible for transmitting 99% of international data traffic systemwide. However, despite being crucial factor in global connectivity, the process of laying subsea cables is still widely misunderstood. This paper aims to address this misconception and to shed lights on the real process of subsea cable laying. A conventional cable laying concept is by mobilizing a dedicated cable lay vessel. However, the main issue in this equation is that the vessel can only be used for cable lay process alone. The above concept above gave an opportunity for Ifactors to venture into an unknown open concept. It is a new technique/process which is modular and easier to setup for a short distance cable lay.
• [04095] Handling Uncertainties for Wastewater Treatment in Oxidation Pond
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zainal Abdul Aziz (Universiti Teknologi Malaysia)
    • Arifah Bahar (Universiti Teknologi Malaysia)
    • Amir Syafiq Hamzah (Universiti Teknologi Malaysia)
  • Abstract : Oxidation pond techniques are effective for wastewater treatment process due to low operational cost. A stochastic model accommodates the correlation between the phototrophic bacteria mPHO and pollutant existing in oxidation pond. The model analyses and handles the uncertainties of this process, particularly the effect of mPHO on the degradation of pollutant. The model parameters estimation use simulated maximum likelihood based on the real data collected from an oxidation pond located in Taman Timor, Johor, Malaysia.

MS [00838] Perspectives in Artificial Intelligence and Machine Learning in Materials Chemistry, 2nd edition

room : D102

• [05561] Fully automatized optimization of ring-opening reactions in lactone derivatives via 2-step machine learning
  • Format : Talk at Waseda University
  • Author(s) :
    • Aleksandar Staykov (Kyushu University)
    • Pierluigi Cesana (kyushu university)
  • Abstract : Cyclization and cycloreversion of organic compounds are fundamental kinetic processes in the design of functional molecules, molecular machines, and nano-switches. We present a fully automatic computational platform for the design of a class of 5- and 6- membered ring lactones by optimizing the ring-opening reaction rate. Starting from a minimal initial parent set, our program generates iteratively cascades of pools of candidate lactone derivatives where optimization and down-selection are performed not requiring human supervision at any stage. We use Density Functional Theory combined with transition state theory to elucidate the exact mechanism leading to the lactone ring opening. Based on the analysis of the reaction pathway and the frontier molecular orbitals, we identify a simple descriptor that can easily correlate with the reaction rate. The program is successful in identifying a large class of lactone derivatives with enhanced ring-opening properties. Our platform is modular and our current implementation for lactone could be further generalized to more complex systems via substitution of the quantum chemical and fingerprinting modules.
• [01724] A Trial for the Realization of Material Pattern Informatics Using Interpretable AI
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoh-ichi Mototake (Hitotsubashi University)
  • Abstract : It has been recently reported that highly accurate classification, regression, and generation can be achieved by interpolative modeling of complex scientific data using machine learning models with high expressive power, such as deep neural networks (DNNs). However, many of the machine learning models used there are nonlinear functions with a large number of parameters, making the interpretation of the training results very difficult. In thermodynamics, Gibbs extended the theory of thermodynamics, which was the theory of heat engines, to chemical reactions, which was a great development in science. This shows that science has been greatly advanced by the scientific insight of human beings, who derive general principles beyond mere interpolation models and boldly extrapolate them. On the other hand, it is sometimes difficult to apply such insights to systems with complex non-periodic structures, such as those found in nonlinear and nonequilibrium phenomena. To address this situation, we believe that it is important to collaborate between machine learning, which is good at building interpolation models for complex data, and humans, who can make bold extrapolations based on scientific insights, and are developing methods for interpreting machine learning training results to bridge the gap between the two. In this presentation, we will discuss our recent research on machine learning frameworks that collaborate with scientists trying to reveal complex pattern dynamics in materials and their applications.
• [05582] Density functional theory analysis for hydrogen sulfide removers with graphene
  • Format : Talk at Waseda University
  • Author(s) :
    • Takaya Fujisaki (Shimane University)
  • Abstract : Methane, attracting attention as a hydrogen carrier for solid oxide fuel cells, can be generated by methane fermentation using biomass, however, it is known to contain some amount of hydrogen sulfide. Since hydrogen sulfide reduces the power generation efficiency of fuel cells, it is desirable to remove as much hydrogen sulfide as possible. In this study, we used density functional theory to understand the hydrogen sulfide removing agent with graphene structure.
• [01335] Understanding the role of defects and disorder in polycrystalline materials
  • Format : Talk at Waseda University
  • Author(s) :
    • Kulbir K Ghuman (Institut national de la recherche scientifique)
  • Abstract : The functionality of the materials used for energy applications is critically determined by the physical properties of small active regions such as dopants, dislocations, interfaces, grain boundaries, etc. The capability to manipulate and utilize the inevitable disorder in materials, whether due to the finite-dimensional defects (such as vacancies, dopants, grain boundaries) or due to the complete atomic randomness (as in amorphous materials), can bring innovation in designing energy materials. With the increase in computational material science capabilities, it is now possible to understand the complexity present in materials due to various defects resulting in pathways required for optimizing their efficiencies. In this talk, I will provide a critical overview of such computational advancements specifically for designing realistic materials with various types of defects. I will discuss the traditional approaches (implemented via tools such as density functional theory, and molecular dynamics) as well as modern approaches such as machine learning that exist for understanding the impact of defects and disorder present in polycrystalline materials, thereby identifying future opportunities for energy materials design and discovery.

MS [00781] Physical and Mathematical Research on Transport on Slippery Surfaces

room : D401

• [03772] Flows through slippery tubes and annuli
  • Format : Talk at Waseda University
  • Author(s) :
    • Sebastian Zimmermann (RPTU Kaiserslautern-Landau)
    • Clarissa Schönecker (RPTU Kaiserlautern-Landau)
  • Abstract : We present analytical models for the flow through tubes and annuli that possess slippery longitudinal slits along their surface. Firstly, these expressions can be employed with an arbitrary local slip length or shear stress being predefined at the slits, corresponding to an arbitrary Newtonian fluid. Secondly, the two solutions for tubes and annuli can be combined such that there is one fluid in the tube and another one in the annulus surrounding the tube.
• [03964] Numerical study of longitudinal flow over liquid infused surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Miyoshi (Imperial College London)
    • Darren G. Crowdy (Imperial College London)
  • Abstract : A numerical method for the computation of two-phase pressure-driven longitudinal flow over liquid-infused surfaces is presented. These surfaces feature a periodic array of circular surface-embedded grooves filled with a subphase fluid that can enhance slip of an upper fluid, of different viscosity, flowing over it. A novelty of the numerical approach is that it deploys techniques from conformal geometry and complex analysis.
• [02965] Viscoplastic Flows through Grooved Superhydrophobic Channels
  • Format : Talk at Waseda University
  • Author(s) :
    • Seyed Mohammad Taghavi (Université Laval)
    • Hossein Rahmani (Université Laval)
  • Abstract : We study the transport of viscoplastic fluids through channels with grooved superhydrophobic walls. To this end, we employ a comprehensive modeling approach and high-resolution numerical simulations and, in particular, consider longitudinal, transverse, and oblique orientations of the grooves. We use the perturbation theory to derive semi-analytical and closed-form solutions for the velocity fields, whose results are validated against our numerical simulations. Finally, we highlight the strong nonlinear effect of viscoplastic rheology and analyze the stabilizing/destabilizing effects of slip conditions on the flow.
• [04260] Jeffery’s paradox for the rotation of a single ‘stick-slip’ cylinder
  • Format : Talk at Waseda University
  • Author(s) :
    • Michael S Siegel (New Jersey Institute of Technology)
    • Ehud Yariv (Technion)
  • Abstract : The two-dimensional fluid velocity due to the rotation of a superhydrophobic or `stick-slip’ cylinder in Stokes flow is determined. We find that in the general case of an aperiodic distribution of stick and slip boundaries there is no solution in which the fluid velocity vanishes at infinity. This is the first example of Jeffery’s paradox, typically associated with the flow due to the counter-rotation of two rigid cylinders, for a single cylinder.

MS [00037] Recent advances in modelling and simulation of interfacial flows

room : D402

• [02292] Interfacial flows and their modelling and control
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexander Wray (University of Strathclyde)
    • Radu Cimpeanu (University of Warwick)
    • Susana Gomes (University of Warwick)
  • Abstract : Interfacial flows are ubiquitous in nature and industry, and modelling, understanding and controlling them has applications everywhere from carbon sequestration to medical diagnostics. As an introduction to this session, we provide an overview of the topic area, particularly with regards to the state of the art and relevant applications. We also discuss our recent work on controlling the full Navier-Stokes equations using reduced-order models as an example of tying together many of these research strands.
• [05417] New perspectives on continuous film flow over non-planar substrate: a family affair
  • Format : Talk at Waseda University
  • Author(s) :
    • Markus Scholle (Heilbronn University )
    • Philip H. Gaskell (Durham University)
  • Abstract : Film flow on curved substrate is investigated theoretically for: (i) continuously-fed, full coverage; (ii) partial coverage following deposition of a fixed liquid volume; (iii) rivulet formation. Using a novel variational formulation uncovers the presence of an interrelated family of flows for 3D axisymmetric geometries and related 2D counterparts. Analytic solutions for local film thickness and the internal flow are obtained, together with rigorous identification of associated timescales, via asymptotic analysis combined with the long-wave approximation.
• [02788] Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel
  • Format : Talk at Waseda University
  • Author(s) :
    • Anna Kalogirou (University of Nottingham)
    • Mark Blyth (University of East Anglia)
  • Abstract : The Rayleigh-Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications, revealing a number of interfacial phenomena including finger-like protrusions, coalescence, saturated travelling waves, and near-segregation of the two fluids. The finer structure of the interface is exposed through asymptotic analysis and is compared to numerical results of the lubrication model as well as direct numerical simulations, displaying an excellent agreement between the three in terms of interfacial structure, wave speed and film thicknesses.
• [04110] Neural network methods for solving interface problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Te-Sheng Lin (National Yang Ming Chiao Tung University)
    • Ming-Chih Lai (National Yang Ming Chiao Tung University, Taiwan)
    • Wei-Fan Hu (National Central University)
    • Yu-Hau Tseng (National University of Kaohsiung)
  • Abstract : Neural networks have emerged as powerful tools for numerically solving partial differential equations. In this talk, we will discuss our recent work using neural network approaches to elliptic interface problems, and possible extensions to deal with models arising from interfacial phenomena. Specifically, we will introduce a structure enforcement layer in the network to enforce the inherent properties of the solutions to given problems, such as discontinuity or periodicity. The structure enforcement layer offers a new approach to solving such problems compared to traditional neural networks, which may struggle to represent discontinuous functions and may not have built-in periodicity.

MS [00280] Canonical Scattering Theory and Application

room : D403

• [02735] Diffraction of acoustic waves by multiple independent semi-infinite arrays.
  • Format : Talk at Waseda University
  • Author(s) :
    • Matthew Allan Nethercote (University of Manchester)
    • Raphael Assier (University of Manchester)
    • Anastasia Kisil (University of Manchester)
  • Abstract : We consider multiple wave scattering problems with several semi-infinite periodic arrays of point scatterers. For each array, a coupled system of equations must be satisfied by the scattering coefficients. All of these systems are solved using the discrete Wiener--Hopf technique and the result leads to a invertible matrix equation. In particular, we look at two arrays forming a wedge interface and will make comparisons with numerical methods that do not rely on the array periodicity.
• [05383] Extending the Unified Transform Method for Periodic Scattering Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shiza Batool Naqvi (University of Cambridge)
    • Lorna Ayton (University of Cambridge)
  • Abstract : The Unified Transform method (also known as Fokas method) is employed in unbounded convex domains to model wave scattering governed by the Helmholtz equation. The method is extended to consider periodic boundary conditions allowing for computation of infinite scattering patterns which have been previously studied using periodic Green's functions and large-dimension Wiener--Hopf matrices. The method is amenable to impedance and elastic surfaces. Furthermore, complex arrangements of scatterers, such as non-parallel cascading plates, are considered.
• [01576] A Mathematical Method to Solve Diffraction Problems with Generalised Linear Boundary Conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Alistair Hales (University of Cambridge)
  • Abstract : The Wiener—Hopf Technique is a popular method used in the analysis of diffraction problems and elsewhere. We present a novel methodology that can solve the gust diffraction problem for a surface with a general linear boundary condition, with the view of applying said solutions to leading or trailing edge noise problems for general (possibly non-rigid) materials. We discuss how solving such a problem is primarily difficult due to the factorization procedure required for the Wiener—Hopf technique to work. However, such boundary conditions may be simplified using a transformation of variables to a trigonometric polynomial, whose roots give the information required to split the scalar kernel into individual factors. This methodology provides insight into the underlying structure of the kernel while also allowing numerical methods to be easily applied thanks to the Maliuzhinets function that originates from wedge diffraction problems. As an initial demonstration of the theory, we compare different canonical choices for impedance boundaries and demonstrate not only how changing the impedance of the surface can affect the solution, but how choosing a correct boundary condition initially may prove cruci
• [03068] Acoustic emission of a vortex ring near a porous edge
  • Format : Talk at Waseda University
  • Author(s) :
    • Huansheng Chen (Lehigh University)
    • Zachary Yoas (General Dynamics Electric Boat)
    • Mitchell Swann (Applied Research Laboratory, Pennsylvania State University)
    • Justin Jaworski (Lehigh University)
    • Michael Krane (Applied Research Laboratory, Pennsylvania State University)
  • Abstract : The sound of a vortex ring in a quiescent fluid passing near a semi-infinite porous edge is investigated analytically to determine its time-dependent pressure signal and directivity in the acoustic far field as a function of a single dimensionless parameter. Results for this configuration furnish an analogue to scaling results from standard trailing-edge noise analyses and permit a direct comparison to companion experiments that circumvent measurement contamination by background noise sources of a mean flow.

MS [00372] Recent advances on computational wave propagation

room : D404

• [01429] Analysis and simulation of carpet cloak model with metamaterials
  • Format : Talk at Waseda University
  • Author(s) :
    • Jichun Li (University of Nevada Las Vegas)
  • Abstract : This talk is concerned about a time-domain carpet invisibility cloak model. Here we consider two new finite element schemes to solve it. Stability and optimal error estimates are proved for both schemes. Numerical results are presented to support our analysis and demonstrate the cloaking phenomenon.
• [01639] Edge elements on nonaffine quadrilateral and hexahedral grids for Maxwell eigenproblem
  • Format : Talk at Waseda University
  • Author(s) :
    • HUOYUAN DUAN (Wuhan University, School of Mathematics and Statistics)
  • Abstract : Most of the edge elements on nonaffine quadrilateral and hexhaedral grids do not satisfy the so-called discrete compactness property. Consequently, they generate spurious eigenmodes and are not spectral correct. We propose some new finite element methods for Maxwell eigenproblems so that all the edge elements on nonaffine quadrilateal and hexhaedral grids are spurious-free and spectral correct. The new methods have been confirmed by theory and numerics.
• [01856] Deriving consistent surface fields for compatible FETD discretizations of Maxwell’s equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Duncan McGregor (Sandia National Laboratories)
  • Abstract : The coupling of electromagnetic energy to a cable is a critical quantity of interest in some engineering applications. These cables can be modelled as internal boundaries with a perfect electric conductor condition. An intuitive method is a loop integral of the magnetic field around the cable. This leads to physical and mathematical concerns. As such, we use Dirichlet-to-Neumann map to compute surface currents. We will describe our method and present numerical results.
• [01860] FDTD Method With Explicit Non-Iterative and Second Order Treatment for Kerr Nonlinearities
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinjie Liu (Delaware State University)
  • Abstract : In this talk, we introduce a new explicit non-iterative FDTD algorithm for solving Maxwell's equations in nonlinear Kerr media. The FDTD method is a widely used numerical technique for solving Maxwell's equations in complex media. Our method balances accuracy and computational cost, offering similar accuracy to Newton's iterative method but at a lower computational expense. The effectiveness of our method is demonstrated by its quadratic convergence rate, as well as several numerical examples such as simulations of four-wave mixing and soliton propagation.

MS [00789] Algorithmic advances in computational quantum mechanics

room : D405

• [03946] Analyzing Non-equilibrium Quantum Many-body Dynamics by Dynamic Mode Decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Chao Yang (Lawrence Berkeley National Lab)
    • Jia Yin (Lawrence Berkeley National Lab)
    • Yuanran Zhu (Lawrence Berkeley National Lab)
  • Abstract : A practical way to compute time-dependent observables of an out-of-equilibrium quantum many-body system is to focus on the single-particle Green's function defined on the Keldysh contour. The equation of motion satisfied by such a Green's function is a set of nonlinear integro-differential equations called the Kadanoff-Baym equations. We will describe numerical methods for solving these equations and show how to use dynamic mode decomposition to reduce their computational complexity.
• [05317] Some mathematical insights on DMET
  • Format : Talk at Waseda University
  • Author(s) :
    • Fabian Maximilian Faulstich (Rensselaer Polytechnic Institute)
  • Abstract : High-accuracy methods are crucial for simulating static correlated systems, but they often scale severely. DMET can solve this by scaling highly accurate solvers. This talk shows that the exact ground-state density matrix is a fixed point of DMET for non-interacting systems, with a unique physical solution in the weakly-interacting regime. DMET is exact to first order in the coupling parameter, and numerical simulations confirm these results. Assumptions behind their validity are also discussed.
• [04977] Efficient algorithms for Brillouin zone and frequency integration
  • Format : Talk at Waseda University
  • Author(s) :
    • Lorenzo Xavier Van Munoz (Massachusetts Institute of Technology)
    • Jason Kaye (Flatiron Institute, Simons Foundation)
    • Sophie Beck (Flatiron Institute, Simons Foundation)
  • Abstract : Brillouin zone integration is a standard operation in electronic structure calculations used to compute numerous physical observables. For integrands with broad features at scale $\eta$, standard equispaced integration methods are highly effective. However, when $\eta$ is small, adaptive methods become necessary to achieve converged results. We extend these adaptive, high-order accurate methods to problems with an additional frequency integral, such as the optical conductivity, and discuss how to control the error in these iterated integrals.
• [04273] Extraction of resonant states in systems with defects
  • Format : Talk at Waseda University
  • Author(s) :
    • Eloise Letournel (CERMICS)
    • Antoine Levitt (Université Paris Saclay (LMO))
    • Luigi Genovese (CEA Grenoble)
    • Ivan Duchemin (CEA Grenoble)
    • Simon Ruget (CERMICS)
  • Abstract : We introduce a numerical method to compute resonances induced by localized defects in crystals. We express the resonance in terms of a “resonance source" strictly localized within the defect region. We then compute a kernel equation, applying against this source the Green's function of the perfect crystal, which we show can be computed efficiently by a complex deformation of the Brillouin zone (BCD).

MS [00140] Interacting particle systems: modeling, learning and applications

room : D407

• [04464] Data-driven discovery of interacting particle systems with Gaussian Processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Sui Tang (University of California Santa Barbara)
    • Charles Kulick (University of California Santa Barabra)
    • Jinchao Feng (Johns Hopkins University)
  • Abstract : We present a data-driven approach for discovering interacting particle models with latent interactions. Our approach uses Gaussian processes to model latent interactions, providing an uncertainty-aware approach to modeling interacting particle systems. We demonstrate the effectiveness of our approach through numerical experiments on prototype systems and real data. Moreover, we develop an operator-theoretic framework to provide theoretical guarantees for the proposed approach. We analyze recoverability conditions and establish the statistical optimality of our approach.
• [03149] The mean field limit of random batch interacting particle systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Lei Li (Shanghai Jiao Tong University)
  • Abstract : The Random Batch Method proposed in our previous work (J Comput Phys, 2020) is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a new model in which particles interact, at discrete time, with randomly selected mini-batch of particles. We investigate the mean-field limit of this model as the number of particles tends to infinity. The mean field limit now exhibits some new features. We will not only justify this mean-field limit (discrete in time) but will also show that the limit approaches to the solution of a nonlinear Fokker-Planck equation as the discrete time step goes to zero.
• [04827] Neural parameter calibration for large-scale multi-agent systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Thomas Gaskin (University of Cambridge)
  • Abstract : I present a method to calibrate multi-agent systems to datasets using neural networks, allowing for uncertainty quantification in a manner that reflects both the noise on the data as well as the non-convexity of the parameter estimation problem. I will discuss applications to various different examples, including learning entire network adjacency matrices, and give a comparative analysis of the method’s performance in terms of speed, prediction accuracy, and uncertainty quantification to classical techniques.
• [05244] Non-local regularization of Semilinear PDE for Probability Density Stabilization
  • Format : Talk at Waseda University
  • Author(s) :
    • Karthik Elamvazhuthi (University of California, Riverside)
  • Abstract : In this talk, I will present some recent work on a particle method for numerically simulating a class of semilinear PDEs that provide strategies for probability density stabilization. These have important applications in problems such as sampling and multi-agent control. We will consider a semilinear diffusion model in which the reaction parameters are to be designed so that the solution of PDE converges to a target probability density. Since the parameters of these PDEs depend on the local density, they are not suitable for implementation on a finite number of particles. We construct a particle method by regularizing the local dependence to construct a non-local PDE. While the nonlocal approximations make numerical implementation easier, their local limits have good analytical properties from the point of view of understanding long-term behavior. Motivated by applications in robotics, the method also easily generalizes to situations where the particle diffusions are degenerate and hence, not elliptic, but only hypoelliptic.

MS [01622] Mathematics for Prediction and Control of Complex Systems

room : D408

• [02251] Sequential data assimilation and data driven control
  • Format : Online Talk on Zoom
  • Author(s) :
    • Sebastian Reich (University of Potsdam)
  • Abstract : Sequential data assimilation can be considered a coupling of measure problem which can be tackled using optimal transport or Schroedinger bridges. In this talk, we will present an approximate bridging approach which leads to a data-driven term being added to the underlying model dynamics. The added control term is of mean-field type and can be implemented easily within a Monte Carlo context. The control term is also closely related to continuous time ensemble Kalman-Bucy filter formulations. One can extend the proposed controlled DA approach to cost functions other than those derived from the data likelihood.
• [02790] Data-driven Reconstruction of Partially Observed Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Pierre Tandeo (IMT Atlantique)
    • Pierre Ailliot (Univ. Brest)
    • Florian Sévellec (CNRS)
  • Abstract : The goal of this work is to obtain predictions of a partially observed dynamical system, without knowing the model equations. To account to those strong assumptions, a combination of machine learning and data assimilation techniques is proposed with the introduction of latent variables. We find that the latent variables inferred by the procedure are related to the successive derivatives of the observed components of the dynamical system.
• [02800] Sensor selection by greedy method for linear dynamical systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shun Takahashi (Tokai University)
    • Kumi Nakai (National Institute of Advanced Industrial Science and Technology )
    • Takayuki Nagata (Tohoku University)
    • Keigo Yamada (Tohoku University)
    • Yasuo Sasaki (Tohoku University)
    • Yuji Saito (Tohoku University)
    • Taku Nonomura (Tohoku University)
  • Abstract : Sensor optimization using a greedy method based on the snapshot-to-snapshot Fisher information matrix, observability Gramian, and Kalman filter indices in linear time-invariant systems is discussed. The objective functions and computational times are compared for the resulting sensor sets with a background of application to sensor selection in large systems.
• [02804] Fast Linear-regression-based Sensor Selection and its Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Yasuo Sasaki (Tohoku University)
    • Yuji Saito (Tohoku University)
    • Takayuki Nagata (Tohoku University)
    • Keigo Yamada (Tohoku University)
    • Taku Nonomura (Tohoku University)
  • Abstract : We consider a ridge-regression-based sensor selection problem in which sensors are selected so that dependent variables can be estimated as easily as possible. For this problem, a fast greedy algorithm is derived by means of one-rank update law of covariance matrices. To verify the effectiveness of this greedy algorithm, it is applied to sensor selection for estimation of the sea surface temperature and for optimal feedback control of flow around a circular cylinder.

MS [01718] On SDP relaxations of polynomial optimization

room : D501

• [01976] Tightness conditions of SDP relaxation for QCQPs with bipartite graph structure
  • Format : Talk at Waseda University
  • Author(s) :
    • Godai Azuma (Tokyo Institute of Technology)
    • Mituhiro Fukuda (Federal University of ABC)
    • Sunyoung Kim (Ewha Womans University)
    • Makoto Yamashita (Tokyo Institute of Technology)
  • Abstract : We discuss a tightness condition of SDP, semidefinite programming, relaxation for QCQPs, quadratically-constrained quadratic programming problems, with bipartite graph structure, and this result generalizes that a condition that the SDP relaxation is tight for QCQPs with diagonal matrices due to Burer and Ye, and a condition based the signs of the elements in input data matrices analyzed by Sojoudi and Lavaei. Our condition to check the tightness of SDP relaxation demands to solve SDP systems, but it requires weaker assumptions than Sojoudi and Lavaei. Our approach also gives another proof for the tightness of SDP relaxations for QCQPs with off-diagonal nonpositive elements by converting such QCQPs into QCQPs with bipartite graph structure.
• [02464] Equivalent Sufficient Conditions for Exact SDP Relaxation and the Saddle Point of Lagrangian Function of QCQP
  • Format : Talk at Waseda University
  • Author(s) :
    • Sunyoung Kim (Ewha W. University)
    • Masakazu Kojima (Chuo University)
  • Abstract : We study global optimality conditions for general quadratically constrained quadratic program $(\rm QCQP)$. For NP-hard nonconvex QCQP, there has been a great interest in the class of QCQPs whose global optimality can be obtained via convex relaxations. The exactness of optimal solutions of QCQP can determined by several methods: First, the optimal solution $X \in S_+^n$ of the semidefinite $(\rm SDP)$ relaxation of nonconvex QCQP is exact if its rank is 1 or the rank of dual optimal solution of the SDP relaxation is n-1 under strong duality. Second, the global optimality of solutions of QCQP can be also determined by the saddle point of the Lagrangian function of QCQP. Third, second-order sufficient condition for the global optimality can also be used. We examine the relationship among the three conditions and prove their equivalence. A QCQP instance is provided to illustrate the equivalent conditions.
• [02214] Approximation Hierarchies for Copositive Cone over Symmetric Cone
  • Format : Talk at Waseda University
  • Author(s) :
    • Mitsuhiro Nishijima (Tokyo Institute of Technology)
    • Kazuhide Nakata (Tokyo Institute of Technology)
  • Abstract : We first provide an inner-approximation hierarchy described by a sum-of-squares constraint for the copositive cone over a general symmetric cone. We second provide inner- and outer-approximation hierarchies described by semidefinite but not by sum-of-squares constraints for the copositive cone over the direct product of a nonnegative orthant and a second-order cone. We also compare them with existing hierarchies. Numerical experiments show that, by combining them, we can solve copositive programming problems more accurately and efficiently.
• [02008] An inexact projected gradient method with rounding and lifting for rank-one semidefinite relaxation of polynomial optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Kim-Chuan Toh (National University of Singapore)
    • Heng Yang (Harvard University)
    • Ling Liang (National University of Singapore)
    • Luca Carlone (MIT)
  • Abstract : We consider solving high-order semidefinite programming (SDP) relaxations of polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. We propose a new algorithmic framework that uses an inexact projected gradient method for solving the SDP, together with acceleration by taking long, but safeguarded, rank-one steps generated by fast local solver for the underlying POP. Our framework achieves state-of-the-art efficiency, scalability, and robustness in solving degenerate rank-one SDPs to high accuracy, even with millions of equality constraints.

MS [02628] Mathematical Modeling on waste reduction through sustainable developmnet

room : D502

MS [01383] Sustainable Logistics and Transportation under Uncertain Environments

room : D505

contributed talk: CT171

room : D514

[00050] Generalized Game Theoretical Model with Multiple Types of Homogeneous Players

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @D514
• Type : Industrial Contributed Talk
• Abstract : We introduce a decision game model with finite number of types and each type has finite number of homogeneous players. We assume that each type of player has similar characteristics and will choose only between two alternative choices or decisions). The preference for each type of players is described by a discrete utility function which gathers the influence of players in the same group and the influence of players from the other groups. We will characterize all pure ''united or separated'' and mixed strategies that form Nash equilibria. The united strategies ensure that all players with same type will make same decision, while separated strategy includes at least one type of players who do not make same decision. We will determine the strategic thresholds for each type that identify the Nash regions in space. As a special case, we consider three types of homogeneous players and use geometry to construct three dimensional regions for Nash equilibria, where the horizontal axis reflects the preference for players of type one, the vertical axis reflects the preference for the players of type two, and the depth axis reflects the preferences for the players of type three, and we characterize all Nash equilibria regions. Finally, we apply our model in economics ''tourist sector'' by introducing a resort model for three types of tourists distributed among two resorts and determine the competitive Nash Equilibrium prices for given preference for the three types of tourists.
• Classification : 91A06, 91A10, 91A35, 91A43, 91A11
• Format : Talk at Waseda University
• Author(s) :
  • Abdelrahim Said Mousa (Birzeit University)

[00600] A Two Timescale Evolutionary Game Theoretic Approach to Multi-Agent Learning

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @D514
• Type : Contributed Talk
• Abstract : We propose a two timescale evolutionary game theoretic approach to solving multiagent reinforcement learning problems. This new approach enables us to avoid the computationally expensive step of solving exact equilibrium in each iteration. It provably converges to epsilon-Nash equilibria without imposing the global optima or saddle point conditions, two restrictive assumptions that are typically needed in the literature. The numerical experiments show the computationally efficiency of the algorithm.
• Classification : 91A15, 91A22, 68T05, 37N40, Reinforcement learning; Multi-agent system
• Format : Talk at Waseda University
• Author(s) :
  • Nan Chen (The Chinese University of Hong Kong)
  • Chengli Ren (The Chinese University of Hong Kong)

[00053] How predators choose their prey to maximize their utility functions by using switching prey

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @D514
• Type : Contributed Talk
• Abstract : In this work, we model the relationship between prey and predators by studying the interactive behavior of this prey-predator model and using the change of prey. The objective is to maximize the profit function of each predator by seeking the strategy provided by each predator to maximize its profit. To do so, we maximize this utility function being constrained by balance equations between biomass and trophic, and we show that this last problem is completely equivalent to finding the Generalized Nash Equilibrium Point. To calculate it, we use the conditions of KKT and we show that it is indeed a Problem of Linear Complementarity.
• Classification : 91A06, 91B06, 92B05, 15A03, 15A30
• Format : Online Talk on Zoom
• Author(s) :
  • Asmaa IDMBAREK (LAMS, Hassan II University of Casablanca, Casablanca, Morocco)
  • Yamna ACHIK (LAMS, Hassan II University of Casablanca, Casablanca, Morocco)
  • Hajar NAFIA (LAMS, Hassan II University of Casablanca, Casablanca, Morocco)
  • Imane AGMOUR (LAMS, Hassan II University of Casablanca, Casablanca, Morocco)
  • Youssef EL FOUTAYENi (LAMS, Hassan II University of Casablanca, Casablanca, Morocco)

[02555] A Mean Field Game Model for Renewable Investment under Uncertainty

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @D514
• Type : Contributed Talk
• Abstract : We consider a stylized model for investment into renewable power plants under long-term uncertainty. Risk-averse agents face heterogeneous weather conditions and a common noise including demand trends. The objective of each agent is to maximize profit by controlling investment at discrete time steps. We prove that the N-player game admits a Nash equilibrium that converges to the unique solution of a mean field game. The numerical experiments emphasize the impact of risk aversion and heterogeneity.
• Classification : 91A16, 49N80, 91A80, 91A50
• Author(s) :
  • Célia Escribe (Ecole Polytechnique)
  • Josselin Garnier (Ecole Polytechnique)
  • Emmanuel Gobet (Ecole Polytechnique)

[00188] Two-Phase Modelling of Plaque Growth in Early Atherosclerosis

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @D514
• Type : Contributed Talk
• Abstract : We discuss the early stage of atherosclerotic plaque formation within arteries. The production of foam cells characterizes such plaque. Foam cells generate from the differentiated form of monocytes (called macrophages) owing to oxidized low-density lipoprotein (ox-LDL) cholesterol intake. Initially, plaque radius grows exponentially and later on, it stabilizes with time. Such behaviour is due to the death of foam cells owing to the toxicity of excess ox-LDL intake, although ox-LDL enhances foam cell proliferation.
• Classification : 92C35, 92-10, 76M20, 35B20, 92B05
• Format : Talk at Waseda University
• Author(s) :
  • Abdush Salam Pramanik (Department of Mathematics, University of North Bengal)
  • Bibaswan Dey (Department of Mathematics, University of North Bengal)

MS [00935] Applied mathematics in industry: Success stories of collaboration between academia and industry in Mexico

room : D515

• [01745] P&L Attribution and Risk Management
  • Format : Talk at Waseda University
  • Author(s) :
    • Joyce Vega (Universidad Nacional Autónoma de México)
  • Abstract : In this session I will talk about the concept of profit and loss attribution in risk management as a predictive and explanatory model of financial market movements in investment portfolios through Taylor expansion, and associated concepts of risk factors as components of a price function of a financial instrument. Finally, I will also present an applied example of this model.
• [01753] Building an university-based knowledge transfer network for the financial sector: The case of Fin-ML
  • Format : Online Talk on Zoom
  • Author(s) :
    • Manuel Morales (Université de Montréal)
  • Abstract : In 2017, the Fin-ML Network was created within the Université de Montréal with the goal of training the next generation of applied mathematicians and statisticians working at the intersection of data-science, machine learning, quantitative finance and business intelligence. In the past five years, it has become a knowledge transfer center fostering collaboration between industry and academia around data-centric value creation for businesses in the financial sector. This collaboration is now international as we have started partnering with the innovation ecosystem in two Mexican states. This talk will narrate this success story while showcasing some of the applied projects our researchers have been working on.
• [01912] Applied mathematics in industry: Success stories of collaboration between academia and industry in Mexico
  • Format : Online Talk on Zoom
  • Author(s) :
    • Cipriano Arturo Santos (Tecnologico de Monterrey)
  • Abstract : The applied collaboration between educational institutions in mathematics and industry is complicated not only from a scientific and technological point of view but also due to intellectual property legislation, organization, response time, and confidentiality. This mini-symposium will present successful real cases of applying mathematics directly to technological development in Mexico and some ideas for achieving greater collaboration.

MS [00223] Stochastic optimization and stochastic variational inequalities

room : A201

• [02880] Dynamic Stochastic Projection Method for Multistage Stochastic Variational Inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • Hailin Sun (Nanjing Normal University)
    • Bin Zhou (Nanjing Normal University)
    • Jie Jiang (Chongqing University)
  • Abstract : Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an $\mathcal{O}(\frac{1}{\epsilon^2})$ convergence rate regarding the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM.
• [02891] A two-stage stochastic variational inequality model
  • Format : Talk at Waseda University
  • Author(s) :
    • Min Li (Beijing Jiaotong University)
    • Chao Zhang (Beijing Jiaotong University)
    • Mingxv Ding (Beijing Jiaotong University)
    • Ruipu Lv (Beijing Jiaotong University)
  • Abstract : This paper first proposes a new nonsmooth two-stage stochastic equilibrium model of medical supplies in epidemic management. The first stage addresses the storage in the pre-disaster phase, and the second stage focuses on the dynamic distribution in the post-disaster phase. The uncertainties are the numbers of infected people treated in multiple hospitals. The model is further approximated and transformed to a monotone two-stage stochastic variational inequality (SVI) model that is computationally tractable.
• [02899] Discrete approximation for two-stage stochastic variational inequalities
  • Format : Talk at Waseda University
  • Author(s) :
    • Jie Jiang (Chongqing University)
    • Hailin Sun (Nanjing Normal University)
  • Abstract : In this paper, the discrete approximation of two-stage stochastic variational inequalities has been investigated when the second stage problem has multiple solutions. First, a discrete approximation scheme is given by a series of models with the aid of merit functions. After that, the convergence relationships between these models are analysed, which therefore yields the convergence guarantee of the proposed discrete approximation scheme. Finally, we use the well-known progressive hedging algorithm to report some numerical results and to validate the effectiveness of the discrete approximation approach.
• [05136] Iteratively sampling scheme for stochastic optimization with variable number sample path
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dali ZHANG (Shanghai Jiao Tong University)
    • Shuang HAO (Shanghai Jiao Tong University)
    • Ming Dong (Shanghai Jiao Tong University)
  • Abstract : Optimal search methods are proposed for solving optimization problems with analytically unobtainable objectives. This paper proposes a method by incorporating sampling schemes into the directional direct search with variable number sample path and investigates its effectiveness in solving stochastic optimization problems. We also explore the conditions on sample sizes at each iteration under which the convergence in probability can be guaranteed. Finally, a set of benchmark problems are numerically tested to show the effectiveness in different sampling schemes.

MS [00521] Recent advances on non-convex optimization in inverse problems, imaging and machine learning

room : A206

• [02446] Convergence rate analysis of a Dykstra-type projection algorithm
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaozhou Wang (The Hong Kong Polytechnic University)
    • Ting Kei Pong (The Hong Kong Polytechnic University)
  • Abstract : We extend the Dykstra’s projection algorithm to find projections onto the intersection of linear preimages of closed convex sets. The algorithm only makes use of projections onto the latter sets and operations by the linear maps and their adjoints in every iteration. Explicit convergence rate is derived when each set is $C^{1,\alpha}$-cone reducible for some $\alpha\in (0,1]$, under standard relative interior conditions. Concrete examples are constructed to illustrate the necessity of some of our assumptions.
• [04336] Critical points of the projection onto the set of low rank tensors
  • Format : Talk at Waseda University
  • Author(s) :
    • Shenglong Hu (Hangzhou Dianzi University)
  • Abstract : In 2009, SIAM von Neumann prize-winner Yousef Saad proposed the open problem on characterizing the convergence rate of the classical alternating polar decomposition method for low rank orthogonal tensor approximation problem. Actually, this problem was initiated by Gene Golub in 2001 for the rank one case, and received considerable study in the past twenty years. In 2015, concrete examples were given showing that the convergence rate may be sublinear, linear and superlinear. In this talk, we show that for a generic tensor, the algorithm converges linearly without any further assumption by studying the critical points of the projection onto the set of low rank tensors.
• [05256] Nonconvex Semi-algebraic Optimization: From Exact to Convergent Conic Program Relaxations
  • Format : Talk at Waseda University
  • Author(s) :
    • Jeya Jeyakumar (UNSW Sydney)
  • Abstract : Semi-algebraic optimization is the study of optimization problems where the feasible set is defined in terms of polynomial inequalities, called a semi-algebraic set. In addition to the usual tools of nonlinear optimization, such as convex analysis and linear algebra, powerful techniques of real algebraic geometry, such as representation theorems for polynomials, and conic programming methods, such as semi-definite programming and copositive programming, can be employed to study these problems. In this talk, I will describe the key results in this area, highlighting our recent work on the development of exact conic programming relaxations and convergent hierarchy of conic programming relaxations for classes of semi-algebraic optimization problems.

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

room : A207

• [03085] Gradient methods using Householder transformation with application to hypergraph partitioning
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Zhang ( Suqian University)
    • Jingya Chang (Guangdong University of Technology)
    • Zhili Ge (, Nanjing Normal University of Special Education)
    • Zhou Sheng (Anhui University of Technology)
  • Abstract : In this paper, we propose a constraint preserving algorithm for the smallest Z-eigenpair of the compact Laplacian tensor of an even-uniform hypergraph, where Householder transform is employed and a family of modified conjugate directions with sufficient descent is determined. Besides, we prove that there exists a positive step size in the new constraint preserving update scheme such that the Wolfe conditions hold. Based on these properties, we prove the convergence of the new algorithm. Furthermore, we apply our algorithm to the hypergraph partitioning and image segmentation, numerical results are reported to illustrate the efficiency of the proposed algorithm.
• [03102] Solving saddle point problems: a landscape of primal-dual algorithm with larger stepsizes
  • Format : Talk at Waseda University
  • Author(s) :
    • Fan Jiang (Nanjing University of Information Science and Technology)
    • Hongjin He (Ningbo University)
    • Zhiyuan Zhang (Xiamen University)
  • Abstract : We consider a class of saddle point problems frequently arising in the areas of image processing and machine learning. In this paper, we propose a simple primal-dual algorithm, which embeds a general proximal term induced with a positive definite matrix into one subproblem. It is remarkable that our algorithm enjoys larger stepsizes than many existing state-of-the-art primal-dual-like algorithms due to our relaxed convergence-guaranteeing condition. Moreover, our algorithm includes the well-known primal-dual hybrid gradient method as its special case, while it is also of possible benefit to deriving partially linearized primal-dual algorithms. Finally, we show that our algorithm is able to deal with multi-block separable saddle point problems. In particular, an application to a multi-block separable minimization problem with linear constraints yields a parallel algorithm. Some computational results sufficiently support the promising improvement brought by our relaxed requirement.
• [03200] Inexact variable metric proximal incremental aggregated gradient algorithm for nonconvex nonsmooth optimization problem
  • Author(s) :
    • zehui Jia (Nanjing University of Information Science and Technology)
    • junru Hou (Nanjing University of Information Science and Technology)
    • xingju Cai (Nanjing Normal University)
  • Abstract : This paper focuses on the problem that minimizing the sum of a nonconvex smooth function and a nonsmooth convex function, in which the smooth term is in the form of finite sum. In order to solve the problem efficiently, we introduce the idea of incremental aggregation and two different inexact criterions to the variable metric proximal gradient (VMPG) algorithms, and then propose the inexact variable metric proximal incremental aggregated gradient (iVMPIAG) algorithms, i.e., iVMPIAG-I, iVMPIAG-II. Under the Kurdyka-Łojasiewicz (KL) property, we show the global convergence of iVMPIAG-I and iVMPIAG -II. When the Łojasiewicz exponent is known, we can prove the convergence rate of iVMPIAG-I with respect to the objective function value and the convergence rate of iVMPIAG-II with respect to the iterative sequence. Note that, for the convergence analysis of iVMPIAG-I, a critical tool is introduced, i.e., the incremental aggregated forward-backward (FB) envelope, which is a continuously differential function and can cover the FB envelope as a special case. Based on this tool, we define a continuously differentiable surrogate function, which equals to the value of the objective function at the stationary point. Finally, we present the efficiency of the iVMPIAG method for large-scaled image restoration problem.
• [03253] A Restricted Dual PRSM for a Strengthened DNN Relaxation for QAP
  • Format : Talk at Waseda University
  • Author(s) :
    • Naomi Graham (University of British Columbia)
    • Hao Hu (Clemson University)
    • Jiyoung Im (University of Waterloo)
    • Xinxin Li (Jilin University)
    • Henry Wolkowicz (University of Waterloo)
  • Abstract : Splitting methods in optimization arise when one can divide an optimization problem into two or more simpler subproblems. They have proven particularly successful for relaxations of problems involving discrete variables. We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the particularly difficult, NP-hard quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. In particular, we show how to exploit redundant constraints in the subproblems. Our strengthened bounds exploit these new subproblems, as well as new dual multiplier estimates, to improve on the bounds and convergence results in the literature.

MS [01036] Progress in Mathematical Programming Methods and Applications

room : A208

• [02296] New MIP presolving techniques in the Cardinal Optimizer
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gerald Gamrath (COPT GmbH)
  • Abstract : Presolving is an essential component of modern MIP solvers. Besides model cleanup, it identifies structures in the problem and tightens the formulation before the branch-and-cut search starts. In this talk, we discuss common structures in real-world instances and show how a mathematical analysis of those structures resulted in new presolving reductions implemented in the Cardinal Optimizer (COPT). The impact of the new techniques is demonstrated in computational experiments.
• [03882] Realization of smart factories using MIP
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroki Ishikura (Kyushu University)
  • Abstract : Smart factories have become widely used for more efficient production activities recently. In collaboration with Rohto Pharmaceutical Co. (Rohto), we have conducted research to realize smart factories. In this talk, we will introduce mobility optimization related to automated warehouses. Rohto uses an automated warehouse to manage a large volume of various items. By optimizing the mobility of automated warehouses, production activities can be streamlined, and factory operations can be made more efficient.
• [02009] Benders' decomposition approach for the integrated long-haul and local VRP
  • Format : Talk at Waseda University
  • Author(s) :
    • Junko Hosoda (Hitachi, Ltd.)
    • Stephen J. Maher (Quantagonia GmbH)
    • Yuji Shinano (Zuse Institute Berlin )
    • Christoffer Villumsen (Hitachi, Ltd.)
  • Abstract : A supply chain management problem that integrates the determination of consolidation locations with the coordination of long-haul and local vehicle routing is a complicated problem. A Benders' decomposition approach is used to solve this problem. The delivery area and consolidation locations are computed in the master problem, and the long-haul and local vehicle routes are computed in the subproblems. The effectiveness of the decomposition is discussed in the presentation.
• [05535] An efficient solver for multi-objective onshore wind farm siting and network integration
  • Format : Talk at Waseda University
  • Author(s) :
    • Jaap Pedersen (Zuse Insitute Berlin)
    • Jann-Michael Weinand (Forschungszentrum Jülich GmbH, Institute of Energy and Climate Research)
    • Daniel Rehfeldt (Zuse Insitute Berlin)
  • Abstract : Existing planning approaches for onshore wind farm siting and network integration often do not meet minimum cost solutions or social and environmental considerations. In this talk, we present an approach for the multi-objective optimization of turbine locations and their network connection using the Quota Steiner tree problem. We design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. Although our case studies in selected regions of Germany show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, network integration must be simultaneously optimized in order to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision making and help optimize wind farms in large regions in the future.

MS [02445] Advances in Optimization II

room : A502

• [05543] Optimal Diagonal Preconditioning: Theory and Practice
  • Format : Talk at Waseda University
  • Author(s) :
    • Yinyu Ye (Stanford University)
  • Abstract : Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and to speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice, most lack guarantees on reductions in condition number, and the degree to which we can improve over existing heuristic preconditioners remains an important question. In this paper, we study the problem of optimal diagonal preconditioning, that achieves maximal reduction in the condition number of any full-rank matrix by scaling its rows and/or columns with positive numbers. We first reformulate the problem as a quasi-convex optimization problem and provide a simple algorithm based on bisection. Then we develop an interior point algorithm with $O(\log(1/\epsilon))$ iteration complexity. Next, we specialize to one-sided optimal diagonal preconditioning problems, and demonstrate that they can be formulated as standard dual SDP problems. We then develop efficient customized solvers for the SDP approach and study the empirical performance of our optimal diagonal preconditioning procedures through extensive experiments. Our findings suggest that optimal diagonal preconditioners can significantly improve upon existing heuristics-based diagonal preconditioners at reducing condition numbers, and our SDP approach can find such optimal preconditioners efficiently for large matrices. We also extend our SDP approach to compute optimal mixtures of base preconditioners, which further improves its scalability and applicability.
• [03259] Smart Initial Basis Selection for Linear Programs
  • Format : Talk at Waseda University
  • Author(s) :
    • Yong Zhang (Huawei Technologies Canada Co., Ltd)
  • Abstract : The simplex method, introduced by Dantzig more than half a century ago, is still to date one of the most efficient methods for solving large-scale linear programming (LP) problems. While the simplex method is known to have the finite termination property under mild assumptions, the number of iterations until optimality largely depends on the choice of initial basis. Existing strategies for selecting an advanced initial basis are mostly rule-based. These rules usually require extensive expert knowledge and empirical study to develop. Yet, many of them fail to exhibit consistent improvement, even for LP problems that arise in a single application scenario. In this paper, we propose a learning-based approach for initial basis selection. We employ graph neural networks as a building block and develop a model that attempts to capture the relationship between LP problems and their optimal bases. In addition, during the inference phase, we supplement the learning-based prediction with linear algebra tricks to ensure the validity of the generated initial basis. We demonstrate through extensive experiments with state-of-the-art simplex solvers that the proposed strategy can achieve substantial speedup and consistently outperforms existing rule-based methods. Furthermore, we extend the proposed approach to generating restricted master problems for column generation methods and present encouraging numerical results.
• [04683] Interior Point Methods are Not Worse Than Simplex
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Dadush (CWI)
    • Xavier Allamigeon (Inria, CMAP, CNRS, Ecole Polytechnique)
    • Bento Natura (Georgia Tech)
    • Georg Loho (University of Twente)
    • Laszlo Vegh (London School of Economics)
  • Abstract : We develop a path-following IPM whose number of iterations is at most $O(n^{1.5} \log n)$ times the number of segments of any piecewise linear curve traversing the wide neighborhood of the central path. Our IPM matches the number of iterations of any path following IPM up to this polynomial factor and admits an $O(2^n n^{1.5} \log n)$ upper bound. The latter result complements an exponential lower bound of Allamigeon et al (SIAGA 18) for IPMs.
• [03175] Analysis of Algorithms on Growing Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuji Kijima (Shiga University)
  • Abstract : Real networks are often dynamic. Nevertheless, very few is known about the theoretical analysis of algorithms on dynamic networks. This talk is concerned with some analysis techniques for dynamics on networks with a moderately increasing number of vertices regarding the growing speed.

MS [00437] Climate Risks: From Modelling to Applications

room : A510

• [01677] Optimal ecological transition path of a credit portfolio distribution, based on Multidate Monge-Kantorovich formulation
  • Format : Talk at Waseda University
  • Author(s) :
    • Emmanuel Gobet (Ecole Polytechnique)
    • Clara Lage (Ecole polytechnique and Univ. Lyon1)
  • Abstract : Accounting for climate transition risks is one of the most important challenges in the transition to a low-carbon economy. Banks are encouraged to align their investment portfolios to CO2 trajectories fixed by international agreements, showing the necessity of a quantitative methodology to implement it. We propose a mathematical formulation for this problem and a multistage optimization criterion for a transition between the current bank portfolio and a target one. The optimization problem combines the Monge-Kantorovich formulation of optimal transport, for which the cost is defined according to the financial context, and a credit risk measure. We show that the problem is well-posed, and can be embedded into a saddle-point problem for which Primal-Dual algorithms can be used. We design a numerical scheme that is able to solve the problem in available time, with nice scalability properties according to the number of decision times; its numerical convergence is analysed. Last we test the model using real financial data, illustrating that the optimal portfolio alignment may differ from the naive interpolation between the initial portfolio and the target.
• [01674] Optimal Dynamic Contracts and Environmental Pollution
  • Format : Talk at Waseda University
  • Author(s) :
    • Jerome Detemple (Boston University)
    • Hao Xing (Boston University)
  • Abstract : We examine optimal dynamic contracts when production generates harmful pollution. We derive optimal consumption, effort and environmental investment of the agent and solve for the optimal contract offered by the principal. We then solve for a stationary pollution equilibrium in an economy with a continuum of polluting firms. The optimal contract rewards for financial performance and self-pollution mitigation. We study the impact of model parameters on contractual structure, managerial decisions, and the stationary pollution distribution.
• [05305] Optimal Impact Portfolios with General Dependence and Marginals
  • Format : Talk at Waseda University
  • Author(s) :
    • Andrew Lo (MIT)
    • Lan Wu (Peking University)
    • Ruixun Zhang (Peking University)
    • Chaoyi Zhao (Peking University)
  • Abstract : Impact investing typically involves ranking and selecting assets based on a non-financial impact factor, such as the environmental, social, and governance (ESG) score and the prospect of developing a disease-curing drug. We develop a framework for constructing optimal impact portfolios and quantifying their financial performances. Under general bivariate distributions of the impact factor and residual returns from a multi-factor asset-pricing model, the construction and performance of optimal impact portfolios depend critically on the dependence structure (copula) between the two. We derive a general representation theorem to characterize the distribution of induced order statistics (returns of impact-ranked assets), which allows us to explicitly and efficiently compute the optimal portfolio weights under any copula. The optimal weights depend on the tail characteristics of the copula, as well as whether the marginal distribution of residual returns is skewed or heavy-tailed. Our framework requires the estimation of only a constant number of parameters as the number of assets grows, providing a more regularized and robust approach compared to traditional Markowitz portfolios.
• [01585] Using NLP to Analyze Corporate Communication
  • Format : Online Talk on Zoom
  • Author(s) :
    • Markus Leippold (University of Zurich)
  • Abstract : Corporate climate disclosures are considered an essential prerequisite to managing climate-related financial risks. At the same time, current disclosures are imprecise, inaccurate, and greenwashing-prone. We introduce a deep learning approach to enable comprehensive climate disclosure analyses by fine-tuning the climateBert model. From 14,584 annual reports of the MSCI World index firms from 2010 to 2020, we extract the amount of cheap talk, defined as the share of precise versus imprecise climate commitments. We then test various hypotheses by linking three different climate initiatives, namely the Task Force on Climate-Related Financial Disclosure, the Science-Based Targets Initiative, and the Climate Action 100+, to the economic channels of signaling, credibility, and active engagement. In particular, we ask whether these initiatives decrease cheap talk by disciplining companies in how they define and disclose actionable climate commitments in their annual reports.

contributed talk: CT179

room : A511

[00894] ODE models relating irrigation to kidney bean yield

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A511
• Type : Industrial Contributed Talk
• Abstract : Chippewa Valley Bean, located in Wisconsin, USA, is the world’s largest processor of dark red kidney beans and works with farmers over several states. Current trends in farming are pressuring producers to generate higher yields with fewer resources, particularly water resources. This project describes our work creating ODE models that describe the relationship between irrigation inputs, soil parameters, and kidney bean yields that CVB can use to advise farmers for productive yet sustainable practices.
• Classification : 92-10
• Format : Talk at Waseda University
• Author(s) :
  • Tyler Skorczewski (University of Wisconsin Stout)
  • Keith Wojciechowski (University of Wisconsin Stout)

[01103] Mechanoelectric effects in cardiac function

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A511
• Type : Contributed Talk
• Abstract : To date the role of the different mechanoelectric feedback $($MEF$)$ mechanisms is not clear in the cardiac function. Using a multiscale $($from cellular to organ level$)$ 3D-0D closed loop fluid-electromechanical framework implemented in the Cardiac Arrhythmia Research Package $($CARP$)$ software, we perform computer simulations to explore the effect of two MEF mechanisms in healthy cardiac function and under the Left Bundle Branch Block pathology.
• Classification : 92-10, 92Bxx
• Format : Talk at Waseda University
• Author(s) :
  • Argyrios Petras (RICAM-Johann Radon Institute for Computational and Applied Mathematics)
  • Matthias AF Gsell (Medical University of Graz)
  • Christoph M Augustin (Medical University of Graz)
  • Jairo J Rodriguez Padilla (Centre Inria d’Université Côte d’Azur)
  • Alexander Jung (Medical University of Graz)
  • Marina Strocchi (King's College London)
  • Frits Prinzen (Maastricht University)
  • Steven Niederer (King's College London)
  • Gernot Plank (Medical University of Graz)
  • Edward J Vigmond (Liryc, Electrophysiology and Heart Modeling Institute)

[02222] Unfolding operator in Heisenberg group and its applications

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A511
• Type : Contributed Talk
• Abstract : After the development of multi-scale convergence in the 1990s, the periodic unfolding approach is one of the most effective methods for studying multi-scale problems like homogenization in the Euclidean setup. This talk will discuss the periodic unfolding operator in the Heisenberg group. Analogous to the Euclidean unfolding operator, we prove all the required properties. We apply the unfolding operator to homogenize an optimal control problem subject to a state equation having high contrast diffusive coefficients.
• Classification : 35Rxx
• Format : Talk at Waseda University
• Author(s) :
  • Abu Sufian (TIFR- Centre for Applicable Mathematics)
  • Akambadath Keerthiyil Nandakumaran (Indian Institute of Science, Bangalore, India)

[00859] A mathematical model of immunotherapy: CD19 relapses in B leukemia

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A511
• Type : Contributed Talk
• Abstract : B-cell Acute Lymphoblastic Leukemia (B-ALL) is the most common type of pediatric leukaemia. For relapsing patients, a treatment possibility is chimeric antigenic receptor (CAR)-T cells, which recognize target cells with the antigen CD19, expressed in B-ALL. We show a mathematical model based on partial differential equations and focus on how CAR-T cell therapy can lead to positive or negative CD19 relapses. The analysis presented represents real-life scenarios, where optimal treatment can be studied.
• Classification : 92-10, 37N25, 35Q92
• Format : Online Talk on Zoom
• Author(s) :
  • Salvador Chulián (Department of Mathematics, University of Cádiz)
  • Álvaro Martínez-Rubio (Department of Mathematics, University of Cádiz)
  • Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
  • María Rosa (Department of Mathematics,)

[00191] Two-Phase Modelling of Subcutaneous Injection of Drugs

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A511
• Type : Contributed Talk
• Abstract : Various drugs and vaccines are administered through the subcutaneous pathway. The adipose cells within the subcutaneous layer impart structural anisotropy. We address the mechanical response of the adipose tissue in terms of the computed stress fields to understand the pain a patient realizes. Tissue anisotropy instigates the interstitial fluid to generate one or more eddies. Eddies help a low viscous injected drug homogenize when the skin pinching height is high at the injection apply area.
• Classification : 92C35, 92B05, 92C50, 35B20, 92-10, Mathematical Modeling of Problems on Biological Phenomena
• Format : Online Talk on Zoom
• Author(s) :
  • Bibaswan Dey (Department of Mathematics, University of North Bengal)
  • Abdush Salam Pramanik (Department of Mathematics, University of North Bengal)
  • Timir Karmakar (Department of Mathematics, National Institute of Technology Meghalaya, India)
  • Kalyan Saha (Department of Mathematics, University of North Bengal)

MS [00924] Calibration and Validation of Mathematical Models for Biological Systems

room : A512

• [02727] The role of bacterial chemotaxis in microbial symbiosis
  • Format : Online Talk on Zoom
  • Author(s) :
    • Douglas Brumley (The University of Melbourne)
  • Abstract : Bacterial motility, symbioses, and marine nutrient cycling unfold at the scale of individual microbes, and are inherently dynamic. In this talk, I will outline how iteratively combining video-microscopy, image processing and mathematical modelling can resolve dynamic microscale processes which underpin the ecology of microbes. I will also demonstrate how the highly-resolved processes at the scale of individual cells can be connected to bulk measurements at the population-level through calibrated mathematical models.
• [04509] Multi-scale modelling of the uterus and the 12 Labours project
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alys Rachel Clark (University of Auckland)
    • Shawn Means (University of Auckland)
    • Claire Miller (University of Auckland)
    • Mathias Roesler (University of Auckland)
    • Amy Garrett (University of Auckland)
    • Leo Cheng (University of Auckland)
  • Abstract : Uterine contractions contribute to fertility, menstruation, and delivery of babies, and the uterus has unique properties compared to other smooth muscle organs (including extensive stretch in pregnancy without contraction). Here, I present cell-to-tissue models of the uterus which form part of the 12 Labours project. This project takes a data-driven and reproducible approach to modelling physiological systems, which aims to integrate models into clinical workflows and provide feedback to wearable devices that monitor the uterus.
• [02752] Bayesian discovery of mechanics and signaling during collective cell migration
  • Format : Online Talk on Zoom
  • Author(s) :
    • Simon Martina Perez (Oxford)
    • Ruth E. Baker (University of Oxford)
  • Abstract : Collective cell migration results from a complex interplay of cell-cell interactions and whole-tissue mechanics. Experimental data enables Bayesian inference to identify the role of mechanics and cell-cell interactions. While mathematical models can be identified with sufficiently detailed data, the relationship between observation noise and uncertainty in the learned models remains unexplored. We explore how to combine data sets to quantify uncertainty, and draw mechanistic conclusions about the underlying biophysical process in morphogenesis and cancer invasion.
• [05213] 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: CT180

room : A601

[00697] Vicsek-Kuramoto system in collective dynamics and their macroscopic equations

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A601
• Type : Contributed Talk
• Abstract : In this project we investigate a 'Vicsek-style' model, where noisy self-propelled particles align orientation and angular velocity through interaction with their neighbours. This work has been inspired by the model introduced by Chen, C. et al. Nature (2017) to describe the behaviour of dense colony of bacteria, which self-organize into robust collective oscillatory motion. The main focus is to investigate how individual-level behaviours influence the emergence of macroscopic patterns.
• Classification : 92B05, 82C31
• Format : Talk at Waseda University
• Author(s) :
  • Carmela Moschella (University of Vienna )

[00725] Role of CXCL12 in regulation of T cell invasion

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A601
• Type : Contributed Talk
• Abstract : In this study, we investigate the mutual interactions between the CD8+ T cells and the CXCL12 that prevent T cell invasion by developing mathematical models that involve taxis-reaction-diffusion. We apply the mathematical model to a Boyden invasion assay used in the experiments to demonstrate that the over-expressed CXCL12 can prevent T cell infiltration into tumor. Moreover, we consider tumor-immune dynamics by a hybrid approach and investigate the fundamental mechanism of cytokine shield.
• Classification : 92B05, 92C17, 92C45, 92C50
• Format : Talk at Waseda University
• Author(s) :
  • Junho Lee (Konkuk University)
  • Yangjin Kim (Konkuk University)
  • Chaeyoung Lee (Korea University)

[00480] Mathematics, the Mind and Alzheimer's disease: Systematical progression on brain graphs

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A601
• Type : Contributed Talk
• Abstract : Neurodegenerative diseases, Alzheimer's disease (AD) in particular, present a clear challenge to modern medicine due to brain delicate in vivo environment and limited insight from the human whole nervous system. Mathematical network models of dementia, such as AD, offer a path forward that can be deployed using the multitude of anatomical brain-graph data from real human patients. The dynamical processes of the model support front-like propagation on networks, where an initial localized perturbation grows and systematically invades all nodes in the network. The main question is to understand its overall dynamics. For instance, if a process starts at a seed location, how long will it take to appear at other locations, and then develop through a full-scale invasion, leading to dementia for the brain? The arrival-time problem, that consists in determining the time it takes for a quantity of interest to reach a certain level at each node, greatly depends on the coupling dynamics between nodes. In this talk, I address a question to extract estimates for the dynamics motivated by the study of toxic protein propagation in neurodegenerative diseases: if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? My research demonstrates that different estimates can give their important insights to understand the dynamics and, in particular, analytical methods to estimate and compute the arrival times are extremely powerful and can capture essential features in AD.
• Classification : 92B05, General biology and biomathematics
• Format : Talk at Waseda University
• Author(s) :
  • Prama Setia Putra (Mathematical Institute, University of Oxford)
  • Prama Setia Putra (Mathematical Institute, University of Oxford)
  • Alain Goriely (Mathematical Institute, University of Oxford)

[00713] Mathematical Modeling of Lymphatic Filariasis-Buruli ulcer co-infection

• Session Time & Room : 3D (Aug.23, 15:30-17:10) @A601
• Type : Industrial Contributed Talk
• Abstract : A mathematical model for Lymphatic Filariasis -Buruli ulcer co-infection is explored to provide a theoretical analysis of the disease's dynamics. The disease free equilibrium is proved to be locally asymptotically stable; the model was found to be showing transcritical and backward bifurcation, time dependent controls are incorporated to obtain necessary conditions for optimal control of the diseases. Numerical simulation results suggest best strategy in controlling the diseases is using all the controls at the same time.
• Classification : 92B05, 37G10
• Author(s) :
  • Helen Olaronke Edogbanya (Federal University Lokoja, Kogi State)
  • Helen Olaronke Edogbanya (Federal University Lokoja)
  • Zamurat Ayobami Adegboye (Institute of Mathematical and Physcical Sciences, IMSP-UAC, Dangbo)

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

room : A617

• [04054] Folding transformations for q-Painleve equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mikhail Bershtein (Kavli IPMU, Landau Institute and Skoltech)
  • Abstract : Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces. Based on joint work with A. Shchechkin [arXiv:2110.15320]
• [04739] Laguerre (q-Laguerre) Weight Recurrence and Geometric Theory of Painlevé equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jie HU (Jinzhong University)
  • Abstract : Sakai's geometric theory of Painlevé equations is used to identify difference or differential equations with corresponding Painlevé equations. In this talk we will consider two classes of examples of recurrence coefficients of semi-classical orthogonal polynomials: Laguerre weight and the deformed $q$-Laguerre weight. We will gives the identification procedure on how to deduce related solutions of canonical discrete Painlevé equations from coefficients. Meanwhile, we also give the explicit birational function of variables achieving that reduction.

MS [00523] Implicit methods for hyperbolic problems and their extensions and applications

room : A618

• [01684] Implicit and semi-implicit well-balanced finite volume methods for general 1d systems of balance laws
  • Format : Talk at Waseda University
  • Author(s) :
    • Carlos Parés (University of Málaga)
    • Irene Gómez-Bueno (University of Málaga)
    • Manuel Jesús Castro (University of Málaga)
    • Sebastiano Boscarino (University of Catania)
    • Giovanni Russo (University of Catania)
  • Abstract : In this work a general family of implicit and semi-implicit well-balanced finite volume numerical methods for nonlinear hyperbolic systems of balance laws will be presented. These methods are obtained by extending a general strategy introduced by some of the authors to design high-order well-balanced explicit methods. This strategy, based on the computation of local steady states, will be combined with implicit RK or IMEX solvers in time. Different applications will be shown.
• [01665] SHALLOW-WATER MODEL: IMPLICIT FULLY WELL-BALANCED METHODS IN THE LAGRANGE-PROJECTION FRAMEWORK
  • Format : Talk at Waseda University
  • Author(s) :
    • Celia Caballero Cárdenas (Universidad de Málaga)
    • Manuel Jesús Castro Díaz (Universidad de Málaga)
    • Tomás Morales de Luna (Universidad de Malaga)
    • María de la Luz Muñoz-Ruiz (Universidad de Málaga)
    • Christophe Chalons (Université Versailles Saint-Quentin-en-Yvelines)
  • Abstract : We propose fully well-balanced Lagrange-Projection finite volume schemes for the shallow-water model. This two-step approach separates acoustic and transport phenomena, allowing for implicit-explicit and large time step schemes with CFL restriction based on slower transport waves.
• [01664] Hyperbolic systems with stiff relaxation: asymptotic-preserving and well-balanced schemes
  • Format : Talk at Waseda University
  • Author(s) :
    • Irene Gómez-Bueno (University of Málaga)
    • Sebastiano Boscarino (University of Catania)
    • Manuel Jesús Castro Díaz (University of Málaga)
    • Carlos Parés (University of Málaga)
    • Giovanni Russo (University of Catania)
  • Abstract : We consider hyperbolic systems depending on a stiff parameter $\varepsilon$: when $\varepsilon$ is small, numerical schemes may produce spurious results. Implicit-explicit Runge–Kutta schemes have been widely used for their time evolution. Our goal is to design high-order asymptotic-preserving methods which are at the same time well-balanced for the asymptotic limit system.
• [01673] MIRK methods and applications in RRMHD and neutrino transport equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Isabel Cordero-Carrión (University of Valencia)
    • Samuel Santos-Pérez (University of Valencia)
    • Martin Obergaulinger (University of Valencia)
  • Abstract : We present the Minimally-Implicit Runge-Kutta $($MIRK$)$ methods for the numerical resolution of hyperbolic equations with stiff source terms. We apply these schemes to the resistive relativistic magnetohydrodynamic $($RRMHD$)$ and the M1 neutrino transport equations. Previous approaches rely on Implicit-Explicit Runge-Kutta schemes. The MIRK methods are able to deal with stiff terms producing stable numerical evolutions and their computational cost is similar to the standard explicit methods.