MS and CT list / Aug. 24, 17:40-19:20.

MS [00283] Recent developments in mathematical imaging and modeling in magnetic particle imaging

room : G301

• [05030] Implicit neural representations for super-resolution in magnetic particle imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Franziska Schrank (RWTH Aachen University)
    • Volkmar Schulz (RWTH Aachen University)
  • Abstract : Magnetic particle imaging is a medical imaging technology based on the non-linear magnetization of magnetic nanoparticles. For image reconstruction, the received signal from the excitation of the nanoparticles is converted into the particles’ concentration distribution via the system matrix, which is commonly measured in a calibration scan. We propose to parametrize this system matrix using implicit neural representations, enabling to super-resolve it or to reduce the matrix’ acquisition time by processing an undersampled matrix.
• [05026] Reducing displacement artifacts in multi-patch magnetic particle imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Marija Boberg (University Medical Center Hamburg-Eppendorf)
    • Tobias Knopp (University Medical Center Hamburg-Eppendorf)
    • Martin Möddel (University Medical Center Hamburg-Eppendorf)
  • Abstract : Magnetic particle imaging determines the spatial distribution of superparamagnetic nanoparticles within a small field-of-view. Multi-patch approaches can expand the field-of-view at the cost of artifacts caused by field imperfections. Time-consuming calibration scans can reduce these displacement artifacts by measuring system matrices for each patch. In this contribution, only one central system matrix is used, which is warped according to the underlying magnetic fields, resulting in low calibration times and higher image quality.
• [05158] Deconvolution of direct Chebyshev reconstructions in MPI with neural networks
  • Format : Online Talk on Zoom
  • Author(s) :
    • Mathias Eulers (Universität zu Lübeck)
    • Marco Maass (Universität zu Lübeck)
    • Christine Droigk (Universität zu Lübeck)
    • Alfred Mertins (Universität zu Lübeck)
  • Abstract : Recently, a direct reconstruction method using Chebyshev polynomials for multi-dimensional MPI has been proposed. The reconstruction method weights and sums the frequency components of the voltage signals with tensor products Chebyshev polynomials, followed by a deconvolution step to perform a very fast image reconstruction. Unfortunately, the method is degraded by image artifacts. In this presentation, the method itself will be explained and a data-driven deconvolution model is presented which improves the image quality.

MS [01202] Analysis and modelling of human flows

room : G302

• [03707] Recent Public Data Related with Urban Vehicle Traffic Simulation
  • Format : Talk at Waseda University
  • Author(s) :
    • Takeshi Uchitane (Aichi Institute of Technology)
  • Abstract : Various kinds of social data are available in Japan in order to realize and evaluate vehicle simulations within an urban-scale digital map. In such the social data, open data is becoming more and more common. In our discussion, two case studies of vehicle simulations and related open data are explained. Because the target locations are different between Kobe city and Aichi prefecture, different kinds of open data are required to make appropriate origin-destination pairs.
• [04718] Urban scale pedestrian simulation and analysis around Kobe City center
  • Format : Talk at Waseda University
  • Author(s) :
    • Daigo Umemoto (RIKEN R-CCS)
    • Maiko Kikuchi (NTT DOCOMO, INC)
    • Ayako Terui (NTT DOCOMO, INC)
    • Koutarou Abe (NTT DOCOMO, INC)
    • Ryuushi Shimizu (NTT DOCOMO, INC)
    • Katsuki Hirashige (NTT DOCOMO, INC)
    • Nobuyasu Ito (RIKEN R-CCS)
    • Itsuki Noda (Hokudai)
  • Abstract : We constructed a pedestrian evacuation simulator for Kobe City center, using population based on cell phone demographics provided by NTT DoCoMo, Inc., pedestrian simulator CrowdWalk, and Open Street Map with manually added signals. The evacuation time was initially simulated as 25,685 seconds. Decentralizing evacuation routes reduced it to 17,780 seconds. The signal removal further reduced it to 9,550 seconds. The signal removal alone gave 12,475 seconds: interestingly, overall reduction was about 50% in both cases.
• [02895] Potential field of human flow extracted by Hodge-Kodaira decomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Takaaki Aoki (Shiga university, japan)
    • Shota Fujishima (Hitotsubashi University)
    • Naoya Fujiwara (Tohoku University)
  • Abstract : People are moving daily from one location to another for commuting, shopping, entertainment, schools, etc. Human movements provide vital information for unfolding the actual shapes of cities. Here, we show the potential of human flows using the orthogonal decomposition of the combinatorial Hodge theory for the origin-destination matrix. The potential landscape visualizes an intuitive perspective of the urban structure behind the massive movements and helps us examine the complex spatial structures in contemporary metropolitan areas.
• [03549] Towards science of multi-scale human flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Naoya Fujiwara (Tohoku University)
  • Abstract : In this talk, we present our recent findings in data analysis and mathematical models of human mobility, with an emphasis on characteristics of different temporal and spatial scales. The examples include data analysis of evacuation behaviors for severe disasters, change in the mobility patterns after COVID-19 pandemic, and mathematical models for long-term migration patterns. These results would provide hints to obtain a general framework for studying and understanding human mobility.

MS [01029] Extremal Combinatorics and Probabilistic Combinatorics

room : G304

• [04621] Spanning trees with bounded number of leaves in $K_{1,p}$-free graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kenta Ozeki (Yokohama National University)
  • Abstract : Matthews and Sumner proved that a connected $K_{1,3}$-free graph contains a Hamiltonian path if the graph satisfies a certain minimum degree condition. Extending this result, it has been widely studied about the existence of a spanning $k$-ended tree in $K_{1,3}$-free or $K_{1,4}$-free graphs with $k \geq 2$, and in $K_{1,5}$-free graphs with $k=4,6$, where a $k$-ended tree is a tree with at most $k$ leaves. With this situation in mind, in this talk, we pose a conjecture on a spanning $k$-ended tree in $K_{1,p}$-free graphs, and show two partial answers to the conjecture: One solves the case $p=5$ completely, and the other proves the conjecture asymptotically for all $p \geq 6$. This is a joint work with Masao Tsugaki (Tokyo University of Science) and partially with Masahiro Kimura (Yokohama National University).
• [04636] Hadwiger’s conjecture for some graphs with independence number two
  • Format : Talk at Waseda University
  • Author(s) :
    • Guiying YAN (Academy of Mathematics and Systems Science’Chinese Academy of Sciences)
    • Qiang Zhou (Academy of Mathematics and Systems Science’Chinese Academy of Sciences)
  • Abstract : Hadwiger’s conjecture is difficult to prove even for graphs with independence number two. Recently, Daniel Carter found the conjecture is true for H-free graphs if H is some particular graphs of 6, 7, 8 or 9 vertices with the help of computers. In this talk, we will introduce this conjecture is true if H is one of four special graphs with 6 or 7 vertices mathematically.
• [05371] On Connectivities of Edge-Colored Graphs
  • Format : Talk at Waseda University
  • Author(s) :
    • Kiyoshi Yoshimoto (Nihon University)
  • Abstract : In this talk, we consider two kind of color-connectivities of edge-colored graphs which are generalizing strong connectivity of directed graphs and also the relation is given. Furthremore we show structures of edge-colored complete graphs using the color-connectivities.

contributed talk: CT007

room : G305

[00791] FunFact: Tensor Decomposition, Your Way

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : FunFact simplifies the design of matrix and tensor factorization algorithms. It features a powerful programming interface that augments the NumPy API with Einstein notations for writing concise tensor expressions. Given an arbitrary forward calculation scheme, the package will solve the inverse problem using stochastic gradient descent, automatic differentiation, and multi-replica vectorization. It is GPU- and parallelization-ready thanks to modern numerical linear algebra backends such as JAX/TensorFlow and PyTorch. We demonstrate a variety of use cases.
• Classification : 15-04, 65F55
• Format : Talk at Waseda University
• Author(s) :
  • Daan Camps (Lawrence Berkeley National Laboratory)
  • Yu-Hang Tang (NVIDIA)

[02001] GPU batched sparse solver for XGC fusion plasma collision operator

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : Batched linear solvers solve many small related but independent problems. They are beneficial for GPUs, which require substantial amounts of work to operate efficiently. The XGC gyrokinetic particle-in-cell code for modeling magnetically confined fusion plasma devices employs a LAPACK CPU solver for the collision operator. We describe how Ginkgo's batched solver can be integrated into the collision operator and accelerate the simulation process. We present comparisons for the solve times on A100 GPUs with CPUs.
• Classification : 15-04, 35-04, 76-10
• Format : Talk at Waseda University
• Author(s) :
  • Paul Lin (Lawrence Berkeley National Laboratory)
  • Aditya Kashi (Oak Ridge National Laboratory)
  • Pratik Nayak (Karlsruhe Institute of Technology)
  • Dhruva Kulkarni (Lawrence Berkeley National Laboratory)
  • Aaron Scheinberg (Jubilee Development)
  • Hartwig Anzt (University of Tennessee)

[02429] Differential geometry with extreme eigenvalues in the positive semidefinite cone

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : Geometric data in convex cones appear in a wide range of applications. Of particular interest is the space of symmetric positive definite (SPD) matrices and a variety of associated geometries that have been successfully exploited in medical imaging, neuroscience, and machine learning. In this talk, I will explore the Hilbert and Thompson geometries associated with SPD matrices and show that they offer a natural route to statistics based on extreme eigenvalues with promising computational properties.
• Classification : 15B48, 53C22, 53B20, 53B50, 53C80
• Format : Talk at Waseda University
• Author(s) :
  • Nathaël Da Costa (Nanyang Technological University)
  • Cyrus Mostajeran (Nanyang Technological University)
  • Rodolphe Sepulchre (University of Cambridge)
  • Graham van Goffrier (University College London)

[02414] Quadratic Lie algebras algorithms applied over oscillator algebras

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : Quadratic Lie algebras appear in Mathematics and Physics. Main examples are oscillator and generalized oscillator which are related to space-time models and determine some Lie groups with Lorentz metrics or Lorentzian cones. This variety of algebras with bilinear invariant forms can be built using double extensions from a metric vector space via derivations. In this talk we will see an overview of how all these concepts can be algorithmically obtained. Available in our Github repository.
• Classification : 17B05, 15A63, 17B40, 17B81
• Format : Talk at Waseda University
• Author(s) :
  • Jorge Roldán-López (Universidad de La Rioja)
  • Pilar Benito (Universidad de La Rioja)

[02379] Quasigroups with inverse properties and information protection

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G305
• Type : Contributed Talk
• Abstract : In connection with the computerization of almost all spheres of life, the need for information protection, and therefore for the development of new encryption methods, has grown rapidly. To quickly decipher the information, it is appropriate to use invertible functions having the property of some invertibility of elements, i.e. quasigroups with inverse properties. We investigate varieties of these quasigroups and propose methods for their constructions and applications.
• Classification : 20N05, 08B15, 14L30
• Format : Online Talk on Zoom
• Author(s) :
  • Alla Lutsenko (Vasyl` Stus Donetsk National University)

MS [00484] Matrix Analysis and Applications

room : G306

• [01263] Geometric inequalities for contraction matrices
  • Format : Talk at Waseda University
  • Author(s) :
    • Tin-Yau Tam (University of Nevada, Reno)
  • Abstract : Given two $n\times n$ contraction matrices $W$ and $Z$, i.e., $I-WW^*\ge 0$ and $I-ZZ^*\ge 0$, L.K. Hua's inequalities (1955) assert that $$ \det (I-WW^*)\det (I-ZZ^*) \le |\det (I - WZ^*)|^2\le \det (I+WW^*)\det (I+ZZ^*). $$ In this talk we will present geometry behind Hua's inequalities in the context of elliptical and hyperbolic geometry.
• [01307] The generalized quaternion matrix equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Xin Liu (Macau University of Science and Technology)
    • Cui E Yu (Macau University of Science and Technology)
  • Abstract : We consider the matrix equation $AXB+CX^{\star}D=E$ over the generalized quaternions, where $X^\star$ is one of $X$, $X^\ast$, the $\eta$-conjugate or the $\eta$-conjugate transpose of $X$ with $\eta \in \{i, j, k\}$. We define two new real representations of a generalized quaternion matrix, then we derive the solvability conditions for the mentioned matrix equation. Moreover, we also discuss the existence of $X=\pm X^{\star}$ solutions to the generalized quaternion matrix equation $AXB+CXD=E$.

contributed talk: CT018

room : G401

[00326] Estimating the lowest-order eigenvalue in Sturm-Liouville boundary value problem

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : We investigate a special case of the Sturm–Liouville boundary value problem $($BVP$)$ and examine the BVP in the Schrödinger form. By considering a reciprocal quadratic form of the corresponding invariant function, we estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions. Some combinations of parameter values yield poor spectrum estimates. Other combinations are satisfactorily although the values tend to overestimate results from numerical computations.
• Classification : 34B05, 34B24, 34L15
• Format : Talk at Waseda University
• Author(s) :
  • Natanael Karjanto (Sungkyunkwan University)

[00566] Numerical study of Draw resonance in Fibre spinning using multi-mode constitutive model

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : We study the instability called Draw resonance that occurs in the industrial process of manufacture of thin polymer fibres, called fibre spinning using a multi-mode viscoelastic constitutive equation. We do a linear stability analysis of the equations by carrying out numerical simulations for a varying number of modes in the constitutive equation. We compare our results with those got by using single-mode viscoelastic models and discuss our findings.
• Classification : 34B09, 34B60, 65N25, Polymer flows in industrial processes
• Format : Talk at Waseda University
• Author(s) :
  • Renu Dhadwal (Center for Mathematical Modelling, FLAME University )

[01345] Novel Lyapunov-type Inequality Involving Riesz Fractional Derivative

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : In this work, we obtained necessary condition for the existence of solutions to a fractional boundary value problem involving Riesz fractional derivative, which is defined as a two-sided fractional operator. The approach proposed in this work is based on the reduction of the problem considered to a singular integral equation, then we derive the Lyapunov-type inequalities in a weighted Lebesgue space.
• Classification : 34B10, 34B16, 34B18
• Format : Talk at Waseda University
• Author(s) :
  • Rabah Khaldi (Badji Mokhtar Annaba University)
  • Assia Guezane Laakoud (Badji Mokhtar Annaba University)

[00034] Relative heat flux in nonlocal reaction-diffusion equations and thermoelectric efficiency

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Thermoelectric generators directly convert a temperature difference into electrical energy. To study their efficiency, we consider second-order integro-differential equations describing the steady-state temperature distribution inside thermoelectric generators when the Seebeck coefficient of the thermoelectric material is temperature-independent but the electrical resistivity and thermal conductivity are temperature-dependent. In this talk, we show that the temperature solution is unique and the relative boundary Fourier heat flux can be explicitly written. Therefore, the efficiency has an explicit formula.
• Classification : 34B15, 35A02, 35J25, 34B10, 35K59
• Format : Talk at Waseda University
• Author(s) :
  • Jaywan Chung (Korea Electrotechnology Research Institute)
  • Byungki Ryu (Korea Electrotechnology Research Institute)
  • Hyowon Seo (Kunsan National University)

[01392] Solving a fractional pantograph delay equation

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : We study a pantograph delay equation involving a fractional derivative. Our approach relies basically on the reduction of the considered problem to an equivalent integral equation, then by using fixed point theorems, we prove the existence results. We also discussed the fractional Ambartsumian differential equation, that describes in the classical case the absorption of light by the interstellar matter.
• Classification : 34B05, 26A33, 34A30
• Format : Online Talk on Zoom
• Author(s) :
  • Assia Guezane Laakoud (Badji Mokhtar Annaba University)
  • Rabah Khaldi (Badji Mokhtar Annaba University)

MS [01050] Delay equations in mathematical biology

room : G402

• [04514] An approach to model the bird migration
  • Format : Talk at Waseda University
  • Author(s) :
    • Rongsong Liu (University of Wyoming)
    • Stephen Gourley (Surrey University)
  • Abstract : An approach to modelling bird migration is proposed, in which there is a region where birds do not move but spend time breeding. Birds leave this breeding region and enter a migration flyway. Mathematically, the flyway is a curve parametrised by arc-length. Per-capita mortality along the flyway is both position and age-dependent.
• [05022] Infectious disease dynamics with delayed control on the reproduction number
  • Format : Talk at Waseda University
  • Author(s) :
    • Ferenc A Bartha (Bolyai Institute, University of Szeged)
  • Abstract : We attempt to mitigate an epidemic governed by a compartmental transmission model by introducing an adaptive control based on the effective reproduction number $\mathcal{R}_t$. The control aims to keep $\mathcal{R}_t$ within the prescribed interval $\mathcal{I}$ containing 1 by triggering or lifting non-pharmaceutical interventions affecting the transmission rate. The inherent delay in measuring the control output, i.e. $\mathcal{R}_t$, results in involved dynamics. We analyze the effects of both the choice of $\mathcal{I}$ and of the delay.
• [04371] A delayed epidemic model for behavior change
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshikazu Kuniya (Kobe University)
  • Abstract : In the period of COVID-19, the on/off of strict interventions such as lockdown caused oscillations of reported infected population in many countries. In this study, we formulate a delayed epidemic model with psychological effect that people change their contact frequency according to the recent information on the reported cases. We perform the Hopf bifurcation analysis, and show that time delay and behavior change play an important role in the occurrence of the recurrent epidemic waves.
• [04511] Evolution of maturation delay
  • Format : Talk at Waseda University
  • Author(s) :
    • Gergely Röst (University of Szeged, Hungary)
  • Abstract : We propose a new mathematical model to address the evolution of maturation period, building on the well-studied Nicholson's blowfly equation, formulated as a system of delay differential equations with two delays. We identify the optimal maturation delay, depending on the quality and suitability of the habitat, which is both a globally evolutionary stable and convergence stable strategy. Mathematically interesting questions raised by the invasibility of oscillatory insect populations. Joint work with Xingfu Zou.

contributed talk: CT028

room : G404

[01348] Existence and nonexistence of solutions of thin-film equations with variable exponent spaces

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G404
• Type : Contributed Talk
• Abstract : This works aims at presenting a thin film problem involving variable exponent sources in a bounded domain. Which deals with the existence and nonexistence of solutions under subcritical initial energy. Also determine the global existence of solutions, exponential decay and finite time blow-up of solutions under specific conditions for the proposed model.
• Classification : 35B44, 35D30, 35K70
• Format : Talk at Waseda University
• Author(s) :
  • GNANAVEL Soundararajan (Central University of Kerala)
  • GNANAVEL SOUNDARARAJAN (Central University of Kerala)

[01797] Random dynamics of 2D stochastic Naiver-Stokes equations on the whole space

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G404
• Type : Contributed Talk
• Abstract : In this talk, we consider the 2D stochastic Navier-Stokes equations (SNSE) driven by a linear multiplicative white noise of It\^o type on the whole space. Firstly, we will discuss the existence of a unique bi-spatial $(\mathbb{L}^2(\mathbb{R}^2),\mathbb{H}^1(\mathbb{R}^2))$-pullback random attractor for non-autonomous SNSE with initial data in $\mathbb{L}^2(\mathbb{R}^2)$. Finally, we will discuss the existence of an invariant measure for 2D autonomous SNSE. Also, the uniqueness of invariant measures for $\boldsymbol{f}=\mathbf{0}$ will be addressed.
• Classification : 35B41, 35Q35, 37L55, 37N10, 35R60
• Format : Talk at Waseda University
• Author(s) :
  • Kush Kinra (Indian Institute of Technology Roorkee, Roorkee)
  • Manil T. Mohan (Indian Institute of Technology Roorkee, Roorkee)

[02575] Propagation of Nonlinear Waves in Non-genuinely Nonlinear Characteristic Field

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G404
• Type : Contributed Talk
• Abstract : We consider a quasilinear hyperbolic system of partial differential equations to discuss the evolution of weakly nonlinear waves, where the evolution equation includes quadratic, cubic, and quartic nonlinear terms and the flux function admits two inflection points. We present an example from gasdynamics with analytical and numerical results demonstrating a wide range of wave phenomena, and study the interaction of expansion and compression waves evolving from a rectangular pulse.
• Classification : 35B40, 35B65, 35C20, 35L65, 35L67
• Format : Online Talk on Zoom
• Author(s) :
  • Triveni Prasad Shukla (National Institute of Technology Warangal)

MS [00554] Pattern dynamics appearing in mathematical biology

room : G406

• [01234] Turing's instability by equal diffusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Hirokazu Ninomiya (Meiji University)
  • Abstract : In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of some kinetic system is destabilized by diffusion. In the case of two-component reaction-diffusion systems, however, the diffusion coefficients should be different. This talk presents an example of a two-component kinetic system with a asymptotically stable equilibrium, while the corresponding reaction-diffusion system has a family of unstable stationary solutions that is arbitrarily close to the homogeneous stationary solution.
• [01275] Reaction-diffusion fronts in funnel-shaped domains
  • Format : Talk at Waseda University
  • Author(s) :
    • Mingmin Zhang (Universite Toulouse III - Paul Sabatier)
  • Abstract : We study large-time dynamics of entire solutions to bistable equations in funnel-shaped domains emanating from a planar front in the straight part and moving into the conical part. We prove a dichotomy between blocking and spreading, and show that any spreading solution is a transition front whose level sets have roughly expanding spherical shapes at large times. We provide sufficient conditions on geometry of the domains, under which the solution is blocked or spreads completely.
• [01442] Traveling wave solution in a macroscopic traffic model
  • Format : Talk at Waseda University
  • Author(s) :
    • Kota Ikeda (Meiji UniversityMeiji University)
  • Abstract : Various subjects in traffic dynamics have long posed a challenge. Theoretical approaches have revealed the localized and extended forms of congestion with the propagation velocity of stop-and-go waves in models. In 2001, Lee et al. derived a macroscopic traffic model from an OV model and numerically showed that a traveling pulse appears under a relatively high density of cars. We prove the existence of such a traveling pulse rigorously via a phase plane method.
• [03160] Bistable pulsating fronts in showling oscillating environments
  • Format : Talk at Waseda University
  • Author(s) :
    • Weiwei Ding (South China Normal University)
  • Abstract : In this talk, I will present some progress on reaction-diffusion fronts in spatially periodic bistable media. The results include: existence of pulsating fronts with large periods, existence of and an explicit formula for the limit of front speeds as the spatial period goes to infinity, convergence of pulsating front profiles to a family of front profiles associated with spatially homogeneous equations. This talk is based on joint work with Francois Hamel and Xing Liang.

contributed talk: CT029

room : G501

[01390] Neural Operator for Multidisciplinary Engineering Design

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
• Type : Contributed Talk
• Abstract : Deep learning surrogate models have shown promise in solving PDEs, which enable many-query computations in science and engineering. In this talk, I will first introduce a geometry-aware Fourier neural operator (Geo-FNO) to solve PDEs on arbitrary geometries, inspired by adaptive mesh motion and spectral methods. Furthermore, we study the cost-accuracy trade-off of different deep learning-based surrogate models, following traditional numerical error analysis. Finally, we demonstrate our approach on challenging engineering design problems.
• Classification : 35C99, 65M99, 65Z05, 68T07
• Format : Talk at Waseda University
• Author(s) :
  • Daniel Zhengyu Huang (Caltech)
  • Andrew M. Stuart (Caltech)
  • Elizabeth Qian ( Georgia Tech)
  • Maarten de Hoop (Rice University)

[02689] Double Dirac Cone in Subwavelength Bandstructure

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
• Type : Contributed Talk
• Abstract : In this talk we wish to rigorously justify the existence of the double Dirac point for the super-honeycomb lattice in the subwavelength regime. First, we will give a rigorous characterization of the symmetry conditions. Then, representing the solution by periodic layer potentials when the frequency is nonzero, we can asymptotically solve the band structure by the periodic capacitance matrix. We also study how the perturbation to the inclusions affect the band structure numerically.
• Classification : 35C20
• Format : Talk at Waseda University
• Author(s) :
  • Borui Miao (Tsinghua University)
  • Yi Zhu (Yau Mathematical Sciences Center)

[01224] Collision-induced amplitude dynamics of nD solitons in a perturbed saturable nonlinear medium

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
• Type : Contributed Talk
• Abstract : We study the amplitude dynamics of two-dimensional (2D) fast solitons in an interaction under a framework of coupled (2+1)D nonlinear Schrodinger equations with a saturable nonlinearity and weak perturbation. We derive a theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is mainly based on the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. The theoretical results are validated by numerical simulations with the coupled perturbed nonlinear Schrodinger equations with saturable nonlinearity.
• Classification : 35C08, 35Q51, 35Q60, 78A10, 78M10
• Format : Online Talk on Zoom
• Author(s) :
  • Quan Minh Nguyen (International University, Vietnam National University Ho Chi Minh City)
  • Toan Thanh Huynh (Department of Mathematics, University of Medicine and Pharmacy at Ho Chi Minh City, Vietnam)

MS [01070] PDE Based Image Processing

room : G502

• [02870] A Framework for Motion Estimation with Physics-Based Constraints in Image Sequences
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hirak Doshi (Doctoral Research Scholar)
    • Uday Kiran Nori (Associate Professor)
  • Abstract : Motion estimation using variational models has been a central topic in mathematical image processing for many years. The Horn and Schunck model's variational approach to optical flow motion estimation is a seminal work that has been studied in-depth to develop different variational models for motion estimation. However, the Horn and Schunck model's constancy assumption cannot reflect the reality of actual motion, as deformation effects of fluid, illumination variations, perspective changes, poor contrast, etc., directly affect the important motion parameters. Therefore, physics-dependent motion estimation algorithms have been extensively investigated in the literature. In this paper, we propose a generic framework that captures physics-based constraints for motion estimation as perceived at the smallest intensity level (pixel) of an image sequence. These constraints are introduced as non-conservative terms that capture the loss of particles at the pixel-level, in the minimizing energy functional. We demonstrate our framework with two physics-based constraints, the continuity constraint for fluid motion and the harmonic constraint for capturing rotation in the images. Furthermore, we theoretically justify the effectiveness of our model through the techniques of Augmented Lagrangian and maximal monotone operators. We establish the mathematical well-posedness of the associated PDE in the Hilbert space setting. For the linear case, we perform a decoupling of the associated PDE into diffusion equations on the curl and divergence of the flow field through a diagonalization with the Cauchy-Riemann operator. This decoupling process suggests that our approach preserves the spatial characteristics of the divergence and the vorticities of the flow field. We adapt the first-order primal-dual Chambolle-Pock algorithm to obtain the minimization of our variational problem. We demonstrate the robustness of our approach through velocity plots and use the Average Angular Error (AAE) and End-Point Error (EPE) as performance metrics. We test our algorithm on several relevant datasets and show good results. In particular, for the Middlebury dataset, we show that our algorithm outperforms some of the state-of-the-art Horn and Schunk based flow models. Moreover, for the fluid motion estimation case, a primal-dual implementation of our two-phase refinement model has a faster convergence rate of $O(1/N)$ compared to the $O(1/\sqrt{N})$ convergence rate of a direct primal-dual implementation of the Liu-Shen continuity-based model, where $N$ is the number of iterations. Although we do not have a theoretical proof for this observed efficiency, we provide substantial empirical evidence.
• [03393] On the convergence analysis of DNN for vorticity stream function formulation and application
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rajendra Kumar (Student)
    • Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
    • Ming-Chih Lai (National Yang Ming Chiao Tung University, Taiwan)
  • Abstract : The physics-informed neural network is a completely mesh-free method for partial differential equations. In this paper, We introduce a Physics-informed neural network for the two dimensions Navier-stokes equation in the vorticity-stream function form with boundary conditions. We estimate the error of the physics-informed neural network for vorticity stream function formulation and theoretically establish the convergence of the computational procedure. In Deep neural network representation imposing the boundary condition is one of the main issues. We successfully incorporate periodic boundary conditions in the vorticity stream function formulation which is known for its difficulty in training the model. We have successfully applied PINNS on applications such as the Double shear layer and Taylor vortex problem

MS [00306] Mathematical approaches to nonlinear phenomena with singularities

room : G601

• [03661] Geometric convergence in regularization of inverse problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jose A. Iglesias (University of Twente)
    • Gwenael Mercier (University of Vienna)
    • Kristian Bredies (University of Graz)
    • Otmar Scherzer (University of Vienna)
  • Abstract : We present some results bridging classical regularization theory of ill-posed inverse problems and regularity properties of almost-minimizers of the corresponding regularization energies. In the regime of vanishing noise and regularization parameter, we obtain results of convergence in Hausdorff distance of level sets of minimizers (which can be interpreted as objects to be recovered in an imaging context) and uniform $L^\infty$ bounds. These hold both for the classical total variation, and for some fractional energies.
• [04617] Numerical algorithms for optimization problems of grain boundary motions
  • Format : Talk at Waseda University
  • Author(s) :
    • Shodai Kubota (National Institute of Technology, Miyakonojo College)
    • Ken Shirakawa (Chiba University)
    • Makoto Okumura (Konan University)
  • Abstract : We consider a class of optimal control problems for state problems of one-dimensional systems. Each state problem is associated with the phase-field model of grain boundary motion, proposed by Ryo Kobayashi et al. In this regard, each optimal control problem is prescribed as a minimization problem of a cost. Under suitable assumptions, the convergence of numerical algorithms for optimization problems governed by state systems will be reported as the main theorem of this talk.
• [04370] Temperature optimization problems governed by pseudo-parabolic model of grain boundary motion
  • Format : Talk at Waseda University
  • Author(s) :
    • Ken Shirakawa (Chiba University)
    • Daiki Mizuno (Chiba University)
  • Abstract : In this talk, we consider a class of optimal temperature control problems governed by pseudo-parabolic PDE systems. The PDE systems are based on the KWC-model of grain boundary motion (cf. Kobayashi et al, Physica D, 140, 2000). Under suitable assumptions, we will focus on the Main Theorems, concerned with: the mathematical solvability and parameter dependence of pseudo-parabolic PDE systems and optimal controls; and the first-order necessary optimality conditions for the optimal control problems.
• [04841] On well-posedness of 1-harmonic map flows
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lorenzo Giacomelli (Sapienza University of Rome)
    • Michal Lasica (Institute of Mathematics of the Polish Academy of Sciences)
    • Salvador Moll (Universitat de ValenciaUniversity of Valencia)
  • Abstract : We look at the formal gradient flow of the total variation of a manifold-valued unknown function. After introducing the problem and the state-of-the-art, I will discuss recent results with M. Lasica and S. Moll concerning local/global-in-time well-posedness of Lipschitz solutions and global existence of BV-solutions for one-dimensional domains. Uniqueness, gradient flow structures, and open questions will also be discussed.

MS [00135] Nonlinear PDEs and related diffusion phenomena

room : G602

• [03392] Boundary Regularity of Local and Nonlocal Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Ki-Ahm Lee (Seoul National University)
  • Abstract : In this talk, we are going to discuss boundary regularities of various degenerate local equations and nonlocal equations. Diffusion rates deform undefined geometry related to diffusion and the corresponding distance function makes an important role in the theory of regularity. And then we will also discuss the possible applications.
• [04308] Well-posedness with large data for a weighted porous medium equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Troy Petitt (Politecnico di Milano)
    • Matteo Muratori (Politecnico di Milano (Italy))
  • Abstract : The large data problem for the porous medium equation is to determine the largest class of initial data for which local well-posedness is guaranteed for the Cauchy problem. We review the classical results by Widder for the heat equation $u_t=\Delta u$. The corresponding problem for the porous medium equation $u_t=\Delta u^m$ for $m>1$ was solved in the 1980s. We extend these results for weighted equations $\rho(x)u_t=\Delta u^m$ for $\rho(x)≅|x|^{-\gamma}$ for $\gamma\in(0,2)$.
• [04047] Results on the Stokes eigenvalue problem under Navier boundary conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Alessio Falocchi (Politecnico di Milano)
    • Filippo Gazzola (Politecnico di Milano)
  • Abstract : We study the Stokes eigenvalue problem under Navier boundary conditions in 2D or 3D bounded domains with connected boundary of class $C^1$. Differently from the Dirichlet boundary conditions, zero may be the least eigenvalue. We fully characterize the domains where this happens. We then consider the general version of the problem in any space dimension with $n\geq2$, characterizing the kernel of the strain tensor for solenoidal vector fields with homogeneous normal trace.
• [03585] Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Megumi Sano (Hiroshima University)
  • Abstract : Inspired by Ni's result about the H\'enon equation with nonlinear term which has the strong polynomial growth beyond the Sobolev critical growth, we consider the exponential growth beyond the polynomial growth in a maximization problem. Also we discuss the optimality and the attainability of our maximization problem. Our inequalities are regarded as subcritical versions of the Trudinger-Moser inequalities in the critical Sobolev spaces. This is a joint work with Masahiro Ikeda(RIKEN/Keio Univ.) and Koichi Taniguchi(Tohoku Univ.).

MS [00413] Numerical Methods for Dispersive PDEs and Applications

room : G605

• [05499] Scattering and uniform in time error estimates for splitting method in NLS
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rémi Carles (CNRS & Univ Rennes)
    • Chunmei Su (Tsinghua University)
  • Abstract : We consider the nonlinear Schrödinger equation with a defocusing nonlinearity which is mass-(super)critical and energy-subcritical. We prove uniform in time error estimates for the Lie–Trotter time splitting discretization. This uniformity in time is obtained thanks to a vectorfield which provides time decay estimates for the exact and numerical solutions. This vectorfield is classical in scattering theory and requires several technical modifications compared to previous error estimates for splitting methods.
• [05587] Resonances as a computational tool
  • Format : Online Talk on Zoom
  • Author(s) :
    • Katharina Schratz (Sorbonne University)
  • Abstract : A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full equation into a series of simpler subproblems (e.g., splitting methods). In many situations these classical schemes allow a precise and efficient approximation. This, however, drastically changes whenever non-smooth phenomena enter the scene such as for problems at low regularity and high oscillations. Classical schemes fail to capture the oscillatory nature of the solution, and this may lead to severe instabilities and loss of convergence. In this talk I present a new class of resonance based schemes. The key idea in the construction of the new schemes is to tackle and deeply embed the underlying nonlinear  structure of resonances into the numerical discretization. As in the continuous case, these terms are central to structure preservation and offer the new schemes strong geometric properties at low regularity.
• [01752] Error estimates of numerical methods for the nonlinear Schr\"{o}dinger equation with low regularity potential and nonlinearity
  • Format : Talk at Waseda University
  • Author(s) :
    • Weizhu Bao (National University of Singapore)
    • Chushan Wang (National University of Singapore)
  • Abstract : We prove optimal error bounds of time-splitting methods and the exponential wave integrator for the nonlinear Schr\"{o}dinger equation (\text{(NLSE)}) with low regularity potential and nonlinearity, including purely bounded potential and locally Lipschitz nonlinearity. Arising from different physical applications, low regularity potential and nonlinearity are introduced into the NLSE such as the discontinuous potential or non-integer power nonlinearity, which make the error estimates of classical numerical methods very subtle and challenging.

contributed talk: CT048

room : G701

[01524] Radon measure solutions to compressible Euler equations and applications

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
• Type : Contributed Talk
• Abstract : We proposed a definition of Radon measure solutions to the compressible Euler equations with general constitutive relations. With this definition, we proved the Newton-Busemann law for stationary hypersonic flow passing bodies, constructed delta shock solutions to the Riemann problems of the rectilinear barotropic Euler equations, justified the interpretation of delta shocks as free pistons. This shows the possibility of treating solid-fluid interaction problems by simpler Cauchy problems with solutions in the class of Radon measures.
• Classification : 35R06, 35Q31, 35D99
• Format : Talk at Waseda University
• Author(s) :
  • Hairong Yuan (East China Normal University )
  • Aifang Qu (Shanghai Normal University )

[00614] Sparse spectral methods for fractional PDEs

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
• Type : Contributed Talk
• Abstract : Fractional partial differential equations model nonlocal processes such as wave absorption in the brain, long-range geophysical effects, and Lévy flights. We introduce a spectral method for the fractional Laplacian in one dimension that induces sparse linear systems. We only deal with the coefficients of the expansion and thus time-stepping is fast. We consider a number of examples including the fractional heat and fractional wave propagation equations.
• Classification : 35R11, 65N35, 65M70, 65R10, Numerical Analysis, Nonlocal PDEs
• Format : Talk at Waseda University
• Author(s) :
  • Ioannis P. A. Papadopoulos (Imperial College London)

[01601] Estimation of the Elementary Chirp Model Parameters

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
• Type : Contributed Talk
• Abstract : We propose some estimation techniques to estimate the elementary chirp model parameters. We derive asymptotic properties of least squares estimators (LSEs) and approximate least squares estimators (ALSEs) for the one-component elementary chirp model. We propose sequential LSEs and sequential ALSEs to estimate the multiple-component elementary chirp model parameters and prove that they have the same  theoretical properties as the LSEs. We illustrate the performance of the proposed sequential algorithm on a bat data.
• Classification : 62H12, 62F12
• Format : Talk at Waseda University
• Author(s) :
  • Anjali Mittal (Indian Institute of Technology Kanpur)
  • Rhythm Grover (Indian Institute of Technology Guwahati)
  • Debasis Kundu (Indian Institute of Technology Kanpur)
  • Amit Mitra (Indian Institute of Technology Kanpur)

[02037] Two-stage Bivariate Distribution Estimation based on B-spline approach

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
• Type : Contributed Talk
• Abstract : In this work, we propose a new nonparametric model to estimate distribution functions and densities with bounded support. In addition, we study the asymptotic properties of our estimator such as asymptotic bias, variance and asymptotic normality. The method is illustrated by simulation study and an application to a real data set.
• Classification : 62H10, 62H12, 62H05, 65C20, 60E05
• Format : Online Talk on Zoom
• Author(s) :
  • Nezha Mohaoui (Moulay Ismail University )

[00803] Epilepsy MEG network TERGM analysis

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G701
• Type : Contributed Talk
• Abstract : The brain has a complex structure where different neurons are connected. To study brain activity and disorders, it is important to analyze the functional connectivity of the brain through network analysis. Because of high temporal and spatial resolution, MEG$\text{(magnetoencephalography)}$ can provide useful information for brain network analysis. We analyzed functional connectivity using static/temporal network statistics, MCCA$\text{(multiset canonical correlation analysis)}$, and TERGM$\text{(temporal exponential random graph model)}$ with epilepsy MEG data.
• Classification : 62H22, 62P10
• Format : Talk at Waseda University
• Author(s) :
  • Haeji Lee (Duksung women's university)
  • Jaehee Kim (Duksung women's university)

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

room : G702

• [04052] Wave propagation and stabilization in the Boussinesq–Burgers system
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhi-An Wang (The Hong Kong Polytechnic University )
  • Abstract : This talk will discuss the existence and stability of traveling wave solutions of the Boussinesq– Burgers system describing the propagation of bores. Assuming the fluid is weakly dispersive, we establish the existence of three different wave profiles by the geometric singular perturbation theory alongside phase plane analysis. We further employ the method of weighted energy estimates to prove the nonlinear asymptotic stability of the traveling wave solutions against small perturbations. The technique of taking antiderivative is utilized to integrate perturbation functions because of the conservative structure of the Boussinesq–Burgers system. Using a change of variable to deal with the dispersion term, we perform numerical simulations for the Boussinesq–Burgers system to showcase the generation and propagation of various wave profiles in both weak and strong dispersions. The numerical simulations not only confirm our analytical results, but also illustrate that the Boussinesq– Burgers system can generate numerous propagating wave profiles depending on the profiles of initial data and the intensity of fluid dispersion, where in particular the propagation of bores can be generated from the system in the case of strong dispersion.
• [03930] Hypersonic similarity for steady potential flows over a two dimensional wedge
  • Format : Talk at Waseda University
  • Author(s) :
    • jie kuang (Academy of Mathematics and Systems Science)
    • wei xiang (city university of hong kong)
    • Yongqian Zhang (Fudan University)
  • Abstract : We will talk about our recent results on the hypersonic similarity for the potential flow over a two-dimensional wedge. The convergence is obtained in BV\cap L^1 spaces. Progress on related problems will be presented too.
• [05017] Stability theory for the linear symmetric hyperbolic system with general relaxation
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshihiro Ueda (Kobe University)
  • Abstract : In this talk, we study the dissipative structure for the linear symmetric hyperbolic system with general relaxation. If the relaxation matrix of the system has symmetric properties, Shizuta and Kawashima(1985) introduced the suitable stability condition, and Umeda, Kawashima and Shizuta(1984) analyzed the dissipative structure. On the other hand, Ueda, Duan and Kawashima(2012,2018) focused on the system with non-symmetric relaxation and got partial results. Furthermore, they argued the new dissipative structure called the regularity-loss type. In this situation, this talk aims to extend the stability theory introduced by Shizuta and Kawashima(1985) and Umeda, Kawashima and Shizuta(1984) to our general system. Furthermore, we will consider the optimality of the dissipative structure. If we have time, I would like to discuss some physical models for its application and new dissipative structures.
• [00454] Stability of Riemann shock wave via the method of a-contraction of shifts
  • Format : Talk at Waseda University
  • Author(s) :
    • Moon-Jin Kang (KAIST)
  • Abstract : I will present the so-called "a-contraction with shifts” method. This method is quite useful in studying the stability of Navier-Stokes and Euler flows perturbed from Riemann solution containing a shock wave. First, this method is energy based, and so allows us to seamlessly handle the composite wave of a viscous shock and rarefaction for its long-time behavior. On the other hand, since the method can handle large perturbations of a viscous shock, and so provides the uniform stability of the shock w.r.t. the strength of viscosity, we can prove that the Riemann solution composed of a shock is stable and unique in the class of inviscid limits of solutions to the associated Navier-Stokes system.

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

room : G703

• [03906] Geometric structures in incompressible fluids: vortex and magnetic reconnection
  • Format : Talk at Waseda University
  • Author(s) :
    • Gennaro Ciampa (University of Milan)
  • Abstract : The goal of this talk is to provide examples of smooth solutions of the Navier-Stokes equations such that the topology of the vortex lines changes during the evolution without any loss of regularity. This phenomenon is known as vortex reconnection. We will also discuss the applications to Magnetohydrodynamics: we will construct smooth solutions of the MHD equations such that the topology of the magnetic field lines changes during evolution, providing analytical examples of magnetic reconnection.
• [04219] On maximally mixed equilibria of two-dimensional perfect fluid
  • Format : Talk at Waseda University
  • Author(s) :
    • Michele Dolce (EPFL)
  • Abstract : The motion of a 2D perfect fluid can be described as an area-preserving rearrangement of the initial vorticity that conserves the kinetic energy. In the infinite time limit, vorticity mixing can occur and is conjectured to be a generic phenomenon. We offer a new perspective on the ``maximally mixed states" introduced by Shnirelman by proving that many of them can be obtained as minimizers of a variational problem and we discuss some of their properties.
• [03417] Quasi-periodic invariant structures in incompressible fluids
  • Format : Talk at Waseda University
  • Author(s) :
    • Luca Franzoi (New York University Abu Dhabi)
    • Nader Masmoudi (New York University Abu Dhabi)
    • RICCARDO MONTALTO (University of Milan)
  • Abstract : In this talk, I present a recent result about the existence of nontrivial steady flows near the Couette flow in the channel $\mathbb{R}\times [-1,1]$ that are quasi-periodic in space and solve the incompressible Euler equations. First, I recall the result of Lin $\&$ Zeng and their construction of periodic flows. Then, I state the main result for space quasi-periodic flows. Finally, I show what are the main issues in our construction and how to solve them.
• [03123] Flows with lower dimensional dissipations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luigi De Rosa (University of Basel)
  • Abstract : In my talk I will describe how to put in a rigorous framework the study of turbulent solutions, i.e. rough fluid flows, whose energy cascade accumulates on lower dimensional sets. This naturally connects to intermittency phenomena which have been playing a major role in the current mathematical research.

MS [02493] Advanced Modelling of Complex Nonlinear Systems

room : G704

• [03289] A Minimal Set of Koopman Eigenfunctions -- Analysis and Numerics
  • Author(s) :
    • Ido Cohen (Technion - Israel Institute of Technology)
  • Abstract : In this talk, we present the most concise linear representation of nonlinear systems based on the theory of Koopman Operator. Here, we define the “basis” of Koopman eigenfunctions from which the whole spectrum of the Koopman operator can be generated and the dynamic is accurately reconstructed. Numerically, the curse of dimensionality in samples vanishes since the inherent geometry constraints. Thus, the suggested method yields the most reduced representation from samples justifying the term \emph{minimal set}.
• [03525] Acoustic Streaming
  • Author(s) :
    • James Friend (University of California San Diego)
  • Abstract : Acoustic streaming is a nonlinear effect from an acoustic wave that can generate rapid fluid flows. We show a new, mathematically challenging approach to its analysis that overcomes past limitations, recasting traditional separation of scales in one variable to separation of spatiotemporal scales, with careful treatment of partial derivatives and the definition of compatibility equations to ensure closure. We provide closed-form solutions to transient acoustic streaming for the first time.
• [04735] The Underlying Correlated Dynamics in Neural Training
  • Author(s) :
    • Guy Gilboa (Technion)
    • Rotem Turjeman (Technion)
    • Tom Berkov (Technion)
    • Ido Cohen (Technion)
  • Abstract : We propose a model of neural-net training which dramatically reduces the dimensionality. Our algorithm, Correlation Mode Decomposition (CMD), yields groups of highly correlated parameters. We achieve a remarkable dimensionality reduction with this approach, where a network of 11M parameters like ResNet-18 can be modeled well using just a few modes. Retraining the network using our model induces a regularization which yields better generalization capacity on the test set.
• [05114] A Nonstochastic Control Approach to Optimization
  • Author(s) :
    • Xinyi Chen (Princeton University and Google AI)
    • Elad Hazan (Princeton University and Google AI)
  • Abstract : Selecting the best hyperparameters, such as the learning rate and momentum, is an important but nonconvex problem. We propose an online nonstochastic control methodology for optimization that can circumvent this nonconvexity and obtain certain global guarantees. The problem of learning the best optimizer can be framed as a feedback control problem over the choice of optimizers. Our method guarantees that we can compete with the best optimizer in hindsight from a class of methods on a given sequence of problems.

MS [00969] Eigenvalue Problems in Electronic Structure Calculations

room : G709

• [04226] Grassmann Extrapolation of Density Matrices for Born–Oppenheimer Molecular Dynamics
  • Format : Online Talk on Zoom
  • Author(s) :
    • Benjamin Stamm (University of Stuttgart)
  • Abstract : Born–Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. We show how converged densities from previous DFT-calculations in the trajectory can be used to extrapolate a new guess for the SCF-iterations. We apply the method to real-life, multiscale, polarizable QM/MM BOMD simulations, showing that sizeable performance gains can be achieved. This is joint-work with É. Polack, G. Dusson and F. Lipparini.
• [04929] Applications of Atomic Cluster Expansion in Electronic Structure Calculations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Liwei Zhang (University of British Columbia)
  • Abstract : Nonlinear eigenvalue problems are quite typical in the field of electronic structure calculations. For decades, people tended to solve them by the so-called self-consistent field iterations method, which suffers from both convergence and numerical efficiency. In this talk, we will introduce a generalized Atomic Cluster Expansion (ACE) framework, which provides a complete and symmetry-preserving basis for approximating equivariant properties, to give rise to a way to skip the self-consistent procedure. We will also cover some potential applications of ACE in the context of post-DFT electronic structure calculation models.
• [04280] Numerical Analysis of the Operator Modification Approach for the Calculation of Band Diagrams of Crystalline Materials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Eric Cancès (CERMICS, École des Ponts and Inria Paris)
    • Muhammad Hassan (Laboratoire Jacques-Louis Lions, Sorbonne Université)
    • Laurent Vidal (CERMICS, École des Ponts and Inria Paris)
  • Abstract : In solid-state physics, electronic properties of crystalline materials are often described by the spectrum of periodic Schrödinger operators. Due to Bloch’s theorem, the numerical computation of quantities of interest involves computing integrals over the Brillouin zone of energy bands, which are piecewise smooth, periodic functions obtained by solving a parametrized elliptic eigenvalue problem. Classic discretization strategies for resolving these eigenvalue problems produce approximate energy bands that are either non-periodic or discontinuous, both of which cause difficulties when employing numerical quadrature. We present here an alternative discretization strategy based on an ad hoc operator modification approach. We derive a priori error estimates for the resulting energy bands and we show that these bands are periodic and can be made arbitrarily smooth (away from band crossings) by adjusting suitable parameters in the operator modification approach. We also present numerical experiments involving a toy model in 1D, graphene in 2D, and silicon in 3D to validate our theoretical results and showcase the efficiency of the operator modification approach.

MS [01272] Interface motion and related topics

room : G710

• [04426] Qualitative and numerical aspects of dynamics of diffusion and transport mechanisms on evolving curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Miroslav Kolar (Czech Technical University in Prague)
  • Abstract : In this talk we discuss the model of diffusion and transport acting on evolving curves. The model is coupled with the geometrical evolution equation for moving interfaces in form $$ \text{normal velocity} = \text{curvature} + \text{force}.$$ This model is being developed within the context of study of the vortex dynamics. The technique of incorporation an artificial tangential velocity for the stabilisation of numerical calculations is discussed and qualitative and quantitative computational results in 2D and 3D are shown.
• [02845] Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization settings
  • Format : Talk at Waseda University
  • Author(s) :
    • Julius Fergy Tiongson Rabago (Kanazawa University)
    • Hirofumi Notsu (Kanazawa University)
  • Abstract : A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow is proposed. Using the shape derivative of the cost associated with the new cost functional, a Sobolev-gradient based descent method is employed to solve the shape optimization problem. For validation and evaluation of the method, numerical experiments are carried out both in two and three dimensions which are compared with the ones obtained via the classical Dirichlet-data tracking approach.
• [03222] Structure-preserving numerical methods for gradient flows of planar closed curves
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoya Kemmochi (Nagoya University)
    • Yuto Miyatake (Osaka University)
    • Koya Sakakibara (Okayama University of Science)
  • Abstract : In this talk, we consider numerical approximation of constrained gradient flows of planar closed curves. We will develop structure-preserving methods for these equations that preserve both the dissipation and the constraints. To preserve the energy structures, we introduce the discrete version of gradients according to the discrete gradient method and determine the Lagrange multipliers appropriately. Some numerical examples are presented to verify the efficiency of the proposed schemes.
• [02751] Motion of Space Curves by Binormal and Normal Curvature
  • Format : Talk at Waseda University
  • Author(s) :
    • Michal BENEŠ (Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague)
    • Miroslav KOLÁŘ (Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague)
    • Daniel ŠEVČOVIČ (Faculty of Mathematics, Physics and Computer Science, Comenius University in Bratislava)
  • Abstract : We discuss the motion of closed non-intersecting space curves by curvature in binormal and normal directions with application in vortex dynamics. We formulate the general motion law in space by binormal and normal curvature and mention its analytical properties. The finite-volume scheme allows to solve the motion numerically with stabilization by the tangential velocity redistributing discretization nodes. We demonstrate behavior of the solution on several computational studies combining normal and binormal velocity and mutual interactions.

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

room : G801

• [03353] Double-Zero-Index metamaterials
  • Format : Talk at Waseda University
  • Author(s) :
    • Ying Wu (KAUST)
    • Changqing Xu (KAUST)
    • Keqiang Lyu (KAUST)
    • Guancong Ma (Hong Kong Baptist University)
    • Yun Lai (Nanjing University)
  • Abstract : Wave propagating in a medium with two constitutive parameters vanishing (double-zero index media) does not accumulate any phase retardation. Such a medium is not mathematically interesting but also bears unusual functionalities, such as wave front engineering, cloaking of objects and wave tunnelling. I will report our progresses on realizing double-zero index materials in two and three dimensions for electromagnetic and acoustic waves and discuss their special characteristics.
• [04938] Rigidity and Elasticity of Kirigami and Origami Metamaterials
  • Format : Talk at Waseda University
  • Author(s) :
    • Ian Tobasco (University of Illinois Chicago)
  • Abstract : Kirigami metamaterials combine elasticity and geometry to create unusual bulk deformations. We derive a partial differential equation (PDE) for periodic kirigami, along with a strain-gradient like homogenized energy. Minimizing this energy amongst PDE solutions predicts the kirigami’s deformation, as we demonstrate via experiments and simulations. Time permitting, we present analogous results for origami. A key step in our analysis is a rigidity inequality showing that the metamaterial’s deformation is approximated by local mechanism motions.
• [03863] The macroscopic behavior of the Kagome lattice metamaterial
  • Format : Talk at Waseda University
  • Author(s) :
    • Xuenan Li (New York University)
  • Abstract : Mechanism-based metamaterials are synthetic materials that exhibit microscale buckling in response to mechanical deformation. These artificial materials are like elastic composites, but more degenerate, since they can deform with zero elastic energy. We call such deformations with zero elastic energy mechanisms. My research focuses mainly on a rich example, the Kagome lattice metamaterial. This particular material has a huge variety of mechanisms, which might seem incompatible with having a meaningful macroscopic energy at first sight. In this talk, I will discuss the large-scale behavior of the kagome lattice metamaterial as a nonlinear homogenization problem and present our analysis of the well-defined macroscopic energy on this highly degenerate metamaterial. Our macroscopic theory reveals that compressive conformal maps achieve zero effective energy. I will also discuss the adequacy of our macroscopic theory with various numerical experiments. The theory is joint work with Robert Kohn, and the numerical results are joint work with Katia Bertoldi and Bolei Deng.
• [04196] Rayleigh waves in 2D extremal materials
  • Format : Online Talk on Zoom
  • Author(s) :
    • Gengkai Hu (School of Aerospace Engineering, Beijing Institute of Technology)
    • Yu Wei (School of Aerospace Engineering, Beijing Institute of Technology)
  • Abstract : Rayleigh waves are guaranteed in Cauchy materials with positive definite elasticity tensors. However it's proved that 2D extremal materials with Rank-deficient elasticity tensors cannot support Rayleigh waves, they can appear if the second gradient effect is considered. Microstructural models corresponding to the examined continuum models of Cauchy and second gradient elasticity are constructed, both continuum and discrete models agree very well in terms of the velocity and ellipticity for the predicted Rayleigh waves.

contributed talk: CT056

room : G802

[00610] Input-output finite time stabilization for nonlinear networked control systems

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
• Type : Contributed Talk
• Abstract : In this talk, we discuss the problem of input-output finite time stabilization for nonlinear networked control systems with network induced delay. The nonlinear system can be linearized by fuzzy model with weighted membership functions. Memory event-triggering mechanism incorporated to reduce frequent packets transmission. The sufficient stabilization conditions are developed in the form of linear matrix inequalities with aid of Lyapunov stability theory. Finally, numerical example is provided to demonstrate the viability of the suggested approach.
• Classification : 37N35, 34A34, 93D15, 93D25, 93C42
• Format : Talk at Waseda University
• Author(s) :
  • Marshal Anthoni Selvaraj (Anna University Regional Campus Coimbatore)

[00880] Disturbance rejection based modified repetitive control design for stabilization of Takagi–Sugeno fuzzy systems

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
• Type : Contributed Talk
• Abstract : In this talk, the aim is to obtain a disturbance rejection based repetitive control design for the stabilization of Takagi–Sugeno fuzzy systems in presence of aperiodic disturbances. By employing Lyapunov approach, a new set of conditions is derived in the form of linear matrix inequalities to obtain the control gains for ensuring the robust stabilization of the addressed fuzzy systems. Further, numerical simulations are provided to verify the supremacy of the designed control scheme.
• Classification : 37N35, 93B51, 93D15, 93D25, 93C42
• Format : Talk at Waseda University
• Author(s) :
  • Antony Crispin Sweety Charles Selvaraj (Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore)

[02393] Effect of adding reactions on the chemical reaction network sensitivity

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
• Type : Contributed Talk
• Abstract : Biological functions arise from the complex dynamics of reaction networks comprising numerous reactions and chemicals. However, network information is often inaccurate and diverse across species. Previously, we developed the "Structural Sensitivity Analysis", which enables the responses of reaction systems to parameter perturbations to be determined solely from network topology. In this study, we investigate how small alterations to network structure affect system behavior. The results can be classified into five distinct cases based on topology.
• Classification : 37N25
• Author(s) :
  • Atsuki Hishida
  • Atsuki Hishida (Kyoto University)
  • Atsushi Mochizuki (Kyoto University)

[00834] Analytical Solution for Linearized Diffusive Wave with Concentrated Lateral Inflow

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
• Type : Contributed Talk
• Abstract : We present a solution for flow depth and discharge at different locations of a finite prismatic channel for linearized diffusive wave approximation with concentrated lateral inflow subjected to water discharge as the upstream boundary and flow depth as the downstream boundary. Laplace transform is used to find the analytical solution. We present some results to show the effect of Peclet number and the point of confluence on discharge and flow depth.
• Classification : 44A10, 35Q35, 86A05, Hydraulics, River Mechanics
• Format : Online Talk on Zoom
• Author(s) :
  • Shiva Kandpal (Indian Institute of Technology Guwahati)
  • Swaroop Nandan Bora (Indian Institute of Technology Guwahati)

[01844] Operational Matrix Based Numerical Scheme for Fractional Differential Equations

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
• Type : Contributed Talk
• Abstract : Fractional calculus is active in many engineering and physics disciplines due to their non-local properties. This non integer order derivative performs well in systems where the next state depends not only on the current state but also upon all of its previous states. Modeling such systems and determining their precise solutions are current research topics of interest. Since finding exact solutions for fractional differential equations is more challenging, developing numerical techniques is a trending research topic. In this paper, we propose the spectral collocation method based on the operational matrix of orthogonal basis polynomials to find the approximate solution of fractional differential equations. Different orthogonal and non orthogonal basis polynomials are considered for the approximation, and a comparative study is made. The operational matrix of fractional order derivatives of basis polynomials is derived as a product of matrices. This matrix together with the collocation method, is employed to transform the fractional differential equations into a set of algebraic equations, which is easier to tackle. The perturbation method is applied to show the stability of the discussed method. The solution achieved by this method is more precise than those obtained from the existing methods like the variational iterational, adomian decomposition method, and finite difference method.
• Classification : 44Axx, 33C50, 65N35, Fractional Calculus
• Author(s) :
  • Ashish Awasthi (National Institute of Technology Calicut)
  • Poojitha S (National Institute of Technology Calicut)

MS [00696] Scientific Machine Learning for Inverse Problems

room : G808

• [03211] Learning Stochastic Closures Using Sparsity-Promoting Ensemble Kalman Inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinlong Wu (University of Wisconsin-Madison)
    • Tapio Schneider (California Institute of Technology)
    • Andrew Stuart (California Institute of Technology)
  • Abstract : Closure models are widely used in simulating complex dynamical systems such as turbulence and climate change, for which direct numerical simulation is often too expensive. Although it is almost impossible to perfectly reproduce the true system with closure models, it is often sufficient to correctly reproduce time-averaged statistics. Here we present a sparsity-promoting, derivative-free optimization method to estimate model error from time-averaged statistics. Specifically, we show how sparsity can be imposed as a constraint in ensemble Kalman inversion (EKI), resulting in an iterative quadratic programming problem. We illustrate how this approach can be used to quantify the model error in the closures of dynamical systems. In addition, we demonstrate the merit of introducing stochastic processes to quantify model error for certain systems. We also present the potential of replacing existing closures with purely data-driven closures using the proposed methodology. The results show that the proposed methodology provides a systematic approach to estimating model error in the closures of dynamical systems.
• [03315] Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion
  • Format : Talk at Waseda University
  • Author(s) :
    • xueyu zhu (Department of Mathematics, University of Iowa)
    • andrew pensoneault (Department of Mathematics, University of Iowa)
  • Abstract : Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for PDE-based inverse problems. Existing inference approaches are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI). We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost.
• [02563] Neural operator acceleration of PDE-constrained Bayesian inverse problems: Error estimation and correction
  • Format : Talk at Waseda University
  • Author(s) :
    • Lianghao Cao (The University of Texas at Austin)
    • Thomas O'Leary-Roseberry (The University of Texas at Austin)
    • Prashant K. Jha (The University of Texas at Austin)
    • J. Tinsley Oden (The University of Texas at Austin)
    • Omar Ghattas (The University of Texas at Austin)
  • Abstract : In this talk, we explore using neural operators to accelerate infinite-dimensional Bayesian inverse problems (BIPs) governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained attention in recent years for their ability to approximate nonlinear mappings between function spaces, particularly the parameter-to-solution mappings of PDEs. On the one hand, the computational cost of BIPs can be drastically reduced if the large number of PDE solves required in posterior characterization are replaced with evaluations of trained neural operators. On the other hand, reducing error in the resulting BIP solutions via reducing approximation error of the neural operators in training can be challenging and unreliable. We provide an a-priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably reduce error of neural operator predictions to be used in BIPs, we consider correcting predictions of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can possibly achieve a quadratic reduction of its approximation error. Finally, we provide a numerical example based on the deformation of hyperelastic materials. We demonstrate that the posterior representation produced using neural operators is greatly and consistently enhanced by the error correction, while still retaining substantial computational speed ups.
• [01533] Ensemble Kalman inversion with dropout in Scientific Machine Learning for Inverse Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuigen Liu (National University of Singapore)
    • Sebastian Reich (Universität Potsdam)
    • Xin Thomson Tong (National University of Singapore)
  • Abstract : Ensemble Kalman inversion (EKI) is an ensemble-based method to solve inverse problems. However, EKI can face difficulties when dealing with high-dimensional problems using a fixed-size ensemble, due to its subspace property where the ensemble always lives in the subspace spanned by the initial ensemble. To address this issue, we propose a novel approach using dropout technique to mitigate the subspace problem. Compared to the conventional localization approach, dropout avoids the complex designs in the localization process. We prove that EKI with dropout converges in the small ensemble settings, and the complexity of the algorithm scales linearly with dimension. Numerical examples demonstrate the effectiveness of our approach.

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

room : G809

MS [00342] Localized waves in nonlinear discrete systems

room : F308

• [00812] Universality Classes for Nonlinear Wave Thermalization
  • Format : Talk at Waseda University
  • Author(s) :
    • Sergej Flach (Institute for Basic Science)
  • Abstract : We study the slowing down of thermalization of many-body dynamical systems upon approaching integrable limits. We identify two fundamentally distinct long-range and short-range classes. The long-range class results in a single parameter scaling of the Lyapunov spectrum, with the rescaled spectrum approaching an analytical function. The short-range class results in a rescaled Lyapunov spectrum approaching a non-analytic function through an exponential suppression of all Lyapunov exponents relative to the largest one.
• [01278] Numerical experiment on nonlinear localized oscillation propagating in a mass-spring chain
  • Format : Talk at Waseda University
  • Author(s) :
    • Yosuke Watanabe (Setsunan University)
    • Yusuke Doi (Osaka University)
  • Abstract : Nonlinear localized oscillations excited and propagated in a mass-spring chain are studied. Letting the mass at one end of the chain driven sinusoidally at high frequency and large amplitude, localized oscillations can be excited intermittently near the end and propagated down the chain one after another at a constant speed. This phenomenon is known as supratransmission. We have experimentally observed the supratransmission by a mechanical mass-spring chain which emulates the Fermi-Pasta-Ulam one of beta type. The experimental results are compared with the numerical ones.
• [01274] Moving Intrinsic Localized Modes Created by Transforming Wavenumber-frequency Spectrum of a Static Intrinsic Localized Mode in FPUT-NKG Mixed Lattices
  • Format : Talk at Waseda University
  • Author(s) :
    • Masayuki Kimura (Setsunan University)
    • Kosuke Kawasaki (Kyoto University)
    • Shinji Doi (Kyoto University)
  • Abstract : Intrinsic localized mode $($ILM$)$, also known as discrete breather $($DB$)$, is a spatially localized vibration in nonlinear lattices. It is well known that ILM can travel the lattices without decay of energy localization for a long period of time. In this study, initial values of moving ILMs with arbitrary speed are created by transforming the wavenumber-frequency spectrum of a static ILM. We will discuss the characteristics of the created moving ILMs.
• [00992] Structure of pairwise interaction symmetric lattice for moving discrete breather
  • Format : Talk at Waseda University
  • Author(s) :
    • Yusuke Doi (Osaka University)
    • Kazuyuki Yoshimura (Tottori University)
  • Abstract : The mobility of discrete breathers is an essential issue from the viewpoint of energy transport in microstructure and nanostructures. In this presentation, we construct a nonlinear lattice with long-range interaction, which supports the smooth mobility of the discrete breather by considering the invariance of the interaction potential to a certain mapping corresponding to the translational manipulation of the waveform. Numerical results on the dynamics of the discrete breather in the constructed lattice are also presented.

MS [02083] Integrable Aspects of Nonlinear Wave Equations, Solutions and Asymptotics

room : F309

• [05580] Darboux transformation and soliton solutions for a generalized Sasa-Satsuma equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Zuo-nong Zhu (Shanghai Jiao Tong University)
    • Hongqian Sun (Shanghai Jiao Tong University)
  • Abstract : Sasa-Satsuma equation is an important integrable equation. In this talk, we will investigate a generalized Sasa-Satsuma equation introduced by Geng and Wu. Darboux transformation and soliton solutions including hump-type, breather-type solitons for the generalized Sasa-Satsuma equation are constructed.
• [05584] Rogue waves and solitons of nonlinear integrable/nearly integrable systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhenya Yan (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : In this talk, we mainly discuss some properties of rogue waves and solitons of some nonlinear integrable/nearly integrable systems, which include stability, interactions and excitations of solitons, and rogue wave structures.
• [05579] The modified KdV equation on the background of elliptic function solutions
  • Format : Talk at Waseda University
  • Author(s) :
    • Liming Ling (South China University of Technology)
  • Abstract : In this talk, we first introduce the spectral stability and orbital stability of the elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation with respect to subharmonic perturbations and construct the corresponding breather solutions to exhibit the unstable or stable dynamic behavior. On the other hand, by using the Darboux-Backlund transformation, we construct multi-elliptic-localized wave solutions. The asymptotic analysis of these multi-elliptic-localized wave solutions is also involved in this talk.
• [04134] Pattern Transformation in Higher-Order Lumps of the Kadomtsev-Petviashvili I Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Bo Yang (Ningbo University)
  • Abstract : Pattern formation in higher-order lumps of the Kadomtsev-Petviashvili I equation at large time is analytically studied. For a broad class of these higher-order lumps, we show that two types of solution patterns appear at large time. The first type of patterns comprises fundamental lumps arranged in triangular shapes, which are described analytically by root structures of the Yablonskii-Vorob'ev polynomials. As time evolves from large negative to large positive, this triangular pattern reverses itself along the x-direction. The second type of patterns comprise fundamental lumps arranged in non-triangular shapes in the outer region, which are described analytically by nonzero-root structures of the Wronskian-Hermit polynomials, together with possible fundamental lumps arranged in triangular shapes in the inner region, which are described analytically by root structures of the Yablonskii-Vorob'ev polynomials. When time evolves from large negative to large positive, the non-triangular pattern in the outer region switches its x and y directions, while the triangular pattern in the inner region, if it arises, reverses its direction along the x-axis. Our predicted patterns at large time are compared to true solutions, and excellent agreement is observed.

MS [00088] Machine learning in infinite dimensions

room : F311

• [04018] Learning PDE operators with neural networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Elizabeth Qian (Georgia Institute of Technology)
  • Abstract : The term ‘surrogate modeling’ in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations such as those arising from numerical solution of partial differential equations (PDEs). Surrogate modeling is an enabling methodology for many-query computations in science and engineering which include iterative methods in optimization and sampling methods in uncertainty quantification. Over the last few years several approaches to surrogate modeling for PDEs using neural networks have emerged motivated by successes in using neural networks to approximate nonlinear maps in other areas. In principle the relative merits of these different approaches can be evaluated by understanding for each one the cost required to achieve a given level of accuracy. However the absence of a complete theory of approximation error for these approaches makes it difficult to assess this cost-accuracy trade-off. In this talk we provide a careful numerical study of this issue comparing a variety of different neural network architectures for operator approximation across a range of problems arising from PDE models in continuum mechanics.
• [04864] Learning solution operators for PDEs with uncertainty
  • Format : Talk at Waseda University
  • Author(s) :
    • Emilia Magnani (University of Tübingen)
    • Nicholas Krämer (University of Tübingen)
    • Runa Eschenhagen (University of Cambridge)
    • Philipp Hennig (University of Tübingen)
    • Lorenzo Rosasco (University of Genova & MIT)
  • Abstract : We provide a Bayesian formulation of the problem of learning solution operators of PDEs in the formalism of Gaussian processes. We extend this treatment to recent deep architectures (neural operators) that have shown promising results to tackle this task. We provide them with uncertainty estimates through methods from Bayesian deep learning. Finally, we consider particular types of operators (convolutions) and investigate the process of learning these in the context of functional regression in inverse problems.
• [04774] Unsupervised Learning of the Total Variation Flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Tamara G Grossmann (University of Cambridge)
    • Sören Dittmer (University of Cambridge)
    • Yury Korolev (University of Bath)
    • Carola-Bibiane Schönlieb (University of Cambridge)
  • Abstract : The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradientflow observes desirable features for images and enables texture analysis. The standard numerical approach requires solving multiple non-smooth optimisation problems, this is often prohibitively expensive. We propose the TVflowNET, a neural network approach to compute the solution. We significantly speed up the computation time and show that the TVflowNET approximates the TV flow solution with high fidelity.
• [03051] On solving/learning nonlinear PDEs with GPs
  • Format : Talk at Waseda University
  • Author(s) :
    • Houman Owhadi (California Institute of Technology)
  • Abstract : We present a simple, rigorous, and unified framework for solving and learning arbitrary nonlinear PDEs with GPs. The proposed approach inherits the error bounds of kernel interpolation methods and the near-linear complexity of linear solvers for dense kernel matrices. Its generalization to high-dimensional PDEs comes with error bounds exhibiting a tradeoff between dimensionality and regularity. Parts of this talk are joint work with Pau Batlle Franch, Yifan Chen, Bamdad Hosseini, Florian Schäfer, and Andrew Stuart.

MS [00426] Variational methods for thin structures and free-boundary problems

room : F312

• [02741] Long time behavior and stability of surface diffusion flow
  • Format : Talk at Waseda University
  • Author(s) :
    • Antonia Diana (Scuola Superiore Meridionale )
  • Abstract : We present a long-time existence and stability result for the surface diffusion flow in the flat torus. According to this flow, smooth hypersurfaces move with the outer normal velocity given by the Laplacian of their mean curvature. We show that if the initial set is sufficiently ``close’’ to a stable critical set for the volume-constrained Area functional, then the flow exists for all times and asymptotically converges to a ``translation’’ of the critical set.
• [03626] Graphical solutions to one-phase problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Yu (National University of Singapore)
    • Max Engelstein (University of Minnesota-Twin Cities)
    • Xavier Fernandez-Real (Ecole Polytechnique Federale de Lausanne)
  • Abstract : The free boundaries of solutions (critical points of the functional) to the one-phase problem can have rich geometry. Such richness can be reduced by imposing the graphical condition. In this talk, we show that if homogeneous minimizers are trivial in dimension k, then graphical solutions are trivial in dimension k+1. This works for both the classical one-phase problem as well as its thin counterpart. This talk is based on a joint work with Max Engelstein (Minnesota) and Xavier Fernandez-Real (EPFL).
• [04656] Regularity of the optimal shapes for a class of integral functionals
  • Format : Online Talk on Zoom
  • Author(s) :
    • Bozhidar Velichkov (Università di Pisa)
  • Abstract : This talk is dedicated to the regularity of solutions to the following variational problem $$\min\Big\{J(\Omega)\ :\ \Omega\subset D\Big\},$$ where $D\subset \mathbb{R}^d$ is a given bounded open set and $J$ is a functional of the form $$J(\Omega)=\int_\Omega j(x,u_\Omega)\,dx+|\Omega|\,,$$ where $j:D\times \mathbb{R}\to\mathbb{R}$ is a given "cost function" and $u_\Omega$ is the solution to $$-\Delta u_\Omega=f(x)\quad\text{in}\quad\Omega\ ,\qquad u_\Omega\in H^1_0(\Omega)\,,$$ where $f:D\to\mathbb{R}$ is a fixed function. We will discuss the case $j(x,u_\Omega)=-g(x)u_\Omega$, which leads to a free boundary system of the form \begin{align*} -\Delta u_\Omega=f(x)&\quad\text{in}\quad\Omega\\ -\Delta v_\Omega=g(x)&\quad\text{in}\quad\Omega\\ u_\Omega=v_\Omega=0&\quad\text{on}\quad\partial \Omega\\ |\nabla u_\Omega||\nabla v_\Omega|=1&\quad\text{on}\quad\partial \Omega \end{align*} We will show that, if the functions $f$ and $g$ are positive and comparable, and if the dimension $d$ of the ambient space is $2$, $3$, or $4$, then any optimal set $\Omega$ is $C^{1,\alpha}$ smooth (and solves the above system in the classical sense). The talk is based on joint works with Giorgio Tortone (University of Pisa) and Francesco Paolo Maiale (Scuola Normale Superiore), and on a joint work with Giuseppe Buttazzo (University of Pisa), Francesco Paolo Maiale (Scuola Normale Superiore), Dario Mazzoleni (University of Pavia), and Giorgio Tortone (University of Pisa).
• [04579] Min-max minimal surfaces with contact angle conditions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Luigi De Masi (University of Padova)
  • Abstract : Existence and regularity of minimal surfaces (i.e. stationary points for area functional) has been an active topic of research for the last decades. When minimizing strategies produce just trivial solutions, min-max methods may be successfully used. In this talk, based on a joint work with G. De Philippis, I will discuss min-max construction of a minimal surface $\Sigma$ in a container $\mathcal{M} \subset \mathbb{R}^3$ which meets $\partial \mathcal{M}$ with a fixed angle.

MS [00675] New trends in (optimal) control theory

room : F401

• [01796] Surveillance-evasion games with visibility constraints
  • Format : Talk at Waseda University
  • Author(s) :
    • Carlos Esteve-Yague (University of Cambridge)
  • Abstract : In this talk, I consider a two-player zero-sum game in which the payoff involves the visibility of the players. First, I will present a new analysis of the boundary conditions for the associated Hamilton-Jacobi-Isaacs HJI equation. As we shall see, these boundary conditions turn out to be non-trivial, and the regularity is related to the curvature of the obstacles. Then, using a new notion of visibility, I will introduce suboptimal feedback strategies for the players which can be proven to approximate the optimal feedback given by the solution of the HJI equation. The main advantage of using these suboptimal feedback controls is that they are computationally efficient and are scalable to the case of multiple players.
• [01823] Steering undulatory micro-swimmers in a fluid flow through reinforcement learning
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zakarya El-Khiyati (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
    • Raphaël Chesneaux (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
    • Laetitia Giraldi (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
    • Jérémie Bec (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
  • Abstract : The talk deals with optimal navigation policies for thin, deformable microswimmers, which progress in a viscous fluid flow by propagating a sinusoidal undulation along their slender body. The swimmer has to compete with the drifts, strains, and deformations inflicted by the external flow. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. A study of the swimming strategies selected set will be provided.
• [02637] Optimization problems under uncertainty
  • Format : Online Talk on Zoom
  • Author(s) :
    • teresa scarinci (Università di Cassino e del Lazio Meridionale)
  • Abstract : The study of models with uncertainty plays an important role in scientific numerical simulations. This class of problems is strongly utilized in engineering, biology, and finance. In this talk, we discuss the importance of including uncertainty in optimal control. Randomness can be utilised to model applications where the data of the problem -- such as the dynamic, the coefficients, or the time delay -- are not known a priori and one knows only statistical information.

contributed talk: CT069

room : F403

[02321] Anisotropic perimeter approximation for topology optimization

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
• Type : Contributed Talk
• Abstract : Perimetric type functionals are known to be difficult to handle directly within topology optimization algorithms because of their high sensitivity to topology changes. I will present a Gamma-convergence approximation of an anisotropic variant of the perimeter which is built upon the solution of an elliptic boundary value problem. I will discuss the advantages of such a construction over local approximations, and show applications to the optimal design of supports in additive manufacturing.
• Classification : 49Q10, 49Q20, 49Q05
• Format : Talk at Waseda University
• Author(s) :
  • Samuel Amstutz (Ecole polytechnique)
  • Beniamin Bogosel (Ecole polytechnique)

[00680] Computing p-Harmonic Descent Directions for Shape Optimization

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
• Type : Contributed Talk
• Abstract : Recent development in shape optimization suggests enhanced results by using a $p$-harmonic approach to determine descent directions. Therefore, we present the extension of an algorithm to solve the occurring vector-valued $p$-Laplace problem subject to a boundary force without requiring an iteration over the order $p$ and thus compute higher-order solutions efficiently. Results are verified by numerical experiments in a fluid dynamic setting.
• Classification : 49Q10, 49M41
• Format : Talk at Waseda University
• Author(s) :
  • Henrik Wyschka (University of Hamburg)
  • Martin Siebenborn (University of Hamburg)
  • Winnifried Wollner (University of Hamburg)

[00619] Optimal Transport for Positive and Unlabeled Learning

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
• Type : Contributed Talk
• Abstract : Positive and unlabeled learning (PUL) aims to train a binary classifier based on labeled positive samples and unlabeled Samples, which is challenging due to the unavailability of negative training samples. This talk will introduce a novel optimal transport model with a regularized marginal distribution for PUL. By using the Frank-Wolfe algorithm, the proposed model can be solved properly. Extensive experiments showed that the proposed model is effective and can be used in meteorological applications.
• Classification : 49Q22, 68T01
• Format : Talk at Waseda University
• Author(s) :
  • Jie ZHANG (University of Hong Kong)
  • Yuguang YAN (Guangdong University of Technology)
  • Michael Ng (University of Hong Kong)

[00122] Exact expansion of functions using partial derivatives: sensitivity analysis

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
• Type : Contributed Talk
• Abstract : Expansions of functions such as Taylor’ series, ANOVA and anchored decompositions are widely used for approximating and analyzing complex mathematical models. We propose a novel and exact expansion of functions using their cross-partial derivatives, the distribution functions and densities of the input variables. In uncertainty quantification and multivariate sensitivity analysis, such expansion allows for developing a dimension-free computation of sensitivity indices for dynamic models, and for proposing new lower and upper bounds of total indices.
• Classification : 49Q12, 46G10, 46G99
• Format : Online Talk on Zoom
• Author(s) :
  • Matieyendou LAMBONI (université de Guyane)

MS [00888] Geometric Shape Generation I: Structures

room : F411

• [05391] Singularity of Arc- and Spiral-shaped Miura-ori as Rigid-Flat-Foldable Origami Pattern
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Tagawa (Mukogawa Women's University)
  • Abstract : Arc- and spiral-shaped Miura-ori is rigid flat-folding Origami pattern and one variational type of Miura-ori. Geometric folding lines of the spiral-shaped Miura-ori are obtained by arraying quadrilaterals with identical internal angles in the same column. The arc-shaped Miura-ori is obtained by setting equal edge lengths of the quadrilaterals in the radial direction. This study investigates the singularity of an arc- and spiral-shaped Miura-ori among the generalized Miura-ori.
• [03876] A first-order method for large-scale eigenvalue optimization problems in topology optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Akatsuki Nishioka (The University of Tokyo)
    • Mitsuru Toyoda (Tokyo Metropolitan University)
    • Mirai Tanaka (The Institute of Statistical Mathematics)
    • Yoshihiro Kanno (The University of Tokyo)
  • Abstract : Eigenvalue optimization problems arise in many situations in topology optimization when considering robustness, vibration and buckling. As topology optimization problems are often very large-scale, the semidefinite programming approach is sometimes too computationally costly. We propose an efficient optimization algorithm based on the smoothing method for large-scale eigenvalue problems. The proposed method only uses the first-order derivative of the objective function, and thus has low computational cost per iteration. It also has convergence guarantee.
• [03320] Recent advances on tension-compression mixed shell form-finding
  • Format : Talk at Waseda University
  • Author(s) :
    • Masaaki Miki (The University of Tokyo)
  • Abstract : In architecture, thin surface structures that can withstand gravity with no bending action are called shells. Shells have special geometries that enable them to stream gravitational force toward the ground along their forms with in-plane stresses only; the process of finding these special forms is called form-finding. Researchers have pointed out that in shell form-finding, the problem can be formulated using two surfaces: the shell itself and another surface called Airy's stress function. In 2022, a novel NURBS-based computational approach that can properly handle mixed tension–compression stress states was presented by Miki et al. (note that similar methods were first introduced in Ciang Yu-Chou). Because the solutions are repretented by NURBS, the partial derviatvies can be computed at any point. This enables many kind of computations. In this talk, we present what kind of compuation turns possible based on the solutions obatined by the proposed method.
• [02771] Developable surfaces with curved folds
  • Format : Talk at Waseda University
  • Author(s) :
    • Miyuki Koiso (Kyushu University)
  • Abstract : Developable surfaces are surfaces which can be unfolded into the plane preserving the length of all curves on the surface. Since developable surfaces with curved folds are constructed by bending a flat sheet, they have many applications in manufacturing objects. In this talk, we give conditions of piecewise-smooth surfaces for being developable in terms of curvatures. We also discuss variational problems for developable surfaces, geometric characterizations of their optimal solutions, and their applications to architecture.

MS [00879] Stochastic analysis in mathematical finance

room : F412

• [03804] Constrained optimal stopping under a regime-switching model
  • Format : Talk at Waseda University
  • Author(s) :
    • Takuji Arai (Keio University)
  • Abstract : We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions of the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.
• [04565] Remarks on pathwise Itô calculus in infinite dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuki Hirai (National Institute of Technology, Tsuruoka College)
  • Abstract : The Itô–Föllmer calculus, pioneered by Föllmer (1981), is a deterministic counterpart to classical Itô's stochastic calculus. It has recently been receiving increasing attention from the viewpoint of its financial applications. In this talk, we extend some results in the Itô–Föllmer calculus to infinite dimensional settings.
• [03809] Systemic Risk and Overconfidence under Stochastic Environment
  • Format : Talk at Waseda University
  • Author(s) :
    • Li-Hsien Sun (National Central University)
  • Abstract : We propose an optimal portfolio problem based on the mean variance criterion based on the relative performance with the feature of overconfidence. Namely, investors intend to maximize the distance between the average and minimize the their own variance as well. In the meantime, they also consider the better return than the real one due to overconfidence. We illustrate systemic risk by applying the probability of the large number of defaults. Finally, the influence of overconfidence is discussed through numerical analysis.
• [03808] Smoothness of Directed Chain Stochastic Differential Equations and Its Applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomoyuki Ichiba (University of California Santa Barbara )
  • Abstract : On a filtered probability space for the space of continuous functions, we shall consider a system of stochastic equations called directed chain stochastic differential equations for a pair of stochastic processes whose marginal distributions in the path space are identical and their joint distribution is uniquely determined by the system of equations with the distributional constraints. In this talk we discuss the smoothness of the solutions of the equations under some regular conditions and introduce its applications of such systems to the stochastic filtering problem and to the generative adversarial network problem in finance.

MS [02435] Scaling Limits of Interacting Particle Systems

room : E501

• [03511] Graphon mean field systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ruoyu Wu (Iowa State University)
    • Erhan Bayraktar (University of Michigan)
    • Suman Chakraborty (Uppsala University)
  • Abstract : We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with (random) weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness of the graphon particle system is established. A law of large numbers result is proved as the system size increases and the underlying graphons converge.
• [03358] Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zimo Hao (Bielefeld University)
  • Abstract : In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^p$-interactions as well as for the moderate interaction particle systems on the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of the SDEs for particle systems with singular interaction. To this end, we extend the results on strong well-posedness of Krylov and R\"ockner to the case of mixed $L^{\boldsymbol{p}}$-drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang's entropy method and Zvonkin's transformation.
• [03721] Nonlocal approximation of nonlinear diffusion equations
  • Format : Talk at Waseda University
  • Author(s) :
    • José Antonio Carrillo (University of Oxford)
    • Antonio Esposito (University of Oxford)
    • Jeremy S.-H. Wu (UCLA)
  • Abstract : Nonlinear diffusion equations are ubiquitous in several real world applications. They were introduced to analyse gas expansion in a porous medium, groundwater infiltration, and heat conduction in plasmas, to name a few applications in physics. In this talk, I will present recent joint work with José A. Carrillo and Antonio Esposito concerning a nonlocal approximation inspired by the theory of gradient flows for a general family of equations closely related to the porous medium equation with m>1. Our approximation is inspired by recent ideas to use (nonlocal) interaction equations to approximate (local) diffusion equations. We prove under very general assumptions that weak solutions to our nonlocal approximation converge to weak solutions of the original local equation. One byproduct of our analysis is the development of a deterministic particle method for numerically approximating solutions to nonlinear diffusion equations.
• [04156] Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zebang Shen (ETH Zürich)
    • Zhenfu Wang (Peking University)
  • Abstract : We extend the concept of self-consistency for the Fokker-Planck equation (FPE)(Shen et al., 2022) to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of particles under drift and diffusion, MVE accounts for the additional inter-particle interactions, which are often highly singular in physical systems. Two important examples considered in this paper are the MVE with Coulomb interactions and the vorticity formulation of the 2D Navier-Stokes equation. We show that a generalized self-consistency potential controls the KL-divergence between a hypothesis solution to the ground truth, through entropy dissipation. Built on this result, we propose to solve the MVEs by minimizing this potential function, while utilizing the neural networks for function approximation. We validate the empirical performance of our approach by comparing with state-of-the-art NN-based PDE solvers on several example problems.

MS [00322] Methodological advancement in rough paths and data science

room : E502

• [01994] Optimal approximation with path signatures
  • Format : Talk at Waseda University
  • Author(s) :
    • Emilio Ferrucci (University of Oxford)
  • Abstract : Path signatures have been used extensively as a way of representing the information encoded in multimodal data streams. This choice of a feature set is motivated by the famous universality result of Hambly & Lyons, 2010 and the fact that a broad class of parametrisation-invariant functions of a stream can be arbitrarily well approximated as linear functions of its signature. However, not much is known on the quantitative aspects of such approximations, and, just like Taylor approximations of smooth functions, they can converge slowly. Moreover, just like monomials in a real variable, the signature may fail to be a basis, meaning a function on paths does not have a canonical coefficient corresponding to each coordinate iterated integral. In this talk we explore ways of addressing these issues.
• [01279] Using AI to Accelerate (S)PDE Solving
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qi Meng (Microsoft Research)
  • Abstract : Partial differential equations play an important role in science and engineering. Recently, AI emerged as a disruptive technique on scientific computing and could break the computational bottleneck on solving complex PDE systems via training deep neural network models. In this talk, I will introduce our recent work on AI accelerated PDE solving including DeepVortexNet and DLR-Net, which uses probabilistic representation and regularity features to achieve robust supervision signal and well-generalized neural network architecture, respectively.
• [00769] Markov Chain Cubature for Bayesian Inference
  • Format : Online Talk on Zoom
  • Author(s) :
    • James Foster (University of Bath)
  • Abstract : Markov Chain Monte Carlo is widely regarded as the "go-to" approach for Bayesian inference and, due to the theory of stochastic differential equations, many physics-inspired MCMC algorithms can scale to high dimensions. In this talk, we consider an alternative to Monte Carlo for SDE simulation known as "Cubature on Wiener Space". In particular, by applying SDE cubature and resampling particles in a spatially balanced manner, we introduce a novel interacting particle algorithm for Bayesian inference.
• [01377] Iterated integrals of Gaussian fields and ill-posedness of heat equations
  • Author(s) :
    • Ilya Chevyrev (University of Edinburgh)
  • Abstract : In this talk, I will present a probabilistic method to show norm inflation, and thus local ill-posedness, for non-linear heat equations above scaling criticality. One of the motivations is a proof that the DeTurck-Yang-Mills heat flow is ill-posed on any Banach space that carries the 3D Gaussian free field, which complements recent well-posedness results. The method is inspired by work of Lyons, 1991, on iterated integrals of Brownian paths. Based on arXiv:2205.14350.

MS [00936] Recent advances in applications for large-scale data assimilation and inverse problems.

room : E504

• [05372] Level-set parameterisations for Ensemble Kalman Inversion
  • Format : Online Talk on Zoom
  • Author(s) :
    • Marco Iglesias (University of Nottingham)
  • Abstract : We discuss a level-set approach to parameterise unknown interfaces and discontinuous properties with the Ensemble Kalman Inversion (EKI) framework for inverse problems. We demonstrate the applicability of this approach to solve various inverse problems where the unknown is a discontinuous property arising from the presence of an anomalous material/tissue. We will present numerical examples with applications to (i) non-destructive testing of composite materials, (ii) ground penetrating radar and (iii) magnetic resonance elastography.
• [05415] Data assimilation for estimating nonlinear dynamics in earthquakes
  • Format : Online Talk on Zoom
  • Author(s) :
    • Femke Cathelijne Vossepoel (Delft University of Technology)
    • Hamed Ali Diab-Montero (Delft University of Technology)
    • Arundhuti Banerjee (Delft University of Technology)
    • Celine Marsman (Utrecht University)
    • Ylona van Dinther (Utrecht University)
  • Abstract : The highly nonlinear dynamics of earthquake sequences and the limited data availability make it very difficult, if not impossible, to forecast earthquakes. State- and parameter estimation with data assimilation can improve estimates and forecasts of earthquake sequences. We illustrate the challenges of data assimilation in earthquake simulation with a range of models using several ensemble data-assimilation methods, including the particle filter, the ensemble Kalman filter, the adaptive Gaussian mixture filter, and the particle flow filter.
• [05358] Analysis of a localized ensemble Kalman-Bucy filter with sparse observations
  • Format : Talk at Waseda University
  • Author(s) :
    • Gottfried Hastermann (University of Potsdam)
    • Jana de Wiljes (University of Potsdam)
  • Abstract : With large scale availability of precise real time data, their incorporation into physically based predictive models, became increasingly important. This procedure of combining the prediction and observation is called data assimilation. One especially popular algorithm of the class of Bayesian sequential data assimilation methods is the ensemble Kalman filter which successfully extends the ideas of the Kalman filter to the non-linear situation. However, in case of spatio-temporal models one regularly relies on some version of localization, to avoid spurious oscillations. In this work we develop a-priori error estimates for a time continuous variant of the ensemble Kalman filter, known as localized ensemble Kalman-Bucy filter. More specifically we aim for the scenario of sparse observations applied to models from fluid dynamics and space weather.
• [05397] Edge-preserving inversion with 𝛼-stable priors
  • Format : Talk at Waseda University
  • Author(s) :
    • Jarkko Suuronen (LUT University)
    • Tomás Soto (LUT University)
    • Neil Chada (Heriot Watt University)
    • Lassi Roininen (LUT University)
  • Abstract : The 𝛼-stable distributions are a family of heavy-tailed and infinitely divisible distributions that are well-suited as prior distributions to edge-preserving inversion in the context of (discretization of) infinite-dimensional continuous-time statistical inverse problems. In this talk we present a new hybrid approximation method well-suited to the application of such priors.

MS [02163] Recent Developments in Stochastic Numerics and Computational Finance

room : E505

• [03150] An Approximation Scheme for Path-Dependent BSDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Hyungbin Park (Seoul National University)
    • Ji-Uk Jang (Seoul National University)
  • Abstract : In this work, we study an approximation scheme for solutions to forward-backward stochastic differential equations (FBSDEs) with non-anticipative coefficients. When the non-anticipative coefficients have Fréchet derivatives or can be approximated by non-anticipative functionals having Fréchet derivatives, we show the Picard-type iteration converges to the FBDSE solution and provide its convergence rate. Using this result, we establish a numerical method for solutions of second-order parabolic path-dependent partial differential equations. To achieve this, weak approximation of martingale representation theorem (Cont, Rama, and Yi Lu. “Weak approximation of martingale representations." Stochastic Processes and their Applications 2016) is employed. Our results generalize the scheme for Markovian cases in (Bender, Christian, and Robert Denk. “A forward scheme for backward SDEs." Stochastic processes and their applications, 2007)
• [03659] Practical high-order recombination algorithms for weak approximation of stochastic differential equations : Recursive patch dividing and its effects to singularities of terminal conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Syoiti Ninomiya (Tokyo Institute of Technology)
    • Yuji Shinozaki (Bank of Japan)
  • Abstract : This study proposes practically feasible implementation algorithms of the high-order recombination to apply to the weak approximation problem of SDEs, by extending and refining the work of Lyons and Litterer(2012). Specifically, new recursive patch dividing algorithms, which are based on the refined patch radius criteria, are proposed. Our numerical experiments demonstrate that the new recursive patch dividing algorithms are still efficient even when the terminal condition $f$ becomes more singular.
• [03645] Extended Milstein scheme for hypoelliptic diffusions
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuga Iguchi (University College London)
    • Toshihiro Yamada (Hitotsubashi University)
  • Abstract : For a wide class of diffusion processes, precisely hypoelliptic diffusions, we propose an effective and simple numerical scheme as an extension of Milstein scheme that outperforms Euler-Maruyama (EM) scheme (and standard Milstein scheme), though they share the same convergence rate in a weak sense. Analytic error term for the new scheme is derived and compared with that for EM scheme under non-smooth test functions. The effectiveness of the proposed scheme is also shown through numerical experiments for hypoelliptic diffusions appearing in finance.
• [03489] Wong-Zakai approximation for stochastic PDEs and HJM model
  • Format : Talk at Waseda University
  • Author(s) :
    • TOSHIYUKI NAKAYAMA (MUFG Bank, Ltd.)
  • Abstract : We talk about semi-linear stochastic differential equation (SPDE) driven by a finite dimensional Brownian motion. $$dX(t)=(AX(t)+b(X(t)))dt+\sum_{j=1}^r\sigma_j(X(t))dB^j(t),\quad X(0)=x_0.$$ Our goal is to establish a convergence rate with the generator $A$ which is allowed to be the infinitesimal generator of an arbitrary strongly continuous semigroup. Finally, we will introduce an application example for SPDE called HJMM that appears in mathematical finance. This talk is based on a co-authored paper with Stefan Tappe.

contributed talk: CT091

room : E506

[00668] Solution of Non-linear Problems Through Variant of Newton’s Method with Applications in Engineering

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
• Type : Contributed Talk
• Abstract : Various non-linear problems that formulated from sciences and engineering like Combustion problems, Chemistry of rainwater, Heat problems, etc. are difficult to solve with analytical methods. So, the approximate solution of such non-linear problems is obtained through iterative methods. Hence, we will discuss variant of Newton’s method and its validity in terms of a convergence order, minimum computation cost, time, and efficiency over existing techniques.
• Classification : 65H10, 41A58, 65Y20, Numerical Analysis
• Format : Talk at Waseda University
• Author(s) :
  • Sonia Bhalla (Chandigarh University)

[01309] Deep Learning Methods for BSDEs/PDEs in Finance

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
• Type : Contributed Talk
• Abstract : In this work we present both a multistep deep learning method with automatic differentiation for the resolution of nonlinear PDEs and BSDEs and an adaptation of the Deep BSDE method for Quadratic BSDE and HJB equations. An approximation error result and error rate is proved for the schemes when using a class of networks with sparse weights. Applications to finance including CVA, portfolio optimisation under exponential utility and options pricing will be presented.
• Classification : 65Cxx, 65Nxx, 60Hxx, 91Gxx, 68T07
• Format : Talk at Waseda University
• Author(s) :
  • Daniel Bussell (UCL)

[00008] Semi Analytic Solution for Coupled (n+1)-dimensional Viscous Burgers' Equation using Homotopy Perturbation Method

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
• Type : Contributed Talk
• Abstract : Semi analytic solution for coupled (n+1)-dimensional non-linear viscous Burgers' equation has been obtained by Homotopy Perturbation Method. Potential of prescribed semi analytical technique is specifically examined for (3+1)-dimensional non-linear Burgers' equation with very small kinematic viscosity factor has not been considered yet. Numerical experiments with illustrated absolute error and 3D graphical presentation testify the reliability of the technique. All the computational procedure has been done using MATLAB.
• Classification : 65H20, 65N12, 65N15, 35C10
• Format : Online Talk on Zoom
• Author(s) :
  • Shelly Arora (Punjabi University, Patiala)
  • Atul Pasrija (Punjabi University, Patiala)
  • Sukhjit Singh Dhaliwal (SLIET, Longowal)

[02614] Convergence of a Second-Order Scheme for Nonlocal Traffic Flow Problems

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
• Type : Contributed Talk
• Abstract : In this work, we focus on the construction and convergence analysis of a second-order numerical scheme for traffic flow models that incorporate non-local conservation laws to capture the interaction between drivers and the surrounding density of vehicles. Specifically, we combine MUSCL-type spatial reconstruction with strong stability preserving Runge-Kutta time-stepping to devise a fully discrete second-order scheme for these equations. We show that this scheme satisfies a maximum principle and obtain bounded variation estimates. Also, the scheme is shown to admit L1- Lipschitz continuity in time. Subsequently, employing the Kolmogorov's theorem with a modification and using a Lax-Wendroff type argument, the convergence of this scheme to the entropy solution of the underlying problem is established. Numerical examples are presented to validate our theoretical analysis. Additionally, we extend our analysis to two dimensional non-local problems, for which we present a positivity preserving second-order scheme. While first-order methods are typically reliable in computational fluid dynamics, higher-order methods can provide more accurate solutions at the same computational cost, especially for problems in two or three dimensions. Our proposed scheme thus has important implications for accurately approximating traffic flow equations, and our theoretical analysis provides a solid foundation for its practical implementation.
• Classification : 35L65, 65M12, 65M08
• Format : Talk at Waseda University
• Author(s) :
  • Nikhil Manoj (Indian Institute of Science Education and Research, Thiruvananthapuram)
  • Sudarshan Kumar K (IISER Thiruvananthapuram)
  • GD Veerappa Gowda (Center for Applicable Mathematics, TIFR Bangalore)

[00028] Riemann problem for the Chaplygin gas equations for several classes of non-constant initial data

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E506
• Type : Contributed Talk
• Abstract : Using the differential constraint method, a class of exact solutions is obtained for the homogeneous quasilinear hyperbolic system of partial differential equations describing Chaplygin gas equation; these solutions exhibit linearly degenerate that leads to the formation of contact discontinuities. In fact, in this paper, we solved the gen- eralized Riemann problem through a characteristic shock(s). For several classes of non-constant and smooth initial data, the solution to the generalized Riemann problem is presented.
• Classification : 35L67
• Format : Talk at Waseda University
• Author(s) :
  • Akshay Kumar (University of Hyderabad)
  • Radha R (University of Hyderabad)

MS [01054] Scalable Solvers for Multiphysics Problems

room : E507

• [05039] Immersed Mesh Methods for Coupled Multiphysics Problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Rolf Krause (Euler Institute, USI, Lugano)
    • Patrick Zulian (Euler Institute, USI, Lugano)
    • Maria Nestola (Euler Institute, USI, Lugano)
  • Abstract : We present overlapping domain domain decomposition methods coupling different discretizations in the volume, along surfaces, or between surfaces and volumes. Central element of our approach is a massively parallel discrete $L^2$ projection, which allows for stable variational transfer between different physical models. Examples from fluid structure interaction (FSI), i.e. artificial heart valves, or flow in fracture networks, as well as from contact mechanics coupled with FSI illustrate our approach.
• [04232] Robust nonlinear domain decomposition methods for problems with micro-heterogeneous structures
  • Format : Talk at Waseda University
  • Author(s) :
    • Alexander Heinlein (Delft University of Technology (TU Delft))
    • Axel Klawonn (University of Cologne)
    • Martin Lanser (University of Cologne)
  • Abstract : Nonlinear domain decomposition methods (DDMs) are efficient alternatives to classical Newton-Krylov-DDMs. In contrast to the latter ones, in nonlinear DDMs, the nonlinear partial differential equation is decomposed into subdomains before linearization, which often improves the nonlinear convergence behavior. To obtain robustness applying nonlinear DDMs to heterogeneous multiscale or multiphysics problems, a global and coarse second level should be included. In this talk, several two-level nonlinear Schwarz methods for heterogeneous problems are discussed and compared.
• [04600] Towards a scalable multilevel domain decomposition solver for immersed boundary finite element method
  • Format : Talk at Waseda University
  • Author(s) :
    • Jakub Sistek (Institute of Mathematics of the Czech Academy of Sciences)
  • Abstract : We develop multilevel balancing domain decomposition by constraints (BDDC) method tailored to the solution of the linear systems arising in the context of immersed boundary FEM with parallel adaptive grid refinement. A crucial challenge is presented by fragmenting of subdomains. We present these concepts, the challenges, our implementation, and numerical results for the Poisson problem on complex geometries from engineering. This is joint work with Fehmi Cirak, Eky Febrianto, Matija Kecman, and Pavel Kus.

MS [00825] Numerical Time Integration Algorithms and Software for Machine Learning

room : E508

• [04991] The Roles of Numerical Time Integration Algorithms and Software in the Machine Learning Revolution
  • Format : Talk at Waseda University
  • Author(s) :
    • Cody Balos (Lawrence Livermore National Lab)
  • Abstract : Recently large language models like OpenAI’s ChatGPT have sparked mainstream discussion of Artificial Intelligence and Machine Learning. Meanwhile, in the scientific community there has been an increased interest in Scientific Machine Learning (SciML) and a substantial shift in funding opportunities towards work with at least some ML component. In this talk, I will explore some examples of how numerical time integration algorithms and software, which have been critical to scientific computing for decades, are playing a part in this ML revolution. As part of this exploration, I will also discuss what we are doing in the SUNDIALS time integration library to enable ML applications. LLNL-ABS-847841.
• [03318] TransNet: Transferable Neural Networks for Partial Differential Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zezhong Zhang (Florida State University)
    • Feng Bao (Florida State University)
    • Lili Ju (University of South Carolina)
    • Guannan Zhang (Oak Ridge National Laboratory)
  • Abstract : Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as its formulation and/or data of its solution for pre-training. In this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using PDE information. The construction of the feature space involves re-parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space. Theoretical analysis shows the high quality of the produced feature space, i.e., uniformly distributed neurons. Extensive numerical experiments verify the outstanding performance of our method, including significantly improved transferability, e.g., using the same feature space for various PDEs with different domains and boundary conditions, and the superior accuracy, e.g., several orders of magnitude smaller mean squared error than the state of the art methods.
• [04020] Dissipative residual layers for unsupervised implicit parameterization of data manifolds
  • Format : Online Talk on Zoom
  • Author(s) :
    • Viktor Reshniak (Oak Ridge National Laboratory)
  • Abstract : We propose an unsupervised technique for implicit parameterization of data manifolds. In our approach, the data is assumed to belong to a lower dimensional manifold in a higher dimensional space, and the data points are viewed as the endpoints of the trajectories originating outside the manifold. Under this assumption, the data manifold is an attractive manifold of a dynamical system to be estimated. We parameterize such a dynamical system with a residual neural network and propose a spectral localization technique to ensure it is locally attractive in the vicinity of data. We also present initialization and discuss the regularization of the proposed residual layers that we call dissipative bottlenecks.
• [03338] Improved Parallelism and Memory Performance for Differentiating Stiff Differential Equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Christopher Vincent Rackauckas (Julia Hub, Pumas-AI, MIT)
  • Abstract : Previous work demonstrated trade-offs in performance, numerical stability, and memory usage for ODE solving and differentiation of solutions. Our new time stepping methods expose more parallelism is shown to accelerate small ODE solves, while new GPU-based ODE solvers demonstrate a 10x performance improvement over Jax and PyTorch-based solvers. New adjoint methods achieve linear cost scaling with respect to parameters in stiff ODEs, as opposed to the cubic of Jax/PyTorch, while limiting the memory scaling.

MS [00107] Randomized numerical linear algebra

room : E603

• [04913] RandBLAS and RandLAPACK - Toward Standard Libraries for RandNLA
  • Format : Talk at Waseda University
  • Author(s) :
    • Riley John Murray (ICSI, LBNL, and UC Berkeley)
    • James Demmel (UC Berkeley)
    • Michael Mahoney (ICSI, LBNL, and UC Berkeley)
    • N. Benjamin Erichson (ICSI and LBNL)
    • Maksim Melnichenko (UT Knoxville)
    • Osman Asif Malik (LBNL)
    • Laura Grigori (INRIA Paris and Sorbonne University)
    • Piotr Luszczek (UT Knoxville)
    • Michal Derezinski (University of Michigan)
    • Miles Lopes (UC Davis)
    • Tianyu Liang (UC Berkeley)
    • Hengrui Luo (LBNL)
    • Jack Dongarra (UT Knoxville)
    • Burlen Loring (LBNL)
    • Parth Nobel (Stanford University)
  • Abstract : This talk concerns an ongoing effort to bring RandNLA further into mainstream computing. It includes highlights from our recently released monograph (arXiv:2302.11474) as well as discussion of software. The software component focuses on our C++ library for sketching called RandBLAS. We showcase RandBLAS' capabilities by using it to implement a recently developed algorithm for pivoted QR decompositions of tall matrices. Experiments show the proposed algorithm is often faster than Intel MKL's unpivoted QR.
• [04810] Error Estimation in Randomized Algorithms for Rank-Revealing Factorizations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Katherine Joyce Pearce (The Oden Institute at the University of Texas at Austin)
    • Chao Chen (The Oden Institute at the University of Texas at Austin)
    • Yijun Dong (The Oden Institute at the University of Texas at Austin)
    • Per-Gunnar Martinsson (The Oden Institute at the University of Texas at Austin)
  • Abstract : Interpolative decompositions involve “natural bases” of row and column subsets of a given matrix that approximately span its row and column spaces. For large-scale problems, randomized sketching can serve as an initial step in skeleton selection. In this talk, we describe an adaptive, parallelizable algorithm applying LU with partial pivoting to randomized sketches to determine a target rank for the approximation. Our algorithm exhibits improved efficiency over adaptive randomized column-pivoted QR while maintaining comparable accuracy.
• [04484] Krylov-aware stochastic trace estimation
  • Format : Talk at Waseda University
  • Author(s) :
    • Tyler Chen (New York University)
    • Eric Hallman (Google)
  • Abstract : We discuss an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat matrix-vector products with $f(\mathbf{A})$ as a black-box to be computed by a Krylov subspace method. Like other algorithms for implicit trace estimation, our approach is based on a combination of deflation and stochastic trace estimation. However, we take a closer look at how products with $f(\mathbf{A})$ are integrated into these approaches which enables several efficiencies not present in previously studied methods. In particular, we describe a Krylov subspace method for computing a low-rank approximation of a matrix function by a computationally efficient projection onto Krylov subspace.
• [04463] How and why to "uncompute" the randomized SVD
  • Format : Talk at Waseda University
  • Author(s) :
    • Ethan Nicholas Epperly (California Institute of Technology)
  • Abstract : The randomized SVD is a low-rank approximation procedure and is a foundational tool in randomized matrix computations. This talk introduces a novel "uncomputing" operation in which the randomized SVD approximation is downdated by deleting different columns from the random test matrix. Two examples of the use of this "uncomputing" primitive are presented: estimating the trace of a matrix accessed only through matrix–vector products and estimating the error of the randomized SVD low-rank approximation.

MS [02411] Recent Advances in Numerical Methods for Nonlinear Equations and Applications

room : E604

• [03040] An Iterative scheme for finding simultaneous roots of nonlinear systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Neus Garrido (Universitat Politècnica de València)
    • Paula Triguero Navarro (Universitat Politècnica de València)
    • Alicia Cordero (Universitat Politècnica de València)
    • Juan Ramón Torregrosa (Universitat Politècnica de València)
  • Abstract : Systems of nonlinear equations usually appear in many real-world applications. We give a general iterative algorithm to approximate simultaneous solutions of systems of nonlinear equations. We show that by adding a general sub-step to any iterative method, a new iterative scheme to approximate simultaneous roots of nonlinear systems with doubled convergence order can be obtained. We add this sub-step to some iterative methods of this domain and analyze the behavior of the new schemes.
• [03925] High-order iterative methods for solving nonlinear systems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alicia Cordero
    • Renso V. Rojas-Hiciano (Pontificia Universidad Católica Madre y Maestra)
    • Juan R. Torregrosa (Universitat Politècnica de València)
  • Abstract : In the last decades, many optimal iterative schemes have been developed for solving nonlinear equations, for simple or multiple roots. However, the amount of vectorial iterative procedures able to estimate the solutions of nonlinear systems could be higher. The computational cost of solving the linear systems involved in each iteration plays a key role in the design, seeking the efficiency of the method. We present a highly efficient scheme for solving nonlinear systems of equations.

MS [00573] Emerging Methods for Shape- and Topology Optimization

room : E605

• [04267] Interface Identification constrained by Local-to-Nonlocal Coupling
  • Author(s) :
    • Matthias Schuster (Trier University)
    • Christian Vollmann (Trier University)
    • Volker Schulz (Trier University)
  • Abstract : Models of physical phenomena that use nonlocal operators are better suited for some applications than their classical counterparts that employ partial differential operators. However, the numerical solution of these nonlocal problems can be quite expensive. Therefore, Local-to-Nonlocal couplings have emerged that combine partial differential operators with nonlocal operators. In this talk, we make use of an energy-based Local-to-Nonlocal coupling that serves as a constraint for an interface identification problem.
• [04673] Total Generalized Variation for Geometric Inverse Problems
  • Author(s) :
    • Lukas Baumgärtner (Humboldt Universität zu Berlin)
    • Stephan Schmidt (Humboldt University Berlin)
    • Roland Herzog (Heidelberg University)
    • Ronny Bergmann (NTNU, Trondheim)
    • Manuel Weiß (Uni Heidelberg (IWR))
    • Jose Vidal-Nunez (University of Alcal ́a de Henares)
  • Abstract : The total variation of the outer normal vector of a shape is discussed in the context of triangulated meshes embedded in 3D. This non-smooth regularizer requires an advanced algorithm to be used in (inverse) shape optimization problems. A split Bregman/ADMM method is used for this purpose. There, the non-smooth objective is split into a smooth shape optimization problem and a simple non-smooth problem. The smooth shape problem is solved by a globalized Newton method. Due to the nature of the regularizer, the first and second-order shape derivatives can not be computed by algorithmic differentiation. Therefore, their analytic form is derived and some of their properties are discussed. Numerical results are presented for mesh denoising problems. An extension, the total generalized variation of the normal, to counteract the so-called staircasing effect is presented.
• [04738] Choice of Inner Product in Shape Gradient Descent
  • Author(s) :
    • Caitriona Jacqueline McGarry (University of Leicester)
    • Alberto Paganini (University of Leicester)
  • Abstract : In optimisation problems with infinite dimensional control spaces, the choice of inner product on the control space affects the gradient, the direction of steepest descent wrt the induced norm. Shape optimisation is no exception, with the control variable in an infinite dimensional function space. We will study the impact on shape optimisation of endowing this space of vector fields with alternatively an $H^1$ or $H^2$ inner product, especially regarding adding or removing corners of a shape.
• [04786] Image and Shape Registration via Transport Equations
  • Author(s) :
    • Stephan Schmidt (University of Trier)
    • Lukas Baumgärtner (Humboldt Universität zu Berlin)
  • Abstract : We consider the use of transport equations as a model for solving inverse and registration problems. Incorporating shape Hessians to facilitate higher order methods have recently made new classes of problems tractable, ranging from the formation of capillary bridges in particle flows to the detection of motion in medical scans as well as mesh registration problems. Special attention is given on how to treat hyperbolic constraints within the setting of moving shapes and images.

MS [00763] Long-time dynamics of numerical methods for nonlinear evolution equations

room : E606

• [04908] Structure-preserving finite element discretization of nonlinear PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Ari Stern (Washington University in St. Louis)
  • Abstract : This talk discusses some recent advances in structure-preserving methods for nonlinear PDEs, combining finite elements in space and geometric integration in time. In particular, we extend some earlier methods and results to a broader class of Hamiltonian PDEs than previously considered, showing that multisymplectic and other conservation laws are preserved. These methods apply on unstructured meshes, not just structured grids, and may be arbitrarily high-order.
• [01990] High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Genming Bai (The Hong Kong Polytechnic University)
    • Jiashun Hu (The Hong Kong Polytechnic University)
    • Buyang Li (The Hong Kong Polytechnic University)
  • Abstract : A class of high-order mass- and energy-conserving methods is proposed for the nonlinear Schr\"odinger equation based on Gauss collocation in time and finite element discretization in space, by introducing a mass- and energy-correction post-process at every time level. The existence, uniqueness and high-order convergence of the numerical solutions are proved. In particular, the error of the numerical solution is $O(\tau^{k+1}+h^p)$ in the $L^\infty(0,T;H^1)$ norm after incorporating the accumulation errors arising from the post-processing correction procedure at all time levels, where $k$ and $p$ denote the degrees of finite elements in time and space, respectively, which can be arbitrarily large. Several numerical examples are provided to illustrate the performance of the proposed new method, including the conservation of mass and energy, and the high-order convergence in simulating solitons and bi-solitons.
• [03931] Geometric two-scale integrators for highly oscillatory system
  • Format : Talk at Waseda University
  • Author(s) :
    • Bin Wang (Xi'an Jiaotong University)
  • Abstract : In this talk, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter. We apply the two-scale formulation approach to the problem and propose two new time-symmetric numerical integrators. The methods are proved to have the uniform second order accuracy at finite times and some near-conservation laws in long times.
• [03985] Structure preserving schemes for Allen--Cahn type equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Yongyong Cai (Beijing Normal University)
  • Abstract : In comparison with the Cahn--Hilliard equation, the classic Allen--Cahn equation satisfies the maximum bound principle (MBP) but fails to conserve the mass. Here, we report the MBP and corresponding numerical schemes for the Allen--Cahn equation with nonlocal constraint for the mass conservation. As an extension, we discuss the case of the convective Allen--Cahn equation.

MS [00843] Innovative numerical methods for complex PDEs

room : E702

• [02261] A tourist’s guide to operator splitting
  • Format : Talk at Waseda University
  • Author(s) :
    • Raymond Spiteri (University of Saskatchewan)
    • Siqi Wei (University of Saskatchewan)
  • Abstract : Operator splitting is the dirty little thing we all do when a differential equation is too hard to solve monolithically. Many questions abound, however, regarding how to split a given problem, and many observations and "common knowledge" lack a theoretical understanding. In this talk, I take you on a tour through some of the practical aspects of operator splitting and while touching on some of the folklore that exists around it.
• [02294] Adaptive exponential Runge--Kutta methods for stiff PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Luan Vu Thai (Mississippi State University)
  • Abstract : Exponential Runge-Kutta methods have shown to be well-suited for stiff parabolic PDEs. Their constructions require solving stiff order conditions which involve matrix functions. Current schemes allow using with constant stepsizes only. In this talk, we will derive new schemes of high order which not only fulfill the stiff order conditions in the strong sense and but also support variable step sizes implementation. Numerical experiments are given to illustrate accuracy and efficiency of the new schemes.
• [02660] The Dual-Wind Discontinuous Galerkin Method for Hamilton-Jacobi Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Aaron Rapp (University of the Virgin Islands)
  • Abstract : A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. This framework allows for the approximation of both primal and variational forms of second order differential equations. In this presentation, we will study the error from using the dual-wind DG derivatives to approximate the the solution to stationary and time-dependent Hamilton-Jacobi equations. Some analytical results will be presented, along with numerical examples that verify these results.
• [05622] Well-balanced positivity-preserving DG methods for Euler equations with gravitation
  • Author(s) :
    • Jie Du (Tsinghua University)
    • Yang Yang (Michigan Technological University)
    • Fangyao Zhu (Michigan Technological University)
  • Abstract : We will look at high order discontinuous Galerkin methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. A well-balanced (WB) positivity-preserving (PP) scheme should be constructed to solve the problem. We reformulate the source term such that it balances with the flux at the steady state. To obtain positive numerical density and pressure, we choose a special penalty coefficient in the Lax-Friedrich flux. Numerical experiments will be shown for the performance of the method.

MS [02438] Recent advances in numerical multiscale methods

room : E703

• [03853] A high-order method for elliptic multiscale problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Roland Maier (University of Jena)
  • Abstract : We present a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The method allows for suitable localization and does not rely on additional assumptions on the domain, the diffusion coefficient, or the exact (weak) solution as typically required for high-order approaches. Rigorous a priori error estimates with respect to the involved discretization parameters are presented and the interplay between these parameters as well as the performance of the method are studied numerically.
• [04038] Hierarchical Attention Neural Operator for Multiscale PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Bo Xu (Shanghai Jiao Tong University)
  • Abstract : Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose significant difficulties for the computer simulation of multiscale PDE models in areas such as reservoir simulation, high-frequency scattering, and turbulence modeling. In this talk, we apply hierarchical attention to a data-driven operator learning problem related to multiscale partial differential equations. An empirical H1 loss function is proposed to counteract the spectral bias of the neural operator approximation for the multiscale solution space. We perform experiments on the multiscale Darcy Flow, Helmholtz equation and Navier-Stokes equation. Our model exhibits noticeably higher accuracy compared to the current neural operator techniques, and it produces state-of-the-art results across a variety of datasets. This is joint work with Xinliang Liu (KAUST) and Lei Zhang (SJTU).
• [04167] An abstract framework for multiscale spectral generalized FEMs
  • Format : Online Talk on Zoom
  • Author(s) :
    • chupeng ma (Great Bay University)
  • Abstract : We present an abstract framework for multiscale spectral generalized FEMs based on locally optimal spectral approximations. A higher convergence rate for the local approximations than previously established is derived under certain conditions. The abstract theory is applied to various problems with strongly heterogeneous coefficients, including convection-diffusion problems, elasticity problems, high-frequency wave problems (Helmholtz, elastic wave, and Maxwell's equations), and fourth-order problems, both in the continuous and discrete settings.
• [03857] Multiscale multicontinuum problems in fractured porous media: dimension reduction and decoupling
  • Format : Talk at Waseda University
  • Author(s) :
    • Maria Vasilyeva (Texas A&M University-Corpus Christi)
  • Abstract : We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. The presented decoupling technique separates equations for each continuum that can be solved separately, leading to a more efficient computational algorithm with smaller systems and faster solutions. This approach is based on the additive representation of the operator with semi-implicit approximation by time, where the continuum coupling part is taken from the previous time layer. We extend and investigate this approach for multiscale approximation on the coarse grid using the nonlocal multicontinuum method. We show that the decoupled schemes are stable, accurate, and computationally efficient.

MS [00737] Numerical methods for semiconductor devices simulation and the computational lithography

room : E704

• [01985] An efficient iterative scheme for the coupled Schrödinger-Poisson equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Wenhao Lu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : We propose an efficient iterative scheme for solving the coupled Schrödinger-Poisson equations in three-dimensions. In this scheme, the series of electron densities is truncated to a sum of finite terms, and only a finite number of eigenvalues are computed at each iteration step. The convergence analysis is also presented. We present numerical results that demonstrate the properties of the proposed scheme.
• [01922] Dispersion Analysis of CIP-FEM for Helmholtz Equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Haijun Wu (Nanjing University)
    • Yu Zhou (Nanjing University)
  • Abstract : When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number $k$ increases, known as `pollution effect' which is directly related to the phase difference between the exact and numerical solutions, caused by the numerical dispersion. In this paper, we propose a dispersion analysis for the continuous interior penalty finite element method (CIP-FEM) and derive an explicit formula of the penalty parameter for the $p^{\rm th}$ order CIP-FEM on tensor product (Cartesian) meshes, with which the phase difference is reduced from $\mathcal{O}\big(k(kh)^{2p}\big)$ to $\mathcal{O}\big(k(kh)^{2p+2}\big)$. Extensive numerical tests show that the pollution error of the CIP-FE solution is also reduced by two orders in $kh$ with the same penalty parameter.
• [01779] Efficient Simulation Algorithm for FinFET and Gate-All-Around FET
  • Format : Talk at Waseda University
  • Author(s) :
    • Lang Zeng (Beihang University)
  • Abstract : In this talk, our self-developed device simulator based on the framework of Mode space method will be introduced which can accurately and efficiently simulate the current characteristic of FinFET and GAA FET. In our hybrid framework, the 3D device is divided into 2D cross-sectional direction with closed boundary condition and 1D transport direction with open boundary condition. Our simulator is designed by modular concept that different physical models can be picked and combined freely.
• [01757] A finite element method for the Schr\"{o}dinger-Poisson model
  • Format : Talk at Waseda University
  • Author(s) :
    • Weiying Zheng (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : We propose a finite element method for solving the coupled Schr$\ddot{\rm o}$dinger-Poisson equations in three-dimensions. The series of electron density is truncated into the sum of finite terms. Sharp estimates are proved for both the truncation error and the finite element discretization error. A robust iterative scheme is proposed to solve the nonlinearly coupled problem.

MS [00633] Unconventional numerical methods for advection-diffusion PDEs

room : E705

• [03915] Dissipation-based WENO stabilization of high-order finite element methods for hyperbolic problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Dmitri Kuzmin (TU Dortmund University)
    • Joshua Vedral (TU Dortmund University)
  • Abstract : We propose a new kind of weighted essentially nonoscillatory (WENO) schemes to high-order finite element discretizations of hyperbolic conservation laws. In contrast to WENO-based limiters for DG approximations, our approach uses a reconstruction-based smoothness sensor to blend the numerical viscosity operators of high- and low-order stabilization terms. The so-defined hybrid approximation introduces low-order nonlinear diffusion in the vicinity of shocks, while preserving the high-order accuracy of the baseline discretization in regions where the exact solution is smooth. The underlying reconstruction procedure performs Hermite interpolation on stencils consisting of a mesh cell and its neighbors. The amount of numerical dissipation depends on the relative differences between partial derivatives of reconstructed candidate polynomials and those of the consistent finite element approximation. All derivatives are taken into account by the employed smoothness sensor. To assess the accuracy of our WENO scheme, we derive error estimates and perform numerical experiments. In particular, we prove that the consistency error of the nonlinear stabilization is of the order p+1/2, where p is the polynomial degree. For uniform meshes and smooth exact solutions, the experimentally observed rate of convergence is as high as p+1.
• [04012] A Residual Distribution Approach to Isotropic Wave Kinetic Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Steven Walton (Los Alamos National Laboratory)
  • Abstract : We present a Petrov-Galerkin Residual Distribution (PG-RD) approach to solve isotropic wave kinetic equations (WKEs). The RD method is well-known for its ability to accurately solve advection dominated flow problems due to its intrinsic multi-dimensional upwinding property. While WKEs are nonlinear and non-local integro-differential equations, very different from the historical applications of RD methods, the energy flux of the equations we consider is local. We show that the PG-RD method derived generalizes a finite volume scheme given in a previous work. Analysis of the convergence properties of the method is also provided. The method is verified against established theoretical work for isotropic WKEs.
• [04019] High order Flux Reconstruction schemes for turbulent flows and spectral analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • ROMARIC SIMO TAMOU (IFPEN)
    • JULIEN BOHBOT (IFPEN)
    • JULIEN COATLÉVEN (IFPEN)
    • VINCENT PERRIER (INRIA)
    • QUANG HUY TRAN (IFPEN)
  • Abstract : This study focuses on evaluating Flux Reconstruction schemes for turbulent flows. For these schemes, we perform new analyses of their dissipation and dispersion properties, and we find consistent results with the classical analysis. Ultimately, we evaluate the effect of the high order and correction functions on the DNS of Taylor-Green vortex. This work provides valuable insights into the performance of FR schemes for turbulent flows and presents a promising new approach for analyzing their stability.
• [04429] The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
  • Format : Talk at Waseda University
  • Author(s) :
    • Erik Chudzik
    • Christiane Helzel (Heinrich-Heine Universität)
  • Abstract : We present the first implementation of the Active Flux method on Cartesian grids with adaptive mesh refinement: A new finite volume method for hyperbolic conservation laws, that was introduced by Eymann and Roe, which uses a continuous, piecewise quadratic reconstruction and Simpson’s rule to compute numerical fluxes. Point values at grid cell interfaces together with cell averages are used to compute the reconstruction. The resulting method is third order accurate and has a compact stencil in space and time.

MS [01088] Differential Equations meet Data: Scientific Machine Learning for Cardiovascular Applications

room : E708

MS [00837] Particle Methods for Bayesian Inference

room : E709

• [04766] Wasserstein Steepest Descent Flows for Discrepancy Flows with Riesz Kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Johannes Hertrich (TU Berlin)
    • Robert Beinert (TU Berlin)
    • Gabriele Steidl (TU Berlin)
  • Abstract : We introduce Wasserstein steepest descent flows based on the geometric Wasserstein tangent space. These are locally absolutely continuous curves in the Wasserstein space whose tangent vectors point into a steepest descent direction of a given functional. This allows the use of Euler forward schemes instead of minimizing movement schemes introduced by Jordan, Kinderlehrer and Otto. Under certain assumptions, we show that there exists a unique Wasserstein steepest descent flow which coincides with the Wasserstein gradient flow. For the special example of interaction energies with non-smooth Riesz kernels, we derive analytic formulas for the corresponding Wasserstein steepest descent flows.
• [04729] Neural Wasserstein Gradient Flows for Discrepancies with Riesz Kernels
  • Format : Talk at Waseda University
  • Author(s) :
    • Fabian Altekrüger (HU Berlin/ TU Berlin)
    • Johannes Hertrich (TU Berlin)
    • Gabriele Steidl (TU Berlin)
  • Abstract : Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. For the interaction energy we provide analytic formulas for Wasserstein schemes starting at a Dirac measure. Finally, we illustrate our neural MMD flows by numerical examples.

MS [00639] Analytical and computational aspects of topological photonics

room : E710

• [03761] TE band structure of high contrast honeycomb photonic crystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Maxence Cassier (Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France)
    • Michael Weinstein (Dept of Applied Physics & Applied Mathematics, and Dept. of Mathematics, Columbia University, New-York, United States)
  • Abstract : We analyse the propagation of transverse electric (TE) waves in a two dimensional honeycomb photonic medium. This medium consists of a homogeneous bulk of fixed permittivity and an array of high permittivity dielectric inclusions centered at the vertices of a honeycomb lattice. Our mathematical results, supported by numerical simulations, give detailed local information about the conical crossings of dispersion surfaces (Dirac points) as well as global information about the high contrast behavior of dispersion surfaces.
• [03902] Super band gaps and interface modes in one-dimensional quasicrystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Bryn Davies (Imperial College London)
    • Lorenzo Morini (Cardiff University)
    • Richard Craster (Imperial College London)
  • Abstract : Quasicrystalline photonic crystals show significant potential (large spectral gaps and robustness) but are underutilised in applications due to the lack of efficient modelling techniques. In this work, we show that periodic (supercell) approximations give accurate predictions of the main spectral gaps of Fibonacci quasicrystals. This is based on characterising the growth of the underlying recursion relation and corroborates the existence of previously observed “super band gaps”. We also present a strategy for creating interface modes.
• [03872] Mathematical theory for the interface mode in a waveguide bifurcated from a Dirac point
  • Format : Talk at Waseda University
  • Author(s) :
    • Jiayu QIU (Hong Kong University of Science and Technology)
    • Junshan LIN (Auburn University)
    • Peng XIE (Hong Kong University of Science and Technology)
    • Hai ZHANG (Hong Kong University of Science and Technology)
  • Abstract : In this talk, we present our new results on the existence of a bound state in a waveguide consisting of two semi-infinite periodic structures separated by an interface. The two periodic structures are perturbed from the same periodic medium with a Dirac point, and possess a common band gap enclosing the Dirac point. Using the layer potential technique and asymptotic analysis, we are able to overcome the difficulty imposed by the sharp interface.
• [05154] Bloch Waves for Maxwell's Equations in High-Contrast Photonic Crystals
  • Format : Talk at Waseda University
  • Author(s) :
    • Robert Paul Viator (Swarthmore College)
    • Robert Lipton (Louisiana State University)
    • Silvia Jimenez Bolanos (Colgate University)
    • Abiti Adili (University of Massachusetts - Lowell)
  • Abstract : We investigate the Bloch spectrum of a 3-dimensional high-contrast photonic crystal. The Bloch eigen- values, for fixed quasi-momentum, are expanded in a power series in the material contrast parameter in the high- contrast limit, together with a convergence radius, obtained by decomposing an appropriate vectorial Sobolev space into three mutually orthogonal curl-free subspaces. We also identify the limit spectrum in the periodic case. Time permitting, we will describe some geometries which admit this spectral structure.

contributed talk: CT120

room : E711

[00561] Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E711
• Type : Contributed Talk
• Abstract : We introduce new quantum data representations derived from uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits allowing for high storage density. QBArt directly embeds a binary representation in the computational basis and requires a lower number of quantum measurements. We demonstrate quantum algorithms for DNA pattern matching, Hamming weight calculation, complex value conjugation, and O(400) bits image retrieving executed on Quantiunuum, IBMQ, and IonQ QPUs.
• Classification : 68Q12, 81P68, 81P45, 81P16, Quantum encoding and computation on NISQ QPUs
• Format : Talk at Waseda University
• Author(s) :
  • Jan Balewski (National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory)
  • Mercy G. Amankwah (Case Western Reserve University, Cleveland)
  • Roel Van Beeumen (Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory)
  • E. Wes Bethel (Computer Science Department, San Francisco State University)
  • Talita Perciano (Scientific Data Division, Lawrence Berkeley National Laboratory)
  • Daan Camps (National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory)

[00446] Beyond Empirical Risk Minimization: Minimax Risk Classifiers

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E711
• Type : Contributed Talk
• Abstract : The empirical risk minimization (ERM) approach for supervised learning has been the workhorse of machine learning. However, ERM methods strongly rely on the specific training samples available and cannot easily address scenarios affected by distribution shifts and corrupted samples. This talk presents a learning framework based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). MRC learning is based on expectation estimates and does not strongly rely on specific training samples.
• Classification : 68Q32, 68T05, 68T37, 68T01, Machine Learning, Supervised Classification
• Format : Talk at Waseda University
• Author(s) :
  • Santiago Mazuelas (Basque Center for Applied Mathematics (BCAM))

[00716] Resource Efficient Boolean Function Solver on Quantum Computer

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E711
• Type : Contributed Talk
• Abstract : Grover's algorithm is the best-known quantum search algorithm for problems when classical ones cannot outperform brute-force search. We propose several novel techniques to improve efficiency in solving boolean equations under Grover's algorithm framework. A W-cycle circuit construction strategy and a greedy compression technique are proposed for the oracle to reduce quantum resource usage. A randomized Grover's algorithm further reduces the circuit depth. Numerical results on boolean quadratic equations demonstrate the advantage of the proposed techniques.
• Classification : 68Q12, 81P68
• Format : Talk at Waseda University
• Author(s) :
  • Xiang Li (Fudan University)
  • Hanxiang Shen (Fudan University)
  • Yingzhou Li (Fudan University)
  • Weiguo Gao (Fudan University)

[02686] Double Conical degeneracy on band structures of periodic Schrödinger operators

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @E711
• Type : Contributed Talk
• Abstract : Our work investigates double Dirac cones occurring near fourfold degenerate points in the band structures of certain operators. It is known that such degeneracy originates in the symmetries of operators. Thus, we introduce a new symmetric structure-the super honeycomb structure and an innovative method to incorporate all the symmetries. Both rigorous proof and numerical simulation of the existence of double Dirac cones in the bands of Schroedinger operators with super honeycomb symmetries will be shown.
• Classification : 68Q25, 68R10, 68U05
• Format : Talk at Waseda University
• Author(s) :
  • Ying Cao (Tsinghua University)

MS [02109] Recent Advances on Numerical Analysis of Integral and Integro-differential Equations

room : E802

• [04726] Mean square exponential stability and practical mean square exponential stability of stochastic delay differential equations driven by G-Brownian motion and Euler-Maruyama approximations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Haiyan Yuan (Heilongjiang institute of technology)
  • Abstract : This paper investigates the mean-square (MS) exponential stability and the practical mean square (PMS) exponential stability of stochastic delay differential equations driven by G-Brownian motion (G-SDDEs) and the numerical solution generated by Euler-Maruyama (EM) method. We present a weaker condition to prove the MS exponential stability of G-SDDEs instead of choosing a Lyapunov function under the case that the origin is an equilibrium point. In order to study whether the performance of G-SDDEs near an unstable equilibrium point is acceptable, we introduce the practical stability and establish a new generalized Gronwall inequality based on which we prove the PMS exponential stability of G-SDDEs. We also study the numerical approximations for G-SDDEs. We first establish the stability equivalence between the discrete EM method and the continuous EM method, then we prove that the continuous EM method can reproduce the MS exponential stability and the PMS exponential stability of G-SDDEs under some restrictions on the step size. Furthermore, two numerical experiments are conducted to con- firm our theoretical results.
• [02676] Superconvergent postprocessing of the continuous and discontinuous Galerkin methods for nonlinear Volterra integro-differential equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Lijun Yi (Shanghai Normal University)
    • Mingzhu Zhang (Shanghai Normal University)
  • Abstract : In this talk, we introduce novel postprocessing techniques for improving the accuracy of the CG and DG methods for nonlinear Volterra integro-differential equations. We first show that the CG and DG method superconverge at the nodal points of the time partition. We further prove that the postprocessed CG and DG approximations converge one order faster than the unprocessed CG and DG approximations in the $L^2$-, $H^1$- and $L^{\infty}$-norms. As a by-product of the postprocessed superconvergence results, we construct several a posteriori error estimators and prove that they are asymptotically exact. Numerical examples are presented to verify the theoretical results.

MS [01072] Data-Driven Methods in Scientific Machine Learning

room : E803

• [05632] Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
  • Format : Talk at Waseda University
  • Author(s) :
    • Victor Churchill (Trinity College)
    • Dongbin Xiu (The Ohio State University)
  • Abstract : Flow map learning has shown promise for data-driven modeling of unknown dynamical systems. A remarkable feature is the capability of producing accurate predictive models for partially observed systems, even when their exact mathematical models do not exist. We present an overview of the framework, as well as the important computational details for its successful implementation. A set of well defined benchmark problems are presented in full numerical detail to ensure accessibility for cross-examination and reproducibility.

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

room : E804

• [03514] Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis
  • Format : Talk at Waseda University
  • Author(s) :
    • Yusuke Imoto (Kyoto University)
  • Abstract : We have developed a novel noise reduction method for single-cell RNA sequencing (scRNA-seq) data, RECODE, to resolve the curse of dimensionality (COD) in high-dimensional data analysis. RECODE can reduce technical noises in scRNA-seq data based on high-dimensional statistics theory. In this talk, we will explain biological verification, applicability, and recent progress of RECODE. Moreover, we will overview mathematical/informatical grand challenges in single-cell data science, which is the theme of this minisymposium, at the beginning.
• [05223] Trajectory inference framework by entropic Gaussian mixture optimal transport
  • Format : Talk at Waseda University
  • Author(s) :
    • Toshiaki Yachimura (Tohoku University)
  • Abstract : In 1957, C.H. Waddington introduced the epigenetic landscape for cell differentiation. Recently, many attempts have been made to reconstruct this conceptual model from gene expression data. In this talk, I will introduce scEGOT, a novel trajectory inference framework of cell differentiation for time series scRNA-seq data based on Entropic Gaussian mixture optimal transport. scEGOT allows us to infer the dynamics of gene expression associated with cell differentiation. This talk is based on the WPI-ASHBi project.
• [03619] Dissecting cell identity via network inference and in-silico gene perturbation
  • Author(s) :
    • Kenji Kamimoto (Washington University in St.Louis)
  • Abstract : Single-cell omics technology enables the acquisition of multi-dimensional data in a high-throughput manner, revealing diverse and heterogeneous cellular identities. However, understanding biological events from a gene regulatory networks (GRNs) perspective remains difficult. Here, we have developed a new method, CellOracle, for the inference and analysis of GRNs. The method can perform in silico transcription factor perturbations, simulating the consequent changes in cell identity and promoting new mechanistic insights into the regulation of cell identity.
• [03878] Experimental guidance for discovering genetic networks from time series
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomas Gedeon (Montana State University)
    • Breschine Cummins (Montana State University)
    • Steve Haase (Duke University)
    • Konstantin Mischaikow (Rutgers University)
  • Abstract : We describe an iterative network hypothesis reduction from time-series data in which dynamic expression of individual, pairs, and entire collections of genes are used to infer core network models. The result of our work is a computational pipeline that prioritizes targets for genetic perturbation to experimentally infer network structure. We apply this computational pipeline to synthetic and yeast cell-cycle data.

MS [00184] Recent advances in data-driven methods for inverse problems

room : E811

• [05430] Are neural operators really neural operators?
  • Format : Online Talk on Zoom
  • Author(s) :
    • Rima Alaifari (ETH Zurich)
  • Abstract : In operator learning, it has been observed that proposed models may not behave as operators when implemented, questioning the very essence of what operator learning should be. We contend that some form of continuous-discrete equivalence is necessary for an architecture to genuinely learn the underlying operator, rather than just discretizations of it. Employing frames, we introduce the framework of Representation equivalent Neural Operator (ReNO) to ensure operations at the continuous and discrete level are equivalent.
• [04722] Plug-and-Play Models for Large-Scale Computational Imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Ulugbek Kamilov (Washington University in St. Louis)
  • Abstract : Computational imaging is a rapidly growing area that seeks to enhance the capabilities of imaging instruments by viewing imaging as an inverse problem. Plug-and-Play Priors (PnP) is one of the most popular frameworks for solving computational imaging problems through integration of physical and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods to provide state-of-the-art imaging algorithms. PnP models alternate between minimizing a data-fidelity term to promote data consistency and imposing a learned image prior in the form of an “image denoising” deep neural network. This talk presents a principled discussion of PnP, its theoretical foundations, its implementations for large-scale imaging problems, and recent results on PnP for the recovery of continuously represented images. We present several applications of our theoretical and algorithmic insights in bio-microscopy, computerized tomography, and magnetic resonance imaging.
• [02097] Learned proximal operators meets unrolling for limited angle tomography
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tatiana Alessandra Bubba (University of Bath)
    • Subhadip Mukherjee (University of Bath)
    • Luca Ratti (University of Genoa)
    • Andrea Sebastiani (University of Bologna)
  • Abstract : In recent years, limited angle tomography has become a challenging testing ground for several theoretical and numerical studies, where both variational regularisation and data-driven techniques have been investigated extensively. I will present a hybrid reconstruction framework where the proximal operator of an accelerated unrolled scheme is learned to ensure suitable theoretical guarantees. The recipe relays on the interplay between sparse regularisation, harmonic analysis, microlocal analysis and Plug and Play methods.
• [04626] Plug-and-Play sampling for inverse problems in imaging
  • Format : Talk at Waseda University
  • Author(s) :
    • Julie Delon (Université Paris Cité)
    • Rémi Laumont (Technical University of Denmark,)
    • Marcelo Pereyra (Heriot-Watt University)
    • Andrés Almansa (Université Paris Cité)
    • Valentin De Bortoli (Ecole Normale Supérieure)
  • Abstract : In a Bayesian framework, image models are used as priors or regularisers and combined to explicit likelihood functions to define posterior distributions. These posterior distributions can be used to derive Maximum A Posteriori (MAP) estimators, leading to optimization problems that are generally well studied and understood. Sampling schemes can also be used to explore more finely these posterior distributions, derive other estimators, quantify uncertainties or perform other advanced inferences. In a manner akin to Plug \& Play (PnP) methods in optimization, these sampling schemes can be combined with denoising neural networks approximating the gradient of a log-prior on images. In this talk, we will focus on these PnP sampling schemes, which raise important questions concerning the correct definition of the underlying Bayesian models or the computed estimators, as well as their regularity properties, necessary to ensure the stability of the numerical schemes.

MS [00703] Combining machine learning with domain decomposition and multilevel methods

room : E812

• [03764] A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training
  • Format : Talk at Waseda University
  • Author(s) :
    • Axel Klawonn (University of Cologne)
    • Martin Lanser (University of Cologne)
    • Janine Weber (University of Cologne)
  • Abstract : In this talk, a novel domain decomposition-based CNN-DNN (convolutional/deep neural network) architecture is presented that naturally supports a model parallel training strategy and that is loosely inspired by two-level domain decomposition methods. Experimental results for different 2D image classification problems are shown as well as for the classification of 3D computer tomography (CT) scans. The results show that the proposed approach can significantly accelerate the required training time without losing accuracy in most cases.
• [03312] DNN-MG: A Hybrid Neural Network/Finite Element Method
  • Format : Talk at Waseda University
  • Author(s) :
    • Nils Margenberg (Helmut Schmidt University Hamburg)
    • Robert Jendersie (Otto von Guericke University Magdeburg)
    • Christian Lessig (Otto von Guericke University Magdeburg)
    • Thomas Richter (Otto von Guericke University Magdeburg)
  • Abstract : The Deep Neural Network Multigrid Solver (DNN-MG) augments classical finite element simulations in fluid-dynamics by deep neural networks to improve the computational efficiency. To achieve this, it combines a geometric multigrid solver with a DNN that is used when a full resolution of the effects is not feasible or efficient. Our method's efficiency, generalizability, and scalability is demonstrated through applications to 3D benchmark simulations of the Navier-Stokes equations.
• [05268] Combining physics-informed neural networks with multilevel domain decomposition
  • Format : Online Talk on Zoom
  • Author(s) :
    • Alexander Heinlein (Delft University of Technology (TU Delft))
    • Victorita Dolean Maini (University of Strathclyde)
    • Siddhartha Mishra (ETH Zurich)
    • Ben Moseley (ETH Zurich)
  • Abstract : Physics-informed neural networks (PINNs) are a powerful approach for solving problems related to differential equations. However, PINNs often struggle to solve differential equations when they have high frequency and/or multi-scale solutions. In this work, we improve the performance of PINNs in this regime by combining them with domain decomposition. We build on the existing finite basis physics-informed neural networks (FBPINNs) framework and show that adding multilevel modelling to FBPINNs improves their performance.
• [04823] Enhancing training of scientific machine learning applications
  • Format : Talk at Waseda University
  • Author(s) :
    • Alena Kopanicakova (Brown University)
  • Abstract : Scientific machine learning has shown potential in creating efficient surrogates for complex multiscale and multiphysics problems. However, the computational cost of training these surrogates is prohibitively high.We propose a training procedure that utilizes the layer-wise decomposition of a deep neural network in order to construct a nonlinear preconditioner for the standard L-BFGS optimizer.The convergence properties of the novel training method will be analyzed by means of numerical experiments.

MS [02386] Recent advances on theory and algorithms in deep learning applications

room : E817

• [03440] Vanilla Feedforward Neural Networks as a Discretization of Dynamical Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Yongqiang Cai (Beijing Normal University)
  • Abstract : Deep learning has made significant progress in the fields of data science and natural science. Some studies have linked deep neural networks to dynamical systems, but the network structure is restricted to a residual network. It is known that residual networks can be regarded as a numerical discretization of dynamical systems. In this talk, we consider the traditional network structure and prove that vanilla feedforward networks can also be used for the numerical discretization of dynamical systems, where the width of the network is equal to the dimensions of the input and output. Our proof is based on the properties of the leaky-ReLU function and the numerical technique of the splitting method for solving differential equations. Our results could provide a new perspective for understanding the approximation properties of feedforward neural networks.
• [03441] Phase Diagram of Initial Condensation for Two-layer Neural Networks
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhengan Chen (Shanghai Jiao Tong University)
    • Yuqing Li (Shanghai Jiao Tong University)
    • Tao Luo (Shanghai Jiao Tong University)
    • Zhangchen Zhou (Shanghai Jiao Tong University)
    • Zhiqin Xu (Shanghai Jiao Tong University)
  • Abstract : The phenomenon of distinct behaviors exhibited by neural networks under varying scales of initialization remains an enigma in deep learning research. In this paper, based on the earlier work by Luo et al.~\cite{luo2021phase}, we present a phase diagram of initial condensation for two-layer neural networks. Condensation is a phenomenon wherein the weight vectors of neural networks concentrate on isolated orientations during the training process, and it is a feature in non-linear learning process that enables neural networks to possess better generalization abilities. Our phase diagram serves to provide a comprehensive understanding of the dynamical regimes of neural networks and their dependence on the choice of hyperparameters related to initialization. Furthermore, we demonstrate in detail the underlying mechanisms by which small initialization leads to condensation at the initial training stage.
• [03386] Robust Full Waveform Inversion: A Source Wavelet Manipulation Perspective
  • Format : Talk at Waseda University
  • Author(s) :
    • Chenglong Bao (Tsinghua University)
    • Lingyun Qiu (Tsinghua University)
    • Rongqian Wang (Tsinghua University)
  • Abstract : Full-waveform inversion (FWI) is a powerful tool for high-resolution subsurface parameter reconstruction. Due to the existence of local minimum traps, the success of the inversion process usually requires a good initial model. Our study primarily focuses on understanding the impact of source wavelets on the landscape of the corresponding optimization problem. We thus introduce a decomposition scheme that divides the inverse problem into two parts. The first step transforms the measured data into data associated with the desired source wavelet. Here, we consider inversions with known and unknown sources to mimic real scenarios. The second sub-problem is the conventional full waveform inversion, which is much less dependent on an accurate initial model since the previous step improves the misfit landscape. A regularized deconvolution method and a convolutional neural network are employed to solve the source transformation problem. Numerical experiments on the benchmark models demonstrate that our approach improves the gradient's quality in the subsequent FWI and provides a better inversion performance.
• [02945] Learning robust imaging model with unpaired data
  • Format : Talk at Waseda University
  • Author(s) :
    • Chenglong Bao (Tsinghua University)
  • Abstract : In this talk, in the unpaired data regime, we discuss our recent progress in building AI-aided robust models and their applications in image processing. Leveraging the Bayesian inference framework, our model combines classical mathematical modeling and deep neural networks to improve interpretability. Experimental results on various real datasets validate the advantages of the proposed methods.

MS [01868] An introduction of “Journal of Machine Learning” for applied mathematicians

room : E818

• [02982] Generalization ability and memorization phenomenon of distribution learning models
  • Format : Talk at Waseda University
  • Author(s) :
    • Hongkang Yang (Princeton University, Program in Applied and Computational Mathematics)
  • Abstract : Generative models and density estimators suffer from the memorization phenomenon (i.e. convergence to the finite training samples) as training time goes to infinity. This deterioration is in contradiction to the empirical success of models such as StableDiffusion and GPT-3. We resolve this paradox by proving that distribution learning models enjoy implicit regularization during training. Specifically, prior to the onset of memorization, their generalization errors at early-stopping escape from the curse of dimensionality.
• [04035] Approximation of Functionals by Neural Network without Curse of Dimensionality
  • Format : Talk at Waseda University
  • Author(s) :
    • Yahong Yang (The Hong Kong University of Science and Technology)
    • Tianyu Jin (The Hong Kong University of Science and Technology)
    • Yang Xiang (Hong Kong University of Science and Technology)
  • Abstract : In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\sqrt{m})$ where m is the size of networks, which overcomes the curse of dimensionality. Then, the proposed method is employed in several numerical experiments, such as evaluating the energy functionals and solving Poisson equations by the aforementioned network at one or a few given points.
• [02256] Approximation of Functionals by Neural Network without Curse of Dimensionality
  • Format : Talk at Waseda University
  • Author(s) :
    • Yahong Yang (Hong Kong University of Science and Technology)
    • Yang Xiang (Hong Kong University of Science and Technology)
  • Abstract : In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $O(1/\sqrt{m})$ where $m$ is the size of networks. In other words, the error of the network is no dependence on the dimensionality respecting to the number of the nodes in neural networks. The key idea of the approximation is to define a Barron space of functionals.
• [02998] Ab-Initio Study of Interacting Fermions at Finite Temperature with Neural Canonical Transformation
  • Format : Talk at Waseda University
  • Author(s) :
    • Hao Xie (Institute of Physics, Chinese Academy of Sciences)
    • Linfeng Zhang (DP Technology/AI for Science Institute)
    • Lei Wang (Institute of Physics, Chinese Academy of Sciences)
  • Abstract : We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is imple- mented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quan- tum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further ex- tensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.

MS [01136] Advances in Variational Models and PDEs for Images

room : E819

• [01712] Application of weighted TV flow to material science problems
  • Format : Online Talk on Zoom
  • Author(s) :
    • Prashant Athavale (Clarkson University)
    • Emmanuel Atindama (Clarkson University)
    • Peter Lef (Clarkson University)
    • Gunay Dogan (National Institute of Standards and Technology)
  • Abstract : Several variational and partial differential equation (PDE)-based image processing methods can restore noisy crystallographic orientation data. We discuss restoration approaches, such as the classical total variation-based methods to diffusion PDEs. However, such methods are parameter-dependent, making them challenging in practice. Our work discusses an algorithm to restore noisy orientation data and circumvent the parameter selection problem by using weighted total variation flow, a nonlinear diffusion applied to the noisy orientation map.
• [04202] Rank-One Prior: Real-Time Scene Recovery
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tieyong Zeng (The Chinese University of Hong Kong)
  • Abstract : Scene recovery is a fundamental imaging task with several practical applications, including video surveillance and autonomous vehicles, etc. In this talk, we provide a new real-time scene recovery framework to restore degraded images under different weather/imaging conditions, such as underwater, sand dust and haze. A degraded image can actually be seen as a superimposition of a clear image with the same color imaging environment (underwater, sand or haze, etc.). Mathematically, we can introduce a rank-one matrix to characterize this phenomenon, i.e., rank-one prior (ROP). Using the prior, a direct method with the complexity is derived for real-time recovery. For general cases, we develop ROP to further improve the recovery performance. Comprehensive experiments of the scene recovery illustrate that our method outperforms competitively several state-of-the-art imaging methods.
• [02233] Multispectral Image Restoration by Structured Eigendecomposition
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhantao MA (The University of Hong Kong)
    • Michael Kwok-Po NG (The University of Hong Kong)
  • Abstract : We propose and study the opponent transformation for multispectral images. We generalize the well-known opponent transformation for color images and use it to bring the generalized opponent transformation total variation (GOTTV) multispectral image restoration model. By inheriting the crucial properties of the opponent transformation, the minimization formula of the GOTTV can be simplified and solved by the ADMM. Numerical examples are presented to demonstrate that the performance of the new GOTTV is well.

MS [02130] Fluid-structure interactions in geophysical flows

room : E820

• [04383] A simple model on what drives continental drifts
  • Format : Talk at Waseda University
  • Author(s) :
    • Jinzi Mac Huang (New York University Shanghai)
  • Abstract : It is well known that the continents of earth do not stay in place, and thermal convection in Earth’s mantle is believed to be the driving force of these motions. How does mantle convection couple to the continental drift? Does the moving continent affect the mantle motion beneath it? We address these questions through a simple fluid-structure interaction model, exploring the fluid mechanical origin of continental drift and the possibility of modeling tectonic plate interactions.
• [05512] Computing the diffusivity of a particle subject to dry friction with colored noise
  • Format : Talk at Waseda University
  • Author(s) :
    • Laurent Mertz (City University of Hong Kong)
    • Josselin Garnier (Polytechnique)
  • Abstract : Experimental studies and numerical simulations have been devoted to the motion of an object subjected to a dry friction and an external random force. The experimental and numerical observations suggest that the variance of the object displacement grows linearly with time. Here, the variance growth rate is called diffusivity. The goal of this paper is to propose efficient stochastic simulation methods for computing the diffusivity when the external random force is white or colored noise.
• [04815] The Formation of Karst Pinnacles
  • Format : Online Talk on Zoom
  • Author(s) :
    • Nick Moore (Colgate University)
  • Abstract : Recent experiments demonstrate how dissolution, in conjunction with gravitationally-induced convective flows, can create sharp geometric features. These laboratory-created structures give insight into geological features known as karst pinnacles. A new computational approach reveals convergence to a morphological attractor with high, yet finite, tip curvature. These results reverse previous hypotheses on shock formation (i.e. finite-time blowup of tip curvature), agree well with laboratory experiments, and enable simple estimates for the age of geological structures.

MS [00435] Multiscale Numerical Methods for Complex Fluids

room : D101

• [05555] Moisture-induced weakening of adhesion between polymers and metals
  • Format : Talk at Waseda University
  • Author(s) :
    • Shuji Ogata (Nagoya Institute of Technology)
  • Abstract : Adhesive bonding has attracted renewed interest from the manufacturing industry due to its role in creating composite materials and multimaterial designs with the desired arrangements of polymers and metals. In the present work, we theoretically addressed a fundamental problem of the moisture-induced adhesion weakening between polymers (or resin) and metal from a novel viewpoint of (de)protonation of them in water.
• [03509] Modelling and Simulation of Capillary Origami in Three Dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Zhixuan Li (National University of Singapore)
    • Weiqing Ren (National University of Singapore)
  • Abstract : Capillary origami involves folding a planar object into a 3D structure using capillary force, and has many important applications such as the fabrication of microelectromechanical systems. In this work, we propose a three-dimensional model of the droplet-on-sheet system with a pinned contact line. The system energy consists of interfacial energies caused by surface tensions and the elastic energy of the thin sheet given by nonlinear Koiter's model. We derive the governing equations of the static equilibrium using a variational approach. We then propose a numerical algorithm to find the equilibrium via a relaxation dynamics. We use the subdivision element method for discretization of the sheet, which provides $C^1 \cap H^2$ basis functions, and a modified area-minimizing functional for maintaining the mesh quality of the discrete droplet surface. Our numerical simulations demonstrate first-order and second-order convergence in time and space, respectively, and are in good agreement with physical experiments. Specifically, for a triangular sheet, we present phase diagrams of folding, which exhibit rich and fully three-dimensional behaviors not captured by previous two-dimensional models. Our results provide new insights into the mechanics of capillary folding and can inform the design of microfabrication techniques.
• [04590] Multiscale simulation of a polymer melt flow between two coaxial cylinders under nonisothermal conditions
  • Format : Talk at Waseda University
  • Author(s) :
    • Takashi Taniguchi (Kyoto University)
    • Takeshi Sato (Kyoto University)
    • Yuji Hamada (Kyoto University)
  • Abstract : We successfully extend a multiscale simulation (MSS) method to nonisothermal wellentangled polymer melt flows between two coaxial cylinders. In the multiscale simulation, the macroscopic flow system is connected to a number of microscopic systems through the velocity gradient tensor, stress tensor and temperature. At the macroscopic level, in addition to the momentum balance equation, we consider the energy balance equation, where heat generation plays an important role not only in the temperature distribution but also in the flow profile.
• [05592] Flow-type dependent rheologies and multiscale simulations
  • Format : Talk at Waseda University
  • Author(s) :
    • Giulio Giuseppe Giusteri (University of Padua)
    • Francesca Tedeschi (University of Padua)
    • Maria Lukácová-Medvid'ová (Johannes Gutenberg University of Mainz)
    • Leonid Yelash (Johannes Gutenberg University of Mainz)
  • Abstract : The importance of taking into consideration the dependence on the local flow type of the response of non-Newtonian fluids in multiscale data-driven simulations will be highlighted. A framework to organize data in mixed flows and reconstruct the stress tensor will be reviewed. Then, an algorithm to take into account the flow-type dependence in a consistent way will be presented by discussing paradigmatic planar flows implied by data obtained with a FENE-type model for polymer chains.

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

room : D102

• [03299] Investigation on the hyper-reduction approach for the contact-impact simulation
  • Format : Talk at Waseda University
  • Author(s) :
    • SANGJOON SHIN (Seoul National University)
    • Seung-Hoon Kang (Seoul National University)
    • Minho Hwang (Seoul National University)
    • Yongse Kim (Republic of Korea Air Force)
    • Haeseong Cho (Jeonbuk National University)
  • Abstract : In the multi-body finite element analysis, the contact algorithm usually requires huge computational cost to capture the temporal/spatial discontinuity on the contact surface. This presentation will investigate the projection-based reduced-order model for the contact-impact simulation. Discrete empirical interpolation method (DEIM) will be employed among the hyper-reduction approaches for computation acceleration. Treatment on each nonlinear component, internal and contact force vectors, will be examined for the generation of DEIM basis and sparse sampling.
• [05003] Manifold-Augmented Deep learning-based Approach for Prediction of Airfoil Aerodynamic Performance at Low Reynolds Number
  • Format : Talk at Waseda University
  • Author(s) :
    • Seongwoo Cheon (Jeonbuk National University)
    • Hyejin Kim (Jeonbuk National University)
    • Seokhui Ryu (Gyeongsang National University)
    • Haeseong Cho (Jeonbuk National University)
    • Hakjin Lee (Gyeongsang National University)
  • Abstract : Computational fluid dynamics (CFD) analysis usually gives an accurate performance, better reliability, but it requires intensive computational time and cost. In this study, the deep learning-based MOR framework is proposed to predict the aerodynamic performance of airfoils. For this purpose, the proper orthogonal decompostion (POD), autoencoder (AE), and variational autoencoder (VAE) is carried out to gather the latent vectors from full-order snapshot matrix. Moreover, a novel generative model using projection-based manifold learning is proposed to overcome the lack of data due to the computational cost of CFD analysis and augment the training data.
• [05436] High-dimensional regression using partition of unity networks (POU-Net)
  • Format : Online Talk on Zoom
  • Author(s) :
    • Eric Felix Darve (Stanford University)
    • Tiffany Fan (Stanford University)
    • Nathaniel Trask (Sandia National Laboratories)
    • Marta D'Elia (Stanford University)
  • Abstract : High-dimensional regression problems present challenges in scientific and engineering applications. Conventional approaches like polynomial interpolation become computationally expensive as the dimensionality increases exponentially. Sparse grids and radial basis function regression have been developed as alternatives, but they suffer from high computational costs, low accuracy, and instability in some cases. Deep Neural Networks (DNNs) have proven to be a reliable regression method for high-dimensional problems. However, designing an optimal DNN structure, weight initialization, and achieving high accuracy with the optimizer pose difficulties, making error control challenging in engineering and scientific applications. Additionally, reproducibility is often problematic. To address these issues, we introduce POU-Net and its variants. POU-Net takes advantage of DNNs’ dimensionality reduction and regression capabilities. Additionally, it utilizes the reliability, accuracy, and computational efficiency of polynomial interpolation within the reduced dimension. Our approach enables robust and accurate regression across a wide range of input dimensions. We evaluate the proposed method using various benchmarks and applications, comparing its performance to state-of-the-art techniques.

contributed talk: CT146

room : D401

[01094] Variational iteration Method for Shallow Water Waves

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D401
• Type : Contributed Talk
• Abstract : Variational iteration method, VIM, is employed to solve analytic solutions of shallow water wave equations. For its linearized models we compute a periodic numerical example, and a symbolic one with unprescribed initial conditions and parameters. Both examples are found their explicit exact solutions by VIM. Then we turn to some nonlinear models and obtain their highly accurate approximate solutions. We concluded that VIM is very effective for shallow water wave problems and other nonlinear PDEs.
• Classification : 76M30, 35F55, 35C05, 35C10, shallow water wave
• Format : Talk at Waseda University
• Author(s) :
  • Tzon-Tzer Lu (Department of Applied Mathematics, National Sun Yat-sen University)

[02670] Glacier sliding as a viscous fluid flow modulated by cavitation

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D401
• Type : Contributed Talk
• Abstract : Glacial ice slides due to lubrication by a thin film of water. Separation of ice from the bed results in water-filled cavities that modulate the stress balance, with important implications for glacier flow. We model the problem as a linearised Stokes flow over a wavy boundary. Complex variable methods are used to solve a Riemann-Hilbert problem that is coupled to a kinematic equation for cavity size. The model is used to discuss glacier friction laws.
• Classification : 76M40, 86A40, 76D07, 76M45
• Format : Talk at Waseda University
• Author(s) :
  • Ian Hewitt (University of Oxford)

[00784] A Lagrangian-finite difference scheme for solving viscoelastic fluid flows

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D401
• Type : Contributed Talk
• Abstract : In this work, we will present a new numerical scheme that combines the Generalized Lie Derivative in a Lagrangian framework with the finite difference method. The viscoelastic models with the upper-convected time derivative term are rewritten in order to improve the stability of the method. Moreover, the proposed scheme can also be applied to study the High Weissenberg Number Problems.
• Classification : 76M20, 76A10, 65M50
• Format : Talk at Waseda University
• Author(s) :
  • jose Alberto Cuminato (University of São Paulo)
  • Cassio Machiavelli Oishi (São Paulo State University)
  • Debora de Oliveira Medeiros (University of São Paulo)

[01580] Fast Summation for the Barotropic Vorticity Equations

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D401
• Type : Contributed Talk
• Abstract : The barotropic vorticity equations describe the conservation of absolute vorticity for a fluid on a rotating sphere. When transformed appropriately, one can rewrite these with a Biot-Savart integral, and with a Lagrangian discretization, one can arrive at a discretized system with an update taking the form of a N-body sum. In this talk, I present a fast summation technique that reduces the asymptotic complexity of this sum from $O(N^2)$ to $O(N\log{N})$ with a new spherical tree code, suitable for a wide range of problems in geophysical fluid dynamics.
• Classification : 76M28, 76U99, 65M75, 86A08
• Format : Talk at Waseda University
• Author(s) :
  • Anthony Chen (University of Michigan, Ann Arbor)

[01420] A stochastic solution to inverse problems in thermo-fluid problems

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D401
• Type : Contributed Talk
• Abstract : Inverse problems find their applications in various thermo-fluid systems. The present work aims to develop a computational framework using fast Bayesian inference, which leads to forward uncertainty propagation in various thermo-fluid models and solves the corresponding inverse problems. The framework leverages the polynomial chaos expansions (PCEs) to generate a computationally efficient and statistically equivalent surrogate model of the computationally expensive forward model and dimensionality reduction based on Karhunen-Loeve (K-L) expansion.
• Classification : 76M21, 80A23, 86A22
• Format : Online Talk on Zoom
• Author(s) :
  • SUFIA KHATOON (Indian Institute of Technology Delhi)

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

room : D402

• [05505] Analytical solution to the elliptic PDE of shelf wave with the relaxation of semi-geostrophic approximation
  • Format : Talk at Waseda University
  • Author(s) :
    • Hui Wu (East China Normal University)
  • Abstract : The response of a wide shelf to sub-inertial and barotropic offshore pressure signals from the shelf edge was investigated. By relaxing the semi-geostrophic approximation, an elliptical wave structure equation was formulated and solved with the integral transform method. It was found that when the imposed offshore signal has an along-shelf length scale similar to the shelf width, it can efficiently break the potential vorticity barrier and propagate towards the coast, producing a significant coastal sea-level set-up. Thereafter, the pressure signal reflects from the coast or the sloping topography, producing a transient eddy and propagates to the downshelf. The intensities of the coastal set-up and the eddy increase as the along-shelf scale of the sub-inertial signal decreases or when its timescale is close to the inertial period. For a signal with longer timescale, the eddy is insignificant. The nature of the shelf response is controlled by the shelf conductivity κ≡r⁄((fsB) ), in which r is the Rayleigh friction coefficient, f is the Coriolis parameter, s is the shelf slope, and B is the shelf width, respectively. For a given offshore signal, coastal set-up increases with κ. For large κ, the eddy energy is concentrated at low modes, producing a large eddy, whereas a small κ produces a small eddy. The proposed theory can explain coastal sea-level fluctuations under eddy impingement in the Mid-Atlantic Bight or other similar areas.
• [05534] Two-grid Finite Element Decoupling Scheme for the Mixed Navier-Stokes/Darcy Model
  • Author(s) :
    • Yanren Hou (Xi'an Jiaotong University)
  • Abstract : For the mixed steady-state Navier-Stokes/Darcy model with BJS interface condition, a two-grid FEM based decoupling scheme is analyzed in the talk. The well-posedness of the discrete system and its optimal error estimation are obtained.
• [05325] On discrete shape gradients of boundary type for PDE-constrained shape optimizations
  • Format : Talk at Waseda University
  • Author(s) :
    • Wei Gong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Shape gradients have been widely used in numerical shape gradient descent algorithms for shape optimization. The two types of shape gradients, i.e., the distributed one and the boundary type, are equivalent at the continuous level but exhibit different numerical behaviors after finite element discretization. To be more specific, the boundary type shape gradient is more popular in practice due to its concise formulation and convenience in combining with shape optimization algorithms but has lower numerical accuracy. In this talk we provide a simple yet useful boundary correction for the normal derivatives of the state and adjoint equations, motivated by their continuous variational forms, to increase the accuracy and possible effectiveness of the boundary shape gradient in PDE-constrained shape optimization. We consider particularly the state equation with Dirichlet boundary conditions and provide a preliminary error estimate for the correction. Numerical results show that the corrected boundary type shape gradient has comparable accuracy to that of the distributed one. Extensions to other type of PDE-constrained shape optimizations are also considered, including the interface identification problems, the eigenvalue problems, the Stokes and Navier-Stokes problems. Moreover, we give a theoretical explanation for the comparable numerical accuracy of the boundary type shape gradient with that of the distributed shape gradient for Neumann boundary value problems.

MS [00497] Advances in numerical methods for nonlinear optics

room : D404

• [05175] Local time-integration for wave equations
  • Format : Online Talk on Zoom
  • Author(s) :
    • Constantin Carle (Karlsruhe Institute of Technology)
    • Marlis Hochbruck (Karlsruhe Institute of Technology)
  • Abstract : For the spatially discretized acoustic wave equation, stability of explicit time integration schemes such as the leapfrog scheme can only be guaranteed under a CFL condition. In the case of locally refined meshes, this condition is the main bottleneck for the efficiency of explicit schemes. To overcome this issue, we introduce local time-stepping and locally implicit schemes and present a rigorous error analysis.
• [02186] Discontinuous Galerkin Time-Domain methods for nonlinear active media on unstructured grids
  • Format : Online Talk on Zoom
  • Author(s) :
    • Stéphane Descombes (Université Côte d'Azur, CNRS, Inria, LJAD)
    • Stéphane Lanteri (Université Côte d'Azur, Inria, CNRS, LJAD)
    • Cédric Legrand (Université Côte d'Azur, Inria, CNRS, LJAD)
  • Abstract : We present a Discontinuous Galerkin Time-Domain method for solving the system of Maxwell equations coupled to the rate equations modeling light interaction with gain media.

MS [00605] Recent advances in theory and application of quantum computing technology

room : D405

• [03609] mpiQulacs: A Distributed Quantum Computer Simulator for A64FX-based Cluster Systems
  • Format : Talk at Waseda University
  • Author(s) :
    • Masafumi Yamazaki (Fujitsu LTD.)
    • Satoshi Imamura (Fujitsu LTD.)
    • Takumi Honda (Fujitsu LTD.)
    • Akihiko Kasagi (Fujitsu LTD.)
    • Akihiro Tabuchi (Fujitsu LTD.)
    • Hiroshi Nakao (Fujitsu LTD.)
    • Naoto Fukumoto (Fujitsu LTD.)
    • Kohta Nakashima (Fujitsu LTD.)
  • Abstract : Quantum computer simulators running on classical computers are essential for understanding real quantum states and developing emerging quantum applications. In particular, state-vector simulators, which store the complete state vector in memory can be used to analyze the behavior of all types of quantum applications. Here, we briefly introduce a distributed state-vector simulator and describe its distributed implementation and optimization. Finally, we present the scaling performance of the large-scale simulation using an A64FX-based cluster system.
• [04257] Examples of application of CMOS annealing
  • Format : Talk at Waseda University
  • Author(s) :
    • Akiko Masaki (Hitachi, Ltd.)
    • Kaho Takahashi (Hitachi, Ltd.)
    • Kazuo Ono (Hitachi, Ltd.)
    • Taro Aratani (National Institute of Maritime, Port and Aviation Technology)
    • Takahiro Majima (National Institute of Maritime, Port and Aviation Technology)
  • Abstract : Hitachi has developed CMOS annealing technology as a next-generation computing technology that can solve large-scale, complex optimization problems at high speed. In this talk, we will introduce some examples of practical applications of CMOS annealing technology. In particular, we will present examples of applications that are proving effective in the field of public infrastructure, where there are large-scale problems that cannot be solved by conventional computing technologies.
• [04116] Outline and present development status of CMOS annealing
  • Format : Talk at Waseda University
  • Author(s) :
    • Masanao Yamaoka (Hitachi, Ltd.)
  • Abstract : Today, optimization processing is important for various fields. The CMOS annealing technology, which is a new-paradigm computing technology inspired by quantum computers, was developed to accelerate the optimization processing for the new value creation. By utilizing semiconductor technology, CMOS annealing can achieve large-scale integration and can be easily implemented for the practical usage. In this talk, the outline of CMOS annealing will be introduced with some examples of actual applications as a present development status.

MS [00449] Atomistic simulations in the exascale era

room : D407

• [05409] Quantum-Mechanical Shadow Born-Oppenheimer Molecular Dynamics for Distributed Computing
  • Format : Talk at Waseda University
  • Author(s) :
    • Anders Niklasson (LANL)
  • Abstract : We present recent developments of quantum-mechanical shadow Born-Oppenheimer molecular dynamics for simulations with tens-of-thousands of atoms using distributed, linear scaling, graph-based electronic structure calculations [Negre, Wall, and Niklasson, J. Chem. Phys. 158, 074108 (2023)].
• [05380] Compressing, resampling and forecasting atomic simulations with descriptor vectors
  • Format : Online Talk on Zoom
  • Author(s) :
    • Thomas D Swinburne (CNRS )
  • Abstract : We show atomic descriptor functions give a metric latent space for atomic simulations, where sparse snapshots can be interpolated and complex transitions (e.g. yeilding) can be linearly classified. When descriptors are unimodal, latent trajectories can be resampled and forecasted by a vector autoregressive model, with a Mahalanobis extrapolation grade. The approach is applied to challenging, large-scale simulations of dislocation plasticity. A strategy to optimise resources is proposed, maximising the estimated information yield of additional effort.
• [05479] Structure modeling with large-scale DFT and machine-learning methods
  • Format : Talk at Waseda University
  • Author(s) :
    • Tsuyoshi Miyazaki (National Institute for Materials Science (NIMS))
  • Abstract : To overcome the size limitation of DFT calculations, we have developed a large-scale and linear-scaling DFT code CONQUEST. Using CONQUEST, we can investigate the atomic and electronic structures of large and complex materials containing many thousands of atoms. In this talk, I introduce the recent progress of CONQUEST, together with a newly proposed method to analyze the local atomic structures observed in the DFT-MD simulations of complex systems.

contributed talk: CT170

room : D408

[02415] Propagation of epistemic uncertainty though a multi-layerd geometrically exact beam

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D408
• Type : Contributed Talk
• Abstract : Uncertainty is ever-present in engineering. In this work, we demonstrate the effect of parameter uncertainty on a carbon spring prosthetic foot. The prosthesis is built with multiple layers of carbon fibre laminate. This layered structure is accounted for via homogenisation of the material parameters in the geometrically exact beam model of the prosthesis. Homogenising the material parameters introduces additional uncertainty. The resulting uncertain deformation envelopes and stored energy envelopes are examined.
• Classification : 90C70, 70E55, 74-XX
• Format : Talk at Waseda University
• Author(s) :
  • Eduard Sebastian Scheiterer (Institute of Applied Dynamics - Friedrich-Alexander Universität Erlangen-Nürnberg)
  • Sigrid Leyendecker (Institute of Applied Dynamics - Friedrich-Alexander Universität Erlangen-Nürnberg)

[02367] Applying the 2 Steps SLP method to the UC-ACOPF problem

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D408
• Type : Contributed Talk
• Abstract : The Unit Commitment (UC) problem is a widely used tool for the daily management of power transmission networks in modern economies. While the classical UC is a mixed-integer linear problem, when the AC Power Flow (ACPF) equations are included as constraints it becomes a mixed-integer nonlinear problem (MINLP). The 2-Step SLP method has been successfully applied to solving MINLP problems for gas networks, and here we will analyze its performance for power networks.
• Classification : 90Cxx
• Format : Talk at Waseda University
• Author(s) :
  • Dolores Gómez (Universidade de Santiago de Compostela)
  • Alfredo Ríos-Albores (Universidade de Santiago de Compostela)
  • Pilar Salgado (Universidade de Santiago de Compostela)

[02584] Malmquist Productivity Index under Fuzzy Environment

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D408
• Type : Contributed Talk
• Abstract : Malmquist productivity index (MPI) is widely used to estimate the productivity change by calculating the relative performance of homogeneous organizations for different time periods using data envelopment analysis (DEA). Although in real-world applications, traditional MPI method is tedious due to ambiguous or imprecise data. Thus, traditional DEA is integrated with fuzzy. In this study, novel integrated MPI method is proposed under fuzzy environment. To show the applicability and effectiveness of the proposed model, numerical example is also discussed.
• Classification : 90C70, 90C05, 90B50
• Author(s) :
  • Shivi Agarwal (Birla Institute of Technology and Science, Pilani)
  • Trilok Mathur (Birla Institute of Technology and Science, Pilani)
  • Swati Goyal (Birla Institute of Technology and Science, Pilani)

[00972] Reducing Communication in Federated Learning with Variance Reduction Methods

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D408
• Type : Contributed Talk
• Abstract : In Federated Learning $\text{(}$FL$\text{)}$, inter-client heterogeneity and partial participation of clients at each communication cause client sampling error. We control this client sampling error by developing a novel single-loop variance reduction algorithm. While sampling a small number of clients, the proposed FL algorithms require provably fewer or at least equivalent communication rounds compared to any existing method, for finding first and even second-order stationarypoints in the general nonconvex setting, and under the PL condition.
• Classification : 90Cxx, 68Wxx, 68Txx
• Author(s) :
  • Kazusato Oko (The University of Tokyo, AIP RIKEN)
  • Shunta Akiyama (The University of Tokyo)
  • Tomoya Murata ( The University of Tokyo, NTT DATA Mathematical Systems Inc.)
  • Taiji Suzuki (The University of Tokyo, AIP RIKEN)

[02039] Intelligent Computing Models for Super-large Protein Complex Prediction

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D408
• Type : Contributed Talk
• Abstract : Improved from our Fast Fourier Transform based prediction methods, recently we have designed new artificial intelligence enhanced computing models to predict the super-large protein complex structures, which can give out results from monomer sequences and show good results and promise advances.
• Classification : 92B20, 68T07
• Format : Talk at Waseda University
• Author(s) :
  • Xinqi Gong (Renmin University of China)

MS [01065] Mathematics and its Applications of Risk and Decision

room : D501

• [04299] Optimal reinsurance with multivariate risks and dependence uncertainty
  • Format : Talk at Waseda University
  • Author(s) :
    • Tolulope Rhoda Fadina (University of Essex)
    • Tolulope Fadina (University of Essex)
  • Abstract : We study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the reinsurance is purchased by the insurer for each line of business respectively. For the risk vector generated by the multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk including Expected Shortfall as a special case, and general premium principles satisfying certain conditions. To be more practical, the minimization of the total risk is conducted with both budget constraints and expected profit constraints. For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be convex or concave.
• [04329] Irreversible consumption habit under ambiguity: Singular control and optimal G-stopping time
  • Format : Talk at Waseda University
  • Author(s) :
    • HOI YING WONG (The Chinese University of Hong Kong)
    • Kyunghyun Park (Nanyang Technological University)
    • Kexin Chen (The Hong Kong Polytechnic University)
  • Abstract : Consider robust utility maximization with an irreversible consumption habit, where an agent concerned about model ambiguity is unwilling to decrease consumption and must simultaneously contend with a disutility (i.e., an adjustment cost) due to a consumption increase. While the optimization is a robust analog of singular control problems over a class of consumption-investment strategies and a set of probability measures, it is a new formulation that involves non-dominated probability measures of the diffusion process for the underlying assets in addition to singular controls with an adjustment cost. This paper provides a novel connection between the singular controls in the optimization and the optimal G-stopping times in a G-expectation space, using a duality theory. This connection enables to derive the robust consumption strategy as a running maximum of the stochastic boundary, which is characterized by a free boundary arising from the optimal G-stopping times. The duality, which relies on arguments based on reflected G-BSDEs, is achieved by verifying the first-order optimality conditions for the singular control, the budget constraint equation for the robust strategies, and the worst-case realization under the non-dominated measures.
• [05330] On/Off Shore Currency Rate Discrepancy
  • Format : Talk at Waseda University
  • Author(s) :
    • Samuel Drapeau (Shanghai jiao Tong university )
    • Xuan Tao (Shanghai Jiao Tong University)
  • Abstract : Most developing countries (especially in Asia) adopted a tight control of foreign capital in order to protect their economy from abrupt capital outflows in period of crisis. As those economies developed and opened up to foreign financial investment, they often set up off shore currency exchange markets to facilitate the transfer of capital. This is for instance the case of China where the on shore rmb (CNY) was complemented with an off shore market for trading this currency (CNH). Theoretically, the face value from a domestic viewpoint of the currency is the same regardless of on/off shore origin. And indeed, when observing the spot rate, the CNY and the CNH rate only differ marginally. However, when looking at the price of futures for longer maturity, there is a significant discrepancy (in the CNY/CNY case, up to 4% when corrected for maturity). This is puzzling as the future face value follows the same principle as the present one. In the present work we propose a continuous time equilibrium in two similar market which are scholastically coupled. This solution of which is given by a coupled quadratic jump diffusion FBDE that provide an equilibrium price on both markets. We then use a second equilibrium to price futures and therefore provide some interpretations as for the price discrepancy observed on the market. This is a joint work with Xuan Tao, Peng Luo, Wang Tan and Wang Tao
• [04244] Portfolio Selection, Periodic Evaluations and Risk Taking
  • Format : Talk at Waseda University
  • Author(s) :
    • Alex Sing-lam Tse (University College London)
    • Harry Zheng (Imperial College London)
  • Abstract : We present a continuous-time portfolio selection problem faced by an agent with S-shaped preference who maximizes the utilities derived from the portfolio's periodic performance over an infinite horizon. The periodic reward structure creates subtle incentive distortion. In some cases, local risk aversion is induced which discourages the agent from risk taking in the extreme bad states of the world. In some other cases, eventual ruin of the portfolio is inevitable and the agent underinvests in the good states of the world to manipulate the basis of subsequent performance evaluations. We outline several important elements of incentive design to contain the long-term portfolio risk.

MS [00467] Volatility modeling in finance

room : D502

• [04764] Does the Term-Structure of Equity At-the-Money Skew Really Follow a Power Law?
  • Format : Talk at Waseda University
  • Author(s) :
    • Mehdi El Amrani-Zirifi (Bloomberg LP)
    • Julien Guyon (Ecole des Ponts ParisTech)
  • Abstract : Using two years of S&P 500, Eurostoxx 50, and DAX data, we empirically investigate the term-structure of the at-the-money-forward (ATM) skew of equity indexes. While a power law (2 parameters) captures the term-structure well away from short maturities, the power law fit deteriorates considerably when short maturities are included. By contrast, 3-parameter shapes such as time-shifted or capped power laws, are shown to fit well regardless of whether short maturities are included or not.
• [04899] Fast exact joint S&P 500/VIX smile calibration in discrete and continuous time
  • Format : Talk at Waseda University
  • Author(s) :
    • Florian Bourgey (Bloomberg L.P.)
    • Julien Guyon (Ecole des Ponts ParisTech)
  • Abstract : We introduce the Newton--Sinkhorn and implied Newton algorithms which significantly speed up the Sinkhorn algorithm that (Guyon, Risk, April 2020) used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a purely forward Markov functional model, we show how to build a continuous-time extension of the previous discrete-time model. We also compute model-free bounds on S&P 500 options that show the importance of taking VIX smile information into account. Extensive numerical tests are conducted.
• [03758] Joint calibration to SPX and VIX options with signature-based models
  • Format : Talk at Waseda University
  • Author(s) :
    • Christa Cuchiero (University of Vienna)
    • Guido Gazzani (University of Vienna)
    • Janka Möller (University of Vienna)
    • Sara Svaluto-Ferro (University of Verona)
  • Abstract : We consider a stochastic volatility model where the dynamics of the volatility are described by linear functions of the signature of a primary process. Under the assumption that this process is polynomial, we can express the log-price and the VIX squared as linear functions of the signature of an (augmented) primary process. This feature can be efficiently used for calibration purposes since the signature samples can be easily precomputed. We also propose a Fourier approach for VIX and SPX options exploiting that the signature of the augmented primary process is an infinite dimensional affine process.
• [03638] Neural Joint SPX/VIX Smile Calibration
  • Format : Talk at Waseda University
  • Author(s) :
    • Scander Mustapha (Princeton University)
    • Julien Guyon (CERMICS, Ecole des Ponts ParisTech)
  • Abstract : We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures, and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable loss allows us to fit market data for multiple S&P 500 and VIX maturities. A one-factor Markovian stochastic local volatility model is shown to fit both smiles and VIX futures within bid-ask spreads. The joint calibration actually makes it a pure path-dependent volatility model, confirming the findings in \[Guyon, 2022, The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew\].

contributed talk: CT176

room : D505

[01216] Neural network in option pricing

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D505
• Type : Contributed Talk
• Abstract : Black-Scholes model is the universally accepted model for computing option prices. While its is robust and easy to use, it has many flaws. Moreover, it failed spectacularly in 1987 during the wall street crash. This has led to proliferation of many extensions to the Black-Scholes model. Most extensions focus on relaxing the constant volatility assumption by incorporating randomness in the volatility. Whilst it provides slightly better estimation to option prices, it is computationally expensive to implement. Moreover, most of these models do not have closed-form solutions With advancement in computational techniques, neural network has been increasingly used to price options. Not only, does it outperform conventional stochastic volatility models, it does not require assumption on the statistical characteristics of assets and volatility distribution. A typical neural network consists of three layers: input, hidden, and output. It uses a supervised learning method based on the generalisation of the least mean square error (LMS) algorithm. A gradient descent method is used to minimise the cost function, which is the mean square difference between the target and actual net output. More advanced neural networks (deep learning architectures), such as a Recurrent Neural Network (RNN) and its variant Long Short-Term Memory (LSTM), are useful for taking care of the time-series nature of financial data. The general architecture of the convolutional neural network-based LSTM model includes an input layer, one or more convolutional layers, long short-term memory layer(s), dense layer(s), and an output layer. In this research, we will attempt to predict Strait Times Index (STI) which is one of the most regularly traded options in Singapore Exchange (SGX). After pre-processing and cleaning the data, the input (stock price, time to maturity and volatility and output (option prices) , variables will be extracted for training and testing the models. Various hyperparameters (optimizers, learning rate, hidden layers, activation functions, etc.) will be optimised to generate the best model for the prediction of the option pricing. A comparison of the accuracy of the prediction of option pricing will be performed for three models, namely convolutional neural network-based LSTM, Multilayer Perceptron neural network N and the Black Scholes option pricing model. Different metrics (root mean squared error, mean absolute error, and mean absolute percentage error) will be used to compare the performance of the models.
• Classification : 91G15, 91G20
• Format : Talk at Waseda University
• Author(s) :
  • Abby Chee Hong Tan (Universiti Brunei Darussalam)

[02592] Pricing American barrier options with transaction costs

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D505
• Type : Contributed Talk
• Abstract : When transaction costs in trading underlying stocks are considered, far more modelling effort is needed for pricing options, as a unique fair price between the holder and writer no longer exists. It becomes even more complicated for American and exotic options. In this talk, we shall discuss the valuation of American barrier options with transaction costs and examine the impact of transaction costs on option pricing, particularly on how they affect the optimal exercise boundary.
• Classification : 91G20, 60G40, Mathematical finance
• Format : Talk at Waseda University
• Author(s) :
  • Xiaoping Lu (University of Wollongong)

[00964] The Valuation of Real Options for Risky Barrier to Entry with Hybrid Stochastic and Local Volatility and Stochastic Investment Costs

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D505
• Type : Contributed Talk
• Abstract : Real options are sorts of investment choices which support agents in making better decisions in management strategic cases as well as reducing uncertainty in investment simultaneously. In this paper, we present the new model for investors to handle uncertain environments in investment flexibly: First, we adopt a hybrid stochastic and local volatility model to efficiently describe the external uncertain environment affecting the value of the project in decision making cases, and we set up the investment cost as geometric Brownian motion to illustrate the value of the opportunity costs which arise from things given up by choosing to invest in complex decision making circumstances. We derive partial differential equations for the value of real options and then use asymptotic analysis to obtain analytical solutions for that of the real options. In addition, we analyze the price accuracy of the approximated formulas compared to the solutions obtained from Monte-Carlo simulation. Finally, we investigate the effects of various parameters related to stochastic volatility on real options numerically to observe economic implications.
• Classification : 91G20
• Format : Talk at Waseda University
• Author(s) :
  • Donghyun Kim (Pusan National University)
  • Yong Hyun Shin (Sookmyung Women's University)
  • Ji-Hun Yoon (Pusan National University)

[02334] A generalized integral equation formulation for pricing American options under regime-switching model

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D505
• Type : Contributed Talk
• Abstract : In this paper, we present a generalized integral equation formulation for American put options under regime-switching model, with a goal of improving computational efficiency in mind, particularly when the number of regimes, $n$ is large. Given that the integral equation approach is characterized with its excellent trade off between maximizing analytical tractability and minimizing numerical discretization, our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of an originally simultaneously involved $n$-PDEs so that they can be solved recursively at the numerical solution stage. While some numerical examples are provided to demonstrate the implementation of the new approach and its efficiency, it is anticipated that the very same theorem can be used to reduce the computational burden if other numerical approaches are adopted.
• Classification : 91G20, 91-10
• Format : Talk at Waseda University
• Author(s) :
  • Yawen Zheng (University of Wollongong)
  • Song-Ping Zhu (University of Wollongong)

[02330] Representation Learning for Continuous Single-cell Biology with Graph Neural Networks

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D505
• Type : Contributed Talk
• Abstract : Single-cell RNA sequencing provides high-resolution transcriptomics to study cellular dynamic processes, yet its high-dimensionality, sparsity, and noises undermine the performance of downstream analysis. We propose a deep learning framework based on Variational Graph AutoEncoder to learn a low-dimensional representation that preserves global information and local continuity. By applying pseudotemporal ordering to the extracted features, we show that the model accurately preserves the dynamic cell trajectories of real and synthetic scRNA-seq datasets.
• Classification : 92B20, 68T05, Machine Learning, Bioinformatics
• Format : Talk at Waseda University
• Author(s) :
  • Chengkai Yang (The University of Tokyo)

contributed talk: CT182

room : D514

[00320] Sensing the electrical world: modelling to understand aerial electroreception

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D514
• Type : Contributed Talk
• Abstract : Bees and spiders (and other arthropods) can sense naturally occurring electrical fields. This recent discovery expands our view of how such organisms explore their environments, revealing previously unknown sensory capabilities. This talk consists of three topics: 1) the physical and biological feasibility of this sense, 2) how interactions between sensory hairs alter their sensitivity to different stimuli, and 3) the new sensory possibilities (e.g., object identification) and biological implications of this sense (e.g., decision-making).
• Classification : 92C10, 92C05, 74F10, 92C42
• Format : Talk at Waseda University
• Author(s) :
  • Ryan Palmer (University of Bristol)
  • Daniel Robert (University of Bristol)
  • Isaac Chenchiah (University of Bristol)

[02615] Theory of the cell motility mechanism in the absence of adhesions

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D514
• Type : Contributed Talk
• Abstract : The existing paradigm of the cell motility cycle does not hold for in vivo cell movement in complex 3D environments. In physiologically relevant environments, cells frequently use pressure-driven round membrane protrusions for locomotion. The role of substrate adhesion is minimal, and it remains unknown if and how a cell can migrate without any adhesions. Here, we leverage modeling and computational tools to reveal the step-by-step cycle of locomotion for cells that use blebs as leading-edge protrusions in confined environments. We show that cells cannot effectively migrate when the cell cortex is a purely elastic material, even with asymmetric channel geometry. Cells migrate effectively if actin turnover is included with a viscoelastic description for the cortex. Lastly, we compare with previous experimental findings and identify the spatiotemporal force distribution during a motility cycle.
• Classification : 92Bxx, 76Zxx
• Format : Talk at Waseda University
• Author(s) :
  • Calina Anamaria Copos (Northeastern University)
  • Calina Copos (Northeastern University)
  • Wanda Strychalski (Case Western Reserve University)

[02158] Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D514
• Type : Contributed Talk
• Abstract : The mammalian circadian clock is based on a self-sustaining transcriptional-translational negative feedback loop. This machinery is expected to suffer from the heterogeneous arrival time distribution of clock protein from the noisy intracellular environment at the nucleus; however, mammals exhibit robust daily rhythms of physiological and behavioral processes, including sleep and hormone secretion. We explore under which condition the circadian clock compensates for the heterogeneity by a modeling approach.
• Classification : 92BXX, 92Cxx
• Format : Talk at Waseda University
• Author(s) :
  • Seokjoo Chae
  • Dae Wook Kim (University of Michigan)
  • Seunggyu Lee (Korea University)
  • Jae Kyoung Kim (KAIST)

[02529] Application of machine learning to predict dynamics of epidemiological models that incorporate human behavior

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D514
• Type : Contributed Talk
• Abstract : In this work, we present modeling, analysis and simulation of a mathematical epidemiological model which incorporates human social, behavioral, and economic interactions. We discuss an approach based in Physics-Informed Neural Network, which is capable of predicting the dynamics of a disease described by modified compartmental models that include parameters, and variables associated with the governing differential equations. Finally, human behavior is modeled stochastically and it is included in the compartmental models.
• Classification : 92Bxx, 92-04, 92-05
• Format : Talk at Waseda University
• Author(s) :
  • Alonso Gabriel Ogueda Oliva (George Mason University)
  • Padmanabhan Seshaiyer (George Mason University)

[01908] Quantifying Cytoskeletal Dynamics and Remodeling from Live-imaging Microscopy Data

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @D514
• Type : Contributed Talk
• Abstract : The shape of biological cells emerges from dynamic remodeling of the cell’s internal scaffolding, the cytoskeleton. Hence, correct cytoskeletal regulation is crucial for the control of cell behaviour, such as cell division and migration. A main component of the cytoskeleton is actin. Interlinked actin filaments span the body of the cell and contribute to a cell’s stiffness. The molecular motor myosin can induce constriction of the cell by moving actin filaments against each other. Capturing and quantifying these interactions between myosin and actin in living cells is an ongoing challenge. For example, live-imaging microscopy can be used to study the dynamic changes of actin and myosin density in deforming cells. These imaging data can be quantified using Optical Flow algorithms, which locally assign velocities of cytoskeletal movement to the data. Extended Optical Flow algorithms also quantify actin recruitment and degradation. However, these measurements on cytoskeletal dynamics may be influenced by noise in the image acquisition, by ad-hoc parameter choices in the algorithm, and by image pre-processing steps. Here, we use in silico data to understand conditions under which Optical Flow is applicable. We found the condition to guarantee the method has a good performance is that the displacement has to be in a proper proportion as the object size. We test our methods using data on actin densities in larval epithelial cells of Drosophila pupae. The development of our Optical Flow method will be a starting point for identifying differences in cytoskeletal movement and remodeling under experimental perturbations. Our method will be applicable to other datasets in which flow fields are present.
• Classification : 92-10, 92-08, 92BXX, 37CXX, 76-10
• Format : Online Talk on Zoom
• Author(s) :
  • Carey Li (University of St Andrews)

MS [01149] Sparse optimization techniques and applications

room : D515

• [05058] A new matrix factorization for sparse representation of over-determined systems
  • Format : Talk at Waseda University
  • Author(s) :
    • NAJIYA K Z (PhD Scholar)
    • C S Sastry (IIT Hyderabad)
  • Abstract : This presentation aims at discussing a novel method that finds a sparse approximation of a matrix system y ̴ Ax (where A has a bigger row size compared to its column size). While highlighting the need for such an approximation through some applications, the presentation realizes its objective via a new matrix factorization. Besides, it compares and contrasts the proposed method with established ones that have similar objectives.
• [05060] Sparse optimization-based ERT algorithms for multiphase flows
  • Format : Talk at Waseda University
  • Author(s) :
    • NAJIYA K Z (PhD Scholar)
    • Shantam Gulati (IIT Hyderabad)
  • Abstract : We discuss applications of the compressed sensing framework mainly in the field of Electrical Impedance tomography (EIT). EIT is a scanning technique that draws a relationship between the impedance inside the domain and the current to voltage map on the boundary at the electrodes. In particular, we wish to address the ill-posed inverse problem in the circular domain. The idea is to draw comparisons and improve upon the existing techniques with L 1 and the weighted-norm approaches.
• [05061] Hardware-friendly binary frames for sparse optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • NAJIYA K Z (PhD Scholar)
    • Prasad Theeda (Vellore Institute of Technology)
    • Pradip Sasmal
  • Abstract : Binary matrices are preferred as compressed sensing (CS) matrices because they are hardware-friendly and support low-complexity sparse recovery algorithms. In this talk, we discuss that the disjunctness property of a binary matrix, which has been used in non-adaptive group testing, can also be very useful for recovering sparse signals. Disjunct matrices are particularly well-suited as compressed sensing matrices because they can support a non-iterative, fast sparse recovery algorithm.

MS [02491] Mathematics of Epidemics: modelling, data analysis, and control

room : A201

• [03458] Exploring the dynamics of contagion models with stages
  • Format : Talk at Waseda University
  • Author(s) :
    • Guy Katriel (Braude College of Engineering)
  • Abstract : We study models which are similar to classical epidemiological models, but in which becoming `contagion' involves a process with several stages. Such mechanisms are natural when considering phenomena of `social contagion' - the transmission of beliefs, behaviors. It is shown that these models display a variety of nonlinear behaviors that are absent in the corresponding `classical' epidemiological models, including: bistability, critical transitions, endogenous oscillations, and excitability. These phenomena, and the bifurcations involved, are studied by a combination of analytical and numerical means. We thus suggest that two-stage (or multi-stage) contagion can serve as a possible explanatory mechanism for some of the complex dynamical phenomena observed in social life.
• [04574] Mathematical modeling of COVID-19 transmission with pandemic response in South Korea
  • Format : Talk at Waseda University
  • Author(s) :
    • Yongin Choi (National Institute for Mathematical Sciences)
    • Kyeongah Nah (National Institute for Mathematical Sciences)
  • Abstract : In this study, we investigated the effects of control policies on the COVID-19 outbreak in South Korea using a transmission dynamics model, where its transmission rate is estimated by a machine-learning algorithm. Our findings showed that the effectiveness of these policies varied across different waves of the epidemic and was influenced by various factors, such as vaccination coverage and mobility levels. Our findings emphasize the importance of a data-driven approach to evaluate COVID-19 policies.
• [03885] Front propagation �in an epidemiological model with mutations
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Matano (Meiji University)
    • Quentin Griette (Université Le Havre Normandie)
  • Abstract : We consider a reaction-diffusion system describing the propagation of disease that involves mutation of the pathogen. More precisely this is an S-I-S epidemic model with diffusion in which two types of pathogens appear (wild and mutant). We assume that mutation occurs reciprocally between the two types at a certain rate. The resulting reaction-diffusion system has a peculiar feature: it is of the cooperative nature for small density of infected population while it is of the competitive nature for large density. This model was introduced by Q.Griette and G.Raoul in 2016 for a spatially homogeneous environment. Similar systems were also studied slightly later by L.Girardin and by E.Crooks et al, also for the spatially homogeneous case. In this talk, I will consider this system in spatially periodic environments and present the following results: (1) existence of traveling waves; (2) spreading speed of infection when starting from localized initial data; (3) stability and asymptotic profile of propagating fronts. I will also discuss the homogenization limit of the problem when the spatial period of the environment tends t
• [05100] Resolving the enigma of COVID-19 outbreaks in Iquitos and Manaus
  • Format : Talk at Waseda University
  • Author(s) :
    • lewi stone (RMIT University)
    • Daihai He (Hong Kong Polytechnic University)
  • Abstract : The nearby cities of Iquitos (Peru) and Manaus (Brazil) experienced the world’s highest infection and mortality rates during the first 2020 COVID-19 wave. Key studies suggested >70% of the Manaus population was infected, and thus close to herd immunity and protected. It remains an enigma as to why a deadly second wave followed in Manaus. We present a data-driven model of epidemic dynamics in Iquitos to help explain and model events in Manaus

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

room : A206

• [02734] Continuous Newton-like Methods featuring Inertia and Variable Mass
  • Format : Talk at Waseda University
  • Author(s) :
    • Camille Castera (University of Tübingen)
    • Hedy Attouch (IMAG, Université Montpellier, CNRS)
    • Jalal Fadili (ENSICAEN, Normandie Université, CNRS, GREYC)
    • Peter Ochs (University of Tübingen)
  • Abstract : Towards designing new algorithms that benefit from the best of both first- and second-order optimization methods, we introduce a new dynamical system, called VM-DIN-AVD, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the acceleration, called variable mass. For strongly convex optimization, we provide guarantees on how the Newtonian and inertial behaviors of the system can be non-asymptotically controlled by means of this variable mass. A connection with the Levenberg-Marquardt --or regularized Newton's-- method is also made. We then show the effect of the variable mass on the asymptotic rate of convergence of the dynamics, and in particular, how it can turn the latter into an accelerated Newton method. We present numerical experiments supporting our findings.
• [01611] Inertial quasi-Newton methods for monotone inclusion
  • Format : Talk at Waseda University
  • Author(s) :
    • Shida Wang (Universität Tübingen)
    • Jalal Fadili (Normandie Univ, ENSICAEN)
    • Peter Ochs (Universität Tübingen)
  • Abstract : We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent operator. A change of the metric makes its computation hard even for (otherwise in the standard metric) simple operators. In order to fully exploit the advantage of adapting the metric, we develop a new efficient resolvent calculus for a low-rank perturbed standard metric, which accounts exactly for quasi-Newton metrics. Moreover, we prove the convergence of our algorithms, including linear convergence rates in case one of the two considered operators is strongly monotone. Beyond the general monotone inclusion setup, we instantiate a novel inertial quasi-Newton Primal-Dual Hybrid Gradient Method for solving saddle point problems. The favourable performance of our inertial quasi-Newton PDHG method is demonstrated on several numerical experiments in image processing.
• [05250] Extrapolated Proximal Algorithms for Nonconvex and Nonsmooth Min-max problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Peter Wu (UNSW)
    • Guoyin Li (The University of New South Wales)
    • Minh Dao (RMIT)
  • Abstract : In this talk, we consider an extrapolated proximal algorithm for solving nonsmooth and nonconvex minmax problems. We establish convergence of the full sequence to a stationary point under some gentle assumptions. If time permits, numerical experiment on its application to multi-domain robust sparse learning will be presented.
• [05578] Global stability of first-order methods for coercive tame functions
  • Format : Talk at Waseda University
  • Author(s) :
    • Cédric Josz (Columbia University)
    • Lexiao Lai (Columbia University)
  • Abstract : We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable model-dependent regularity assumptions, this result applies to the random reshuffling and momentum and the random-permutations cyclic coordinate descent method.

MS [01545] Interplay between controllability and qualitative aspects of stochastic dynamical systems

room : A207

• [03022] Small-time control of bilinear PDEs via infinite-dimensional Lie brackets
  • Format : Online Talk on Zoom
  • Author(s) :
    • Eugenio Pozzoli (Università di Bari)
  • Abstract : We consider PDEs with multiplicative control terms, such as Schrödinger, heat and wave equations. Following a bilinear control strategy recently introduced by Duca and Nersesyan, that is a small-time asymptotic of conjugated dynamics, we investigate some approximate controllability properties of these systems, which hold in arbitrarily small times. We moreover comment on the relation between the controllability properties of the systems and the Lie brackets (a.k.a. commutators) of the operators that generate the dynamics.

MS [02285] New Trends in Tensor Networks and Tensor Optimization

room : A208

• [05508] Singular Value Decomposition of Dual Matrices and its Application to Traveling Wave Identification in the Brain
  • Format : Talk at Waseda University
  • Author(s) :
    • Tong Wei (Fudan University)
    • Weiyang Ding (Fudan University)
    • Yimin Wei (Fudan University)
  • Abstract : atrix factorization in dual number algebra, a hypercomplex system, has been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves using the singular value decomposition of dual matrices. Theoretically, we propose the compact dual singular value decomposition (CDSVD) of dual complex matrices with explicit expressions as well as a necessary and sufficient condition for its existence. Furthermore, based on the CDSVD, we report on the optimal solution to the best rank-k approximation under a newly defined quasi-metric in dual complex number system. The CDSVD is also related to the dual Moore-Penrose generalized inverse. Numerically, comparisons with other available algorithms are conducted, which indicate the less computational cost of our proposed CDSVD. Next, we employ experiments on simulated time-series data and a road monitoring video to demonstrate the beneficial effect of infinitesimal parts of dual matrices in spatiotemporal pattern identification. Finally, we apply this approach to the large-scale brain fMRI data and then identify three kinds of traveling waves, and further validate the consistency between our analytical results and the current knowledge of cerebral cortex function.
• [03043] Multilinear Pseudo-PageRank for Hypergraph Partitioning
  • Format : Talk at Waseda University
  • Author(s) :
    • Yannan Chen (South China Normal University)
  • Abstract : In this talk, we establish the higher-order pseudo-PageRank model, which is formulated as a multilinear system with nonnegative constraints. The coefficient tensor of the multilinear system is a kind of Laplacian tensor of the uniform hypergraph and no dangling corrections are involved. Then, a tensor splitting algorithm is utilized for solving the higher-order pseudo-PageRank problem, of which solutions exist but may not be unique. Numerical experiments illustrate that the proposed higher-order pseudo-PageRank method is powerful and effective for hypergraph partitioning problems.
• [04276] Tensorial Time Series Prediction via Tensor Neural Differential Equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Mingyuan Bai (RIKEN AIP)
  • Abstract : The recent decade has witnessed the surge of models and applications in multi-dimensional, i.e., tensorial time series analysis, where their entanglement of different aspects of data, i.e., modes, appeals to both academia and industry, and raises a number of challenges for modeling and analysis. To address these challenges, we aim to introduce tensor neural differential equations for tensorial time series analysis, including tensor neural ordinary differential equations and tensor neural controlled differential equations, etc.
• [03838] A gradient projection method for semi-supervised hypergraph clustering problems
  • Format : Talk at Waseda University
  • Author(s) :
    • Jingya Chang (Guangdong University of Technology)
  • Abstract : We use the hypergraph related tensor to construct an orthogonal constrained optimization model for the semi-supervised hypergraph problems, which is solved by a retraction method. A nonmonotone curvilinear search is implemented to guarantee reduction in the objective function value. Experiments on synthetic hypergraph and hypergraph given by real data demonstrate the effectivity of our method.

contributed talk: CT197

room : A502

[02590] Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Images and Videos Inpainting

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @A502
• Type : Contributed Talk
• Abstract : The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image. In this talk we apply such NSS prior to enhance the robust quaternion matrix completion (QMC) method and significantly improve the inpainting performance. A patch group based NSS prior learning scheme is proposed to learn explicit NSS models from natural color images. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new joint NSS-base QMC method is also presented to solve the color video inpainting problem based quaternion tensor representation. The numerical experiments on large-scale color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.
• Classification : 94A08, 68U10
• Format : Talk at Waseda University
• Author(s) :
  • Zhigang Jia (Jiangsu Normal University)

[02595] Image recovery under non-Gaussian noise

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @A502
• Type : Contributed Talk
• Abstract : Cauchy noise, as a typical non-Gaussian noise, appears frequently in many important fields, such as radar, medical, and biomedical imaging. Here, we focus on image recovery under Cauchy noise. Instead of the celebrated total variation or low-rank prior, we adopt a novel deep-learning-based image denoiser prior to effectively remove Cauchy noise with blur. To preserve more detailed texture and better balance between the receptive field size and the computational cost, we apply the multi-level wavelet convolutional neural network (MWCNN) to train this denoiser. Frequently appearing in medical imaging, Rician noise leads to an interesting nonconvex optimization problem, termed as the MAP-Rician model, which is based on the Maximum a Posteriori (MAP) estimation approach. As the MAP-Rician model is deeply rooted in Bayesian analysis, we want to understand its mathematical analysis carefully. Moreover, one needs to properly select a suitable algorithm for tackling this nonconvex problem to get the best performance. Indeed, we first present a theoretical result about the existence of a minimizer for the MAP-Rician model under mild conditions. Next, we aim to adopt an efficient boosted difference of convex functions algorithm (BDCA) to handle this challenging problem. Theoretically, using the Kurdyka-Lojasiewicz (KL) property, the convergence of the numerical algorithm can be guaranteed.
• Classification : 94A08, 68U10
• Format : Talk at Waseda University
• Author(s) :
  • Tingting WU (Nanjing University of Posts and Telecommunications)

[00578] Secret Sharing Scheme with Perfect Concealment by Quasigroup

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @A502
• Type : Contributed Talk
• Abstract : A secret sharing scheme was introduced by Shamir in 1979. A quasigroup is equivalent to a Latin square. The concept of perfect concealment is also called perfect security. The word ‘security’ describes a property of a phenomena, and the word ‘concealment’ describes an action which makes a phenomenon. In this talk, we force an action rather than a property, and we give new construction of secret sharing scheme with perfect concealment by quasigroup.
• Classification : 94A62, 05B15, 20N05, 60B99
• Format : Talk at Waseda University
• Author(s) :
  • Tomoko Adachi (Shizuoka Institute of Science and Technology)
  • Izumi Takeuti (National Institute of Advanced Industrial Science and Technology)

[02380] PDE methods for joint reconstruction-segmentation of images

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @A502
• Type : Contributed Talk
• Abstract : In practical image segmentation tasks, the image must first be reconstructed from indirect/damaged/noisy observations. Traditionally, reconstruction-segmentation would be performed in sequence: first reconstruct, then segment. Joint reconstruction-segmentation performs reconstruction and segmentation simultaneously, using each to guide the other. Past joint reconstruction-segmentation has employed relatively simple segmentation algorithms, e.g. Chan–Vese. This talk will describe how joint reconstruction-segmentation can be performed using Bhattacharyya-flow-based segmentation (Michailovich et al., 2007) and graph-PDE-based segmentation (Merkurjev et al., 2013).
• Classification : 94A08, 35Q93, 35R02
• Format : Talk at Waseda University
• Author(s) :
  • Jeremy Michael Budd (California Institute of Technology )
  • Franca Hoffmann (California Institute of Technology )
  • Allen Tannenbaum (Stony Brook University)
  • Yves van Gennip (Technische Universiteit Delft)
  • Carola-Bibiane Schönlieb (University of Cambridge)
  • Jonas Latz (Heriot-Watt University)

[02139] Normalizing Flows Based Mutual Information Estimation

• Session Time & Room : 4E (Aug.24, 17:40-19:20) @A502
• Type : Contributed Talk
• Abstract : Mutual Information is a measure of mutual dependence on random quantities without specific modelling assumptions. However, estimating mutual information numerically from high-dimensional data remains a difficult problem. We propose a principled mutual information estimator based on a generalization of normalizing flows. The proposed method uses an autoregressive structure in estimating mutual information with estimating marginal and joint entropy simultaneously. Empirical results demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.
• Classification : 94a17, 62b10, 68t07, 68t09
• Format : Talk at Waseda University
• Author(s) :
  • Haoran Ni (University of Warwick)
  • Martin Lotz (University of Warwick)

MS [00029] New Trends in Structural and Engineering Optimization

room : A508

• [04641] Topology optimization reducing the dynamic instability of squeal noise
  • Format : Talk at Waseda University
  • Author(s) :
    • SolJi Han (Hanyang University)
    • GilHo Yoon (hanyang university)
  • Abstract : This study focuses on topology optimization considering the dynamic instability of squeal noise. In this study, the instability value caused by the frictional force is analysed through the eigenvalue analysis, and the sensitivity is calculated by left and right eigenvectors. With the present development, it is possible to optimize a structure that effectively reduces the instability value. To verify this study, several optimization examples are considered.
• [03974] Structural simulation and optimization to improve the quality of metal additive manufacturing
  • Format : Talk at Waseda University
  • Author(s) :
    • Akihiro Takezawa (Waseda University)
  • Abstract : Reduction of the residual warpage generated through fabrication is an emerging issue in metal laser powder bed fusion additive manufacturing (AM). Regarding the minimization of the residual warpage of the lattice infill structures, simultaneous optimization of the laser hatching orientation and lattice density distribution is conducted in this study to confirm their synergetic effect.
• [03594] Machine-learning assisted topology optimization with structural gene inheritance
  • Format : Talk at Waseda University
  • Author(s) :
    • Weisheng Zhang (Dalian University of Technology)
    • Sung-Kie Youn (KAIST)
    • Xu Guo (Dalian University of Technology)
  • Abstract : A machine-learning assisted topology optimization approach is proposed for structural design with structural gene inheritance. This work establishes a novel framework to systematically integrate structural topology optimization with subjective human design preferences. To embed the structural gene into the design, neural style transfer technique is adopted to measure and generate the prior knowledge from a reference image with the concerned structural gene (such as biological characteristic, artistic flavor and manufacturing requirement, etc.). By using different convolutional layers in the VGG-19 model-based CNN, both the style and content of the structural gene can be constructed from low to high levels of abstraction. The measured knowledge can then be integrated into pixel-based topology optimization as a formal similarity constraint. Both 2D and 3D problems are solved to illustrate the effectiveness of the proposed approach where the inheritance of the structural gene can be achieved in a systematic manner.

MS [00739] Inequalities and entropy with applications

room : A510

• [02721] The permutation entropy and its applications on full-scale compartment fire data
  • Format : Talk at Waseda University
  • Author(s) :
    • Flavia-Corina Mitroi-Symeonidis (Department of Applied Mathematics Academy of Economic Studies Calea Dorobanti 15-17, Sector 1 010552 Bucharest)
  • Abstract : Given the sparse literature on the usefulness of the entropy in characterizing fire data, we investigate the order characteristics of the compartment fire based on experimental data. We compare known algorithms dedicated to the extraction of the underlying probabilities, checking their suitability to point out the abnormal values and structure of the time series. We claim that the permutation entropy is suitable to detect the occurrence of the flashover and unusual data in fire experiments.
• [02772] A Spectral Analysis of The Correlated Random Walk
  • Format : Talk at Waseda University
  • Author(s) :
    • Akihiro Narimatsu (The University of Fukuchiyama)
    • Yusuke Ide (Nihon University)
  • Abstract : In this talk, we consider a spectral analysis of the Correlated Random Walk with the isospectral coin cases. In the Szegedy's quantum walk, our method gives the arcsine law as the lower bound of the time averaged distribution.
• [05367] On a class of k-entanglement witnesses
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroyuki Osaka (Ritsumeikan University)
  • Abstract : Recently, Yang et al.showed that each 2-positive map acting from $\mathcal{M}_3(\mathbb{C})$ into itself is decomposable. It is equivalent to the statement that each PPT state on $\mathbb{C}^3\otimes\mathbb{C}^3$ has Schmidt number at most 2. It is a generalization of Perez-Horodecki criterion which states that each PPT state on $\mathbb{C}^2\otimes\mathbb{C}^2$ or $\mathbb{C}^2\otimes\mathbb{C}^3$ has Schmidt rank 1 i.e. is separable. Natural question arises whether the result of Yang at al. stays true for PPT states on $\mathbb{C}^3\otimes\mathbb{C}^4$. This question can be considered also in higher dimensions. We construct a positive maps which is suspected for being a counterexample. More generally, we provide a class of positive maps $\Phi_a$ between matrix algebras whose $k$-positivity properties can be easily controlled. The estimate bounds on the parameter a are better than those derived from the spectral conditions considered by Chru\'{s}ci\'{n}ski and Kossakowski. We found that in case where dimensions are differ by one we can give explicit analytic formula for parameter a that guarantee $k$-positivity. As an apllication we show that $\Phi_a$ detects $k$-entanglement. This is mainly based on joint work with Tomasz Mlynik and Marcin Marciniak (arXiv:2104.14058v4, 2022).
• [03537] Violation of Bell's Inequality by Classical Correlation via Adaptive Dynamics
  • Format : Talk at Waseda University
  • Author(s) :
    • Satoshi Iriyama (Tokyo University of Science)
  • Abstract : Ohya introduced the adaptive dynamics as subclasses of information dynamics. The notion of adaptive dynamics is helpful to find out characteristic factors in complex systems. In 2001, the chameleon effect proposed by Accardi et al. is the classical dynamics adopting that the local acts of observation may disturb local measurement, and its experimental implementation which can violate Bell's inequality was shown. In this talk, mathematical foundations of the chameleon dynamics and its applications are explained.

MS [00305] Computational Modeling on Biomedical Diseases

room : A511

• [00317] Role of senescent tumor cells and macrophages in building a cytokine shield in the tumor microenvironment: mathematical modeling
  • Format : Talk at Waseda University
  • Author(s) :
    • Yangjin Kim (Konkuk University)
    • Junho Lee (B)
    • Chaeyoung Lee (Korea University)
    • Sean Lawler (Brown University)
  • Abstract : Cellular senescence can induce dual effects (promotion or inhibition) on cancer progression. While immune cells naturally respond and migrate toward various chemotactic sources from the tumor mass, various factors including senescent tumor cells (STCs) in the tumor microenvironment (TME) may affect this chemotactic movement. In this work, we investigate the mutual interactions between the tumor cells and the immune cells (T cells and macrophages) that either inhibit or facilitate tumor growth by developing a mathematical model that consists of taxis-reaction-diffusion equations and receptor kinetics for the key players in the interaction network. We first apply a mathematical model to a transwell Boyden chamber invasion assay used in the experiments to illustrate that STCs can play a pivotal role in negating immune attack through tight regulation of intra- and extra-cellular signaling molecules. In particular, we show that senescent tumor cells in cell cycle arrest can block intratumoral infiltration of CD8+ T cells by secreting a high level of CXCL12, which leads to significant reduction its receptors, CXCR4, on T cells, and thus impaired chemotaxis. Macrophages also play an important role in mediating or inhibiting given signaling pathways between different cells in TME. The predictions of nonlinear responses to CXCL12 were in good agreement with experimental data. We tested several hypotheses on immune-tumor interactions under various biophysical- and biochemical- conditions in the tumor microenvironment and developed new concepts for anti-tumor strategies targeting senescence induced immune impairment.
• [00373] Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles
  • Format : Talk at Waseda University
  • Author(s) :
    • Qiantong Liang (City University of Hong Kong)
    • Wing-Cheong Lo (City University of Hong Kong)
  • Abstract : We develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. Our simulations demonstrate that DIPs can slow down the growth of virus particles and make the spread of virus more patchy.
• [01228] Modeling about prediction and improvement of therapeutic efficacy of immune checkpoint inhibitors
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiulan Lai (Renmin University of China)
  • Abstract : Immune checkpoint inhibitors have been shown to be highly successful against some solid metastatic malignancies, but the overall patient response rate is limited due to the interpatient heterogeneity. In this project, we explored the effect of favorable and unfavorable gut bacteria on the therapeutic efficacy of anti-PD-1 against cancer by modeling the tumor-immune-gut microbiome interactions, and further examined the predictive markers of responders and non-responders to anti-PD-1. The dynamics alteration of PD-L1 expression status during cancer evolution and treatment are also obstacles for PD-1/PD-L1 inhibitors. We established a comprehensive modeling and computational framework for estimating the dynamic alternation of PD-L1 heterogeneity during cancer progression and treatment, and predicting the overall survival of patients.
• [01252] Travelling waves of a new glioma invasion model.
  • Format : Talk at Waseda University
  • Author(s) :
    • Ryan Thiessen (University of Alberta)
  • Abstract : Recently a detailed study of in-vivo glioma invasion patterns in the healthy brain tissue of living mice shows that specialized cancer cells build a network similar to a healthy brain neuronal network. We develop a model for this new phenomenon via a kinetic formulation. After making some simplifying assumptions, we arrive at a reaction-diffusion model. In this talk, I will explore travelling waves for the simplified new glioblastoma model.

MS [01952] Mathematical models of morphogenesis and morphological deformation in living organisms

room : A512

• [02830] A kinetic model for sol-gel transition of teleost muscular proteins
  • Format : Talk at Waseda University
  • Author(s) :
    • Yuri Kominami (The University of Tokyo)
  • Abstract : Various enzymatic reactions have a critical role in control of cellular function in living tissue. The enzymes can be activated in the tissue after organismal death and cause post-mortem changes. The enzymes delivered from animal tissue are also activated during food processing and affect product attributes. In this talk, the enzymatic reactions during sol-gel transition of teleost muscular proteins will be addressed and a kinetic model will be discussed.
• [03680] Mathematical model for dynamics of endothelial cells in sprouting angiogenesis
  • Format : Talk at Waseda University
  • Author(s) :
    • Tatsuya Hayashi (Yamato University)
  • Abstract : Angiogenesis is a morphogenic process that involves the emergence of new blood vessels from an existing vascular network. We propose a mathematical model based on the characteristic movements of endothelial cells in angiogenesis. In this presentation, we show that our model is able to reproduce the coordinated linear and rotational movements observed in a two-cell state, as well as angiogenic morphogenesis and the effects of cell adhesion molecules in a multicellular simulation.
• [04407] Measurement and mathematical analysis of organ morphogenetic processes
  • Format : Talk at Waseda University
  • Author(s) :
    • Yoshihiro Morishita (RIKEN Center for Biosystems Dynamics Research)
  • Abstract : The physical processes that govern the formation of almost all organs, namely, collective cell motion and tissue-level deformation, remain largely unknown. However, recent advances in microscopy have enabled the measurement and quantification of these dynamics. In this study, we investigate the early development of the forebrain and heart and present our findings on the morphogenetic rules that underlie their formation, based on our analysis of the measured morphogenetic dynamics.
• [03395] A mathematical model for the evolution of low-grade gliomas before and after radiotherapy
  • Format : Talk at Waseda University
  • Author(s) :
    • Mathilde Badoual (Paris Cité University)
    • Leo Adenis (CNRS)
    • Stephane Plaszczynski (CNRS)
    • Jean-Eric Campagne (CNRS)
    • Basile Grammaticos (CNRS)
    • Johan Pallud (Sainte-Anne Hospital)
  • Abstract : Diffuse low-grade gliomas are slowly growing tumors that mainly affect adults around 40 years old and are incurable. After tens of years, they transform inexorably into more aggressive forms, jeopardizing the patient’s life. Mathematical modeling could help clinicians to have a better understanding of the underlying biological process involved in the evolution of these tumors and their response to treatments. We present here a model of evolution of these tumors, based on a PDE that describes the evolution of the cell density and the effect of radiotherapy. This model is used to fit clinical data (MRI scans), and to predict the regrowth time after radiotherapy.

contributed talk: CT180

room : A601

[00300] Coupling macro-micro simulations in complex fluids

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : Some of the most remarkable properties and functions served by some complex fluids originate from the interplay between external fields and microstructural dynamics. From a computational point of view this generates a set of challenges related to the need of coupling dynamics at different length and times scales, sometimes spanning several orders of magnitude. Micro-macro simulations have gained a lot of recognition within the field because these methods allow capturing full dynamics at the macroscale without losing resolution at the microscale. In this talk, we will review our efforts to couple existing macroscopic solvers for the Navier-Stokes equations with microstructural dynamics described by Langevin-type equations. In particular, we will discuss dumbbells models -under viscometric and capillary thinning flows fields- and parallel computing using GPUs.
• Classification : 92B05, 76A05, 76A10, 76D05, 97M60
• Format : Talk at Waseda University
• Author(s) :
  • Paula A Vasquez (University of South Carolina)
  • Michael Cromer (RIT)

[00035] Effects of toxicity and zooplankton selectivity under seasonal pattern of viruses on plankton dynamics

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : A mathematical model for the interacting dynamics of phytoplankton-zooplankton is proposed. The phytoplankton have ability to take refuge and release toxins to avoid over predation by zooplankton. The zooplankton are provided some additional food to persist in the system. The phytoplankton are assumed to be affected directly by an external toxic substance whereas zooplankton are affected indirectly by feeding on the affected phytoplankton. We incorporate seasonal variations in the model, assuming the level of nutrients, refuge and the rate of toxins released by phytoplankton as functions of time. Our results show that when high toxicity and refuge cause extinction of zooplankton, providing additional food supports the survival of zooplankton population and controls the phytoplankton population. Prey refuge and additional food have stabilizing effects on the system; higher values of the former results in extinction of zooplankton whereas phytoplankton disappear for larger values of the latter. Seasonality in nutrients level and toxins released by phytoplankton generates higher periodic solutions while time-dependent refuge of phytoplankton causes the occurrence of a period-three solution. The possibility of finding additional food for zooplankton may push back the ecosystem to a simple stable state from a complex dynamics.
• Classification : 92B05, 92D25, 92D30, 37A50, 34D05
• Format : Online Talk on Zoom
• Author(s) :
  • Samares Pal (University of Kalyani)

[00375] Modelling Typhoid Fever Transmission: Optimal control and Cost-Effectiveness Analysis

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Industrial Contributed Talk
• Abstract : Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of limited clinical efficacy of antibiotics administer to patients suffering from the disease with optimal control and cost-effectiveness analysis. Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of clinical efficacy of antibiotics administer to patients suffering from the disease. The basic reproduction number is analytically computed, and existence and local stability condition of disease-free equilibrium is investigated. Subsequently, the global sensitivity analysis of the model parameters is computed. The optimal control and cost-effectiveness analysis were also computed. Our results suggest that hygiene practice and awareness campaign, and disinfection or sterilization or bacteria decay control is the most cost-effective in eliminating the disease from the population and from preventing the susceptible individuals from contracting the bacteria disease.
• Classification : 92BXX, 92-XX, 92-10, 91-XX, 91-10, Mathematical modeling of infectious disease(Biomathematics)
• Author(s) :
  • kazeem Austin TIJANI (Federal University of Agriculture(J. S Tarka university), Makurdi)
  • Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria )
  • Iortyer Reuben GWERYINA (Federal university of Agriculture(J.S. Tarka University), Makurdi))

[00892] Predicting response to pediatric leukemia with flow cytometry data

• Session Time & Room : 3C (Aug.23, 13:20-15:00) @A601
• Type : Contributed Talk
• Abstract : 15% of children with B-cell acute lymphoblastic leukemia fail to achieve response or long-term remission. With new treatments being developed to provide an alternative for this subset of patients, an improved risk classification at diagnosis can help to plan and prepare for this eventuality. Flow cytometry is currently used to characterize the leukemic clone but it has no prognosis value. In this work we use flow cytometry data at diagnosis from 250 pediatric patients from hospitals in Spain to find features associated with response by means of an array of computational methods.
• Classification : 92Bxx
• Author(s) :
  • Alvaro Martínez-Rubio (University of Cadiz)
  • Salvador Chulián (University of Cádiz)
  • Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
  • Víctor Manuel Pérez-García (University of Castilla-La Mancha)
  • María Rosa (University of Cadiz)

MS [00498] Approximation and modeling with manifold-valued data

room : A615

• [04608] Structure-preserving Model Order Reduction on Manifolds
  • Format : Talk at Waseda University
  • Author(s) :
    • Patrick Buchfink (University of Stuttgart)
    • Silke Glas (University of Twente)
    • Bernard Haasdonk (University of Stuttgart)
    • Benjamin Unger (University of Stuttgart)
  • Abstract : Approximation on manifolds has become a highly researched field in Model Order Reduction (MOR) for problems with slowly decaying Kolmogorov $n$-widths. However, many MOR techniques do not respect the structure of the underlying equations during the reduction. In this talk, we present a new differential geometric formulation of MOR on pseudo-Riemannian manifolds. It allows us to geometrically understand and unify existing structure-preserving MOR techniques for Hamiltonian and Lagrangian systems.
• [03709] The Difference of Convex Algorithm on Riemannian Manifolds
  • Format : Online Talk on Zoom
  • Author(s) :
    • Ronny Bergmann (NTNU, Trondheim)
    • Orizon Pereira Ferreura (IME/UFG, Goiâna)
    • Elisanderson Meneses Santos (Instituto Federal de Educação, Ciência e Tecnologia do Maranhão, Barra do Corda)
    • João Carlos de Oliveira Souza (Department of Mathematics, Federal University of Piauí, Teresina)
  • Abstract : In this talk we propose a difference of convex algorithm (DCA) on Riemannian manifolds to solve optimisation problems involving a difference of two functions. We establish both its relation to recently introduced Fenchel duality on manifolds, and its wwell-posedness. On Hadamard manifolds, we prove that every cluster point of the sequence generated by the algorithm is a cluster point. Finally, we illustrate that several optimisation problems can be written as difference of convex (DC) functions on manifolds, and that some Euclidean problems that are differences of non-convex problems become DC problems when rephrased on a manifold. Numerical examples illustrate that such a rephrasing even for DC problems is beneficial numerically.
• [02950] Symplectic model order reduction via Riemannian optimization
  • Format : Talk at Waseda University
  • Author(s) :
    • Bin Gao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
  • Abstract : Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a so-called symplectic Stiefel manifold, Riemannian optimization is preferred, because one can borrow ideas from unconstrained optimization methods after preparing necessary geometric tools. Retraction is arguably the most important one which decides the way iterates are updated given a search direction. Two retractions have been constructed so far: one relies on the Cayley transform and the other is designed using quasi-geodesic curves. In this talk, we propose a new retraction that is based on an SR matrix decomposition. We prove that its domain contains the open unit ball which is essential in proving the global convergence of the associated gradient-based optimization algorithm. Moreover, we consider the symplectic model order reduction of Hamiltonian systems with various examples. The extensive numerical comparisons reveal the strengths of the proposed optimization algorithm.
• [05465] Hirotugu Akaike's Analysis of Gradient Descent: 70 years later
  • Format : Talk at Waseda University
  • Author(s) :
    • Pok Yin Thomas Yu (Drexel University)
  • Abstract : It is very well known that when the exact line search gradient descent method is applied to a convex quadratic objective, the worst-case rate of convergence (among all seed vectors) deteriorates as the condition number of the Hessian of the objective grows. By an elegant analysis by H. Akaike in 1959, it is generally believed -- but not proved -- that in the ill-conditioned regime the ROC for almost all initial vectors, and hence also the average ROC, is close to the worst case ROC. We complete Akaike's analysis using the theorem of center and stable manifolds. Our analysis also makes apparent the effect of an intermediate eigenvalue in the Hessian by establishing the following somewhat amusing result: In the absence of an intermediate eigenvalue, the average ROC gets arbitrarily fast -- not slow -- as the Hessian gets increasingly ill-conditioned. We discuss in passing some contemporary applications of exact line search GD to polynomial optimization problems arising from imaging and data sciences and, if time allows, formulate an open problem related to accelerated GD methods.

MS [00341] Graph Coloring

room : A617

• [02669] Flows and coloring of triangle-free graphs on surfaces
  • Format : Talk at Waseda University
  • Author(s) :
    • Zdeněk Dvořák (Charles University)
  • Abstract : The near-quadrangulations of surfaces, i.e., graphs where almost all faces have length four, play an important role in the theory of 3-colorability of triangle-free graphs on surfaces. We present a powerful approach to coloring near-quadrangulations using nowhere-zero flows and explore its applications. In particular, we show a connection between the maximum edgewidth of triangle-free non-3-colorable graphs on a given surface and a long-standing conjecture concerning the maximum width of polytopes containing no integer points.
• [02782] Alon-Tarsi number of planar graphs
  • Format : Online Talk on Zoom
  • Author(s) :
    • Xuding Zhu (Zhejiang Normal University)
    • Yangyan Gu (Zhejiang Normal University)
  • Abstract : This talk presents a simple proof of the result that planar graphs have Alon-Tarsi number at most 5, and that each planar graph $G$ has a matching $M$ such that $G-M$ has Alon-Tarsi number at most 4. The former result is a strengthening of Thomassen’s result that planar graphs are 5-choosable, and the latter result implies that every planar graph $G$ has a matching $M$ such that $G-M$ is online 4-choosable, which is a generalization of Cushing-Kierstead’s result that planar graphs are 1-defective 4-choosable.
• [02488] Edge-colourings, hamiltonian cycles, and a problem of Kotzig
  • Format : Online Talk on Zoom
  • Author(s) :
    • Carol T. Zamfirescu (Ghent University)
  • Abstract : This talk concerns proper edge-colourings of regular graphs in which certain colour pairs form hamiltonian cycles -- such a pair is called perfect. We present a theorem solving Kotzig's problem asking whether planar 5-regular graphs exist admitting an edge-colouring in which all ten pairs are perfect. If time permits, we shall also discuss certain edge-colouring enumeration problems. This talk is based on joint work with Nico Van Cleemput.
• [03108] Coloring Graphs with Forbidden Minors
  • Format : Online Talk on Zoom
  • Author(s) :
    • Zi-Xia Song (University of Central Florida)
    • Michael Lafferty (University of Central Florida)
  • Abstract : Hadwiger's Conjecture from 1943 states that every graph with no $K_{t}$ minor is $(t-1)$-colorable; it remains open for all $t\ge 7$. Jakobsen in 1971 proved that every graph with no $\mathcal{K}_7^{-2}$ minor is $6$-colorable. In this talk, we present our recent work that every graph with no $\mathcal{K}_8^{-4}$ minor is $7$-colorable, and every graph with no $\mathcal{K}_9^{-6}$ minor is $8$-colorable, where $\mathcal{K}_t^{-s}$ denote the family of graphs obtained from $K_t$ by removing $s$ edges.

MS [00082] Development in fractional diffusion equations: models and methods

room : A618

• [04911] Uniqueness for inverse source problems for time-fractional diffusion-wave equations
  • Format : Talk at Waseda University
  • Author(s) :
    • Masahiro Yamamoto (The Univ. Tokyo)
  • Abstract : For time-fractional diffusion-wave equations, $\partial_t^{\alpha} u(x,t) = -Au + \mu(t)f(x)$ for $x\in \Omega, 0
• [02617] Fractional diffusion equation with psi-Hilfer derivative
  • Format : Talk at Waseda University
  • Author(s) :
    • M. Manuela Rodrigues (University of Aveiro, Portugal)
  • Abstract : We consider the multidimensional time-fractional diffusion equation with $\psi$-Hilfer derivative. An integral representation of the solution to the associated Cauchy problem involving Fox H-functions is obtained. Fractional moments of arbitrary order are computed. Series representations of the first fundamental solution are presented. Some plots of the fundamental solution are presented for particular choices of the function $\psi$ and the fractional parameters. Joint work with N. Vieira (UA - CIDMA), M. Ferreira (IPLeiria~ \& ~ CIDMA)
• [02623] On the $\psi$-Hilfer time-fractional telegraph equation in higher dimensions
  • Format : Talk at Waseda University
  • Author(s) :
    • Nelson Vieira (CIDMA - University of Aveiro)
  • Abstract : We consider the time-fractional telegraph equation in $\mathbb{R}^n \times \mathbb{R}^+$ with $\psi$-Hilfer fractional derivatives. For the solution, we present an integral representation involving Fox H-functions of two variables, and in terms of double series. For $n=1$, we prove the conditions under which we can interpret the first fundamental solution as a probability density function. Some plots of the fundamental solutions are presented. Joint work with M. Ferreira $($IPLeiria & CIDMA$)$ and M.M. Rodrigues $($CIDMA$)$.
• [02767] The fundamental solution to the space fractional diffusion equation
  • Format : Talk at Waseda University
  • Author(s) :
    • Piotr Rybka (University of Warsaw)
    • Tokinaga Namba (Nippon Steel Corporation)
    • Shoichi Sato (University of Tokyo)
  • Abstract : We consider a one dimensional diffusion equation equation involving the divergence of the Caputo space derivative of order less than one. We construct a self-similar solution, $\mathcal{E}$, which permits us to derive the representation formulas for boundary value problem on the half line. We also present properties of $\mathcal{E}$, and we show the infinite speed of signal propagation. This is a joint research with T.Namaba and S.Sato.