Abstract : The minisymposium "recent advances in data-driven modeling and computational methods" covers a wide range of topics including topological data analysis, physics-informed neural networks, and data-driven modeling and numerical methods. It provides a platform for experts and junior researchers to exchange ideas and share knowledge in these areas.
This minisymposium is organized by the East Asia section of SIAM (EASIAM), and the organizers and speakers represent a broad list of countries covered by SIAM. We hope the minisymposium would provide an ideal opportunity for communication among EASIAM members, and to promote EASIAM internationally.
Organizer(s) : Yoshinobu Kawahara, Yao Yao, Zhiwen Zhang
[02896] Topological Data Analysis Experience in Malaysia: A Survey
Format : Talk at Waseda University
Author(s) :
Fatimah Abdul Razak (Universiti Kebangsaan Malaysia)
Mohd Salmi Md Noorani (Universiti Kebangsaan Malaysia)
Abstract : Topological Data Analysis (TDA) is used to detect qualitative features in datasets. It is often combined with techniques from Machine Learning, Time Series Analysis as well as Complex Network Analysis to achieve better predictions and classifications. This presentation outlines our experiences of using TDA to investigate several Malaysian data sets in order to predict floods and financial crises, classify different levels of air quality within a certain time window as well as detecting critical transitions.
[03038] A Reaction Network Analysis of Insulin Signaling
Format : Talk at Waseda University
Author(s) :
Angelyn Lao (De La Salle University)
Abstract : The insulin signaling system is an important metabolic system that initiates the uptake of glucose into the cell. This reduced ability of cells to use available insulin for energy metabolism is viewed as a common factor in diseases such as obesity, type 2 diabetes, metabolic syndrome, and cancer, and more recently to brain insulin resistance in connection with mild cognitive impairment and Alzheimer’s disease (AD). The complexity of the insulin signaling system, both in terms of the number of molecular components involved as well as the intricate combination of positive and negative feedback loops, clearly warrants the application of mathematical modeling and computational tools. This talk presents the construction of the insulin signaling reaction network and the analysis of its robustness and stability using Chemical Reaction Network Theory.
[03583] Comparing Lagrangian Particle Dispersion Models in Turbulent Flows: A Data-Driven Approach
Format : Talk at Waseda University
Author(s) :
Nurul Huda Mohd Ramli (Universiti Brunei Darussalam)
Haziq Jamil (Universiti Brunei Darussalam)
Abstract : This talk introduces a data-driven method for comparing two Lagrangian stochastic particle models in turbulent flows: the random flight model (RFM) and the simpler random displacement model (RDM). The RFM offers a more realistic representation of eddy velocities but can pose computational challenges. Using a Bayesian approach to infer the models' parameters, the objective is to provide a better understanding of their dynamics and assist researchers in selecting the appropriate model for their specific needs.
[03912] Error estimates of numerical methods for the Dirac equation
Format : Talk at Waseda University
Author(s) :
Ying Ma (Beijing University of Technology)
Jia Yin (Lawrence Berkeley National Laboratory)
Yue Feng (Sorbonne Université)
Lizhen Chen (Beijing Computational Science Research Center)
Abstract : The Dirac equation is a relativistic wave equation which plays an important role in relativistic quantum physics and provides a natural description of relativistic spin-1/2 particles. In this talk, we present numerical methods including several finite difference methods, the symmetric and asymmetric exponential wave integrator Fourier pseudospectral methods and establish the error estimates for the discretization of the Dirac equation in different regimes. Extensive numerical results are reported to support our error estimates.
[04021] A learning-based projection method for model order reduction of transport problems
Format : Talk at Waseda University
Author(s) :
ZHICHAO PENG (Hong Kong University of Science and Technology)
Fengyan Li (Rensselaer Polytechnic Institute)
Min Wang (University of Houston)
Abstract : Due to the slow decay of the Kolmogorov n-width for transport problems, classical linear reduced order model (ROM) may be inefficient. To address this issue we propose a learning-based projection method following an offline-online decomposition framework. A moving low dimensional subspace is learned offline, and in the online stage, the full order problem is projected onto the learned subspace to reduce computational cost. We also numerically demonstrate the performance of the proposed method.
[04197] An iterative algorithm for POD basis adaptation
Format : Talk at Waseda University
Author(s) :
Zhizhang Wu (The University of Hong Kong)
Zhiwen Zhang (The University of Hong Kong)
Abstract : To construct reduced-order models using POD for convection-diffusion equations, fine-grid solvers are needed to obtain accurate solution snapshots for small diffusivities, while coarse-grid solvers are sufficient for large diffusivities. We develop an iterative algorithm that adapts the POD basis functions extracted at large diffusivities for the construction of reduced-order models at small diffusivities without resorting to fine-grid solvers. Convergence analysis and numerical results are provided to confirm the effectiveness of our method.
[04384] Heat on hypergraph and its application to network analysis
Format : Talk at Waseda University
Author(s) :
Masahiro Ikeda (RIKEN)
Abstract : In this talk, I will introduce the joint works with Atsushi Miyauchi (Tokyo Univ.), Yuuki Takai(KIT) and Yuichi Yoshida (NII). They are about heat on hypergraph and its application to network analysis. I will introduce the background of their papers and the fundamental notions for community detection of networks. First I review the notion of Laplacian and Cheegerʼs inequality for the usual undirected graph. After that, I introduce the definition of the (submodular) Laplacian for hypergraphs and the heat on them. I also introduce several properties of the Laplacian and heat such as maximal monotonicity of the Laplacian. Especially I explain well-definedness of the heat and the Personalized PageRank for hypergraphs. Moreover, I introduce applications of their properties to the community detection on hypergraphs. If time permitted, I will introduce recent works about submodular Laplacian with Uchida (Oita Univ.).
[04987] Convergence Rate Analysis for Deep Ritz Method
Format : Talk at Waseda University
Author(s) :
Jerry Zhijian Yang (Wuhan University)
Abstract : We provide a rigorous numerical analysis on deep Ritz method (DRM) for second order elliptic equations with Neumann boundary conditions. We establish the first nonasymptotic convergence rate in H1 norm for DRM using deep networks with ReLU2 activation functions. Our study also shed light on how to set the hyperparameter of depth and width to achieve the desired convergence rate in terms of number of training samples.
