Seminars on Numerical Algorithms, Analyses, and Applications: Wasserstein Hamiltonian Flow and Its Structure Preserving Numerical Scheme

：崔建波（香港理工大学）
：2024-11-11 10:00
：海韵园行政楼C503

报告人：崔建波（香港理工大学）

时  间：2024年11月11日10:00

地  点：海韵园行政楼C503

内容摘要:

We study discretizations of Hamiltonian systems on the probability density manifold equipped with the L2-Wasserstein metric. For low dimensional problems, based on discrete optimal transport theory, several Wasserstein Hamiltonian flows (WHFs) on graph are derived. They can be viewed as spatial discretizations to the original systems. By regularizing the system using Fisher information, we propose a novel regularized symplectic scheme which could preserve several desirable longtime behaviors. Furthermore, we use the coupling idea and WHF to propose a supervised learning scheme for some high-dimensional problem. If time permits, we will talk about more details on solving high-dimensional Hamilton-Jacobi equation via the density coupling and supervised learning.

个人简介：

Jianbo Cui is currently a faculty member at the Hong Kong Polytechnic University. Dr. Cui received his Ph.D. from Chinese Academy of Sciences in 2019. He subsequently served as a visiting assistant professor at Georgia Institute of Technology from 2019-2021. Dr. Cui’s current research interests include computational optimal transport, and numerical analysis of ordinary and partial differential equations. Dr. Cui has received support from NSFC and RGC, and has published academic papers in leading international journals, such as SIAM Journal on Numerical Analysis, Mathematics of Computation, SIAM Journal on Scientific Computing, SIAM Journal on Applied Mathematics, SIAM Journal on Mathematical Analysis, SIAM Journal on Control and Optimization, SIAM/ASA Journal on Uncertainty Quantification, and Journal of Computational Physics.

 

联系人：陈黄鑫