报告题目：Wasserstein Hamiltonian Flow and Its Structure Preserving Numerical Schemes

报告时间：2024-11-25   15:00-16:00

报 告 人：崔建波   副教授   （香港理工大学）

报告地点：理学院东北楼四楼报告厅（404）

Abstract:We study discretizationsof 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 discretizationsto the original systems. By regularizing the system using Fisher information, we propose a novel regularized symplecticscheme 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.