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Applied and computational Analysis Seminars

Wasserstein Hamiltonian flow and its structure preserving numerical scheme

With Jianbo Cui (The Hong Kong Polytechnic University)

Wasserstein Hamiltonian flow and its structure preserving numerical scheme

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.

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