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math.NA2025
A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
Jianbo Cui, Shu Liu, Haomin Zhou
We propose a supervised learning scheme for the first order Hamilton--Jacobi PDEs in high dimensions. The scheme is designed by using the geometric structure of Wasserstein Hamilto…
math.NA2025
A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
Hao Wu, Shu Liu, Xiaojing Ye +1
In this paper, we propose a new method to compute the solution of time-dependent Schrödinger equation (TDSE). Using push-forward maps and Wasserstein Hamiltonian flow, we reformul…
math.NA2024
Parameterized Wasserstein Gradient Flow
Yijie Jin, Shu Liu, Hao Wu +2
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduc…