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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 reformula…
math.NA2024★ 2 cited
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…
math.NA2024
Approximation of Solution Operators for High-dimensional PDEs
Nathan Gaby, Xiaojing Ye
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By em…