52 citations · 89 across the 15 of their papers we have counts for
5 papers · 1 filter
Primal-dual hybrid gradient algorithms for computing time-implicit Hamilton-Jacobi equations
Tingwei Meng, Wenbo Hao, Siting Liu +2
Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications spanning physics, optimal control, game theory, and imaging sciences. This research introduces…
A first-order computational algorithm for reaction-diffusion type equations via primal-dual hybrid gradient method
Shu Liu, Siting Liu, Stanley Osher +1
We propose an easy-to-implement iterative method for resolving the implicit (or semi-implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the n…
In-Context Operator Learning with Data Prompts for Differential Equation Problems
Liu Yang, Siting Liu, Tingwei Meng +1
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new…
High order computation of optimal transport, mean field planning, and mean field games
Guosheng Fu, Siting Liu, Stanley Osher +1
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However,…
A kernel formula for regularized Wasserstein proximal operators
Wuchen Li, Siting Liu, Stanley Osher
We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the Wasserstein proximal operator usi…