9 citations · 48 across the 27 of their papers we have counts for
7 papers · 1 filter
Numerical Analysis on Neural Network Projected Schemes for Approximating One Dimensional Wasserstein Gradient Flows
Xinzhe Zuo, Jiaxi Zhao, Shu Liu +2
We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapp…
Deep JKO: time-implicit particle methods for general nonlinear gradient flows
Wonjun Lee, Li Wang, Wuchen Li
We develop novel neural network-based implicit particle methods to compute high-dimensional Wasserstein-type gradient flows with linear and nonlinear mobility functions. The main i…
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…
A primal-dual approach for solving conservation laws with implicit in time approximations
Siting Liu, Stanley Osher, Wuchen Li +1
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an…
Generalized Unnormalized Optimal Transport and its fast algorithms
Wonjun Lee, Rongjie Lai, Wuchen Li +1
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the optim…