3 papers
cs.LG2025
Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport
Yesom Park, Shu Liu, Mo Zhou +1
We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By…
math.OC2025
Accelerated Markov Chain Monte Carlo Algorithms on Discrete States
Bohan Zhou, Shu Liu, Xinzhe Zuo +1
We propose a class of discrete state sampling algorithms based on Nesterov's accelerated gradient method, which extends the classical Metropolis-Hastings (MH) algorithm. The evolut…
math.NA2024
A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations
Shu Liu, Stanley Osher, Wuchen Li
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtai…