3 citations · 8 across the 17 of their papers we have counts for
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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…
Gradient-adjusted underdamped Langevin dynamics for sampling
Xinzhe Zuo, Stanley Osher, Wuchen Li
Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from…
Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems
Mo Zhou, Stanley Osher, Wuchen Li
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural n…
Convergence of Noise-Free Sampling Algorithms with Regularized Wasserstein Proximals
Fuqun Han, Stanley Osher, Wuchen Li
In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be…
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…
Fisher information dissipation for time inhomogeneous stochastic differential equations
Qi Feng, Xinzhe Zuo, Wuchen Li
We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irrevers…