3 citations · 8 across the 17 of their papers we have counts for
17 papers
A Kernel Formula for Kinetic Fokker-Planck Equations
Fuqun Han, Wuchen Li
We derive an explicit one-step kernel formula for the kinetic Fokker-Planck equation. The construction begins with a reference dynamics admitting an explicit transition kernel and…
Deep Kinetic JKO schemes for Vlasov-Fokker-Planck Equations
Wonjun Lee, Li Wang, Wuchen Li
We introduce a deep neural network-based numerical method for solving kinetic Fokker Planck equations, including both linear and nonlinear cases. Building upon the conservative dis…
Accelerated Regularized Wasserstein Proximal Sampling Algorithms
Hong Ye Tan, Stanley Osher, Wuchen Li
We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles,…
Sparse Transformer Architectures via Regularized Wasserstein Proximal Operator with Prior
Fuqun Han, Stanley Osher, Wuchen Li
In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the…
Preconditioned Regularized Wasserstein Proximal Sampling
Hong Ye Tan, Stanley Osher, Wuchen Li
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed…
Simulating Fokker-Planck equations via mean field control of score-based normalizing flows
Mo Zhou, Stanley Osher, Wuchen Li
The Fokker--Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simu…
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…
Variational conditional normalizing flows for computing second-order mean field control problems
Jiaxi Zhao, Mo Zhou, Xinzhe Zuo +1
Mean field control (MFC) problems have vast applications in artificial intelligence, engineering, and economics, while solving MFC problems accurately and efficiently in high-dimen…
Splitting Regularized Wasserstein Proximal Algorithms for Nonsmooth Sampling Problems
Fuqun Han, Stanley Osher, Wuchen Li
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the…
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…
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 Damping algorithms for optimization
X. Zuo, S. Osher, W. Li
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrain…