212 citations · 625 across the 54 of their papers we have counts for
60 papers
Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals
Hong Ye Tan, Stanley Osher, Wuchen Li
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in…
Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models
Wuchen Li, Jiaxi Zhao
We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distrib…
Minimal Wasserstein Surfaces
Wuchen Li, Tryphon T. Georgiou
In finite-dimensions, minimal surfaces that fill in the space delineated by closed curves and have minimal area arose naturally in classical physics in several contexts. No such co…
Optimal Ricci curvature Markov chain Monte Carlo methods on finite states
Wuchen Li, Linyuan Lu
We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Mark…
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…
Master equations for finite state mean field games with nonlinear activations
Yuan Gao, Wuchen Li, Jian-Guo Liu
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled contin…
Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization
Yifei Wang, Peng Chen, Mert Pilanci +1
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite s…
Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations
Erhan Bayraktar, Qi Feng, Wuchen Li
We study long-time dynamical behaviors of weakly self-consistent Vlasov-Fokker-Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which charac…
Mean field information Hessian matrices on graphs
Wuchen Li, Linyuan Lu
We derive mean-field information Hessian matrices on finite graphs. The "information" refers to entropy functions on the probability simplex. And the "mean-field" means nonlinear w…
Mean field Kuramoto models on graphs
Wuchen Li, Hansol Park
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics…
Controlling conservation laws II: compressible Navier-Stokes equations
Wuchen Li, Siting Liu, Stanley Osher
We propose, study, and compute solutions to a class of optimal control problems for hyperbolic systems of conservation laws and their viscous regularization. We take barotropic com…
A Fast Proximal Gradient Method and Convergence Analysis for Dynamic Mean Field Planning
Jiajia Yu, Rongjie Lai, Wuchen Li +1
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-imp…
Transport information Hessian distances
Wuchen Li
We formulate closed-form Hessian distances of information entropies in one-dimensional probability density space embedded with the L2-Wasserstein metric.
Projected Wasserstein gradient descent for high-dimensional Bayesian inference
Yifei Wang, Peng Chen, Wuchen Li
We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is a…
Wasserstein Proximal of GANs
Alex Tong Lin, Wuchen Li, Stanley Osher +1
We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein informa…
Hypoelliptic entropy dissipation for stochastic differential equations
Qi Feng, Wuchen Li
We study the convergence analysis for general degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to analyze the Fokker-Planck equa…
Tracial smooth functions of non-commuting variables and the free Wasserstein manifold
David Jekel, Wuchen Li, Dimitri Shlyakhtenko
We formulate a free probabilistic analog of the Wasserstein manifold on (the formal Riemannian manifold of smooth probability densities on ), and we us…
Transport information Bregman divergences
Wuchen Li
We study Bregman divergences in probability density space embedded with the -Wasserstein metric. Several properties and dualities of transport Bregman divergences are provided…
Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equations
Qi Feng, Wuchen Li
We formulate explicit bounds to guarantee the exponential dissipation for some non-gradient stochastic differential equations towards their invariant distributions. Our method exte…
Quantum statistical learning via Quantum Wasserstein natural gradient
Simon Becker, Wuchen Li
In this article, we introduce a new approach towards the statistical learning problem to approximate a targ…
A mean field game inverse problem
Lisang Ding, Wuchen Li, Stanley Osher +1
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals int…
Controlling Propagation of epidemics via mean-field control
Wonjun Lee, Siting Liu, Hamidou Tembine +2
The coronavirus disease 2019 (COVID-19) pandemic is changing and impacting lives on a global scale. In this paper, we introduce a mean-field game model in controlling the propagati…
Computational methods for nonlocal mean field games with applications
Siting Liu, Matthew Jacobs, Wuchen Li +2
We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions…
Sub-Riemannian Ricci curvature via generalized Gamma calculus
Qi Feng, Wuchen Li
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group, and Martinet sub-Riemannian st…