19 citations · 75 across the 18 of their papers we have counts for
19 papers
Efficient Computation of Mean field Control based Barycenters from Reaction-Diffusion Systems
Arjun Vijaywargiya, Guosheng Fu, Stanley Osher +1
We develop a class of barycenter problems based on mean field control problems in three dimensions with associated reactive-diffusion systems of unnormalized multi-species densitie…
A Primal-dual hybrid gradient method for solving optimal control problems and the corresponding Hamilton-Jacobi PDEs
Tingwei Meng, Siting Liu, Wuchen Li +1
Optimal control problems are crucial in various domains, including path planning, robotics, and humanoid control, demonstrating their broad applicability. The connection between op…
Wasserstein proximal operators describe score-based generative models and resolve memorization
Benjamin J. Zhang, Siting Liu, Wuchen Li +2
We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstr…
Mean field control of droplet dynamics with high order finite element computations
Guosheng Fu, Hangjie Ji, Will Pazner +1
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, s…
Numerical analysis of a first-order computational algorithm for reaction-diffusion equations via the primal-dual hybrid gradient method
Shu Liu, Xinzhe Zuo, Stanley Osher +1
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct…
Tensor train based sampling algorithms for approximating regularized Wasserstein proximal operators
Fuqun Han, Stanley Osher, Wuchen Li
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evol…
A deep learning algorithm for computing mean field control problems via forward-backward score dynamics
Mo Zhou, Stanley Osher, Wuchen Li
We propose a deep learning approach to compute mean field control problems with individual noises. The problem consists of the Fokker-Planck (FP) equation and the Hamilton-Jacobi-B…
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…
Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation
Guosheng Fu, Stanley Osher, Will Pazner +1
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems.…
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…
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems
Guosheng Fu, Stanley Osher, Wuchen Li
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metr…
High order computation of optimal transport, mean field planning, and mean field games
Guosheng Fu, Siting Liu, Stanley Osher +1
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However,…
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…
Computational Mean-field Games on Manifolds
Jiajia Yu, Rongjie Lai, Wuchen Li +1
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riema…
Controlling conservation laws I: entropy-entropy flux
Wuchen Li, Siting Liu, Stanley Osher
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on con…
Computational Mean-field information dynamics associated with Reaction diffusion equations
Wuchen Li, Wonjun Lee, Stanley Osher
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapu…
Mean field control problems for vaccine distribution
Wonjun Lee, Siting Liu, Wuchen Li +1
With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial…
Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games
Alex Tong Lin, Samy Wu Fung, Wuchen Li +2
We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional inst…
Hessian transport gradient flows
Wuchen Li, Lexing Ying
We derive new gradient flows of divergence functions in the probability space embedded with a class of Riemannian metrics. The Riemannian metric tensor is built from the transporte…