19 citations · 75 across the 18 of their papers we have counts for
7 papers · 1 filter
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…