3 citations · 10 across the 27 of their papers we have counts for
14 papers · 1 filter
Inexact Proximal Point Algorithms for Zeroth-Order Global Optimization
Minxin Zhang, Fuqun Han, Yat Tin Chow +2
This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theo…
VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
Yadi Cao, Yuxuan Liu, Liu Yang +3
In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, ex…
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…
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…
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…
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…
PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws
Liu Yang, Stanley J. Osher
Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs, even of new forms, without any fine-tuning? In-c…
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…