7 papers · 1 filter
Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems
Xingjian Li, Kelvin Kan, Deepanshu Verma +3
This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approac…
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…
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…
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…
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…
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…