7 papers
Learning Mean-Field Games through Mean-Field Actor-Critic Flow
Mo Zhou, Haosheng Zhou, Ruimeng Hu
We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and op…
Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport
Yesom Park, Shu Liu, Mo Zhou +1
We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By…
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…
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…
Variational conditional normalizing flows for computing second-order mean field control problems
Jiaxi Zhao, Mo Zhou, Xinzhe Zuo +1
Mean field control (MFC) problems have vast applications in artificial intelligence, engineering, and economics, while solving MFC problems accurately and efficiently in high-dimen…
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…