Score-based Neural Ordinary Differential Equations and Normalizing Flow for Mean Field Control

In this 1-hour 7-minute talk from the USC Probability and Statistics Seminar, explore how Mean Field Control (MFC) provides a mathematical framework for decision-making in large-scale systems with connections to modern AI and generative models. Learn about a novel approach that computes MFC problems using score-based neural ordinary differential equations (ODEs) and normalizing flows. Discover how this method formulates a system of ODEs to compute both first- and second-order score functions along trajectories, transforming MFC into an unconstrained optimization problem. Understand the regularization technique inspired by Hamilton–Jacobi–Bellman (HJB) equations that improves accuracy. See practical applications including probability flow matching and Wasserstein proximal operators, gaining insights into both theoretical understanding and practical computation in control problems. Presented by Mo Zhou from UCLA.