Mo Zhou, UCLA

Title: Score-based neural ordinary differential equations and normalizing flow for computing mean
field control problems

Abstract: Mean Field Control (MFC) provides a mathematical framework for decision-making in large-scale systems and has strong connections to modern artificial intelligence, particularly generative models. In this talk, I will introduce a novel approach that computes MFC problems using score based neural ordinary differential equations (ODEs) and normalizing flows. Our method formulates a system of ODEs that computes both first- and second-order score functions along trajectories, transforming MFC into an unconstrained optimization problem. To improve accuracy, we introduce a regularization technique inspired by the Hamilton–Jacobi–Bellman (HJB) equations. I will show applications, including probability flow matching and Wasserstein proximal operators, explaining how this approach enhances both theoretical understanding and practical computation in control problems.