Speaker: Mo Zhou, Ph.D.
IDRE Postdoctoral Fellow
Department of Mathematics (UCLA)
University of California Los Angeles
Abstract: Generative models, a cornerstone of modern AI, learn to approximate complex probability distributions and generate realistic data. A key challenge in these models is efficiently computing the “score function,” which helps guide the learning process. Interestingly, a similar challenge arises in mean field control (MFC), a mathematical framework for decision-making in large-scale systems, such as crowd dynamics and financial markets.
In this talk, I will introduce a novel approach that computes MFC problems using score based neural ordinary differential equations (ODEs) and normalizing flows. We develop a system of ODEs to compute both first- and second-order score functions, reframing MFC problems as unconstrained optimization tasks. Our method also introduces a regularization technique inspired by Hamilton–Jacobi–Bellman (HJB) equations, ensuring better accuracy and stability. I will show applications, including probability flow matching and Wasserstein proximal operators, explaining how this approach enhances both theoretical understanding and practical computation in generative modeling and control.