Speaker: Mo Zhou, Ph.D. IDRE Postdoctoral Fellow Department of Mathematics (UCLA) University of California Los Angeles    Place: Virtual (Link to registration)

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.

About the speaker: Dr. Zhou is an Assistant Adjunct Professor in the Department of Mathematics at UCLA, under Professor Stanley Osher’s guidance. He earned his bachelor’s degree in mathematics from Tsinghua University in 2018 and Ph.D. in mathematics from Duke University in 2023, under Professor Jianfeng Lu. During his Ph.D. studies, Dr. Zhou developed advanced deep learning algorithms to overcome the curse of dimensionality and addressed traditional scientific computing challenges, including eigenvalue problems and optimal control problems. Currently, his research focuses on mean-field control and games.