🎓 MSc Program in Data Science and Machine/Statistical Learning
Spring 2025 Lecture Series
📅 Date: Friday, March 21, 2025 | ⏰ Time: 11:00 AM
📍 Location: Meeting Room Vassileios Dougalis, STEP C, KEEK Building, FORTH
Guest Lecture
🔹 Speaker: Markos Katsoulakis, University of Massachusetts Amherst
🔹 Title: Hamilton-Jacobi Equations and Mean-Field Games for Robust Generative Modeling
Abstract
This talk explores the versatility of Hamilton-Jacobi (HJ) equations and mean-field games (MFGs) as a unifying framework for analyzing, designing, and ensuring the robustness of generative models. By connecting MFG formulations to major classes of flow- and diffusion-based generative models—including continuous-time normalizing flows, score-based models, and Wasserstein gradient flows—we show how different choices of particle dynamics and cost functions naturally lead to these models. The mathematical structure of MFGs, based on forward-backward nonlinear PDEs, offers new insights into the design and performance of generative algorithms. For instance, it enables the development of faster, more data-efficient score-based models, robust normalizing flows for learning low-dimensional manifold-supported distributions, and new analyses of diffusion models using nonlinear PDE tools. Another focus of the talk is uncertainty quantification (UQ) and robustness in generative modeling. Using a new Wasserstein uncertainty propagation theorem, we establish that score-based generative models are provably robust to the multiple sources of error in their practical implementation. The regularity theory of HJ equations within the MFG framework underpins this robustness, offering both theoretical guarantees and practical insights into the stability of generative algorithms.