Jia-Jie Zhu: Optimization in the probability space: PDE gradient flows for sampling and inference

Abstract: This talk presents two recent advances in the use of gradient flows for sampling and inference in statistical machine learning. I will introduce the concept of optimal transport and gradient flows in the space of probability measures, highlighting their role as powerful tools in modern analysis and statistical inference. The talk will focus on new PDE analysis results, such as the entropy decay along transport-type gradient flows (including Wasserstein-Fisher-Rao), and I will discuss machine learning and sampling algorithms derived from principled dissipation geometries for PDEs of probability measures.