Georgia Institute of Technology College of Sciences

We introduce proximal optimal transport divergences that provide a unifying variational framework interpolating between classical f-divergences and Wasserstein metrics. From a gradient-flow perspective, these divergences generate stable and robust dynamics in probability space, enabling the learning of distributions with singular structure, including strange attractors, extreme events, and low-dimensional manifolds, with provable guarantees in sample size.

We illustrate how this mathematical structure leads naturally to generative particle flows for reconstructing nonlinear cellular dynamics from snapshot single-cell RNA sequencing data,including real patient datasets, highlighting the role of proximal regularization in stabilizing learning and inference in high dimensions.

Bio: Markos Katsoulakis is a Professor of Applied Mathematics and an Adjunct Professor of Chemical & Biomolecular Engineering at UMass Amherst,  whose research lies at the interface of PDEs, uncertainty quantification, scientific machine learning, and information theory. He serves on the editorial boards of the SIAM/ASA Journal on Uncertainty Quantification, the SIAM Journal on Scientific Computing, and the SIAM Mathematical Modeling and Computation book series. He received his Ph.D. in Applied Mathematics from Brown University and his B.Sc. from the University of Athens. His work has been supported by AFOSR, DARPA, NSF, DOE, and the ERC.