Computational and Applied Mathematics seminar

Abstract: Identifying the dynamics of individual agents from aggregate, population-level data is a key challenge in many applications, ranging from biology to crowd dynamics and traffic systems. In recent years, optimal transport theory has emerged as a powerful tool for modeling large populations of agents, as it bridges a population-level viewpoint with an agent-level viewpoint.

In this talk, I will show how optimal transport can be used to identify agent dynamics from snapshot observations of the full population. This idea extends even to heterogeneous populations, where the observed data results from a superposition of multiple subpopulations, each governed by distinct dynamics. In this case, our method simultaneously separates the population into ensembles and identifies each ensemble’s governing system, using only aggregate snapshot observations.