Statistics Seminar

Date: November 2, 2022

Speaker: Mauro Maggioni

Website: https://mauromaggioni.duckdns.org/

Title: Learning Interaction laws in particle- and agent-based systems

Abstract: We consider systems of interacting agents or particles, which are commonly used for modeling across the sciences. Oftentimes the laws of interaction between the agents are quite simple, for example they depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances. We consider this problem both the mean-field limit (i.e. the number of particles going to infinity) and in the case of a finite number of agents, with an increasing number of observations, albeit in this talk we will mostly focus on the latter case. We cast this as an inverse problem, and present a solution in the simplest yet interesting case where the interaction is governed by an (unknown) function of pairwise distances. We discuss when this problem is well-posed, we construct estimators for the interaction kernels with provably good statistically and computational properties, and discuss extensions to second-order systems, more general interaction kernels, stochastic systems, and to the setting where the variables (e.g. pairwise distance) on which the interaction kernel depends are not known a priori. This is joint work with F. Lu, J.Miller, S. Tang and M. Zhong.