Abstract:

Interacting agent-based systems are ubiquitous in scienc e, from modeling of particles in Physics to prey-predator and colony models in Biology, to opinion dynamics in economics and social sciences. Oftentim es the laws of interactions between the agents are quite simple, for exampl e they depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a syst em of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? W e would like to do this without assuming any particular form for the intera ction laws, i.e. they might be "any" function of pairwise distances. We con sider 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 in creasing number of observations, albeit in this talk we will mostly focus o n the latter case. We cast this as an inverse problem, and study it in the case where the interaction is governed by an (unknown) function of pairwise distances. We discuss when this problem is well-posed, and we construct es timators for the interaction kernels with provably good statistically and c omputational properties. We measure their performance on various examples, that include extensions to agent systems with different types of agents, se cond-order systems, and families of systems with parametric interaction ker nels. We also conduct numerical experiments to test the large time behavior of these systems, especially in the cases where they exhibit emergent beha vior. This is joint work with F. Lu, J.Miller, S. Tang and M. Zhong.

CONTACT:Mauro Maggioni, Johns Hopkins University X-EXTRAINFO: BIO:\nMauro Maggioni works at the intersection between harmonic analysis, approximation theory, high-dimensional probability, statistical and machine learning, model reduction, stochastic dynamical systems, and statistical s ignal processing. He received a Ph.D. in Mathematics from the Washington Un iversity, St. Louis, in 2002; after begin a Gibbs Assistant Professor in Ma thematics at Yale University for 4 years, he moved to Duke University, beco ming Professor in Mathematics, Electrical and Computer Engineering, and Com puter Science in 2013. He is presently a Bloomberg Distinguished Professor of Mathematics, and Applied Mathematics and Statistics at Johns Hopkins Uni versity. He received the Popov Prize in Approximation Theory in 2007, a N.S .F. CAREER award and Sloan Fellowship in 2008, and was nominated inaugural Fellow of the American Mathematical Society in 2013. \n \n\n DTSTAMP:20230925T060856Z DTSTART;TZID=America/New_York:20200911T100000 DTEND;TZID=America/New_York:20200911T110000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR