BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mauro Maggioni (Johns Hopkins University) DTSTART:20201021T170000Z DTEND:20201021T180000Z DTSTAMP:20260423T003239Z UID:MPML/24 DESCRIPTION:Title: Le arning Interaction laws in particle- and agent-based systems\nby Mauro Maggioni (Johns Hopkins University) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nInteracting agent-based sys tems are ubiquitous in science\, from modeling of particles in Physics to prey-predator and colony models in Biology\, to opinion dynamics in econom ics and social sciences. Oftentimes the laws of interactions between the a gents are quite simple\, for example they depend only on pairwise interact ions\, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agent s: given only observed trajectories of the agents in the system\, can we l earn what the laws of interactions are? We would like to do this without a ssuming any particular form for the interaction laws\, i.e. they might be "any" function of pairwise distances. We consider this problem both the me an-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 observat ions\, albeit in this talk we will mostly focus on the latter case. We cas t this as an inverse problem\, and study it in the case where the interact ion is governed by an (unknown) function of pairwise distances. We discuss when this problem is well-posed\, and we construct estimators for the int eraction kernels with provably good statistically and computational proper ties. We measure their performance on various examples\, that include exte nsions to agent systems with different types of agents\, second-order syst ems\, and families of systems with parametric interaction kernels. We also conduct numerical experiments to test the large time behavior of these sy stems\, especially in the cases where they exhibit emergent behavior.\n\nT his is joint work with F. Lu\, J.Miller\, S. Tang and M. Zhong.\n LOCATION:https://researchseminars.org/talk/MPML/24/ END:VEVENT END:VCALENDAR