Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Assistant Professor Fei Lu,Johns Hopkins University
Inviter:	Professor Jialin Hong
Title:	Inverse problems for mean-field equations of interacting particles
Language:	Chinese
Time & Venue:	2023.07.15 09:00-10:00 N226
Abstract:	Systems of self-interacting particles/agents arise in multiple disciplines, such as particle systems in physics, flocking birds and migrating cells in biology, and opinion dynamics in social science. An essential task in these applications is to learn the laws of interaction from data. When the number of agents is large, this task leads to a linear inverse problem for mean-field equations. We study the nonparametric estimation of interaction kernels, and introduce three key new elements: (1) the construction of loss functions that are derivative-free and flexible to adapt to discrete or sampled data; (2) the identifiability of the kernels and ill-posedness of the inverse problem; (3) a data-adaptive RKHS Tikhonov regularization (DARTR) method. If time permits, we will discuss open problems in the generalization to a variational framework for the learning of kernels in operators, a topic that bridges statistical learning with inverse problems.