Center for Stochastic Dynamics Seminar: Nonparametric Learning of Interaction Kernels in Mean-Field Equations of Interacting Particles
Speaker:
Fei Lu, assistant professor of mathematics, Johns Hopkins University
Title:
Nonparametric Learning of Interaction Kernels in Mean-Field Equations of Interacting Particles
Abstract:
Systems of self-interacting particles/agents arise in multiple disciplines, such as particle systems in physics, flocking birds and swarming cells in biology, and opinion dynamics in social science. We present an efficient regression algorithm to estimate the distance-based interaction kernel from data consisting a trajectory of solution of the mean-field PDE, which is the population density of the particles. In particular, we provide a systematic learning theory addressing identifiability and convergence of the estimators. We demonstrate our algorithm on three typical examples: the opinion dynamics with a piecewise linear kernel, the granular media model with a quadratic kernel, and the aggregation-diffusion with a repulsive-attractive kernel. If time permits, I will also discuss a data-adaptive RKHS Tikhonov regularization (DARTR) method for the learning of hidden functions from data in general linear inverse problems.
Meeting ID: 974 8665 9782
Passcode: 423168
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