Center for Stochastic Dynamics Seminar by Jinchao Feng
Jinchao Feng, postdoctoral fellow, Department of Mathematics, Johns Hopkins University
Data-Driven Discovery of Interacting Particle Systems Using Gaussian Processes
Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and collective behaviors. We study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems, and propose a learning approach that models the latent interaction kernel functions as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of interaction kernel function with the pointwise uncertainty quantification, and the other one is the inference of unknown parameters in the non-collective forces of the system. By connecting with a statistical inverse problem, we also establish an operator-theoretical framework to analyze the recoverability via the coercivity of the associated operator and provide a finite sample analysis. The numerical results on prototype systems, including Cuker-Smale dynamics and fish milling dynamics, show that our approach produced faithful estimators from scarce and noisy trajectory data and made accurate predictions of collective behaviors.
Meeting ID: 974 8665 9782
Passcode: 423168Zoom link