Seminar| Institute of Mathematical Sciences
Speaker: Jinchao Feng, Great Bay University
Abstract: In this talk, I will discuss the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and body type. We propose a Gaussian Process-based approach to this problem, where the unknown model parameters are marginalized by Gaussian process priors on latent interaction kernels constrained to dynamics and observational data. This results in a nonparametric model for interacting dynamical systems that accounts for uncertainty quantification. Moreover, we perform a theoretical analysis to interpret the methodology and investigate the conditions under which the kernels can be recovered. We demonstrate the effectiveness of the proposed approach on various prototype systems, including the selection of the order of the systems and the types of interactions.