Learning governing equations of interacting particle systems using Gaussian process regression

Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. The fundamental and challenging goals are to infer individual interaction rules that yield collective behaviors and establish the governing equations. In this paper, we study the data-driven discovery of second-order interacting particle systems with distance-based interaction laws, which are known to have the capability to reproduce a rich variety of collective patterns. We propose a learning approach that models the latent interaction function as a Gaussian process, which can simultaneously fulfill two inference goals: one is the nonparametric inference of interaction function with the pointwise uncertainty quantification, and the other one is the inference of unknown parameters in the non-collective forces of the system. We test the learning approach on Dorsogma model and numerical results demonstrate the effectiveness.