A Numerical Study on Sparse Learning of Interaction Laws in Homogeneous Multiparticle Systems

Abstract

. Multi-agent systems have found wide applications in science and engineering ranging from opinion dynamics to predator-prey systems. A grand challenge encountered in these areas is to reveal the interaction laws between individual agents leading to collective behaviors. In this article, we consider a system of ODEs that is often used in modeling opinion dynamics, where the laws of the interaction are dependent on pairwise distances. We leverage recent advancements in sparsity-promoted algo-rithms and propose a new approach to learning the interaction laws from a small amount of data. Numerical experiments demonstrate the effectiveness and robustness of the proposed approach in a small, noisy data regime and show the superiority of the proposed approach.