Young Researchers Workshop: Ki-Net 2012-2019

Data-driven discovery of emergent states in collective dynamics

Ming Zhong

Johns Hopkins University

We further the investigation of [1] by extending the nonparametric inference approach for learning interaction laws from observations of agent-based dynamical systems to more complex dynamics and interaction kernels. The systems considered involve homogeneous and heterogeneous agents with interaction kernels of multiple variables and parametric forms. Our estimators can provide faithful approximation to interaction laws as well as excellent prediction of both trajectories and the emergent behaviors of the systems in various settings. The estimators, through an optimization procedure, are able to learn from observed data the more elaborate structure of the interaction laws, namely a parametric form. These particular learned estimators can lead to discovery and deeper understanding of fundamental physics in a novel proof of concept of a non-parametric approach to the discovery of the governing equation of planetary motion.

[1]: F. Lu, M. Zhong, S. Tang, and M. Maggioni, Nonparametric inference of interaction laws in systems of agents from trajectory data, PNAS, 116 (29), 14424 – 14433, 2019.