Title: Data-driven Discovery of Emergent Behaviors in Collective Dynamics
We further the investigation of  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.
: 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.