Data-driven coarse graining of many-body systems

First-principle derivations of governing equations for many-body systems have traditionally been based on systematic coarse graining procedures, but classical approaches rely on heuristic assumptions and become intractable for non-ideal systems. Recently, system identification has received renewed interest as machine learning has revolutionized data-driven discovery. Modern algorithms leverage sparsity and physical constraints to discover dynamical governing equations directly from trajectory data. These methods offer a powerful new approach to study the emergence of macroscopic behavior from microscopic physics. We apply system identification algorithms to discover coarse-grained dynamics governing data derived from molecular dynamics simulations. We focus on systems of spherical particles with hard and soft interaction potentials, which exhibit a myriad of collective behaviors including gaseous, liquid, crystalline, glassy, and jammed phases. Our results shine light on the emergence of universal macroscopic dynamics and may aid in the study of intractable disordered systems.