Data driven discovery of system equilibration

The field of dynamical systems is undergoing a revolution. In the last 5 years, many tools have emerged which discover simple governing equations from timeseries data [arXiv:2102.12086 (2021)]. The discovered model is often simpler than the original data generating model! Recently, data driven discovery allows us to observe a transient system’s dimension reduction as it evolved to attractor [J Stat Phys 179, 1028–1045 (2020)]. This capability allows physics to gain traction on long-standing problems. One such problem is Hilbert’s 6^th problem, which challenged physics to formulate the limiting processes that leads from the unequilibrated atomistic systems to equilibrated continuum systems. It has been shown that transient non-equilibrium dynamics explore a larger dimensional space and that some dimensions are removed by fast relaxation towards the equilibrium attractor [Bulletin of the AMS 51.2, 187-246 (2014)]. In this work, we formulate Hilbert’s 6^th problem in an operator framework and use data driven discovery to observe the aforementioned fast relaxation towards the hydrodynamic attractor.