A data-driven statistical description for the hydrodynamics of active matter

Modeling living systems at the collective scale can be very challenging because the individual constituents can themselves be complex and the respective interactions between the constituents may not be fully understood. With the advent of high throughput experiments and in the age of big data, data-driven methods are on the rise to overcome these challenges. Although machine-learning approaches can help quantify correlations between the various players, they do not directly shed light on the underlying physical principles of such systems. Here, we present a data-driven method for obtaining the phase-space density of active matter systems such that the solution to the stochastic dynamic equation for active matter readily emerges, from which time and space dependence of physical order parameters can be readily extracted. If the system is near a steady state, we illuminate how to construct a field theory to subsequently make physical predictions about the system. The method is first developed analytically and subsequently calibrated using simulated data. The method is then applied to an experimental system of particles actively driven by a Serratia marcescens bacterial swarm and in the presence of localized UV light. The analysis demonstrates that the particles are in the steady-state before and sometime after the UV light and obey a Gaussian field theory with a spatially-varying 'mass' in those regimes. This novel yet simple finding is surprising given the complex dynamics of the bacterial swarm. In response to the UV light, we demonstrate that there is a net flow of the particles away from the UV light and that the entropy of the particles increases away from the light. We conclude with a discussion of additional potential applications of our data-driven method such as when the internal structure of the individual constituents dynamically changes to result in a modified stochastic dynamic equation governing the system.