  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 are not 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. To directly
uncover the underlying physical principles, we present a data-driven method for
obtaining the phase-space density 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 {\it Serratia marcescens} bacterial swarm and in the presence of spatially
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.
