  We present a principled data-driven strategy for learning deterministic
hydrodynamic models directly from stochastic non-equilibrium active particle
trajectories. We apply our method to learning a hydrodynamic model for the
propagating density lanes observed in self-propelled particle systems and to
learning a continuum description of cell dynamics in epithelial tissues. We
also infer from stochastic particle trajectories the latent phoretic fields
driving chemotaxis. This demonstrates that statistical learning theory combined
with physical priors can enable discovery of multi-scale models of
non-equilibrium stochastic processes characteristic of collective movement in
living systems.
