Deep Potential: Recovering the gravitational potential from a snapshot
  of phase space
  One of the major goals of the field of Milky Way dynamics is to recover the
gravitational potential field. Mapping the potential would allow us to
determine the spatial distribution of matter - both baryonic and dark -
throughout the Galaxy. We present a novel method for determining the
gravitational field from a snapshot of the phase-space positions of stars,
based only on minimal physical assumptions, which makes use of recently
developed tools from the field of deep learning. We first train a normalizing
flow on a sample of observed six-dimensional phase-space coordinates of stars,
obtaining a smooth, differentiable approximation of the distribution function.
Using the Collisionless Boltzmann Equation, we then find the gravitational
potential - represented by a feed-forward neural network - that renders this
distribution function stationary. This method, which we term "Deep Potential,"
is more flexible than previous parametric methods, which fit restricted classes
of analytic models of the distribution function and potential to the data. We
demonstrate Deep Potential on mock datasets, and demonstrate its robustness
under various non-ideal conditions. Deep Potential is a promising approach to
mapping the density of the Milky Way and other stellar systems, using rich
datasets of stellar positions and kinematics now being provided by Gaia and
ground-based spectroscopic surveys.
