An end-to-end strategy for recovering a free-form potential from a
  snapshot of stellar coordinates
Wassim Tenachi Rodrigo Ibata Foivos I. Diakogiannis
New large observational surveys such as Gaia are leading us into an era of
data abundance, offering unprecedented opportunities to discover new physical
laws through the power of machine learning. Here we present an end-to-end
strategy for recovering a free-form analytical potential from a mere snapshot
of stellar positions and velocities. First we show how auto-differentiation can
be used to capture an agnostic map of the gravitational potential and its
underlying dark matter distribution in the form of a neural network. However,
in the context of physics, neural networks are both a plague and a blessing as
they are extremely flexible for modeling physical systems but largely consist
in non-interpretable black boxes. Therefore, in addition, we show how a
complementary symbolic regression approach can be used to open up this neural
network into a physically meaningful expression. We demonstrate our strategy by
recovering the potential of a toy isochrone system.