Charting galactic accelerations II: how to 'learn' accelerations in the
  solar neighbourhood
  Gravitational acceleration fields can be deduced from the collisionless
Boltzmann equation, once the distribution function is known. This can be
constructed via the method of normalizing flows from datasets of the positions
and velocities of stars. Here, we consider application of this technique to the
solar neighbourhood. We construct mock data from a linear superposition of
multiple `quasi-isothermal' distribution functions, representing stellar
populations in the equilibrium Milky Way disc. We show that given a mock
dataset comprising a million stars within 1 kpc of the Sun, the underlying
acceleration field can be measured with excellent, sub-percent level accuracy,
even in the face of realistic errors and missing line-of-sight velocities. The
effects of disequilibrium can lead to bias in the inferred acceleration field.
This can be diagnosed by the presence of a phase space spiral, which can be
extracted simply and cleanly from the learned distribution function. We carry
out a comparison with two other popular methods of finding the local
acceleration field (Jeans analysis and 1D distribution function fitting). We
show our method most accurately measures accelerations from a given mock
dataset, particularly in the presence of disequilibria.
