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.