Clear Potential: Learning the Dust-Corrected Gravitational Potential of the Milky Way using Masked Autoregressive Flows

We introduce $\texttt{ClearPotential}$, a data-driven and dust-corrected measurement of the local Milky Way's gravitational potential using unsupervised machine learning, without the symmetry assumptions, specific functional forms, and binning required in previous work.The potential is modeled as a neural network, optimized to solve the equilibrium collisionless Boltzmann equation for the observed phase space density of $\textit{Gaia}$ DR3 Red Clump and Red Giant Branch stars within $4~$kpc of the Sun. This density is obtained from data using normalizing flows, and our unsupervised solution to the Boltzmann equation automatically corrects for selection effects from crowding and the dust-driven extinction of starlight.Our fully-differentiable and unbinned machine learning model of the gravitational potential allows us to compute the acceleration and mass density, providing a three-dimensional map of the dark matter density in our local Galaxy.This work provides the clearest map of the local Galactic potential to date and marks an important step in the era of data-driven astrometry.