Deep Potential: Recovering the Gravitational Potential from a Snapshot of Phase Space

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