GalaxyScore: Estimating Local Dark Matter Density in Galaxies with Score Matching

We introduce GalaxyScore, an unsupervised machine learning method for estimating local dark matter density in galaxies using collisionless Boltzmann equation solvers with a stellar kinematics catalog. Current approaches using normalizing flows require computing derivatives of neural network outputs to estimate the probability density derivatives needed for solving these equations, leading to high computational overhead and minor numerical noise. GalaxyScore bypasses the explicit density evaluation by using score matching to directly estimate the log-probability density derivatives from stellar positions and velocities. We anticipate that this direct approach will provide more accurate and computationally efficient solutions compared to existing methods. We demonstrate GalaxyScore on simulated spherical galaxies from the Gaia Challenge Datasets.