We present a novel, data-driven analysis of Galactic dynamics, using
unsupervised machine learning -- in the form of density estimation with
normalizing flows -- to learn the underlying phase space distribution of 6
million nearby stars from the Gaia DR3 catalog. Solving the collisionless
Boltzmann equation with the assumption of approximate equilibrium, we calculate
-- for the first time ever -- a model-free, unbinned, fully 3D map of the local
acceleration and mass density fields within a 3 kpc sphere around the Sun. As
our approach makes no assumptions about symmetries, we can test for signs of
disequilibrium in our results. We find our results are consistent with
equilibrium at the 10% level, limited by the current precision of the
normalizing flows. After subtracting the known contribution of stars and gas
from the calculated mass density, we find clear evidence for dark matter
throughout the analyzed volume. Assuming spherical symmetry and averaging mass
density measurements, we find a local dark matter density of 0.47±0.05GeV/cm3. We fit our results to a generalized NFW, and find a
profile broadly consistent with other recent analyses.Comment: 19 pages, 13 figures, 3 table