Probabilistic Mapping of Dark Matter by Neural Score Matching
  The Dark Matter present in the Large-Scale Structure of the Universe is
invisible, but its presence can be inferred through the small gravitational
lensing effect it has on the images of far away galaxies. By measuring this
lensing effect on a large number of galaxies it is possible to reconstruct maps
of the Dark Matter distribution on the sky. This, however, represents an
extremely challenging inverse problem due to missing data and noise dominated
measurements. In this work, we present a novel methodology for addressing such
inverse problems by combining elements of Bayesian statistics, analytic
physical theory, and a recent class of Deep Generative Models based on Neural
Score Matching. This approach allows to do the following: (1) make full use of
analytic cosmological theory to constrain the 2pt statistics of the solution,
(2) learn from cosmological simulations any differences between this analytic
prior and full simulations, and (3) obtain samples from the full Bayesian
posterior of the problem for robust Uncertainty Quantification. We present an
application of this methodology on the first deep-learning-assisted Dark Matter
map reconstruction of the Hubble Space Telescope COSMOS field.
