Probabilistic Mass Mapping with Neural Score Estimation

Kavli Affiliate: Jia Liu

| First 5 Authors: Benjamin Remy, Francois Lanusse, Niall Jeffrey, Jia Liu, Jean-Luc Starck

| Summary:

Weak lensing mass-mapping is a useful tool to access the full distribution of
dark matter on the sky, but because of intrinsic galaxy ellipticies and finite
fields/missing data, the recovery of dark matter maps constitutes a challenging
ill-posed inverse problem. We introduce a novel methodology allowing for
efficient sampling of the high-dimensional Bayesian posterior of the weak
lensing mass-mapping problem, and relying on simulations for defining a fully
non-Gaussian prior. We aim to demonstrate the accuracy of the method on
simulations, and then proceed to applying it to the mass reconstruction of the
HST/ACS COSMOS field. The proposed methodology combines elements of Bayesian
statistics, analytic theory, and a recent class of Deep Generative Models based
on Neural Score Matching. This approach allows us 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. 3) Obtain samples from the full Bayesian
posterior of the problem for robust Uncertainty Quantification. We demonstrate
the method on the $kappa$TNG simulations and find that the posterior mean
significantly outperfoms previous methods (Kaiser-Squires, Wiener filter,
Sparsity priors) both on root-mean-square error and in terms of the Pearson
correlation. We further illustrate the interpretability of the recovered
posterior by establishing a close correlation between posterior convergence
values and SNR of clusters artificially introduced into a field. Finally, we
apply the method to the reconstruction of the HST/ACS COSMOS field and yield
the highest quality convergence map of this field to date.

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