Probabilistic mass-mapping with neural score estimation^⋆

¹ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
e-mail: benjamin.remy@cea.fr
² Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
³ University College London, Gower St, London, UK
⁴ Berkeley Center for Cosmological Physics, University of California, 341 Campbell Hall, Berkeley, CA 94720, USA
⁵ Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 93720, USA
⁶ Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
⁷ Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
⁸ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

Received: 6 January 2022
Accepted: 29 April 2022

Abstract

Context. Weak lensing mass-mapping is a useful tool for accessing the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies, finite fields, and missing data, the recovery of dark matter maps constitutes a challenging, ill-posed inverse problem

Aims. We introduce a novel methodology that enables the efficient sampling of the high-dimensional Bayesian posterior of the weak lensing mass-mapping problem, relying on simulations to define a fully non-Gaussian prior. We aim to demonstrate the accuracy of the method to simulated fields, and then proceed to apply it to the mass reconstruction of the HST/ACS COSMOS field.

Methods. 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 make full use of analytic cosmological theory to constrain the 2pt statistics of the solution, to understand any differences between this analytic prior and full simulations from cosmological simulations, and to obtain samples from the full Bayesian posterior of the problem for robust uncertainty quantification.

Results. We demonstrate the method in the κTNG simulations and find that the posterior mean significantly outperfoms previous methods (Kaiser–Squires, Wiener filter, Sparsity priors) both for the 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 the S/N of the clusters artificially introduced into a field. Finally, we apply the method to the reconstruction of the HST/ACS COSMOS field, which yields the highest-quality convergence map of this field to date.

Conclusions. We find the proposed approach to be superior to previous algorithms, scalable, providing uncertainties, and using a fully non-Gaussian prior.