Generative modelling for mass-mapping with fast uncertainty quantification

Tobías I. Liaudat, Jessica Whitney, Jason McEwen, Matthijs Mars, Matthew Alexander Price

Abstract: Understanding the nature of dark matter in the Universe is an important goal of modern cosmology. A key method for probing this distribution is via weak gravitational lensing mass-mapping – a challenging ill-posed inverse problem where one infers the convergence field from observed shear measurements. Upcoming stage IV surveys, such as those made by the Vera C. Rubin Observatory and Euclid satellite, will provide a greater quantity and precision of data for lensing analyses, necessitating high-fidelity mass-mapping methods that are computationally efficient and that also provide uncertainties for integration into downstream cosmological analyses. In this work we introduce a novel generative adversarial network (GAN) for mass-mapping, which we call the Mass-Mapping GAN (MMGAN), based on a regularized conditional GAN framework, which generates approximate posterior samples of the convergence field given shear data. We adopt Wasserstein GANs to improve training stability and apply regularization techniques to overcome mode collapse, issues that otherwise are particularly acute for conditional GANs. We train and validate our model on a mock data set modeled after the Cosmic Evolution Survey (COSMOS) before applying it to true COSMOS data. Our approach significantly outperforms the Kaiser–Squires technique and achieves similar reconstruction fidelity as alternative state-of-the-art deep learning approaches. Notably, while alternative approaches for generating samples from a learned posterior are slow (e.g. requiring 10 GPU min per posterior sample), MMGAN can produce a high-quality convergence sample in less than a second.