Decoding Cosmological Information in Weak-Lensing Mass Maps with Generative Adversarial Networks

Galaxy imaging surveys enable us to map the cosmic matter density field through weak gravitational lensing analysis. The density reconstruction is compromised by a variety of noise originating from observational conditions, galaxy number density fluctuations, and intrinsic galaxy properties. We propose a deep-learning approach based on generative adversarial networks (GANs) to reduce the noise in the weak lensing map under realistic conditions. We perform image-to-image translation using conditional GANs in order to produce noiseless lensing maps using the first-year data of the Subaru Hyper Suprime-Cam (HSC) survey. We train the conditional GANs by using 30000 sets of mock HSC catalogs that directly incorporate observational effects. We show that an ensemble learning method with GANs can reproduce the one-point probability distribution function (PDF) of the lensing convergence map within a $0.5-1\sigma$ level. We use the reconstructed PDFs to estimate a cosmological parameter $S_{8} = \sigma_{8}\sqrt{\Omega_{\rm m0}/0.3}$, where $\Omega_{\rm m0}$ and $\sigma_{8}$ represent the mean and the scatter in the cosmic matter density. The reconstructed PDFs place tighter constraint, with the statistical uncertainty in $S_8$ reduced by a factor of $2$ compared to the noisy PDF. This is equivalent to increasing the survey area by $4$ without denoising by GANs. Finally, we apply our denoising method to the first-year HSC data, to place $2\sigma$-level cosmological constraints of $S_{8} < 0.777 \, ({\rm stat}) + 0.105 \, ({\rm sys})$ and $S_{8} < 0.633 \, ({\rm stat}) + 0.114 \, ({\rm sys})$ for the noisy and denoised data, respectively.