A comparative study of cosmological constraints from weak lensing using Convolutional Neural Networks

Abstract: Weak Lensing (WL) surveys are reaching unprecedented depths, enabling the investigation of very small angular scales. At these scales, nonlinear gravitational effects lead to higher-order correlations making the matter distribution highly non-Gaussian. Extracting this information using traditional statistics has proven difficult, and Machine Learning based summary statistics have emerged as a powerful alternative. We explore the capabilities of a discriminative, Convolutional Neural Networks (CNN) based approach, focusing on parameter constraints in the ($\Omega_m$, $\sigma_8$) cosmological parameter space. Leveraging novel training loss functions and network representations on WL mock datasets without baryons, we show that our models achieve $\sim 5$ times stronger constraints than the power spectrum, $\sim 3$ stronger constraints than peak counts, and $\sim 2$ stronger constraints than previous CNN-learned summary statistics and scattering transforms, for noise levels relevant to Rubin or Euclid. For WL convergence maps with baryonic physics, our models achieve $\sim 2.3$ times stronger constraining power than the power spectrum at these noise levels, also outperforming previous summary statistics. To further explore the possibilities of CNNs for this task, we also discuss transfer learning where we adapt pre-trained models, trained on different tasks or datasets, for cosmological inference, finding that these do not improve the performance.