Cosmological constraints from noisy convergence maps through deep learning

Deep learning is a powerful analysis technique that has recently been proposed as a method to constrain cosmological parameters from weak lensing mass maps. Because of its ability to learn relevant features from the data, it is able to extract more information from the mass maps than the commonly used power spectrum, and thus achieve better precision for cosmological parameter measurement. We explore the advantage of convolutional neural networks over the power spectrum for varying levels of shape noise and different smoothing scales applied to the maps. We compare the cosmological constraints from the two methods in the Omega(M) - sigma(8) plane for sets of 400 deg(2) convergence maps. We find that, for a shape noise level corresponding to 8.53 galaxies/arcmin(2) and the smoothing scale of sigma(s) = 2.34arcmin, the network is able to generate 45% tighter constraints. For a smaller smoothing scale of sigma(s) = 1.17 the improvement can reach similar to 50%, while for a larger smoothing scale of sigma(s) = 5.85, the improvement decreases to 19%. The advantage generally decreases when the noise level and smoothing scales increase. We present a new training strategy to train the neural network with noisy data, as well as considerations for practical applications of the deep learning approach.