Cosmological constraints from noisy convergence maps through deep learning

Abstract

Deep learning is a powerful analysis technique that has recently been proposed as a method to constrain cosmological parameters from weak lensing mass maps. Due to 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 (CNN) 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 ΩM −σ8 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 σs = 2.34 arcmin, the network is able to generate 45% tighter constraints. For smaller smoothing scale of σs = 1.17 the improvement can reach ∼ 50%, while for larger smoothing scale of σs = 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.arXiv:1807.08732v2 [astro-ph.CO]

Cosmological constraints with deep learning from KiDS-450 weak lensing maps

“…To reduce the training time, we trained the networks asynchronously on 16 GPUs for 1'500'000 iterations where we fed the network maps from eight cosmological parameter combinations at each iteration. For the network architectures with 10 and 15 residual blocks, it was not necessary to slowly increase the smoothing scale and noise level as in our previous work [23]. However, the network with 25 residual blocks did not converge when trained directly on noisy, smoothed maps.…”

“…As in previous work [23], we used the Ufalcon package [53] to generate the convergence maps. Ufalcon follows the procedure described in the appendix of [54] and uses the Hierarchical Equal Area iso-Latitude Pixelization tool [55] (HEALPix[56]).…”

“…These shells were then used to generate convergence maps. A detailed description of the formalism can be found in [23,53]. The convergence of a given pixel θ pix can be calculated using the Born approximation in the following way…”

“…the output of the last residual block to the desired output size. Similarly to [23], we used a negative log-likelihood loss function…”

“…To generate cosmological constraints using the predictions of the networks we followed the same approach as in previous work [23]. We used the predictions of our test set as summary statistics and perform a standard likelihood analysis.…”