Title: Weak lensing cosmology with convolutional neural networks on noisy data

Weak gravitational lensing is one of the most promising cosmological probes
of the late universe. Several large ongoing (DES, KiDS, HSC) and planned
(LSST, EUCLID, WFIRST) astronomical surveys attempt to collect even deeper
and larger scale data on weak lensing. Due to gravitational collapse, the
distribution of dark matter is non-Gaussian on small scales. However,
observations are typically evaluated through the two-point correlation
function of galaxy shear, which does not capture non-Gaussian features of
the lensing maps. Previous studies attempted to extract non-Gaussian
information from weak lensing observations through several higher-order
statistics such as the three-point correlation function, peak counts or
Minkowski-functionals. Deep convolutional neural networks (CNN) emerged in
the field of computer vision with tremendous success, and they offer a new
and very promising framework to extract information from 2 or 3-dimensional
astronomical data sets, confirmed by recent studies on weak lensing. We
show that a CNN is able to yield significantly stricter constraints of
(σ8,Ωm) cosmological parameters than the power spectrum using convergence
maps generated by full N-body simulations and ray-tracing, at angular
scales and shape noise levels relevant for future observations. In a
scenario mimicking LSST or Euclid, the CNN yields 2.4-2.8 times smaller
credible contours than the power spectrum, and 3.5-4.2 times smaller at
noise levels corresponding to a deep space survey such as WFIRST. We also
show that at shape noise levels achievable in future space surveys the CNN
yields 1.4-2.1 times smaller contours than peak counts, a higher-order
statistic capable of extracting non-Gaussian information from weak lensing
maps.