Cosmological constraints with deep learning from KiDS-450 weak lensing
  maps
  Convolutional Neural Networks (CNN) have recently been demonstrated on
synthetic data to improve upon the precision of cosmological inference. In
particular they have the potential to yield more precise cosmological
constraints from weak lensing mass maps than the two-point functions. We
present the cosmological results with a CNN from the KiDS-450 tomographic weak
lensing dataset, constraining the total matter density $\Omega_m$, the
fluctuation amplitude $\sigma_8$, and the intrinsic alignment amplitude
$A_{\rm{IA}}$. We use a grid of N-body simulations to generate a training set
of tomographic weak lensing maps. We test the robustness of the expected
constraints to various effects, such as baryonic feedback, simulation accuracy,
different value of $H_0$, or the lightcone projection technique. We train a set
of ResNet-based CNNs with varying depths to analyze sets of tomographic KiDS
mass maps divided into 20 flat regions, with applied Gaussian smoothing of
$\sigma=2.34$ arcmin. The uncertainties on shear calibration and $n(z)$ error
are marginalized in the likelihood pipeline. Following a blinding scheme, we
derive constraints of $S_8 = \sigma_8 (\Omega_m/0.3)^{0.5} =
0.777^{+0.038}_{-0.036}$ with our CNN analysis, with
$A_{\rm{IA}}=1.398^{+0.779}_{-0.724}$. We compare this result to the power
spectrum analysis on the same maps and likelihood pipeline and find an
improvement of about $30\%$ for the CNN. We discuss how our results offer
excellent prospects for the use of deep learning in future cosmological data
analysis.
