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

Convolutional neural networks (CNNs) 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 Ωm, the fluctuation amplitude σ8, and the intrinsic alignment amplitude AIA. 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, a different value of H0, or the light cone 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 σ=2.34  arc min. The uncertainties on shear calibration and n(z) error are marginalized in the likelihood pipeline. Following a blinding scheme, we derive constraints on S8=σ8(Ωm/0.3)0.5=0.777-0.036+0.038 with our CNN analysis, with AIA=1.398-0.724+0.779. 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.