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

## TL;DR

This paper demonstrates that convolutional neural networks applied to KiDS-450 weak lensing maps can improve cosmological parameter constraints by about 30% over traditional power spectrum methods, showing promise for future cosmological analyses.

## Contribution

The study introduces a CNN-based analysis pipeline for weak lensing maps that outperforms traditional methods in constraining cosmological parameters, validated on real data with robustness tests.

## Key findings

- CNN yields 30% tighter constraints than power spectrum analysis.
- Robustness of CNN constraints tested against baryonic feedback and simulation uncertainties.
- Constraints obtained: S8=0.777+/-0.037, A_IA=1.398+/-0.751.

## Abstract

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.