Cosmological parameter estimation from large-scale structure deep learning

Shuyang Pan, Miaoxin Liu, Jaime Forero-Romero, Cristiano G. Sabiu, Zhigang Li, Haitao Miao, Xiao-Dong Li

Published 2019-08-28Version 1

We propose a light-weight deep convolutional neural network to estimate the cosmological parameters from simulated 3-dimensional dark matter distributions with high accuracy. The training set is based on 465 realizations of a cubic box size of $256\ h^{-1}\ \rm Mpc$ on a side, sampled with $128^3$ particles interpolated over a cubic grid of $128^3$ voxels. These volumes have cosmological parameters varying within the flat $\Lambda$CDM parameter space of $0.16 \leq \Omega_m \leq 0.46$ and $2.0 \leq 10^9 A_s \leq 2.3$. The neural network takes as an input cubes with $32^3$ voxels and has three convolution layers, three dense layers, together with some batch normalization and pooling layers. We test the error-tolerance abilities of the neural network, including the robustness against smoothing, masking, random noise, global variation, rotation, reflection and simulation resolution. In the final predictions from the network we find a $2.5\%$ bias on the primordial amplitude $\sigma_8$ that can not easily be resolved by continued training. We correct this bias to obtain unprecedented accuracy in the cosmological parameter estimation with statistical uncertainties of $\delta \Omega_m$=0.0015 and $\delta \sigma_8$=0.0029. The uncertainty on $\Omega_m$ is 6 (and 4) times smaller than the Planck (and Planck+external) constraints presented in \cite{ade2016planck}.