Cosmological parameter estimation from large-scale structure deep learning

Abstract

We propose a light-weight deep convolutional neural network (CNN) 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 with a side length of 256 h⁻¹ Mpc, sampled with 128³ particles interpolated over a cubic grid of 128³ voxels. These volumes have cosmological parameters varying within the flat ΛCDM parameter space of 0.16 ≤ Ω_m ≤ 0.46 and 2.0 ≤ 10⁹A_s ≤ 2.3. The neural network takes as an input cubes with 32³ voxels and has three convolution layers, three dense layers, together with some batch normalization and pooling layers. In the final predictions from the network we find a 2.5% bias on the primordial amplitude σ₈ that cannot easily be resolved by continued training. We correct this bias to obtain unprecedented accuracy in the cosmological parameter estimation with statistical uncertainties of δΩ_m=0.0015 and δσ₈=0.0029, which are several times better than the results of previous CNN works. Compared with a 2-point analysis method using the clustering region of 0–130 and 10–130 h⁻¹ Mpc, the CNN constraints are several times and an order of magnitude more precise, respectively. Finally, we conduct preliminary checks of the error-tolerance abilities of the neural network, and find that it exhibits robustness against smoothing, masking, random noise, global variation, rotation, reflection, and simulation resolution. Those effects are well understood in typical clustering analysis, but had not been tested before for the CNN approach. Our work shows that CNN can be more promising than people expected in deriving tight cosmological constraints from the cosmic large scale structure.