Deep learning for cosmological parameter inference from a dark matter halo density field

Abstract

We propose a lightweight deep convolutional neural network (lCNN) to estimate cosmological parameters from simulated three-dimensional dark matter (DM) halo distributions and associated statistics. The training dataset comprises 2000 realizations of a cubic box with a side length of 1000 $h^{-1}\mathrm{Mpc}$, and interpolated over a cubic grid of $300^3$ voxels, with each simulation produced using $512^3$ DM particles and $512^3$ neutrinos. Under the flat $\hat{I}›$CDM model, simulations vary standard six cosmological parameters including $\hat{I}{\text{c◯}}_m$, $\hat{I}{\text{c◯}}_b$, $h$, $n_s$, $\ddot{I}{ƒ}_8$, $w$, along with the neutrino mass sum, $M_{\hat{I}}½$. We find that: 1) within the framework of lCNN, extracting large-scale structure information is more efficient from the halo density field compared to relying on the statistical quantities including the power spectrum, the two-point correlation function, and the coefficients from wavelet scattering transform; 2) combining the halo density field with its Fourier transformed counterpart enhances predictions, while augmenting the training dataset with measured statistics further improves performance; 3) achieving high accuracy in inferring $\hat{I}{\text{c◯}}_m$, $h$, and $\ddot{I}{ƒ}_8$ by the neural network model, while being inefficient in predicting $\hat{I}{\text{c◯}}_b$, { $n_s$}, $M_{\hat{I}}½$ and $w$; 4) { compared to the simple fully connected network trained with three statistical quantities, our CNN yields statistically reduced errors, showing improvements of approximately 23\% for $\hat{I}{\text{c◯}}_m$, 11\% for $h$, 8\% for $n_s$, and 21\% for $\ddot{I}{ƒ}_8$. Additionally, in comparison with the likelihood-based analysis on $P(k)$ data, our CNN provides much tighter constraints on parameters, especially on $\hat{I}{\text{c◯}}_m$ and $\ddot{I}{ƒ}_8$.} Our study emphasizes this lCNN-based novel approach in extracting large-scale structure information and estimating cosmological parameters.

v2: matches the version published in PRD,17 pages,12 figures