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

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 $h^{-1}{\rm Mpc}$, 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 $\Lambda$CDM model, simulations vary standard six cosmological parameters including $\Omega_m$, $\Omega_b$, $h$, $n_s$, $\sigma_8$, $w$, along with the neutrino mass sum, $M_\nu$. 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 $\Omega_m$, $h$, and $\sigma_8$ by the neural network model, while being inefficient in predicting $\Omega_b$, { $n_s$}, $M_\nu$ 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 $\Omega_m$, 11\% for $h$, 8\% for $n_s$, and 21\% for $\sigma_8$. Additionally, in comparison with the likelihood-based analysis on $P(k)$ data, our CNN provides much tighter constraints on parameters, especially on $\Omega_m$ and $\sigma_8$.} Our study emphasizes this lCNN-based novel approach in extracting large-scale structure information and estimating cosmological parameters.