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 $1000\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$ 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, simulations vary standard six cosmological parameters including ${\mathrm{\ensuremath{\Omega}}}_{m}$, ${\mathrm{\ensuremath{\Omega}}}_{b}$, $h$, ${n}_{s}$, ${\ensuremath{\sigma}}_{8}$, and $w$, along with the neutrino mass sum ${M}_{\ensuremath{\nu}}$. We find that (i) 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; (ii) combining the halo density field with its Fourier-transformed counterpart enhances predictions, while augmenting the training dataset with measured statistics further improves performance; (iii) achieving high accuracy in inferring ${\mathrm{\ensuremath{\Omega}}}_{m}$, $h$, and ${\ensuremath{\sigma}}_{8}$ by the neural network model, while being inefficient in predicting ${\mathrm{\ensuremath{\Omega}}}_{b}$, ${n}_{s}$, ${M}_{\ensuremath{\nu}}$, and $w$; and (iv) compared to the simple fully connected network trained with three statistical quantities, our CNN yields statistically reduced errors, showing improvements of approximately 23% for ${\mathrm{\ensuremath{\Omega}}}_{m}$, 11% for $h$, 8% for ${n}_{s}$, and 21% for ${\ensuremath{\sigma}}_{8}$. Additionally, in comparison with the likelihood-based analysis on $P(k)$ data, our CNN provides much tighter constraints on parameters, especially on ${\mathrm{\ensuremath{\Omega}}}_{m}$ and ${\ensuremath{\sigma}}_{8}$. Our study emphasizes this lCNN-based novel approach in extracting large-scale structure information and estimating cosmological parameters.