Power Spectrum Emulators from Neural Networks and Tree-Based Methods

Abstract

We use two subsets of 2000 and 1000 Quijote simulations to build two power spectrum emulators, allowing for fast computations of the non-linear matter power spectrum. The first emulator is built in terms of seven cosmological parameters: the matter and baryon fraction of the energy density of the Universe $\Omega_m$ and $\Omega_b$, the reduced Hubble constant $h$, the scalar spectral index $n_s$, the amplitude of matter density fluctuations $\sigma_8$, the total neutrino mass $M_{\nu}$ and the dark energy equation of state parameter $w$, on scales $k \in [0.015,1.8]\,h/ \rm{Mpc^{-1}}$. The power spectra can be directly determined at redshifts 0, 0.5, 1, 2 and 3, while for intermediate redshifts these can be interpolated. The second emulator is based on five cosmological parameters, $\Omega_m$, $h$, $n_s$, $\sigma_8$ and the amplitude of equilateral non-Gaussianity $f_{\rm NL}^{\rm eq}$, at redshifts 0, 0.503, 0.733, 0.997 for $k \in [0.015,1.8]\,h/ \rm{Mpc^{-1}}$. The emulators are built on machine learning techniques. In both cases we have investigated both neural networks and tree-based methods and we have shown that the best accuracy is obtained for a neural network with two hidden layers. Both emulators achieve a root-mean-squared relative error of less then 5\% for all the redshifts considered on the scales discussed.