Power Spectrum Emulators from Neural Networks and Tree-Based Methods

TL;DR

This paper develops two machine learning-based emulators for the non-linear matter power spectrum using Quijote simulations, enabling rapid and accurate predictions across various cosmological parameters and redshifts.

Contribution

It introduces two novel power spectrum emulators built with neural networks and tree-based methods, covering different parameter spaces and redshift ranges, with high accuracy.

Findings

Neural networks outperform tree-based methods in accuracy.

Emulators achieve less than 5% RMS relative error across scales and redshifts.

The approach enables fast computations for cosmological analyses.

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.