Power Spectrum Emulators from Neural Networks and Tree-Based Methods

TL;DR

Two emulators of 2000 and 1000 Quijote simulations are built, allowing for fast computations of the non-linear matter power spectrum, and it is shown that the best accuracy is obtained for a neural network with two hidden layers.

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 $Ω_m$ and $Ω_b$, the reduced Hubble constant $h$, the scalar spectral index $n_s$, the amplitude of matter density fluctuations $σ_8$, the total neutrino mass $M_ν$ 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, $Ω_m$, $h$, $n_s$, $σ_8$ 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.

Figures (6)

• Figure 1: Comparison of RMSRE as a function of $k$ on the test set for the seven-parameter emulator ($\Omega_m$, $\Omega_b$, $h$, $n_s$, $\sigma_8$, $M_\nu$ and $w$) for the different learning models considered at $z=0$.
• Figure 2: RMSRE for the neural network (with PCA) for redshifts 0, 0.5, 1, 2 and 3 for the emulator involving the sum of neutrino masses and the dark energy equation of state
• Figure 3: Comparison between the interpolated predictions at $z=1$ and the true predictions for the neural network and the CatBoost model. The solid line represents the mean of the ratios of the interpolated predictions and the model predictions at $z=1$, while the shaded areas represent $1\sigma$ error bars.
• Figure 4: Comparison of RMSRE as a function of $k$ on the test set for the five-parameter emulator involving equilateral non-Gaussianity for the different learning models considered.
• Figure 5: RMSRE for the neural network (with PCA) for redshifts 0, 0.503, 0.733 and 0.997 for the five-parameter emulator involving $f_{\rm NL}^{\rm eq}$.