Power spectrum emulators from neural networks and tree-based methods

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 Ωₘ and Ωb, the reduced Hubble constant h, the scalar spectral index nₛ, the amplitude of matter density fluctuations σ₈, the total neutrino mass M_ν and the dark energy equation of state parameter w, on scales k ∈ [0.015,1.8]\,h/ 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, Ωₘ, h, nₛ, σ₈ and the amplitude of equilateral non-Gaussianity fNLeq, at redshifts 0, 0.503, 0.733, 0.997 for k ∈ [0.015,1.8]\,h/ 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.