Pkann – II. A non-linear matter power spectrum interpolator developed using artificial neural networks

Abstract

In this paper we introduce PkANN, a freely available software package for interpolating the non-linear matter power spectrum, constructed using Artificial Neural Networks (ANNs). Previously, using Halofit to calculate matter power spectrum, we demonstrated that ANNs can make extremely quick and accurate predictions of the power spectrum. Now, using a suite of 6380 N-body simulations spanning 580 cosmologies, we train ANNs to predict the power spectrum over the cosmological parameter space spanning $3\sigma$ confidence level (CL) around the concordance cosmology. When presented with a set of cosmological parameters ($\Omega_{\rm m} h^2, \Omega_{\rm b} h^2, n_s, w, \sigma_8, \sum m_\nu$ and redshift $z$), the trained ANN interpolates the power spectrum for $z\leq2$ at sub-per cent accuracy for modes up to $k\leq0.9\,h\textrm{Mpc}^{-1}$. PkANN is faster than computationally expensive N-body simulations, yet provides a worst-case error $<1$ per cent fit to the non-linear matter power spectrum deduced through N-body simulations. The overall precision of PkANN is set by the accuracy of our N-body simulations, at 5 per cent level for cosmological models with $\sum m_\nu<0.5$ eV for all redshifts $z\leq2$. For models with $\sum m_\nu>0.5$ eV, predictions are expected to be at 5 (10) per cent level for redshifts $z>1$ ($z\leq1$). The PkANN interpolator may be freely downloaded from http://zuserver2.star.ucl.ac.uk/~fba/PkANN