A supervised machine learning estimator for the non-linear matter power spectrum - SEMPS

Abstract: In this article, we argue that models based on ML can be very effective in estimating the non-linear matter power spectrum ($P(k)$). We employ the prediction ability of the supervised ML algorithms to build an estimator for the $P(k)$. The estimator is trained on a set of cosmological models, and redshifts for which the $P(k)$ is known, and it learns to predict $P(k)$ for any other set. We review three ML algorithms -- Random Forest, Gradient Boosting Machines, and K-Nearest Neighbours -- and investigate their prime parameters to optimize the prediction accuracy of the estimator. We also compute an optimal size of the training set, which is realistic enough, and still yields high accuracy. We find that, employing the optimal values of the internal parameters, a set of $50-100$ cosmological models is enough to train the estimator that can predict the $P(k)$ for a wide range of cosmological models, and redshifts. Using this configuration, we build a blackbox -- Supervised Estimator for Matter Power Spectrum (SEMPS) -- that computes the $P(k)$ to 5-10$\%$ accuracy up to $k\sim 10 h^{-1}{\rm Mpc}$ with respect to the reference model (cosmic emulator). We also compare the estimations of SEMPS to that of the Halofit, and find that for the $k$-range where the cosmic variance is low, SEMPS estimates are better than that of the Halofit. The predictions of the SEMPS are instantaneous in the sense that it can evaluate up to 500 $P(k)$ in less than one second, which makes it ideal for many applications like visualisations, weak lensing, emulations, likelihood analysis etc.. As a supplement to this article, we provide a publicly available software package.