PkANN - I. Non-linear matter power spectrum interpolation through artificial neural networks

TL;DR

This paper introduces a neural network-based method to accurately interpolate the non-linear matter power spectrum across cosmological parameters, achieving less than 1% error and enabling faster analysis in cosmology.

Contribution

The paper presents a novel ANN approach for interpolating the non-linear matter power spectrum with high accuracy, reducing computational costs compared to traditional simulations.

Findings

Achieves <=1% error in power spectrum interpolation for z<=2

Provides rapid and reliable predictions over the entire parameter space

Improves upon existing matter power spectrum calculators

Abstract

We investigate the interpolation of power spectra of matter fluctuations using Artificial Neural Network (PkANN). We present a new approach to confront small-scale non-linearities in the power spectrum of matter fluctuations. This ever-present and pernicious uncertainty is often the Achilles' heel in cosmological studies and must be reduced if we are to see the advent of precision cosmology in the late-time Universe. We show that an optimally trained artificial neural network (ANN), when presented with a set of cosmological parameters (Omega_m h^2, Omega_b h^2, n_s, w_0, sigma_8, m_nu and redshift z), can provide a worst-case error <=1 per cent (for z<=2) fit to the non-linear matter power spectrum deduced through N-body simulations, for modes up to k<=0.7 h/Mpc. Our power spectrum interpolator is accurate over the entire parameter space. This is a significant improvement over some of the current matter power spectrum calculators. In this paper, we detail how an accurate interpolation of the matter power spectrum is achievable with only a sparsely sampled grid of cosmological parameters. Unlike large-scale N-body simulations which are computationally expensive and/or infeasible, a well-trained ANN can be an extremely quick and reliable tool in interpreting cosmological observations and parameter estimation. This paper is the first in a series. In this method paper, we generate the non-linear matter power spectra using HaloFit and use them as mock observations to train the ANN. This work sets the foundation for Paper II, where a suite of N-body simulations will be used to compute the non-linear matter power spectra at sub-per cent accuracy, in the quasi-non-linear regime 0.1 h/Mpc <= k <= 0.9 h/Mpc. A trained ANN based on this N-body suite will be released for the scientific community.