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