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.Comment: 12 pages, 9 figures, 2 tables, updated to match version accepted by MNRA

A new and flexible method for constructing designs for computer experiments

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.Comment: Published in at http://dx.doi.org/10.1214/09-AOS757 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org