Window function convolution with deep neural network models

Traditional estimators of the galaxy power spectrum and bispectrum are sensitive to the survey geometry. They yield spectra that differ from the true underlying signal since they are convolved with the window function of the survey. For the current and future generations of experiments, this bias is statistically significant on large scales. It is thus imperative that the effect of the window function on the summary statistics of the galaxy distribution is accurately modelled. Moreover, this operation must be computationally efficient in order to allow sampling posterior probabilities while performing Bayesian estimation of the cosmological parameters. In order to satisfy these requirements, we built a deep neural network model that emulates the convolution with the window function, and we show that it provides fast and accurate predictions. We trained (tested) the network using a suite of 2000 (200) cosmological models within the cold dark matter scenario, and demonstrate that its performance is agnostic to the precise values of the cosmological parameters. In all cases, the deep neural network provides models for the power spectra and the bispectrum that are accurate to better than 0.1 per cent on a timescale of 10 $\mu$s.