Fast emulation of two-point angular statistics for photometric galaxy surveys

ABSTRACT We develop a set of machine-learning-based cosmological emulators, to obtain fast model predictions for the C (ℓ) angular power spectrum coefficients, characterizing tomographic observations of galaxy clustering and weak gravitational lensing from multiband photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving, with respect to standard Boltzmann solvers, a speed-up of O (10³) in computing the required statistics for a given set of cosmological parameters, with an accuracy better than 0. 175 per cent (0. 1 per cent for the weak lensing case). This corresponds to 2~{\ per\ cent} of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i) a specific pre-processing optimization, ahead of the training phase, and (ii) an effective neural network architecture. Compared to previous implementations in the literature, we achieve an improvement of a factor of 5 in terms of accuracy, while training a considerably lower amount of neural networks. This results in a cheaper training procedure and a higher computational performance. Finally, we show that our emulators can recover unbiased posteriors when analysing synthetic Stage-IV galaxy survey data sets.