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

We develop a set of machine-learning based cosmological emulators, to obtain fast model predictions for the $C(\ell)$ angular power spectrum coefficients characterising tomographic observations of galaxy clustering and weak gravitational lensing from multi-band photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving a speed-up $\mathcal{O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with respect to standard Boltzmann solvers, with an accuracy better than $0.175\%$ ($<0.1\%$ for the weak lensing case). This corresponds to $\sim 2\%$ or less of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through ($\textit{i}$) a specific pre-processing optimisation, ahead of the training phase, and ($\textit{ii}$) a more effective neural network architecture, compared to previous implementations.