  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.
