A serious concern for semi-analytical galaxy formation models, aiming to simulate multi-wavelength surveys and to thoroughly explore the model parameter space, is the extremely time consuming numerical solution of the radiative transfer of stellar ra
diation through dusty media. To overcome this problem, we have implemented an artificial neural network algorithm in the radiative transfer code GRASIL, in order to significantly speed up the computation of the infrared SED. The ANN we have implemented is of general use, in that its input neurons are defined as those quantities effectively determining the shape of the IR SED. Therefore, the training of the ANN can be performed with any model and then applied to other models. We made a blind test to check the algorithm, by applying a net trained with a standard chemical evolution model (i.e. CHE_EVO) to a mock catalogue extracted from the SAM MORGANA, and compared galaxy counts and evolution of the luminosity functions in several near-IR to sub-mm bands, and also the spectral differences for a large subset of randomly extracted models. The ANN is able to excellently approximate the full computation, but with a gain in CPU time by $sim 2$ orders of magnitude. It is only advisable that the training covers reasonably well the range of values of the input neurons in the application. Indeed in the sub-mm at high redshift, a tiny fraction of models with some sensible input neurons out of the range of the trained net cause wrong answer by the ANN. These are extreme starbursting models with high optical depths, favorably selected by sub-mm observations, and difficult to predict a priori.
The spectral energy distribution of galaxies is a complex function of the star formation history and geometrical arrangement of stars and gas in galaxies. The computation of the radiative transfer of stellar radiation through the dust distribution is
time-consuming. This aspect becomes unacceptable in particular when dealing with the predictions by semi-analytical galaxy formation models populating cosmological volumes, to be then compared with multi-wavelength surveys. Mainly for this aim, we have implemented an artificial neural network algorithm into the spectro-photometric and radiative transfer code GRASIL in order to compute the spectral energy distribution of galaxies in a short computing time. This allows to avoid the adoption of empirical templates that may have nothing to do with the mock galaxies output by models. The ANN has been implemented to compute the dust emission spectrum (the bottleneck of the computation), and separately for the star-forming molecular clouds and the diffuse dust (due to their different properties and dependencies). We have defined the input neurons effectively determining their emission, which means this implementation has a general applicability and is not linked to a particular galaxy formation model. We have trained the net for the disc and spherical geometries, and tested its performance to reproduce the SED of disc and starburst galaxies, as well as for a semi-analytical model for spheroidal galaxies. We have checked that for this model both the SEDs and the galaxy counts in the Herschel bands obtained with the ANN approximation are almost superimposed to the same quantities obtained with the full GRASIL. We conclude that this method appears robust and advantageous, and will present the application to a more complex SAM in another paper.
