The spectral energy distribution (SED) 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 (ANN) algorithm into the spectro-photometric and radiative transfer code grasil in order to compute the SED 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 (MC) 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.