We introduce a new technique based on artificial neural networks which allows us to make accurate predictions for the spectral energy distributions (SEDs) of large samples of galaxies, at wavelengths ranging from the far-ultra-violet to the sub-millimetre and radio. The neural net is trained to reproduce the SEDs predicted by a hybrid code comprised of the GALFORM semi-analytical model of galaxy formation, which predicts the full star formation and galaxy merger histories, and the GRASIL spectro-photometric code, which carries out a self-consistent calculation of the SED, including absorption and emission of radiation by dust. Using a small number of galaxy properties predicted by GALFORM, the method reproduces the luminosities of galaxies in the majority of cases to within 10% of those computed directly using GRASIL. The method performs best in the sub-mm and reasonably well in the mid-infrared and the far-ultra-violet. The luminosity error introduced by the method has negligible impact on predicted statistical distributions, such as luminosity functions or colour distributions of galaxies. We use the neural net to predict the overlap between galaxies selected in the rest-frame UV and in the observer-frame sub-mm at z=2. We find that around half of the galaxies with a 850um flux above 5 mJy should have optical magnitudes brighter than R_AB < 25 mag. However, only 1% of the galaxies selected in the rest-frame UV down to R_AB < 25 mag should have 850um fluxes brighter than 5 mJy. Our technique will allow the generation of wide-angle mock catalogues of galaxies selected at rest-frame UV or mid- and far-infrared wavelengths. Comment: 24 pages, 18 figures. Submitted to MNRAS