Current hydrodynamical and semi-empirical simulations of galaxy formation and evolution have difficulties in reproducing the number densities of IR-detected galaxies. Therefore, a versatile, phenomenological new simulation tool is necessary to reproduce current and predict future observations at IR wavelengths. In this work we generate simulated catalogues starting from the Herschel infrared luminosity functions of different galaxy populations, in order to consider in a consistent way different populations of galaxies and active galactic nuclei. We associated a spectral energy distribution and physical properties, such as stellar mass, star-formation-rate and AGN contribution, to each simulated galaxy using a broad set of empirical relations. We compare the resulting simulated galaxies, extracted up to z$=$10, with a broad set of observational relations. The Spectro-Photometric Realisations of Infrared-selected Targets at all-z (SPRITZ) simulation will allow us to obtain in a fully consistent way simulated observations for a broad set of current and future facilities with photometric capabilities as well as low-resolution IR spectroscopy, like the James Webb Space Telescope (JWST) or the Origin Space Telescope (OST). The derived simulated catalogue contains galaxies and active galactic nuclei that by construction reproduce the observed IR galaxy number density, but it is also in agreement with the observed number counts from UV to far-IR wavelengths, the observed stellar mass function, the star-formation-rate vs. stellar mass plane and the luminosity function from the radio to the X-ray. The proposed simulation is therefore ideal to make predictions for current and future facilities, in particular, but not limited to, those operating at IR wavelengths. The SPRITZ simulation will be publicly available.
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