Context. Star-forming galaxies (SFGs) are the dominant population in the faint radio sky, corresponding to flux densities at 1.4 GHz < 0.1 mJy. A panchromatic approach is essential for selecting SFGs in the radio band and understanding star formation processes over cosmic time. Semi-empirical models are valuable tools to effectively study galaxy formation and evolution, relying on minimal assumptions and exploiting empirical relations between galaxy properties and enabling us to take full advantage of the recent progress in radio and optical/near-infrared (NIR) observations. Aims. In this paper, we develop the Semi-EMPirical model for Extragalactic Radio emission (SEMPER) to predict radio luminosity functions and number counts at 1.4 GHz and 150 MHz for SFGs. SEMPER is based on state-of-the-art empirical relations, with the goal of better understanding the radio properties of high-z, massive galaxy populations. Methods. We combine the redshift-dependent galaxy stellar mass functions obtained from the recent COSMOS2020 catalogue, which exploits deep NIR observations, with up-to-date observed scaling relations such as the galaxy main sequence and the mass-dependent far-infrared/radio correlation across cosmic time. Our luminosity functions are compared with recent observational determinations from the Very Large Array (JVLA), the Low-Frequency Array (LOFAR), the Westerbork Synthesis Radio Telescope (WSRT), the Giant Metrewave Radio Telescope (GMRT) and the Australian Telescope Compact Array (ATCA), along with previous semi-empirical models and simulations. Results. Our semi-empirical model successfully reproduces the observed luminosity functions at 1.4 GHz and 150 MHz up to z ∼ 5 and the most recent number count statistics from radio observations in the LOFAR Two-metre Sky Survey (LoTSS) deep fields. Our model, based on galaxies selected in the NIR, naturally predicts the presence of radio-selected massive and/or dust-obscured galaxies already in place at high redshift (z≥ 3.5), as suggested by recent results from the James Webb Space Telescope (JWST). Our predictions offer an excellent benchmark for upcoming updates from JWST and future ultra-deep radio surveys planned with the Square Kilometre Array (SKA) and its precursors.
