We present a direct comparison between the observed star formation rate functions (SFRF) and the state-of-the-art predictions of semi-analytic models (SAM) of galaxy formation and evolution. We use the PACS Evolutionary Probe Survey (PEP) and Herschel Multi-tiered Extragalactic Survey (HerMES) data-sets in the COSMOS and GOODS-South fields, combined with broad-band photometry from UV to sub-mm, to obtain total (IR+UV) instantaneous star formation rates (SFRs) for individual Herschel galaxies up to z~4, subtracted of possible active galactic nucleus (AGN) contamination. The comparison with model predictions shows that SAMs broadly reproduce the observed SFRFs up to z~2, when the observational errors on the SFR are taken into account. However, all the models seem to under-predict the bright-end of the SFRF at z>2. The cause of this underprediction could lie in an improper modelling of several model ingredients, like too strong (AGN or stellar) feedback in the brighter objects or too low fall-back of gas, caused by weak feedback and outflows at earlier epochs.
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