  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.
