  In theoretical models of galaxy evolution, AGN and star formation (SF)
activity are closely linked and AGN feedback is routinely invoked to regulate
galaxy growth. In order to constrain such models, we compare the hydrodynamical
simulations IllustrisTNG and SIMBA, and the semi-analytical model SAG to the
empirical results on AGN and SF at cosmic noon ($0.75 < z < 2.25$) reported in
Florez et al. (2020). The empirical results are based on a large mass-complete
sample drawn from 93,307 galaxies with and without high X-ray luminosity AGN
($L_X \gtrsim 10^{44}$ erg s$^{-1}$), selected from a 11.8 deg$^2$ area ($\sim
0.18$ Gpc$^3$ comoving volume at $z=0.75-2.25$). The main results of our
comparisons are: (i) SAG and IllustrisTNG both qualitatively reproduce the
empirical result that galaxies with high X-ray luminosity AGN have higher mean
SFR, at a given stellar mass, than galaxies without such AGN. SAG, however,
strongly over-produces the number density of high X-ray luminosity AGN by a
factor of 10 to 100, while IllustrisTNG shows a lack of high X-ray luminosity
AGN at high stellar mass ($M* > 10^{11} \ M_{\odot}$) at $z \sim 2$. (ii) In
SIMBA, the mean SFR of galaxies with high X-ray luminosity AGN is lower than
the SFR of galaxies without such AGN. Contrary to the data, many high X-ray
luminosity AGN in SIMBA have quenched SF, suggesting that AGN feedback, or
other feedback modes in galaxies with such AGN, might be too efficient in
SIMBA.
