  A tightly correlated star formation rate-stellar mass relation of star
forming galaxies, or star-forming sequence (SFS), is a key feature in galaxy
property-space that is predicted by modern galaxy formation models. We present
a flexible data-driven approach for identifying this SFS over a wide range of
star formation rates and stellar masses using Gaussian mixture modeling (GMM).
Using this method, we present a consistent comparison of the $z=0$ SFSs of
central galaxies in the Illustris, EAGLE, and Mufasa hydrodynamic simulations
and the Santa Cruz semi-analytic model (SC-SAM), alongside data from the Sloan
Digital Sky Survey. We find, surprisingly, that the amplitude of the SFS varies
by up to ${\sim} 0.7\,\mathrm{dex}$ (factor of ${\sim} 5$) among the
simulations with power-law slopes range from $0.7$ to $1.2$. In addition to the
SFS, our GMM method also identifies sub-components in the star formation
rate-stellar mass relation corresponding to star-burst, transitioning, and
quiescent sub-populations. The hydrodynamic simulations are similarly dominated
by SFS and quiescent sub-populations unlike the SC-SAM, which predicts
substantial fractions of transitioning and star-burst galaxies at stellar
masses above and below $10^{10} M_\odot$, respectively. All of the simulations
also produce an abundance of low-mass quiescent central galaxies in apparent
tension with observations. These results illustrate that, even among models
that well reproduce many observables of the galaxy population, the $z=0$ SFS
and other sub-populations still show marked differences that can provide strong
constraints on galaxy formation models.
