  Recent years have seen growing interest in post-processing cosmological
simulations with radiative transfer codes to predict observable fluxes for
simulated galaxies. However, this can be slow, and requires a number of
assumptions in cases where simulations do not resolve the ISM. Zoom-in
simulations better resolve the detailed structure of the ISM and the geometry
of stars and gas, however statistics are limited due to the computational cost
of simulating even a single halo. In this paper, we make use of a set of high
resolution, cosmological zoom-in simulations of massive M_star>10^10.5M_sol at
z=2), star-forming galaxies from the FIRE suite. We run the SKIRT radiative
transfer code on hundreds of snapshots in the redshift range 1.5<z<5 and
calibrate a power law scaling relation between dust mass, star formation rate
and 870um flux density. The derived scaling relation shows encouraging
consistency with observational results from the sub-millimeter-selected AS2UDS
sample. We extend this to other wavelengths, deriving scaling relations between
dust mass, stellar mass, star formation rate and redshift and sub-millimeter
flux density at observed-frame wavelengths between 340um and 870um. We then
apply the scaling relations to galaxies drawn from EAGLE, a large box
cosmological simulation. We show that the scaling relations predict EAGLE
sub-millimeter number counts that agree well with previous results that were
derived using far more computationally expensive radiative transfer techniques.
Our scaling relations can be applied to other simulations and semi-analytical
or semi-empirical models to generate robust and fast predictions for
sub-millimeter number counts.
