  We present an application of the da Cunha, Charlot & Elbaz (2008) model of
the spectral energy distribution (SEDs) of galaxies from the ultraviolet to
far-infrared to a small pilot sample of purely star-forming Ultra-Luminous
Infrared Galaxies (ULIRGs). We interpret the observed SEDs of 16 ULIRGs using
this physically-motivated model which accounts for the emission of stellar
populations from the ultraviolet to the near-infrared and for the attenuation
by dust in two components: an optically-thick starburst component and the
diffuse ISM. The infrared emission is computed by assuming that all the energy
absorbed by dust in these components is re-radiated at mid- and far-infrared
wavelengths. This model allows us to derive statistically physical properties
including star formation rates, stellar masses, as well as temperatures and
masses of different dust components and plausible star formation histories. We
find that, although the ultraviolet to near-infrared emission represents only a
small fraction of the total power radiated by ULIRGs, observations in this
wavelength range are important to understand the properties of the stellar
populations and dust attenuation in the diffuse ISM of these galaxies.
Furthermore, our analysis indicates that the use of mid-infrared spectroscopy
from the Infrared Spectrograph on the Spitzer Space Telescope is crucial to
obtain realistic estimates of the extinction to the central energy source,
mainly via the depth of the 9.7-micron silicate feature, and thus accurately
constrain the total energy balance. Our findings are consistent with the notion
that, in the local Universe, the physical properties of ULIRGs are
fundamentally different from those of galaxies with lower infrared luminosities
and that local ULIRGs are the result of merger-induced starbursts. [abridged]
