  In the next decade, deep galaxy surveys from telescopes such as the James
Webb Space Telescope and Roman Space Telescope will provide transformational
data sets that will greatly enhance the understanding of galaxy formation
during the epoch of reionization (EoR). In this work, we present the Deep
Realistic Extragalactic Model (DREaM) for creating synthetic galaxy catalogs.
Our model combines dark matter simulations, subhalo abundance matching and
empirical models, and includes galaxy positions, morphologies, and spectral
energy distributions (SEDs). The resulting synthetic catalog extends to
redshifts $z \sim 12 $, and galaxy masses $\log_{10}(M/M_{\odot}) = 5 $
covering an area of $1\, {\rm deg}^2$ on the sky. We use DREaM to explore the
science returns of a $1\, {\rm deg}^2$ \emph{Roman} UDF, and to provide a
resource for optimizing ultra-deep survey designs. We find that a \emph{Roman}
UDF to $\sim 30\,m_{\rm AB}$ will potentially detect more than $10^6$ $M_{\rm
UV}<-17$ galaxies, with more than $10^4$ at redshifts $z>7$, offering an
unparalleled dataset for constraining galaxy properties during the EoR. Our
synthetic catalogs and simulated images are made publicly available to provide
the community with a tool to prepare for upcoming data.
