  We introduce the DREAMS project, an innovative approach to understanding the
astrophysical implications of alternative dark matter models and their effects
on galaxy formation and evolution. The DREAMS project will ultimately comprise
thousands of cosmological hydrodynamic simulations that simultaneously vary
over dark matter physics, astrophysics, and cosmology in modeling a range of
systems -- from galaxy clusters to ultra-faint satellites. Such extensive
simulation suites can provide adequate training sets for machine-learning-based
analyses. This paper introduces two new cosmological hydrodynamical suites of
Warm Dark Matter, each comprised of 1024 simulations generated using the Arepo
code. One suite consists of uniform-box simulations covering a $(25~h^{-1}~{\rm
M}_\odot)^3$ volume, while the other consists of Milky Way zoom-ins with
sufficient resolution to capture the properties of classical satellites. For
each simulation, the Warm Dark Matter particle mass is varied along with the
initial density field and several parameters controlling the strength of
baryonic feedback within the IllustrisTNG model. We provide two examples,
separately utilizing emulators and Convolutional Neural Networks, to
demonstrate how such simulation suites can be used to disentangle the effects
of dark matter and baryonic physics on galactic properties. The DREAMS project
can be extended further to include different dark matter models, galaxy
formation physics, and astrophysical targets. In this way, it will provide an
unparalleled opportunity to characterize uncertainties on predictions for
small-scale observables, leading to robust predictions for testing the particle
physics nature of dark matter on these scales.
