  Powerful new observational facilities will come online over the next decade,
enabling a number of discovery opportunities in the "Cosmic Frontier", which
targets understanding of the physics of the early universe, dark matter and
dark energy, and cosmological probes of fundamental physics, such as neutrino
masses and modifications of Einstein gravity. Synergies between different
experiments will be leveraged to present new classes of cosmic probes as well
as to minimize systematic biases present in individual surveys. Success of this
observational program requires actively pairing it with a well-matched
state-of-the-art simulation and modeling effort. Next-generation cosmological
modeling will increasingly focus on physically rich simulations able to model
outputs of sky surveys spanning multiple wavebands. These simulations will have
unprecedented resolution, volume coverage, and must deliver guaranteed
high-fidelity results for individual surveys as well as for the
cross-correlations across different surveys. The needed advances are as
follows: (1) Development of scientifically rich and broadly-scoped simulations,
which capture the relevant physics and correlations between probes (2) Accurate
translation of simulation results into realistic image or spectral data to be
directly compared with observations (3) Improved emulators and/or data-driven
methods serving as surrogates for expensive simulations, constructed from a
finite set of full-physics simulations (4) Detailed and transparent
verification and validation programs for both simulations and analysis tools.
(Abridged)
