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Powerful new observational facilities will come online over the next decade,enabling a number of discovery opportunities in the "Cosmic Frontier", whichtargets understanding of the physics of the early universe, dark matter anddark energy, and cosmological probes of fundamental physics, such as neutrinomasses and modifications of Einstein gravity. Synergies between differentexperiments will be leveraged to present new classes of cosmic probes as wellas to minimize systematic biases present in individual surveys. Success of thisobservational program requires actively pairing it with a well-matchedstate-of-the-art simulation and modeling effort. Next-generation cosmologicalmodeling will increasingly focus on physically rich simulations able to modeloutputs of sky surveys spanning multiple wavebands. These simulations will haveunprecedented resolution, volume coverage, and must deliver guaranteedhigh-fidelity results for individual surveys as well as for thecross-correlations across different surveys. The needed advances are asfollows: (1) Development of scientifically rich and broadly-scoped simulations,which capture the relevant physics and correlations between probes (2) Accuratetranslation of simulation results into realistic image or spectral data to bedirectly compared with observations (3) Improved emulators and/or data-drivenmethods serving as surrogates for expensive simulations, constructed from afinite set of full-physics simulations (4) Detailed and transparentverification and validation programs for both simulations and analysis tools.(Abridged)

Snowmass2021 Computational Frontier White Paper: Cosmological Simulations and Modeling