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Despite efforts over several decades, direct-detection experiments have not yet led to the discovery of the dark matter (DM) particle. This has led to increasing interest in alternatives to the Lambda CDM (LCDM) paradigm and alternative DM scenarios (including fuzzy DM, warm DM, self-interacting DM, etc.). In many of these scenarios, DM particles cannot be detected directly and constraints on their properties can ONLY be arrived at using astrophysical observations. The Dark Energy Spectroscopic Instrument (DESI) is currently one of the most powerful instruments for wide-field surveys. The synergy of DESI with ESA's Gaia satellite and future observing facilities will yield datasets of unprecedented size and coverage that will enable constraints on DM over a wide range of physical and mass scales and across redshifts. DESI will obtain spectra of the Lyman-alpha forest out to z~5 by detecting about 1 million QSO spectra that will put constraints on clustering of the low-density intergalactic gas and DM halos at high redshift. DESI will obtain radial velocities of 10 million stars in the Milky Way (MW) and Local Group satellites enabling us to constrain their global DM distributions, as well as the DM distribution on smaller scales. The paradigm of cosmological structure formation has been extensively tested with simulations. However, the majority of simulations to date have focused on collisionless CDM. Simulations with alternatives to CDM have recently been gaining ground but are still in their infancy. While there are numerous publicly available large-box and zoom-in simulations in the LCDM framework, there are no comparable publicly available WDM, SIDM, FDM simulations. DOE support for a public simulation suite will enable a more cohesive community effort to compare observations from DESI (and other surveys) with numerical predictions and will greatly impact DM science.