Compact binary mergers are related to some of the most pressing open problems in astrophysics, including the nature of gravity and matter under extreme conditions, the astrophysical site of production of the heavy elements, and the mechanism powering gamma-ray bursts. In the next years, the LIGO experiment will undergo a series of upgrades that will double its sensitivity. In 2027, following the upgrades, LIGO will start its fifth observing run (O5). LIGO will be joined by the Virgo detector in Italy and KAGRA in Japan to form an international network of detectors. A number of electromagnetic follow-up observations are planned, including with the Vera Rubin telescope, the Nancy Grace Roman Space Telescope, and the James Web Space Telescope. The combined gravitational-wave and electromagnetic data from these observations will encode the answer to some of the most pressing questions in high energy and nuclear astrophysics. The aim of this project is to perform compact binary merger simulations with unprecedented fidelity to unlock them. The team will perform simulations of precessing, eccentric binary black hole mergers and tidally interacting neutron stars at unprecedented resolutions, which will be used to develop new gravitational-wave data analysis pipelines. Such simulations are urgently needed, since systematic uncertainties in current models will dominate over statistical uncertainties for the high signal-to-noise ratio events expected in O5. General-relativistic neutrino-radiation magnetohydrodynamics simulations of a large number of configurations, some of which at very high resolutions, will be performed to characterize the electromagnetic counterpart to binary neutron star mergers. These will include the first full-Boltzmann neutrino-radiation magnetohydrodynamics simulations of these events and the first zoom-in simulations with up to 100 times higher resolution than any extant simulation and resolving, for the first time, the turbulence down to the neutrino viscous scale.