The detection of bright electromagnetic (EM) transients powered by neutron star mergers, supernovae, and other extreme astrophysical events associated with compact objects will play a major role in nuclear astrophysics in the coming years. These events act as cosmic laboratories allowing us to study the properties of high-density matter and the origin of heavy elements. Transients may even reveal particle physics beyond the standard model in conditions that we cannot probe on Earth. The rapidly growing number and variety of observed EM transients now regularly challenge our incomplete theoretical understanding of the transient sky. These limitations inhibit our ability to leverage transient observations for high-energy and nuclear astrophysics. Despite significant improvements to the numerical accuracy and microphysics of numerical simulations, the impact of nuclear physics inputs, approximate physical modeling, and the large range in spatial scales and timescales that need to be resolved remain major issues. This program will address these issues with an interdisciplinary group of nuclear, theoretical, computational physicists and astronomers as we prepare for a new era of EM discovery and anticipated experiments on exotic nuclei.