ore-collapse supernovae (CCSNe) are the tumultuous explosions that accompany the ends of lives of massive stars. After millions of years being seemingly idle, laboriously creating increasingly heavy elements, the star exhausts its fuel supply and, in an instant, is ripped apart. Their innards, consisting of millions of years of nucleosynthesis products, are spread throughout the interstellar medium as fertilizer for the next generation of stars. Left in their wake is a stellar mass compact object – a black hole or neutron star. CCSNe are vital to understanding our own origins. Our understanding of CCSNe is driven by the union of observation and theory. Computational models, constantly leveraging the most advanced supercomputers of the time, provide insights into the central engines powering CCSNe and connect to observations of CCSNe. Observations, providing a goal post and validation for computational models, require a theoretical framework to be interpreted. The work presented in this Dissertation seeks to provide novel approaches to interpreting CCSN observables and develops new computational models for studying the explosion mechanisms of CCSNe.I produce synthetic supernova light curves from high fidelity, neutrino-driven supernova models – the largest such study. Using these light curves, I demonstrate the improved ability of neutrino-driven models to constrain observations. I demonstrate how the imprint from the core structure of the star on the explosion can be seen in observed photometry. In followup work, I build on this and investigate the core structures of a population of observed supernovae. Using a novel Bayesian analysis, I use these inferences to constrain the mass distribution of the stellar population. To demonstrate the ineffectiveness of simplified models to constrain observations, I produce a grid of roughly 2000 light curves and demonstrate that, with these simplified models, the results aredegenerate and ill-constraining. I also report on the development of several open source software projects to further investigate the CCSN explosion mechanism. First, I present the thornado hydrodynamics algorithms. thornado uses a novel high order discontinuous Galerkin approach to modeling the underlying partial differential equations and is posed to power the next generation of models. Next, I present Singularity-Eos, an open source microphysics library for fluid dynamics that is capable of leveraging modern heterogeneous hardware. Finally, I close with a description of Phoebus, a new simulation software for supernovae, compact object accretion, and mergers set to make use of exascale computing resources.
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