Nuclear fission is important for energy production, medicinal applications, nonprolifer-ation efforts, and nucleosynthesis studies. The rapid neutron capture process (r process) contributes to observed abundances of medium- and heavy-mass nuclei, and requires fission data for hundreds of nuclei, most of which lie outside of experimental reach. Therefore, predictive fission models with quantified uncertainties are required. In this thesis, spontaneous fission is described as tunneling through an effective barrier defined using a set collective coordinates, called the potential energy surface (PES), which is computed using nuclear density functional theory (DFT). The half-life is then determined by the tunneling pathway, and the primary fragment yields are approximately determined by its endpoint. Computing uncertainties for these quantities in a Bayesian framework requires tens- to hundreds-of-thousands of calculations, making it computationally infeasible. This problem is exacerbated by the large number of nuclei that participate in the r process. This thesis is divided in two parts. The first discusses the formalism necessary for com- puting spontaneous fission observables. Improvements to the tunneling pathway calculation are presented, and the improved methodology is applied to nuclei with competing fission modes. The second part discusses two strategies for approximating these observables across the r process region of the chart, with quantified uncertainties. The first strategy uses neu- ral networks to emulate the PES. The second uses dimensionality reduction techniques to propagate statistical uncertainties from the energy density functional posterior parameter distribution.
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