Study of Nuclear Structure and Neutron Stars with a Bayesian Neural Network Approach

In this dissertation, we introduce a new approach in building a hybrid nuclear model that combines some existing theoretical models and a \universal" approximator. The goal of such an approach is to obtain new predictions of nuclear masses and charge radii. We begin our study by investigating nuclear masses based on theoretical and experimental values. Nuclear masses are essential for astrophysical applications, such as r-process nucleosynthesis and neutron-star structure. To overcome the intrinsic limitations of the existing ``state-of-the-art" mass models, a renement is generated based on a Bayesian Neural Network (BNN) formalism. A novel BNN approach is applied with the aim of optimizing mass residuals between theory and experiment. A signicant improvement (of about 40%) in the mass predictions of existing models is obtained after BNN renement. Moreover, these improved results are accompanied by proper statistical errors. By constructing a \world average" of these predictions, we obtained a unied mass model that is used to predict the composition of the outer crust of a neutron star. In order to get a better description of nuclear structure, a similar procedure is also implemented in the nuclear charge radius. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are rened through the BNN approach to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. The neural networks function is trained using charge radii residuals between theoretical predictions and experimental data. Although the predictions obtained with density functional theory provide a fairly good description of the experiment, our results show signicant improvement (better than 40%) after BNN renement. Despite the improvement and robust predictions, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain. Overall, we have successfully demonstrated the ability of the BNN approach to signicantly increase the accuracy of nuclear models in the predictions of nuclear masses and charge radii. Extension to other nuclear observables is a natural next step in asserting the eectiveness of the BNN method in nuclear physics.