This paper studies a practical problem in nuclear physics: how to read out a “barrier distribution” from measurements of fusion cross sections. A fusion cross section is a measure of how likely two nuclei are to fuse at a given collision energy. A barrier distribution is a way to summarize how different possible interaction barriers contribute to that fusion probability. Extracting the barrier distribution normally requires taking the second derivative of an energy-weighted cross section, a numerically unstable step that makes the result very sensitive to noisy or sparse data and to the choice of finite-difference step size.

The author tests Bayesian statistical tools as a safer way to extract barrier distributions and their uncertainties. They generate realistic simulated data from a simple model of fusion excitation functions (the thesis discusses the Wong model of reaction cross sections) and then try different inference methods. First they benchmark Gaussian process regression, a common Bayesian method, and then they apply newer Bayesian machine-learning approaches: automated Bayesian neural network (BNN) architectures motivated by recent work. They also calibrate these methods to real experimental data and make their code available as open source.

The main findings are practical. Gaussian processes can produce useful uncertainty estimates but often show aliasing problems at higher energies in the barrier distribution. The BNN architectures tested typically recover the barrier shape more faithfully across the full energy range and give quantified uncertainties. The BNNs can also point out energy regions where uncertainty or model disagreement is large. That information can tell experimentalists where additional measurements would be most useful.

All methods proved fairly robust when the data were sparse or sampled irregularly. However, the single most important factor controlling how well any method works is the size of the experimental uncertainties relative to the signal. Large measurement errors limit the fidelity of the recovered barrier distribution, no matter the statistical method. The work therefore highlights that better precision in experiments is often more valuable than denser sampling alone.