Interpolation of sparse data in hadron physics with Gaussian processes

Ferguson, Ryan Funai (2026) Interpolation of sparse data in hadron physics with Gaussian processes. PhD thesis, University of Glasgow.

Abstract

Hadron physics seeks to understand the structure and dynamics of strongly interacting matter governed by Quantum Chromodynamics; however, the interpretation of experimental data is complicated by their sparse, heterogeneous and multidimensional nature. This thesis develops a Gaussian Process (GP) framework for constructing continuous, uncertainty-aware representations of hadron physics observables across kinematic phase space.
A central contribution is a hyperparameter optimisation strategy designed for sparse datasets. Rather than relying on negative marginal log-likelihood minimisation, hyperparameters are determined using empirical coverage of the GP posterior, with the Wasserstein distance providing a quantitative optimisation criterion. Combined with Particle Swarm Optimisation and physicsinformed parameter boundaries, this provides a systematic procedure for calibrating the predictive uncertainties. A discretised convex hull framework is also developed to distinguish interpolation from extrapolation regions in multidimensional kinematic space, incorporating experimental binning information and allowing the resolution to be controlled independently in each dimension.

The framework is validated using pseudodata and applied to polarisation observables in the γ p→K0Σ+ reaction. The resulting GP surfaces provide continuous representations of the available measurements while retaining quantified predictive uncertainties across the energy-angle plane. A probabilistic multi-dataset combination method is also developed, in which independent GP regressions are combined into probability surfaces rather than reduced to a single averaged fit. Applied to K−p scattering data, this approach preserves non-trivial statistical structures, including separated regions of high probability, and provides a means of retaining differences between experimental constraints near the Λ(1405) region.
Overall, the framework provides a statistical interface between sparse experimental measurements and subsequent theoretical and phenomenological analyses. By retaining both the continuous representation of the observables and their associated uncertainties, it provides a basis for using sparse hadron physics data in analyses requiring information across kinematic phase space, while also identifying regions where the existing experimental constraints are comparatively weak.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: Ireland, Professor David and McKinnon, Dr. Bryan
• Date of Award: 2026
• Depositing User: Theses Team
• Unique ID: glathesis:2026-86320
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Nov 2026 13:54
• Last Modified: 10 Nov 2026 12:22
• Thesis DOI: 10.5525/gla.thesis.86320
• URI: https://theses.gla.ac.uk/id/eprint/86320