Charting new territories: exploring physics datasets through continued fraction regression

This thesis presents a comprehensive analysis of Continued Fraction Regression (CFR) within the framework of Symbolic Regression (SR), a field of machine learning dedicated to extracting symbolic mathematical formulas from data. With a focus on enhancing both the accuracy and interpretability of models, this research delves into the application of CFR to complex predictive challenges, particularly within the domain of physics. The study begins by situating CFR within the broader landscape of machine learning and symbolic regression, detailing its evolution and foundational concepts. We propose integrating an asymmetric loss function within CFR to enhance the precision of upper and lower bound model generation from data and manage uncertainty in critical applications, such as nuclear physics. Empirical applications are demonstrated where CFR is applied to calculate the shear strength contact surface area in rock discontinuities and to estimate nuclear binding energies, with the latter showing superior performance compared to the traditional Liquid Drop Model. The implementation of CFR is thoroughly detailed, from development to testing, highlighting its robustness and effectiveness in scenarios that extend beyond its initial training data. This adaptability underlines CFR’s potential for broad application and its ability to offer precise predictions in new contexts. Furthermore, the thesis explores the contributions made through this study, emphasizing CFR’s unique capability to balance accuracy with interpretability — a critical consideration for future research endeavours. The findings advocate for the development of enhanced feature selection techniques, address the challenges of multi-objective optimisation, and propose a further exploration of CFR’s potential across various scientific and engineering fields. This work not only extends the existing knowledge on symbolic regression but also paves the way for future investigations into its practical implications and theoretical foundations.