PhD Defence - Habib Yousefi Dezdarani

Conformal Prediction for Nuclear Physics 

Abstract

Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this thesis, we apply conformal prediction to quantify uncertainties in nuclear physics and nuclear astrophysics. In particular, we use conformalized quantile regression as a postprocessing step applied to samples generated from Bayesian calculations, constructing uncertainty bands without assuming a specific form for the underlying distribution. We first apply conformal prediction to nucleon-nucleon scattering observables, including the total cross section, differential cross section, and phase shifts. We consider pointwise and Gaussian-process models for truncation errors in chiral effective field theory, as well as phase shifts calculated from chiral interactions. We then apply conformalized quantile regression to form prediction intervals in the neutron-star equation of state. This includes a toy model based on a polytropic equation of state and the Tolman-Oppenheimer-Volkoff equations, posterior samples of neutron-star mass-radius relations, and Quantum Monte Carlo calculations of pure neutron matter. In all cases, conformal-prediction intervals are constructed and validated empirically to test their coverage. Our results show that conformal prediction provides reliable uncertainty bands with finite-sample coverage guarantees, even in the presence of non-Gaussian behavior such as skewness, heavy tails, and heteroscedasticity. These findings highlight conformal prediction as a robust and practical framework for quantifying theoretical uncertainties in nuclear physics. 

Examination Committee

• Dr. Martin Williams, Chair 
• Dr. Alexandros Gezerlis, Advisor 
• Dr. Robert Wickham, Advisory Committee   
• Dr. Eric Poisson, Graduate Faculty 
• Dr. Jeremy Holt, External Examiner (Texas A&M University)