Conformal prediction for uncertainties in nucleon-nucleon scattering

Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to generate uncertainty bands for physical observables in nuclear physics, such as the total cross section and nucleon-nucleon phase shifts. We demonstrate the method's flexibility by considering three scenarios: (i) a pointwise model, where expansion coefficients in chiral effective field theory are treated as random variables; (ii) a Gaussian-process model for the coefficients; and (iii) phase shifts at various energies and partial waves calculated using local interactions from chiral effective field theory. In each case, conformal-prediction intervals are constructed and validated empirically. Our results show that conformal prediction provides reliable and adaptive uncertainty bands even in the presence of non-Gaussian behavior, such as skewness and heavy tails. These findings highlight conformal prediction as a robust and practical framework for quantifying theoretical uncertainties.