Conformal prediction for uncertainties in nucleon-nucleon scattering

TL;DR

This paper introduces the novel application of conformal prediction to nuclear physics, providing reliable, model-agnostic uncertainty bands for nucleon-nucleon scattering observables across various models and energy regimes.

Contribution

It is the first to apply conformal prediction in nuclear physics, demonstrating its effectiveness for uncertainty quantification in complex physical models.

Findings

Conformal prediction yields reliable uncertainty intervals for nuclear observables.

The method adapts well to non-Gaussian behaviors like skewness and heavy tails.

Uncertainty bands are validated empirically across multiple models.

Abstract

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.