标题： 共形预测在核子-核子散射不确定性中的应用 显示英文标题

标题： Conformal prediction for uncertainties in nucleon-nucleon scattering

摘要： 共形预测是一种分布无关且模型无关的不确定性量化方法，它能够提供具有保证覆盖率的有限样本预测区间。 在本工作中，我们首次将共形预测应用于生成核物理中物理可观测量的不确定性带，例如总截面和核子-核子相移。 我们通过考虑三种情况来展示该方法的灵活性： (i) 一个逐点模型，其中手征有效场论中的展开系数被视为随机变量；(ii) 对于系数的高斯过程模型；以及 (iii) 使用手征有效场论中的局部相互作用计算的不同能量和部分波的相移。 在每种情况下，都构建并经验验证了共形预测区间。 我们的结果表明，即使存在非高斯行为，如偏斜和重尾，共形预测也能提供可靠且自适应的不确定性带。 这些发现突显了共形预测作为量化理论不确定性的稳健且实用框架的潜力。 显示英文摘要

摘要： 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.