标题： 基于模型的核可观测量外推的贝叶斯方法 显示英文标题

标题： Bayesian approach to model-based extrapolation of nuclear observables

摘要： 质量或结合能是原子核的基本性质。 它决定了其稳定性以及反应和衰变速率。 量化核结合能对于理解宇宙中元素的起源非常重要。 负责恒星中核合成的天体物理过程通常发生在远离稳定区的地方，此时实验质量尚不清楚。 在这些情况下，必须通过理论预测使用极端外推来提供缺失的核信息。 贝叶斯机器学习技术可以应用于改进预测，充分利用实验质量和计算质量之间偏差所包含的信息。 我们考虑了基于核密度泛函理论的10个全局模型以及两个更经验性的质量模型。 使用贝叶斯高斯过程和贝叶斯神经网络构建了S2n残差和定义理论误差棒的置信区间模拟器。 我们考虑了一个大型训练数据集，涉及2003年之前测量质量的核。 对于测试数据集，我们考虑了2003年后确定质量的奇异核。 然后我们进行了向2n滴线的外推。 尽管高斯过程和贝叶斯神经网络都显著减少了与实验的均方根偏差，但GP表现出更好且更加稳定的性能。 预测能力的提高非常令人惊讶：在测试数据集上得到的均方根偏差与更经验性的模型相似。 我们获得的经验覆盖概率曲线与参考值非常吻合，这对于确保不确定性量化的真实性非常重要，而对预测的估计置信区间使得评估单个模型的预测能力成为可能。 显示英文摘要

摘要： The mass, or binding energy, is the basis property of the atomic nucleus. It determines its stability, and reaction and decay rates. Quantifying the nuclear binding is important for understanding the origin of elements in the universe. The astrophysical processes responsible for the nucleosynthesis in stars often take place far from the valley of stability, where experimental masses are not known. In such cases, missing nuclear information must be provided by theoretical predictions using extreme extrapolations. Bayesian machine learning techniques can be applied to improve predictions by taking full advantage of the information contained in the deviations between experimental and calculated masses. We consider 10 global models based on nuclear Density Functional Theory as well as two more phenomenological mass models. The emulators of S2n residuals and credibility intervals defining theoretical error bars are constructed using Bayesian Gaussian processes and Bayesian neural networks. We consider a large training dataset pertaining to nuclei whose masses were measured before 2003. For the testing datasets, we considered those exotic nuclei whose masses have been determined after 2003. We then carried out extrapolations towards the 2n dripline. While both Gaussian processes and Bayesian neural networks reduce the rms deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power is quite astonishing: the resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. The empirical coverage probability curves we obtain match very well the reference values which is highly desirable to ensure honesty of uncertainty quantification, and the estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models.