AI 中文总结
本文对比五种模型平均方法在核电荷半径预测中的性能，发现NBMA的rms偏差最佳，PCA可提取物理信息且抗新模型干扰，PMM能整合模型优势并合理估计不确定性，模型平均策略兼具高精度与稳健外推能力。
AI 中文摘要
本文研究了五种模型平均方法在核电荷半径预测中的性能，包括算术平均（AM）、加权平均（WM）、朴素贝叶斯模型平均（NBMA）、主成分分析（PCA）和幂调节平均（PMM）方法。采用五种常用的核电荷半径模型作为平均过程的输入，分析了实验数据与原始核模型之间的电荷半径差异，并讨论了考虑模型平均方法后的结果。计算表明，在这五种模型平均方法中，NBMA方法能提供最佳的均方根（rms）偏差；PCA方法可提取有用的物理信息，不仅有助于解释模型差异，还能通过重组主成分提供构建改进经验模型的可行途径；与其他方法在纳入rms偏差更大的新模型时结果会变差不同，PCA方法的rms偏差几乎不受影响；PMM方法能够整合各种核模型的优势，不仅在已知区域还在未知区域都能提供合理的不确定性估计，该方法可自动调整数据不确定性以实现一致性，还能为核电荷半径预测从WM到AM的平滑过渡提供工具。通过2021年后新观测到的66个数据检验了这些模型平均方法的外推能力，计算表明模型平均为核电荷半径预测提供了可靠策略，结合了对已知数据的高精度和对新测量的稳健外推；本文还讨论了钙同位素的电荷半径及其奇偶歧变。
英文摘要
The performance of five model averaging methods, including the arithmetic mean (AM), weighted mean (WM), naive Bayesian model averaging (NBMA), principal component analysis (PCA), and power-moderated mean (PMM) methods, in nuclear charge radius predictions is investigated. Five commonly used nuclear charge radius models are adopted as inputs for the averaging procedures. The charge radius differences between the experimental data and the original nuclear models are analyzed and the results after considering the model averaging methods are also discussed. The calculations show that the NBMA method can provide the best root-mean-square (rms) deviation among these five model averaging methods. The PCA method can extract useful physical information and not only helps to interpret the model differences but also offers a feasible way to construct improved empirical models by recombining the principal components. In contrast to the other methods, whose results worsen upon including a new model with a larger rms deviation, the rms deviation of the PCA method remains almost unaffected. The PMM method is capable of integrating the strengths of various nuclear models and delivering reasonable uncertainty estimates not only in known regions but also in unknown ones. This method can automatically adjust data uncertainties to achieve consistency, and it can provide a tool for a smooth transition of the nuclear charge radius prediction from the WM to the AM. The extrapolation ability of these model averaging methods is checked by 66 newly observed data after year 2021. The calculations show that model averaging offers a reliable strategy for nuclear charge radius predictions, combining high accuracy on known data with robust extrapolation to new measurements. The charge radii and the odd-even staggering in calcium isotopes are also discussed.
Comments18 pages, 10 figures, 3 tables
