超越恒定误差：用于未测量核建模的异方差贝叶斯模型组合
Beyond Constant Error: Heteroscedastic Bayesian Model Combination for Modeling Unmeasured Nuclei
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中文总结 AI 辅助
针对原子核全局模型预测难题，引入基于统计机器学习的贝叶斯模型组合方法及异方差框架，应用于能量密度泛函并聚焦特定同位素链，经实验和合成数据验证，该方法校准指标优且能对粒子滴线进行有统计依据的评估。
中文摘要 AI 辅助
原子核图表中实验难以触及的区域仍是原子核全局模型预测的挑战，包括粒子滴线附近的奇异核、质量和电荷极端情况下的超重元素以及重元素形成的爆炸恒星环境中富含中子的路径。鉴于单个核模型不完善，最好用模型集成进行深度外推。本研究采用基于统计机器学习的贝叶斯模型组合（BMC）方法，为模型集成预测提供可靠的不确定性量化。为解决模型外推到未探索领域时预测能力的固有退化问题，引入异方差BMC框架，将组合理论不确定性视为动态量。将此方法应用于一组现实的能量密度泛函，重点关注Z = 46 - 52同位素链。用实验数据和合成数据严格验证该方法，结果表明所提异方差方法产生了更好的校准指标，并对粒子滴线提供了有统计依据的评估。
英文摘要
Experimentally inaccessible regions of the nuclear chart remain a challenge for global models of atomic nuclei to predict. This includes exotic nuclei near particle drip lines, superheavy elements at the extremes of mass and charge, and the neutron-rich pathways of astrophysical processes in explosive stellar environments where heavy elements are created. Given that individual nuclear models are imperfect, deep extrapolations are best approached using model ensembles, which allow for the systematic combination of diverse theoretical predictions. In this study, we employ the recently introduced Bayesian Model Combination (BMC) method, based on statistical machine learning, that provides robust uncertainty quantification for forecasts using model ensembles. To account for the inherent degradation of predictive power as models extrapolate into the yet-unexplored domain, we introduce a heteroscedastic BMC framework in which the combined theoretical uncertainty is treated as a dynamic quantity. We apply this methodology to an ensemble of realistic energy density functionals with a specific focus on the $Z=46\text{--}52$ isotopic chains. We rigorously validate the approach using both experimental data and synthetic data designed to assess performance in the deep extrapolation regime. Our results demonstrate that the proposed heteroscedastic approach yields superior calibration metrics and provides statistically principled assessments of the particle drip lines.
