摘要
在原子核密度泛函理论框架下,理论预测的不确定度可分为两类:模型内参数不确定度引起的统计误差和模型间系统误差。前者源于参数校准过程中实验数据的误差传递,后者表现为不同模型对同一物理量预测的系统性差异。本文介绍了用于量化这两类不确定度的贝叶斯推断方法,并重点阐述了其两个典型应用:基于机器学习的贝叶斯参数估计在原子核密度泛函参数校准中的应用以及贝叶斯模型平均方法在量化核物质对称能模型间系统不确定度中的应用。
[Background]In nuclear density functional theory(DFT),uncertainties in theoretical predictions can be categorized into two types:statistical errors originating from intra-model parameter uncertainties and systematic errors arising from inter-model discrepancies.The former results from the propagation of experimental uncertainties during parameter calibration,whereas the latter reflects systematic deviations in predicting the same physical quantity across different models.[Purpose]This study aims to review the application of Bayesian uncertainty quantification in nuclear DFT,addressing both intra-and inter-model uncertainties.[Methods]The Bayesian inference approach was first introduced.Subsequently,two representative applications in DFT uncertainty quantification were presented:1)Bayesian parameter estimation utilizing machine learning techniques to quantify parameter uncertainties within the nonlinear relativistic mean field(RMF)model;2)Bayesian model averaging to analyze systematic uncertainties in symmetry energy at 2/3 saturation density between Skyrme energy density functionals and RMF models.[Results]The Bayesian parameter estimation method effectively quantifies statistical intra-model uncertainties,while Bayesian model averaging offers a robust statistical framework for quantifying inter-model uncertainties,enhancing the reliability of nuclear property predictions.[Conclusions]The application of Bayesian inference in both parameter estimation and model averaging provides valuable tools for addressing uncertainties in nuclear physics.
作者
丘梦莹
张振
QIU Mengying;ZHANG Zhen(Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University,Zhuhai 519082,China)
出处
《核技术》
北大核心
2025年第5期53-63,共11页
Nuclear Techniques
基金
国家自然科学基金(No.12235010)资助。
关键词
不确定度量化
模型平均
贝叶斯推断
对称能
原子核密度泛函
Uncertainty quantification
Model averaging
Bayesian inference
Symmetry energy
Nuclear density functional
