基于改进型贝叶斯分类器预测原子核电荷半径

Improved naive Bayesian probability classifier in nuclear charge radius prediction

近年来,机器学习方法(如神经网络、高斯过程等)被广泛用于描述原子核性质.本文基于改进型贝叶斯分类器(iNBP)方法,研究原子核电荷半径R_(C).已有的理论模型给出了电荷半径的全局变化规律,通过iNBP方法,分析数据集中R_(C)的理论结果和实验值的差异,对核结构模型的计算结果进行有效的修正.通过进一步讨论iNBP方法的全局优化能力和外推能力,表明iNBP方法能够用来预测未知原子核的电荷半径.

The nuclear charge radius can provide direct information about the nuclear structure. In recent years, many statistical methods such as neural networks and Gaussian processes have been used to study nuclear charge radii. Based on previous research, this paper proposes an improved naive Bayesian probability(i NBP) classifier to study the nuclear charge radius.The key strategy of the i NBP method is to treat the prediction of nuclear charge radii as a classification problem,interpreting the predicted charge radii as the most reasonable expectations. First, the residuals are divided into groups by the k-means method to generate prior and conditional probabilities. During the calculation, a weight function is introduced to describe the local relationship between the nuclear charge radii. Next, the expected posterior probability is further calculated by the Bayesian formula. We choose the expectation with the highest probability as the final prediction.The reliability of the i NBP method is evaluated by global optimization and extrapolation ability based on three different theoretical models. Using the proposed method, the accuracy of charge radius prediction for the HFB model, RMF model, and the semiempirical formula was improved by 50%, 56%, and 44%, respectively. The calculations also show that the i NBP method has a strong extrapolation ability to predict charge radii in unknown regions in the nuclear chart.By analyzing the charge radii of the isotopes, the i NBP method can reproduce the parity and shell effects in the isotope chains. Combining the global description with the local relationship of nuclear charge radii, the i NBP method allows considerable fine-tuning of the theoretical results of complex nuclear models. The method proposed in this paper can also be used in other areas of nuclear physics.