The Influence of Different Kernel Functions in the Kernel Ridge Regression Method on the Nuclear Charge Radius Predictions  

核岭回归方法中不同核函数对原子核电荷半径预测的影响

作　　者：TANG Lu ZHANG Zhenhua 唐璐;张振华(华北电力大学数理学院,北京102206;河北省物理学与能源技术重点实验室,华北电力大学,河北保定071000)

机构地区：[1]Mathematics and Physics Department,North China Electric Power University,Beijing 102206,China [2]Hebei Key Laboratory of Physics and Energy Technology,North China Electric Power University,Baoding 071000,Hebei,China

出　　处：《原子核物理评论》2024年第4期927-935,共9页Nuclear Physics Review

基　　金：国家自然科学基金资助项目(11875027)。

摘　　要：Using two nuclear models,i)the relativistic continuum Hartree-Bogoliubov(RCHB)theory and ii)the Weizsäcker-Skyrme(WS)model WS*,the performances of nine kinds of kernel functions in the kernel ridge regression(KRR)method are investigated by comparing the accuracies of describing the experimental nuclear charge radii and the extrapolation abilities.It is found that,except the inverse power kernel,all other kernels can reach the same level around 0.015~0.016 fm for these two models with KRR method.The extrapolation ability for the neutron rich region of each kernel depends on the trainning data.Our investigation shows that the performances of the power kernel and Multiquadric kernel are better in the RCHB+KRR calculation,and the Gaussian kernel is better in the WS*+KRR calculation.In addition,the performance of different basis functions in the radial basis function method is also investigated for comparison.The results are similar to the KRR method.The influence of different kernels on the KRR reconstruct function is discussed by investigating the whole nuclear chart.At last,the charge radii of some specific isotopic chains have been investigated by the RCHB+KRR with power kernel and the WS*+KRR with Gaussian kernel.The charge radii and most of the specific features in these isotopic chains can be reproduced after considering the KRR method.通过采用i)相对论连续谱Hartree-Bogoliubov(RCHB)理论以及ii)Weizsäcker-Skyrme(WS)模型WS^(*),本工作比较了在核岭回归(KRR)方法中采用9个不同核函数对原子核电荷半径描述的精度以及模型的外推能力。本工作发现,在这两个模型中使用KRR方法改进它们对于电荷半径的描述时,除了逆幂律核,采用其他核函数计算得到的电荷半径的均方根偏差均能达到0.015~0.016 fm左右;不同核函数对于丰中子区的外推能力依赖于所采用的数据集。研究表明,在RCHB+KRR的计算中,幂律核以及多元二次核的外推效果较好;在而WS^(*)+KRR的计算中,高斯核的外推效果较好。此外,也研究了在径向基函数方法中采用不同类型的基函数对于电荷半径的描述能力,其结果与KRR方法类似。随后,通过对整个核素图进行计算,研究了不同核函数对于KRR重构函数的影响。最后,利用考虑幂律核的RCHB+KRR以及高斯核的WS^(*)+KRR方法对一些特定同位素链中原子核的电荷半径进行了研究。考虑KRR方法后,能够很好地再现这些同位素链中原子核的电荷半径以及其中的一些特征。

关 键 词：nuclear charge radius machine learning kernel ridge regression method 

分 类 号：O571.3[理学—粒子物理与原子核物理]