基于决策树方法的奇<i>A</i>核基态自旋预测

温湖峰; 尚天帅; 李剑; 牛中明; 杨东; 薛永和; 李想; 黄小龙

doi:10.7498/aps.72.20230530

摘要

作为原子核的基本性质, 基态自旋一直是原子核数据与核结构基础研究领域的热点. 本文采用决策树方法对核素图上的奇质量数原子核(奇A核), 包括奇质子数原子核(奇Z核)与奇中子数原子核(奇N核), 进行了深入的研究, 并分别训练了奇Z核与奇N核的基态自旋预测模型. 其中在以75%∶25%的比例随机划分训练集与验证集的情况下, 奇Z核的训练集和验证集的正确率分别达到98.9%和79.3%; 奇N核的训练集和验证集的正确率分别达到98.6%和71.6%. 同时, 通过1000次随机选择训练集和验证集进行重复验证, 得到的正确率的标准误差均小于5%, 进一步验证了决策树的可靠性和泛化性能; 另一方面, 决策树的正确率远高于核结构研究中常用的理论模型, 如Skyrme-Hartree-Fock-Bogoliubov (SHFB)理论、协变密度泛函理论(CDFT)、有限程液滴模型等. 接下来, 以所有自旋确定的奇Z核和奇N核为学习集, 对共计254和268个自旋未确定但有推荐值的奇Z核和奇N核的基态自旋值进行了预测, 预测集符合率分别达到68.5%和69.0%. 最后, 选择$Z=59$, $Z=77$, $N=41$以及$N=59$四条奇质量数链, 讨论了决策树的学习(预测)结果与相应原子核的实验(推荐)值, 以及3种理论模型所给出结果的异同, 进一步展示了决策树在原子核基态自旋方面的研究与应用价值.

关键词:

基态自旋 /
奇A核 /
机器学习 /
决策树

Abstract

Ground-state spin, as a fundamental parameter of nucleus, has consistently been a hot topic in research on nuclear data and structure. In this paper, we extensively investigate the odd-mass nuclei (odd-A nuclei) on the nuclide chart by using decision trees, including odd-proton nuclei (odd-Z nuclei) and odd-neutron nuclei (odd-N nuclei), and train ground-state spin prediction models of odd-Z nuclei and odd-N nuclei. In the case of randomly dividing the training set and validation set in a ratio of 75% to 25%, the accuracy rate of the training set and validation set for odd-Z nuclei reach 98.9% and 79.3%, respectively. The accuracy rate of the training set and validation set for the odd-N nuclei reach 98.6% and 71.6%, respectively. At the same time, by 1000 random selections of training set and validation set, after being validated repetitively, the standard error of the accuracy rate obtained can be less than 5%, further verifying the reliability and generalization performance of the decision tree. On the other hand, the accuracy rate of decision tree is much higher than those of theoretical models commonly used in nuclear structure research, such as Skyrme-Hartree-Fock-Bogoliubov, covariant density functional theory, and finite range droplet model. Next, by taking all spin-determined odd-Z nuclei and odd-N nuclei as a learning set, the ground-state spin values for 254 spin undetermined but recommended odd-Z nuclei and 268 spin undetermined but recommended odd-N nuclei are predicted, with the predicted set coincidence rates reaching 68.5% and 69.0%, respectively. Finally, four odd-mass number chains, i.e. Z = 59, Z =77, N = 41, and N = 59, are selected to compare the learning (prediction) results of the decision tree with the experimental (recommended) values of the corresponding nuclei, and to discuss the differences and similarities in the results given by the three theoretical models, thereby further demonstrating the research and application value of the decision tree in the ground-state spin of nuclei.

Keywords:

作者及机构信息

1.
吉林大学物理学院, 长春　130012

2.
安徽大学物理与光电工程学院, 合肥　230601

3.
中国原子能科学研究院, 核数据重点实验室, 北京　102413

通信作者: 李剑, jianli@jlu.edu.cn ; 杨东, dyang@jlu.edu.cn ;

基金项目: 吉林省自然科学基金(批准号: 20220101017JC)、国家自然科学基金(批准号: 11675063, 11875070, 11935001)、核数据重点实验室(批准号: JCKY2020201C157)和安徽省项目(批准号: Z010118169)资助的课题

Authors and contacts

1.
School of Physics, Jilin University, Changchun 130012, China

2.
School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China

3.
Key Laboratory of Nuclear Data, Chinese Academy of Atomic Energy Sciences, Beijing 102413, China

Corresponding author: Li Jian, jianli@jlu.edu.cn ; Yang Dong, dyang@jlu.edu.cn ;

Funds: Project supported by the Natural Science Foundation of Jilin Province, China (Grant No. 20220101017JC), the National Natural Science Foundation of China (Grant Nos. 11675063, 11875070, 11935001), the Key Laboratory of Nuclear Data Foundation, China (Grant No. JCKY2020201C157), and the Anhui Project, China (Grant No. Z010118169)

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 奇A核基态自旋实验值分布, 用不同颜色表示不同自旋值　(a)奇Z核; (b)奇N核

Fig. 1. Experimental ground-state spin of odd-A nuclei: (a) Odd-Z nuclei; (b) odd-N nuclei. Different values are represented by different colors.

下载: 全尺寸图片幻灯片

图 2 训练集和验证集的正确率随最大树深的变化　(a)奇Z核; (b)奇N核

Fig. 2. Change of accuracy of training set and validation set with the maximum depth of decision tree: (a) Odd-Z nuclei; (b) odd-N nuclei

下载: 全尺寸图片幻灯片

图 3 学习集正确率随最大树深的变化

Fig. 3. Change of accuracy of learning set with the maximum depth of decision tree

下载: 全尺寸图片幻灯片

图 4 基于最大树深为11的决策树模型得到的原子核基态自旋学习集和预测集的结果, 其中与实验值相同(不同)的用红色实心(空心)圆圈表示; 与推荐值相同(不同)的用蓝色实心(空心)方块表示; 没有推荐值的用蓝色实心三角表示　(a)奇Z核; (b)奇N核

Fig. 4. Learning set and prediction set of the ground-state spin based on the decision tree model with the maximum depth of 11: (a) Odd-Z nuclei; (b) odd-N nuclei. The one same (different) as the experimental value is represented by a red solid (hollow) circle; the one same (different) as the recommended value is represented by blue solid (hollow) square; those with no recommended value are represented by blue solid triangles.

下载: 全尺寸图片幻灯片

图 5 基于决策树得到的质子数$ Z=59 $、$Z=77$的同位素链, 以及中子数$ N=41 $、$ N=59 $的同中异位素链原子核的基态自旋值, 并与SHFB、CDFT、FRDM预测结果和相应实验值、推荐值结果的比较

Fig. 5. The ground-state spin of $ Z=59 $ and $Z=77$ isotopic chains (left) and $ N=41 $ and $ N=59 $ isotonic chains (right) are obtained based on the decision tree, and compared with the predicted results of SHFB, CDFT, FRDM and the corresponding experimental and recommended values.

下载: 全尺寸图片幻灯片

表 1 最大树深为11时取1000次随机重复验证, 分别得到奇Z核和奇N核的训练集与验证集正确率平均值和正确率标准误差

Table 1. Average and standard error of the accuracy of the training set and the validation set obtained by 1000 random repetitions for odd-Z nuclei and odd-N nuclei, respectively

奇Z核奇N核

训练集验证集训练集验证集

平均值 97.6% 72.3% 96.5% 67.1%

标准误差 1.7% 4.5% 2.4% 4.9%

下载: 导出CSV

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