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核素β-衰变释放的β粒子与γ射线平均能量是计算反应堆衰变热的核心参数,对核设施安全与工程应用至关重要.然而,许多核素的实验数据匮乏,现有理论模型精度难以满足需求.本文基于ENSDF数据库中543个实验数据准确的β-衰变核素(选自1136个β-衰变核素),采用神经网络方法对核素衰变发射的β粒子、γ射线及中微子的平均能量进行预测,对比了三种特征组(分别含特殊特征值T1/2、(1/T1/2)1/5,1/3Q)的模型性能.结果表明:相比特征组含T1/2以及(1/T1/2)1/5的模型,特征组含1/3Q的模型综合表现最佳,其β粒子与中微子预测误差分别为28.11%/56.9%和35.33%/37.76%,并且利用该特征组训练的机器学习模型成功补充了裂变产物区(质量数66-172)291个核素的缺失数据.核素图对比显示,神经网络对规律性较强的β粒子及中微子能量预测与实验吻合较好,但对γ射线(训练误差76.9%)以及奇奇核、幻数附近核素的预测偏差显著.本文证实经验特征值1/3Q可有效提升模型性能,同时揭示了数据规律性与模型泛化能力的关联,为后续融合物理机理优化机器学习模型提供了依据.
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关键词:
- 衰变热 /
- β粒子与γ射线平均能量 /
- 机器学习 /
- 神经网络
The average β and γ energies data of the β——decay nuclei plays an important role in many fields of nuclear technology and scientific research, Such as the decay heat and antineutrino spectrum calculation of different kinds of reactors. However, for many nuclei, the reliable experimental measurements of their average energy are lacking, and the theoretical calculation needs to be improved to meet the accuracy requirements of the technical applications.
In this study, the average β, γ and neutrino energies of the β—decay nuclei were investigated by the neural network approach based on the newly evaluated experimental data of 543 nuclei from a total of 1136 β—decay nuclei. For the neural network approach, three different feature groups are used for model training. Each feature group contains a characteristic feature value (one of the T1/2, (1/T1/2)1/5, and 1/3Q), along with five identical feature values (Z, N, parity of Z, parity of N, and ΔZ).
The three characteristics feature values were selected based on the physical mechanism below:1. the average energy is obviously related with Q value and approximately taken as 1/3Q in the reactor industry. Hence the 1/3Q was selected as one characteristics feature value; 2. the half-live is relative with the Q value of β—decay, and T1/2 was considered; 3. considering the Sargent' s law, (1/T1/2)1/5 ∝ Q, a more accurate (1/T1/2)1/5 value were selected.
As a result, for the feature group of T1/2, the training results for all three types of average energy were unsatisfactory. For the other groups, for the average β energy data, the relative errors are 19.32% and 28.11% for(1/T1/2)1/5 and 1/3Q feature groups in the training set and 82% and 56.9% in the validation set; for the average γ energy, the relative errors were 28.9% and 76.9% for (1/T1/2)1/5 and 1/3Q feature groups and >100% and >100% in the validation set; for the average neutrino energy, the relative errors in the training set were 27.82% and 35.33% for (1/T1/2)1/5 and 1/3Q feature group and 76.32% and 37.76% in the validation set.
Considering the accuracy comparison of the three groups, 1/3Q feature group were selected to predict the average energy data of nuclei in the fission product region (mass numbers ranging from 66 to 172) for which miss reliable experimental data. As a result, we supplemented the average energy data with predicted values for 291 nuclei. Besides, a comparison were performed between the calculated data and the evaluated experimental data through the nuclide chart. It is found that the neural network provides good prediction of the experimental data for the average β and neutrino energies which exhibit relatively strong regularity. However, it shows significant deviations in predictions for average γ energy (relative error in the training set was 76.9%). Large deviation also emerges in the odd-odd nuclei and nuclei near magic numbers. This study confirms that incorporating empirical relationships and physical principles can effectively enhance the performance of the neural network, and simultaneously reveals the relationship between data regularity and model generalization capability. These findings provide a basis for future integration of physical mechanisms to optimize machine learning models.-
Keywords:
- decay heat /
- average β and γ energies /
- machine learning /
- neural networks
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