基于神经网络和决策树算法的裂变产物核(n,2n)反应截面研究

Study of(n,2n)Reaction Cross Section of Fission Product Based on Neural Network and Decision Tree Model

为了大规模预言缺少实验测量的裂变产物核反应截面数据,在整理现有(n, 2n)反应截面5 294个实验数据的基础上,分析相关的物理特征建立实验数据集,分别构建和训练反向传播神经网络和极致梯度提升树模型学习数据。神经网络的隐藏层包含两个子网络,分别由2层各128个神经元构成。极致梯度提升树模型集成了16棵决策树。结果表明,虽然(n, 2n)反应截面实验测量数据大多集中分布在中子入射能量14 MeV附近,且相互之间存在分歧,本工作机器学习模型均可较好描述反应截面的实验测量数据,具有较好的预言能力,对于缺少实验数据的情况同样与评价数据库基本符合。人工神经网络模型在测试集中预测结果与实验数据平均相对偏差小于10%的数据占比超过85%。机器学习方法能为核数据评价研究提供参考。

The neutron induced nuclear reaction cross section of fission products is related with the neutron flux and the reactor burnup,which plays an important role in accurately designing nuclear engineering.To predict(n,2n)[JP2]reaction cross sections especially those without experimental data,the relevant features were analyzed and the experimental data set were established on the basis of sorting out the experimental data recorded in EXFOR library.This work includes 5294(n,2n)cross section measured results,among which a lot of experimental data concentrate around 14 MeV incident energy.Moreover,there may be divergence between measurements due to system error and negligence error.Faced with these real and defective data,researchers discovered laws behind them and established the compound nucleus reaction models.However this means a heavy workload.It would be surprising if machine learning could reach a quantitative level close to the evaluation results.The 8 features include the proton number Z,the mass number A,the single nucleon separation energy of both proton and neutron,the Casten factor,the level density,the pairing correction,and the incident energy.The back propagation artificial neural network(ANN)and decision tree(DT)models were built to learn the experimental data set,respectively,adopting PyTorch and XGBOOST toolboxes.Draw lessons from the variational auto-encoder network,the 2 sub-networks with the same internal structure,which contains 128 neurons in 2 hidden layers,were designed to learn the mean and variance respectively.The boosting model integrates 16 decision trees.The training set includes 4000 uniform and randomly selected data,while the remaining data constitute the test set.The results show that both ANN and XGBOOST models describe the experimental cross section data well,moreover model gives a smooth and continuous curve,indicating a certain predictive ability.For the case of lack of experimental data,the predictions are also basically consistent with the evaluation nuclear reaction data libraries.Compared with the XGBOOST model,the ANN model has somewhat better generalization ability in the range of neutron incident energy above 20 MeV.In the test set,the ANN predictions with a mean absolute percentage error(MAPE)deviation less than 10%from the experimental data account for more than 85%.Therefore we successfully established machine learning models to analysis and predicate(n,2n)reaction cross section.On the other hand,through traditional nuclear reaction models,one can intuitively understand the relationship among physical quantities and build a picture of the reaction mechanism.However,machine learning models are often regarded as difficult to understand black boxes,which is questionable for physicists.In future it is planned to further apply machine learning for the nuclear data research to verify the rationality of the method.