基于贝叶斯机器学习对中子诱发235U裂变的产额-能量关系的研究

核裂变碎片产额是核能发展和核技术应用领域的重要基础数据，但在实验和理论上获得精确且完整的能量依赖的裂变产额到目前为止都非常困难。本文提出采用贝叶斯机器学习方法对所有收集到的中子诱发235U裂变产额实验数据进行了数据融合学习和评价。基于该评价方法对关键裂变碎片的产额 能量关系进行推断，并得到了二维的碎片累积产额分布随入射中子能量的变化关系。所得的二维产额分布能合理地反映裂变模式随能量增加的演化，但目前结果的不确定度较大，有待进一步改进。

Study of Energy Dependence of Neutron-induced Fission Yield of 235U with Bayesian Machine Learning

Nuclear fission fragment yields are the key infrastructure data in the field of nuclear engineering and nuclear applications. However, it is very difficult to obtain accurate and complete energy dependent fission yields by experiments and theories. To supply the application needs, the two dimensional cumulative fission yields of neutron induced fission of 235U are evaluated for energy dependencies and uncertainty qualifications by cross experiment data fusion. The data fusion is aim to include more data correlations to produce more consistent and useful information. In this work, the Bayesian machine learning with a double layer neural network was adopted, which was particularly suitable for dealing with imperfect data. The conventional evaluation methods were not ideal for uncertainty quantifications. Furthermore, the experimental uncertainties of fission yields were taken into account in this work, which was essential for data fusion. This is reasonable that the yields with larger uncertainties would have smaller weights in the data fusion. Previously, the Bayesian evaluation of one dimensional mass yields in terms of Y(A) or Y(Z) was studied. As a further step, this work evaluated the two dimensional yields in terms of Y(N, Z) or Y(A, Z), which are of practical usefulness for developing novel nuclear reactors. The double layer networks with 18×18, 20×20 and 22×22 neutrons were tested and the network structure of 20×20 was chosen. The yield energy relations of some key fragments such as 99Mo, 97Zr, 127Sb, 131I, 140Ba, 143Ce and 147Nd were obtained. The full two dimensional cumulative fission yields at neutron incident energies of 2, 6, 8, 10, and 14 MeV were obtained. The resulted two dimensional fission yields can reasonably describe the energy dependencies of evolution of fission modes. The resulted uncertainties are dependent on specific fragments and incident energies. The evaluated uncertainties includes a background noise about 135, which is still very large. In the future, it is essential to develop physics-informed machine learning to obtain more reliable evaluations. It is promising that Bayesian machine learning can facilitate the maximum utilization of imperfect raw experience data.