Physics-Informed Neural Network Methods for Solving Eigenvalue Problems in Neutron Diffusion Equations

To promote the practical application of Physics-Informed Neural Networks (PINNs) in core physics calculations and to achieve a deep integration of deep learning methods with nuclear physics models, thereby enhancing their potential in complex physical systems, this paper proposes a multi-group neutron diffusion eigenvalue neural network model applicable to various material arrangements. In this model, an adaptive weighting strategy is designed based on the characteristic sampling of the material region, and the flux normalization is not required. By solving the single-group multi-material case and the two-group BIBLIS benchmark problem, the calculation results show that the absolute errors of the k_eff for both cases are 529.6 pcm (1pcm=10⁻⁵) and 112.5 pcm, respectively, and the relative error of each assembly's power is less than 5%. These results preliminarily verify the accuracy and effectiveness of this model. This study, through the combination of physical constraints and neural network models, provides a new technical pathway for the numerical simulation of complex reactor cores and is expected to promote the engineering application of deep learning methods in reactor physics design, safety analysis, and multi-physics coupled calculations.