Deep Neural Network Methods and Software for Solving Eigenvalue Problem of Neutron Diffusion Equation

This paper delves into the machine learning approaches for solving the neutron diffusion eigenvalue problem (NDEP) in the field of nuclear engineering. It begins by outlining the process and methods used by Data-Enabled Physics Informed Neural Network (DEPINN) to solve neutron diffusion equations (NDP) with prior or observational data, as well as how to handle noisy data. For situations where observational data is hard to come by, the paper introduces the basic models of Inverse Power Method Neural Network (IPMNN) and Generalized Inverse Power Method Neural Network (GIPMNN) for solving the smallest eigenvalue problem. Based on these models, a software package for solving eigenvalue problems, AISEA (AI for Science with nuclear Engineering Applications), has been developed. The effectiveness and accuracy of the proposed algorithms have been verified through this software package. The AISEA software package developed in this paper provides a new and efficient numerical solution tool for the field of nuclear engineering.