FC-PINNs: Physics-informed Neural Networks for Solving Neutron Diffusion Eigenvalue Problem with Interface Considerations

Hongtao Bi

doi:10.1016/j.jcp.2025.114311

FC-PINNs: Physics-informed Neural Networks for Solving Neutron Diffusion Eigenvalue Problem with Interface Considerations

2025-08-25

0

PRE

AI

DOI：10.1016/j.jcp.2025.114311

Original

Original request for help

Save

Abstract

En 中文

• To solve for the eigenvalue keff in neutron diffusion eigenvalue problems, we propose the fixed-point transformation technique, allowing us to simultaneously obtain the distribution of eigenfunctions and the accurate numerical values of corresponding eigenvalues by establishing fixed points within the computational domain. The fixed-point transformation technique includes two methods: hard-constraints and soft-constraints. The hard-constraint method directly sets fixed point constraints, while the soft-constraint method indirectly guides the network to converge to fixed points by introducing auxiliary loss functions. These two methods have their advantages in terms of computational accuracy and efficiency, and can be chosen based on the specific requirements of the problem. • To handle contact boundary conditions, we employ computational domain concatenation technology, combining fixed-point constraints with extrapolated boundary constraints to effectively integrate multiple outputs for contact boundary calculations. This method can effectively handle contact and interaction between multiple objects, which is significant for solving practical engineering problems.

Keywords:

fixed-point transformation

eigenvalue problems

neutron diffusion

computational domain concatenation

boundary conditions

FC-PINNs: Physics-informed Neural Networks for Solving Neutron Diffusion Eigenvalue Problem with Interface Considerations

Abstract

Journal

Organization