Expanding the capabilities of physics-informed neural networks through parametrisation for the neutron diffusion equation

Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative for solving systems governed by partial differential equations (PDEs), such as the neutron diffusion equation. Here, conventional PINNs assume fixed PDE parameters, however, in reality, the material parameters inside a nuclear reactor core vary continuously. The variation renders the conventional fixed parameters PINNs unsuitable as the models must be retrained. To address this challenge, a parametric PINNs model is built so inferences can be made on various material properties without the need for retraining. This article aims to demonstrates the capabilities of PINNs in resolving the neutron diffusion equation with fixed parameters in both one-dimensional and two-dimensional geometries and compared to the reference finite difference solver. Then, the functionality of PINNs is extended by training the network across a range of material parameters pertaining to real physical changes in reactor conditions generated through OpenMC. The model is then verified against a reference solver on one-hundred random material properties within the OpenMC generated range, showing good agreement with the reference solution but with a vastly accelerated calculation routine.