Physics-Informed Neural Network Method and Application to Nuclear Reactor Calculations: A Pilot Study

In this paper, the physics-informed neural network (PINN) method is investigated and applied to nuclear reactor physics calculations with neutron diffusion models. The reactor problems were introduced with both fixed-source and eigenvalue modes. For the fixed-source problem, the loosely coupled reactor model was solved with the forward PINN approach, and then, the model was used to optimize the neural network hyperparameters. For the k-eigenvalue problem, which is unique for reactor calculations, the forward PINN approach was modified to expand the capability of solving for both the fundamental eigenvalue and the associated eigenfunction. This was achieved by using a free learnable parameter to approximate the eigenvalue and a novel regularization technique to exclude null solutions from the PINN framework. Both single-energy-group and multiple-energy-group diffusion models were examined in the work to demonstrate the PINN capabilities of solving systems of coupled partial differential equations in reactor problems. A series of numerical examples was tested to demonstrate the viability of the PINN approach. The PINN solution was compared against the finite element method solution for the neutron flux and the power iteration solution for the k-eigenvalue. The error in the predicted flux ranged from 0.63% for simple fixed-source problems up to about 15% for the two-group k-eigenvalue problem. The deviations in the predicted k-eigenvalues from the power iteration solver ranged from 0.13% to 0.92%. These generally acceptable results preliminarily justified the feasibility of PINN applications in reactor problems. The advantageous application potentials as well as the observable computational deficits of the PINN approaches are discussed along with the pilot study.