On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation
For researchers using PINNs for neutron diffusion problems, this provides a simple scaling technique that improves training efficiency and accuracy.
The paper introduces Physics-Based Loss Scaling (PBLS) for Mixed-Formulation PINNs applied to the neutron diffusion equation, which accelerates convergence and improves accuracy across various test cases from 1-group to multigroup and 2D to 3D configurations.
Physics-Based Loss Scaling (PBLS) is introduced for Mixed-Formulation PINNs (MF-PINNs) applied to the neutron diffusion equation. In particular, we propose a new \textit{scaled} loss function based on the material cross sections, which is equivalent to the classical MF-PINN loss, but accelerates the convergence and improves accuracy of MF-PINNs. Several numerical experiments on both the fixed source and the k-eigenvalue problem, from one-group to multigroup cases and from two-dimensional (2D) to three-dimensional (3D) configurations, illustrate the efficiency of the proposed scaling method.