On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation
Numerical Analysis
2026-04-30 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2604.25957,
title = {On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation},
author = {Minh-Hieu Do and François Madiot and Karim Ammar and Nicolas Gérard Castaing},
journal= {arXiv preprint arXiv:2604.25957},
year = {2026}
}