On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation

Minh-Hieu Do; François Madiot; Karim Ammar; Nicolas Gérard Castaing

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arXiv · 2604.25957

On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation

Minh-Hieu Do·François Madiot·Karim Ammar·Nicolas Gérard Castaing

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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.

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Minh-Hieu Do, François Madiot, Karim Ammar, Nicolas Gérard Castaing. 2026-04-27. On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation. https://arxiv.org/abs/2604.25957

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