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

TL;DR

This paper introduces Physics-Based Loss Scaling for MF-PINNs to enhance convergence and accuracy in neutron diffusion problems, validated through diverse numerical experiments.

Contribution

It proposes a novel scaled loss function based on material cross sections that accelerates convergence and improves accuracy of MF-PINNs.

Findings

The scaled loss function accelerates convergence in neutron diffusion simulations.

Numerical experiments demonstrate improved accuracy across various configurations.

The method is effective for both fixed source and k-eigenvalue problems.

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.