Journal Article

Physics-informed neural networks coupled with a residual-driven dynamic weighted Huber loss function

Hou, Bo-Ya, Jing, Xia-Ting, Bai, Yu-Long, Huang, Chun-lin

2025

Overview

Physics-informed neural networks (PINNs) commonly use the mean squared error (MSE) as the loss function. However, this MSE is sensitive to high-residual regions and noise, often causing nonconvergence, overfitting, and loss imbalance during training. To address these challenges, we propose a Huber+ that combines the robustness of the Huber loss with a residual-driven weighting mechanism. The Huber loss transitions smoothly from the MSE for small residuals to the mean absolute error for large residuals, enhancing robustness and accuracy. Furthermore, the dynamic weighting mechanism adaptively adjusts loss weights on the basis of residual variations at each training point, effectively mitigating loss imbalance and enabling PINNs to focus on high-residual regions. To validate the effectiveness of the proposed method, we conduct comparative experiments, ablation studies, and noise sensitivity tests on the Allen–Cahn equation, the Burgers equation, and the Helmholtz equation. The experimental results show that the proposed strategy improves both accuracy and convergence speed.

• Publisher: IOP Publishing
• Subject: Ablation / Burgers equation / dynamic weighting mechanism / Helmholtz equations / Huber loss function / loss function robustness / Neural networks / Noise sensitivity / physics-informed neural networks / residual-driven weighting / Robustness / Weighting