Mitigating Gradient Competition and Capturing PDE Frequency in PINNs

Develop training methodologies and loss formulations for physics-informed neural networks (PINNs) that mitigate gradient competition among multiple objective terms in the loss function and enable accurate representation of the frequency content of the governing partial differential equations. The goal is to ensure stable and accurate training across coupled and multi-physics PDE systems where multiple losses (e.g., PDE residuals, boundary/interface conditions) interact, especially under extreme physical parameter regimes.

Background

The paper studies coupled Stokes–Darcy systems using physics-informed neural networks and shows that extreme physical constants can create ill-conditioned multi-objective losses, leading to gradient competition and training failures.

While the authors introduce MF-PINNs—combining velocity–pressure and stream–vorticity forms with weighted losses—to alleviate these issues and demonstrate improvements, they emphasize that the broader challenge of systematically resolving gradient competition while accurately capturing the frequency content of PDE solutions remains unresolved.