Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

Researchers have developed Domain-aware Fourier Features (DaFFs) to enhance Physics-Informed Neural Networks (PINNs), achieving orders-of-magnitude lower errors and faster convergence. The approach incorporates domain-specific characteristics like geometry and boundary conditions while eliminating the need for explicit boundary condition loss terms, making PINNs more accurate, efficient, and interpretable.

• →Domain-aware Fourier Features (DaFFs) significantly improve PINN performance with orders-of-magnitude lower errors compared to vanilla PINNs.
• →The new approach eliminates the need for explicit boundary condition loss terms and complex loss balancing schemes.
• →DaFFs reduce computational costs and simplify the optimization process for training physics-informed neural networks.
• →An LRP-based explainability framework was developed to extract relevance attribution scores and improve interpretability.
• →The method produces more physically consistent feature attributions compared to traditional PINN approaches.