[2603.02948] Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

Computer Science > Machine Learning arXiv:2603.02948 (cs) [Submitted on 3 Mar 2026] Title:Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results Authors:Alberto Miño Calero, Luis Salamanca, Konstantinos E. Tatsis View a PDF of the paper titled Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results, by Alberto Mi\~no Calero and Luis Salamanca and Konstantinos E. Tatsis View PDF HTML (experimental) Abstract:Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling approach is proposed, which relies on the use of Domain-aware Fourier Features (DaFFs) for the positional encoding of the input space. These features encapsulate all the domain-specific characteristics, such as the geometry and boundary conditions, and unlike Random Fourier Features (RFFs), eliminate the need for explicit boundary condition loss terms and loss balancing schemes, while simplifying the optimization process and reducing the computational cost associated with training. We further develop an LRP-based explainability framework tailored to PINNs, enabling the extraction of relevance attribution scores for the in...