Architecture-Embedded Physics Priors for Mitigating Spectral Bias in Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) struggle to capture high-frequency components of PDE solutions, a failure mode known as spectral bias. Most existing fixes adjust the loss, the sampling, or the input encoding, but the network itself remains agnostic to the equation it is supposed to solve. We take a different route and embed physics priors into the architecture. The network's internal spectrum is shaped to match the spectrum of the target PDE through three components that are trained end-to-end: a bounded coordinate warping that contracts regions where the solution varies sharply, a spectral attention layer driven by the PDE residual that emphasizes physically active Fourier modes, and an inter-harmonic gate that lets low-frequency channels modulate high-frequency ones. We test the design on four forward PDEs (Helmholtz, Wave, Klein--Gordon, Burgers), the Burgers inverse problem, and seismic reconstruction, including Gulf of Mexico field data. Across these tasks, the architecture clearly outperforms seven PINN baselines on accuracy and produces noticeably fewer artifacts. Code will be made publicly available upon acceptance.