Preprint Open access
PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networks
Physics-Informed Neural Networks (PINNs) embed governing equations into deep learning, but enforce them only through loss residuals, leaving highly oscillatory wave behavior to be discovered by optimization. As a result, methods that achieve relative $L_2$ errors below $10^{-3}$ on standard manufactured Helmholtz bench …