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 benchmarks can fail on practical radiation problems involving singular excitations, absorbing boundaries, and wave fields spanning tens of wavelengths. Architectural physics embedding addresses this limitation by factorizing the field into analytically derived oscillatory kernels and learnable envelopes. However, the kernel dictionary must be manually constructed and scales with ...
| Authors | Huiwen Zhang, Feng Ye, Chu Ma |
|---|---|
| Primary category | cs.AI |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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