PE-EK-PINN: Physics Embedding with Evolving Kernel for Scalable Physics-Informed Neural Networks· PE-EK-PINN：用于可扩展物理信息神经网络的物理嵌入与演化内核
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 the number of elementary units, growing exponentially with the depth of hierarchically structured syste
提出 PE-EK-PINN，改进物理信息神经网络，实现更广泛的波场问题建模。
- 核心方法
- 通过物理嵌入和演化内核，将场分解为解析导出的振荡核和可学习的包络，自动构建内核字典，减少手动调整。
- 适合谁读
- 研究人员、工程师、对物理信息神经网络及波场问题感兴趣的学者
- 要解决的问题
- 现有的物理信息神经网络在处理涉及奇异激励、吸收边界等实际辐射问题时表现不佳，相对L2误差难以降低。
- 关键实验
- 在标准Helmholtz基准测试和实际辐射问题上进行了实验，展示了模型的优越性能。
- 主要贡献
- 解决了传统PINN在实际问题中的局限性，提高了对复杂波场问题的建模能力和准确度。
- 意义与局限
- 拓展了物理信息神经网络的应用范围，特别是在电磁学、声学等领域；但自动化内核构建的有效性和泛化能力仍需进一步验证。