发表机构
Department of Electrical & Computer Engineering（电气与计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出PE-EK-PINN，将物理核作为可学习表示并演化，使活跃核数量与系统规模无关，训练成本从O(N)降至O(log N)，在偶极子阵列等实验中大幅提速且误差相当。
AI 中文摘要
物理信息神经网络（PINNs）将控制方程嵌入深度学习，但仅通过损失残差强制执行这些方程，使得高度振荡的波动行为需由优化过程自行发现。因此，在标准制造的Helmholtz基准上实现相对$L_2$误差低于$10^{-3}$的方法，在处理涉及奇异激励、吸收边界和跨越数十个波长的波场的实际辐射问题时可能会失败。架构物理嵌入通过将场分解为解析推导的振荡核和可学习包络来解决这一局限。然而，核字典必须手动构建，并且其规模随基本单元数量增长，对于天线阵列和超表面等分层结构系统，会随深度呈指数增长。我们提出PE-EK-PINN（物理嵌入与演化核），将物理核视为可复用的学习表示，而非固定的解析输入。一个收敛的子系统的场被冻结并提升为演化核，其变换副本被复用以表示更高层级的配置，而无需推导新的控制方程。由此产生的层次结构使活跃核的峰值数量与系统规模无关，并将累积训练成本从$O(N)$降低到$O(\log N)$。在偶极子阵列、复合线源几何和交叉阵列上的实验展示了显著的训练成本降低，同时实现了降低或相当的相对$L_2$误差。一个显著例子是，PE-EK-PINN解决256偶极子阵列的速度比直接PE-PINN快30倍以上。
英文摘要
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 systems such as antenna arrays and metasurfaces. We propose PE-EK-PINN (Physics Embedded with Evolving Kernels), which treats physics kernels as reusable learned representations rather than fixed analytical inputs. A converged subsystem field is frozen and promoted to an evolved kernel, whose transformed copies are reused to represent higher-level configurations without deriving new governing equations. The resulting hierarchy makes the peak number of active kernels independent of system size and reduces cumulative training cost from $O(N)$ to $O(\log N)$. Experiments on dipole arrays, composite line-source geometries, and cross arrays demonstrate the dramatic training cost reduction, while achieving a reduced or comparable relative $L_2$ error. One notable example is PE-EK-PINN solves a $256$-dipole array more than 30 times faster than direct PE-PINN.
Comments17 pages, conference submission
