AI 中文总结
研究电磁散射建模中数据效率瓶颈问题），利用麦克斯韦方程组等变性获变换规则，实现数据增强与等变神经网络构建，在光子晶体平板等上验证有效性，提高数据效率，为物理建模提供框架，确立对称性为统一归纳偏差。
AI 中文摘要
深度学习可通过用神经网络替代昂贵的模拟来加速电磁设备建模，将设计参数映射到散射参数。然而，数据效率仍是核心瓶颈，因训练数据通常通过昂贵的数值模拟生成。本文表明对称性为克服电磁散射问题中的这一限制提供了强大且未充分利用的途径。利用麦克斯韦方程组的等变性，获得将电磁设备对称性映射到其散射参数相应变换的一般变换规则。这实现了系统的数据增强和精确等变神经网络的构建。在离散和连续对称群上实现该框架，并在光子晶体平板和自由形式衍射光栅上证明其有效性。与标准架构相比，纳入对称性将数据效率提高了一个数量级，同时等变模型还能精确执行物理约束。我们的方法具有通用性，是对现有物理信息策略的补充，为构建基于物理的替代模型提供了第一性原理框架，并将对称性确立为计算电磁学及其他领域中数据高效且物理一致学习的统一归纳偏差。
英文摘要
Deep learning can accelerate the modeling of electromagnetic devices by replacing costly simulations with neural networks trained to map design parameters to scattering parameters. However, data efficiency remains a central bottleneck, as training data is typically generated through expensive numerical simulations. Here we show that symmetry provides a powerful and largely untapped route to overcoming this limitation in electromagnetic scattering problems. Leveraging the equivariance of Maxwell's equations, we obtain general transformation rules that map symmetries of electromagnetic devices to corresponding transformations of their scattering parameters. This enables both systematic data augmentation and the construction of exactly equivariant neural networks. We implement the framework for both discrete and continuous symmetry groups and demonstrate its effectiveness on photonic-crystal slabs and free-form diffraction gratings. Incorporating symmetry improves data efficiency by an order of magnitude compared to standard architectures, while equivariant models additionally enforce physical constraints exactly. Our approach is general and complementary to existing physics-informed strategies, provides a first-principles framework for constructing physically grounded surrogate models, and establishes symmetry as a unifying inductive bias for data-efficient and physically consistent learning in computational electromagnetics and beyond.
Comments13 pages, 7 figures
