Symmetry-Informed Deep Learning for Electromagnetic Scattering
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.