Learning light scattering from operator parameter spaces to Galerkin-consistent solution spaces
Efficient and generalizable full-wave simulation is essential for nanophotonic analysis and inverse design, yet existing methods face a tradeoff between the high computational cost of numerical solvers and the limited generalizability of neural operator models for complex optical scattering. Here, we introduce FEMONet, a finite-element-constrained operator-learning framework that learns light scattering from an operator parameter space to a Galerkin-consistent solution space. The operator parameter space encodes the physical entities defining a wave-equation problem, while the variational weak form links this space to the coordinate and physical solution spaces. Integrated with operator-learning networks, FEMONet extends classical solvers from isolated problem instances to parameterized scattering operators. To our knowledge, FEMONet represents the first Galerkin-consistent operator-learning framework for complex-valued optical scattering, grounded in the variational weak form of the governing vector wave equations. Finite-element discretization absorbs spatial derivatives into assembled stiffness matrices and load vectors, removing coordinate-based derivatives of the neural-network output from the physics loss and improving training efficiency. By predicting finite-element expansion coefficients rather than unconstrained field values, the Galerkin-consistent formulation preserves compatible trial and test spaces, achieving high accuracy, stable training, and generalization across dielectric, metallic, arrayed, plasmonic, and three-dimensional nanophotonic structures.