Green-preconditioned dynamic graph neural operator for electromagnetic field prediction in heterogeneous media

Neural-network prediction of electromagnetic fields in heterogeneous media can reduce the computational cost of repeated numerical simulations. However, the commonly used U-shaped convolutional neural network (U-Net) has difficulty reconciling fixed local convolutions with full-field propagation, abrupt material-interface changes, and reflected and transmitted responses. To address this issue, we develop a green-preconditioned dynamic graph neural operator (GP-DGNO) that integrates full-field scattering-baseline prediction, material-interface correction, and propagation of the corrected interface response within a single end-to-end model. A bilateral spectral green-FNO learns the global scattering residual relative to the paired incident field. A material- and geometry-conditioned dynamic graph neural network corrects local interface responses, and an explicit green-propagation head transfers the correction to regions outside the interface. On a locked test set of 336 cases comprising 48 unseen geometry families and seven physical conditions, GP-DGNO achieved a full-field NRMSE of 0.1982 versus 0.2098 for U-Net, a mean reduction of 5.54%, and produced lower error in 214 of 336 cases. Across conditions, GP-DGNO had lower error under weak-scattering, ID, low-frequency, and high-frequency conditions. U-Net had lower error under the MHz and combined frequency-material conditions, with paired confidence intervals excluding zero in both conditions. The full model had higher error than the incident-field prior under weak scattering (0.0462 versus 0.0284) and the combined condition (0.5069 versus 0.5002). The full model reached its best validation result at a mean epoch of 117.0, compared with a mean epoch of 164.7 for U-Net, and used 375.1 MiB of peak training memory versus 696.8 MiB. Under the unified GPU-resident steady-state timing protocol, inference took 12.28 ms per case for GP-DGNO and 7.18 ms for U-Net. These results show that GP-DGNO improves the overall accuracy of electromagnetic-field prediction in heterogeneous media under a unified test protocol and clarify the operating limits of spectral propagation, interface correction, and explicit re-propagation across frequency and material conditions.