Transient Electromagnetic Scattering from Dielectric Structures: Stable Long-Time Prediction with Complete-State Neural Networks

The Finite-Difference Time-Domain (FDTD) method is widely used for time-domain electromagnetic simulations, but its high computational cost limits its application to large-scale problems. Neural surrogate models can accelerate FDTD simulations. However, their long-horizon autoregressive predictions often suffer from error accumulation, numerical instability, and spurious reflections at absorbing boundaries. In this work, we investigate a key factor contributing to the numerical instability of neural FDTD surrogates for free-space problems truncated by convolutional perfectly matched layer (CPML) boundaries. Specifically, we show that the dynamically evolving auxiliary memory variables in the CPML must be incorporated into the autoregressive process and accurately represented and updated. Experiments with a complete electromagnetic-field state representation demonstrate that explicitly retaining and recursively updating the CPML auxiliary variables substantially delays the onset of numerical instability during long-horizon inference. The proposed model maintains bounded-error autoregressive prediction over the evaluated 300-step window on the test set, while the mean relative field L2 error increases only from approximately 0.031 at the 50th step to approximately 0.099 at the 300th step. The complete 300-step prediction has a runtime ratio of approximately 1.41 relative to the GPU reference solver. This provides a matched-device surrogate formulation with lower runtime than the GPU reference implementation for the tested setting. We further conduct extensive tests of the model’s generalization capability. The model maintains consistent transient predictions for different permittivity values, unseen irregular and letter-shaped dielectric structures, as well as photonic structures such as microdisks and microrings within the evaluated windows. These results demonstrate its potential for the rapid time-domain analysis of complex electromagnetic scattering and photonic devices. Overall, the results show that a neural surrogate model combining complete-state representation with analytical CPML memory updates can reduce the inference cost of FDTD simulations while maintaining bounded errors within the evaluated prediction window.