Neural Electromagnetic Simulation Training with Time-reversal Consistency

Conventional electromagnetic wave simulators are characterized by lengthy simulation times, making them unsuitable for computational imaging and photonic inverse problems (such as end-to-end design and iterative reconstruction) that necessitate multiple evaluations of the forward model. Neural network-based electromagnetic wave simulators offer potential speed improvements by several orders of magnitude; however, traditional supervised training methods struggle to accurately capture the true physics involved. Although physics-informed approaches provide some improvement, existing residual-based methods rely solely on local information and must be combined with standard supervised loss. In this work, we introduce Time Reversal Consistency (TRC), a novel physics-based training method that leverages the time reversibility of Maxwell's equations. TRC employs a time-reversed, differentiable finite-difference simulator to compare neural network predictions with a known initial condition. This approach offers both global physics guidance and supervision within a single function. We demonstrate that networks trained with TRC, using only randomized scatterers, generalize effectively to various arbitrarily structured media. We validate our method through the inverse design of a set of angle-to-angle couplers, addressing nearly two orders of magnitude more parameters than previous methods. Our findings indicate that the design quality achieved with TRC closely matches that of designs based on conventional simulators, while reducing design time by 95%.