Hybrid Physics-Informed Neural Network for the Wave Equation With Unconditionally Stable Time-Stepping

This letter introduces a novel physics-informed approach for neural network-based 3-D electromagnetic modeling. The proposed method combines standard leap-frog time-stepping with neural network-driven automatic differentiation for spatial derivative calculations in the wave equation. This methodology effectively addresses the challenge of accurately modeling high-frequency electromagnetic fields with physics-informed neural networks, often characterized as “spectral bias,” in the time domain. We demonstrate that the resultant numerical scheme enables unconstrained time-stepping with respect to stability, in contrast to the finite-difference time-domain method, which is subject to the Courant stability limit. Furthermore, the use of neural networks allows for seamless GPU acceleration. We rigorously evaluate the accuracy and efficiency of this finite-difference automatic differentiation approach, by comprehensive numerical experiments.