Hybrid Physics-Informed Neural Network for the Wave Equation with
Unconditionally Stable Time-Stepping
Abstract
This letter introduces a novel physics-informed approach for neural
network-based three-dimensional 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.