This paper presents a novel method for modeling practical electromagnetic problems in the time domain using a physics-informed deep operator network (PI-DON). The training of the PI-DON is executed in two stages. In the first stage, a neural operator is trained to approximate the curl operator in Maxwell’s equations. In the second stage, the neural curl operator is deployed with problem-specific settings to model electromagnetic fields through an unsupervised training approach, utilizing a physics-informed loss function. This unsupervised training eliminates the need to generate ground-truth data and reduces the volume of training data required, making PI-DON more efficient than traditional deep neural networks. As an electromagnetic solver, PI-DON demonstrates competitive efficiency compared to finite-difference time-domain solvers for a single run, even when accounting for its training time. Moreover, PI-DON shows strong generalizability, allowing for accurate and efficient uncertainty quantification of microwave geometries without additional training. We show the high accuracy, efficiency, and robust generalizability of the PI-DON solver through the modeling and uncertainty quantification of 3-D planar microwave circuits and a metasurface unit cell. To our knowledge, this is the first physics-informed machine learning model applied to realistic 3-D microwave geometries, clearly demonstrating its potential to surpass the efficiency of FDTD when numerous simulations are required.

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.

This paper demonstrates a deep learning based methodology for the rapid simulation of planar microwave circuits based on their layouts. We train convolutional neural networks to compute the scattering parameters of general, two- port circuits consisting of a metallization layer printed on a grounded dielectric substrate, by processing the metallization pattern along with the thickness and dielectric permittivity of the substrate. This approach harnesses the efficiency of convolutional neural networks with pattern recognition tasks and extends previous efforts to employ neural networks for the simulation of parameterized circuit geometries. Training is based on full-wave simulation data generated via the Finite-Difference Time-Domain (FDTD) method over a target frequency range. To accelerate the generation of such data, we build a hybrid neural network including recursive neural network modules, to compensate numerical dispersion errors in coarse-grid FDTD. This novel dispersion compensation scheme allows us to generate accurate FDTD training data from fast, coarse-grid simulations.