Physics-Informed Deep Operator Network for 3-D Time-Domain Electromagnetic Modeling

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.