# Physic-informed deep operator networks for modeling 2D time-domain electromagnetic wave propagation in various media

## TL;DR

A new physics-informed neural network model is proposed to efficiently simulate electromagnetic wave propagation in different environments.

## Contribution

A physics-informed DeepONet is introduced for 2D time-domain EM wave modeling with improved generalization and speed.

## Key findings

- The model generalizes across various source and dielectric inclusion configurations without retraining.
- It achieves FDTD-level accuracy with up to 15 times faster prediction.
- Energy analysis confirms physically consistent wave evolution.

## Abstract

Accurate prediction of time-domain electromagnetic (EM) waves is essential for designing high-frequency systems in complex environments. Traditional finite-difference time-domain (FDTD) solvers become burdensome when handling a large domain, motivating alternative approaches. Physics-informed neural networks (PINNs) offer data-efficient frameworks by embedding physical constraints, but their generalization ability is limited, often requiring retraining when source locations or material configurations change. In this work, we investigate a physics-informed deep operator network (PI-DeepONet), for modeling two-dimensional transient EM wave propagation by incorporating the time-domain Helmholtz equation. Leveraging the operator-learning structure of DeepONet, the proposed framework demonstrates enhanced generalization across diverse excitation and material conditions, including multi-source in free-space and inhomogeneous media. Each trained model predicts wave propagation and scattering for arbitrary source and scatterer configurations, including movable dielectric inclusions. The predicted spatiotemporal fields are quantitatively compared with FDTD simulations to validate accuracy and assess the model’s potential as an efficient surrogate for time-domain EM analysis.

•PI-DeepONet learns a physics-informed operator for 2D transient EM waves•One trained model generalizes across source and dielectric inclusion locations•Matches FDTD with low RMSE and up to 15 times faster full-field prediction•Energy analysis confirmeds bounded, physically consistent time evolution

PI-DeepONet learns a physics-informed operator for 2D transient EM waves

One trained model generalizes across source and dielectric inclusion locations

Matches FDTD with low RMSE and up to 15 times faster full-field prediction

Energy analysis confirmeds bounded, physically consistent time evolution

Physics; Applied sciences