GT-MSMW: A Graph Transformer Framework for Multi-step Prediction of Time-domain Maxwell’s Equations

Huilin Cao, Haoran Sun, Yuxiang Ren, Jingwei Liang, Maokun LI

Keywords: Graph Transformer; Time-domain Maxwell’s Equations; Multi-step Prediction; EGAT

Abstract: Spatiotemporal modeling of electromagnetic fields governed by time-domain Maxwell's equations is essential for simulating and understanding wave propagation and scattering phenomena. However, accurate long-term predictions remains challenging due to the stringent numerical stability requirements and high computational costs inherent in traditional numerical algorithms. We propose **GT-MSMW**, a specialized framework built upon the finite-difference time-domain (FDTD) method, which integrates graph neural networks (GNNs) with a residual Transformer to enable efficient and accurate multi-step forecasting of time-domain Maxwell’s equation solutions for the first time. Unlike previous neural methods that rely on step-by-step autoregressive propagation, **GT-MSMW** directly maps the initial field distribution to the desired state, thus mitigating cumulative errors. To ensure both accuracy and flexibility, the proposed model uses unstructured mesh discretization, GNNs to capture dominant spatial interactions, and the Transformer to model remaining long-range dependencies. Extensive experiments across various 2D and 3D electromagnetic scattering scenarios demonstrate that **GT-MSMW** achieves superior accuracy and generalization, offering a powerful data-driven solver for Maxwell-based simulations.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 8870