Predicting Wave Reflection and Transmission in Heterogeneous Media via Fourier Operator-Based Transformer Modeling

2026-03-31

AI Summary

This study addresses the challenge of efficiently predicting electromagnetic wave propagation in heterogeneous media with material interfaces, where high-fidelity numerical simulations are computationally prohibitive. The authors propose a physics-informed, frequency-embedded vision Transformer-based autoregressive surrogate model, which—novelty—incorporates Fourier operators into its latent space to encode one-dimensional solutions of Maxwell’s equations. Trained on simulation data generated via the finite volume method, the model achieves accurate roll-out predictions beyond 75 time steps with relative errors below 10%, even in the presence of material discontinuities and unknown parameters. It faithfully reproduces key wavenumber spectral characteristics and dynamic interfacial responses, thereby substantially improving both long-term prediction accuracy and computational efficiency compared to conventional approaches.

Abstract

We develop a machine learning (ML) surrogate model to approximate solutions to Maxwell's equations in one dimension, focusing on scenarios involving a material interface that reflects and transmits electro-magnetic waves. Derived from high-fidelity Finite Volume (FV) simulations, our training data includes variations of the initial conditions, as well as variations in one material's speed of light, allowing for the model to learn a range of wave-material interaction behaviors. The ML model autoregressively learns both the physical and frequency embeddings in a vision transformer-based framework. By incorporating Fourier transforms in the latent space, the wave number spectra of the solutions aligns closely with the simulation data. Prediction errors exhibit an approximately linear growth over time with a sharp increase at the material interface. Test results show that the ML solution has adequate relative errors below $10\%$ in over $75$ time step rollouts, despite the presence of the discontinuity and unknown material properties.

Problem

• wave reflection
• wave transmission
• heterogeneous media
• Maxwell's equations
• material interface

Innovation

• Fourier Operator
• Transformer
• Wave Reflection and Transmission
• Surrogate Modeling
• Heterogeneous Media