Predicting Wave Reflection and Transmission in Heterogeneous Media via Fourier Operator-Based Transformer Modeling
arXiv:2604.00132v1 Announce Type: new 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
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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.
Comments: 6 pages, 9 figures, ACDSA 2026
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2604.00132 [cs.LG]
(or arXiv:2604.00132v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.00132
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Zhe Bai [view email] [v1] Tue, 31 Mar 2026 18:37:56 UTC (1,462 KB)
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