Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media

TL;DR

The paper introduces the Windowed Fourier Propagator, a neural operator that efficiently models wave equations in inhomogeneous media by leveraging frequency locality, enabling accurate, explainable simulations with limited training data.

Contribution

It presents a novel neural operator based on frequency locality principles, improving efficiency and generalization in wave equation simulations in complex media.

Findings

Achieves computational efficiency by learning localized frequency propagators.

Generalizes from simple to complex wave states effectively.

Provides an explainable framework for wave modeling.

Abstract

Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs of traditional solvers, we propose the Windowed Fourier Propagator (WFP), a novel neural operator that efficiently learns the solution operator. The WFP's design is rooted in the physical principle of frequency locality, where wave energy scatters primarily to adjacent frequencies. By learning a set of compact, localized propagators, each mapping an input frequency to a small window of outputs, our method avoids the complexity of dense interaction models and achieves computational efficiency. Another key feature is the explicit preservation of superposition, which enables remarkable generalization from simple training data (e.g., plane waves) to arbitrary, complex wave states. We demonstrate that the WFP provides an explainable, efficient and accurate framework for data-driven wave modeling in complex media.