用频域局部性设计神经算子，高效模拟不均匀介质中的波动方程。
Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media
- 基于频率局部性原理，用局部传播器替代密集交互模型。
- 在复杂介质中实现高精度、低计算成本的波场建模。
- 从平面波训练即可泛化到复杂波态，适合物理信息学习场景。
波动方程是描述众多物理现象的基础，但在非均匀介质中求解因解的高度振荡性而计算成本高昂。为克服传统求解器的高开销，我们提出窗口傅里叶传播器（WFP），一种新型神经算子，可高效学习解算子。其设计基于频率局部性物理原理：波能主要散射至相邻频率。通过学习一组紧凑的局部传播器，每个将输入频率映射到小范围输出频率，该方法避免了密集交互模型的复杂性，实现计算效率提升。另一关键特性是显式保持叠加性，使模型能从简单训练数据（如平面波）泛化至任意复杂波态。实验表明，WFP提供了一种可解释、高效且准确的数据驱动波场建模框架。
原文摘要 · Abstract (English)
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.
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