用物理约束神经算子高效预测波场，少样本下仍准确。
An effective physics-informed neural operator framework for predicting wavefields
- 输入背景波场与速度模型，输出散射波场，融合偏微分方程约束
- 少样本下实现高分辨率预测，高频波场精度显著优于纯数据驱动方法
- 适合地震反演等需要物理一致性建模的地球物理应用
求解波动方程是地球物理应用的基础。然而，赫姆霍兹方程的数值求解面临巨大的计算和内存挑战。为此，我们提出一种物理信息卷积神经算子（PICNO），用于高效求解赫姆霍兹方程。PICNO以均匀介质对应的背景波场和速度模型为输入函数空间，输出散射波场。其训练过程直接嵌入偏微分方程约束，使神经算子不仅能拟合数据，还能捕捉波传播的物理规律。即使训练样本有限，PICNO仍能实现高分辨率、合理准确的预测，并在高频波场预测上显著优于纯数据驱动的卷积神经算子（CNO）。这些特性对后续波形反演具有重要意义。
原文摘要 · Abstract (English)
Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional neural operator (PICNO) to solve the Helmholtz equation efficiently. The PICNO takes both the background wavefield corresponding to a homogeneous medium and the velocity model as input function space, generating the scattered wavefield as the output function space. Our workflow integrates PDE constraints directly into the training process, enabling the neural operator to not only fit the available data but also capture the underlying physics governing wave phenomena. PICNO allows for high-resolution reasonably accurate predictions even with limited training samples, and it demonstrates significant improvements over a purely data-driven convolutional neural operator (CNO), particularly in predicting high-frequency wavefields. These features and improvements are important for waveform inversion down the road.
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