An effective physics-informed neural operator framework for predicting wavefields

TL;DR

This paper introduces a physics-informed neural operator framework that efficiently predicts wavefields by integrating PDE constraints, significantly improving accuracy and resolution over traditional data-driven methods, especially for high-frequency wave predictions.

Contribution

The paper presents a novel physics-informed convolutional neural operator (PICNO) that incorporates PDE constraints into training, enabling high-resolution wavefield predictions with limited data.

Findings

PICNO outperforms purely data-driven models in wavefield prediction.

PICNO achieves high-resolution predictions with limited training samples.

Significant improvements in high-frequency wavefield prediction are demonstrated.

Abstract

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.