An effective physics-informed neural operator framework for predicting wavefields

• URL: http://arxiv.org/abs/2507.16431v1
• Date: Tue, 22 Jul 2025 10:22:30 GMT
• Title: An effective physics-informed neural operator framework for predicting wavefields
• Authors: Xiao Ma, Tariq Alkhalifah,
• Abstract summary: We introduce a physics-informed convolutional neural operator (PICNO) to solve the Helmholtz equation efficiently.<n> PICNO takes 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.<n>It allows for high-resolution reasonably accurate predictions even with limited training samples.
• Score: 10.94738894332709
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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