An effective physics-informed neural operator framework for predicting wavefields
This addresses computational bottlenecks in geophysical applications like waveform inversion, though it appears incremental as an enhancement to existing neural operator frameworks.
The researchers tackled the computational and memory challenges of solving the Helmholtz equation for wavefields by introducing a physics-informed convolutional neural operator (PICNO), which integrates PDE constraints during training to predict scattered wavefields from background wavefields and velocity models, achieving significant improvements over purely data-driven methods, especially for high-frequency predictions.
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.