An Effective Physics‐Informed Neural Operator Framework for Predicting Wavefields

Abstract Solving the wave equation is fundamental for many geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics‐informed convolutional neural operator (CNO) (PICNO) to solve the Helmholtz equation efficiently. 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 partial differential equation 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 CNO, particularly in predicting high‐frequency wavefields. These features and improvements are important for waveform inversion down the road.