Underwater sound field prediction conventionally relies on numerically solving the Helmholtz equation, which is computationally expensive and struggles to meet real-time requirements. This study presents the shallow water Fourier neural operator (SWFNO), an end-to-end model based on the Fourier neural operator, for the rapid and accurate prediction of the amplitude and phase of two-dimensional underwater sound fields in shallow water environments with variable sound speed profiles (SSPs). To enhance the model's generalization capability, we design a hybrid sample generation scheme combining Gaussian random fields with simulated shallow water SSPs, constructing a training dataset that balances randomness and physical plausibility. Simulation results demonstrate that SWFNO achieves high sound field prediction accuracy on both test sets and generalization datasets containing actual ocean SSPs, demonstrating its robustness to out-of-distribution samples. Furthermore, the model exhibits super-resolution prediction capability, enabling high-resolution sound field prediction without retraining, and achieves a speedup of over an order of magnitude compared to the traditional spectral method for large-scale samples. These results indicate that SWFNO is an efficient and accurate surrogate model for underwater acoustic propagation, offering a promising route toward real-time, high-fidelity, and intelligent sound field prediction in complex marine environments.
Zhang et al. (Fri,) studied this question.