Supplementary file 1_A Fourier Neural Operator-enhanced parabolic equation framework for highly efficient underwater acoustic field prediction.pdf

The challenges of high computational complexity as well as the corresponding long time consumption are like the Achilles’ Heel in the traditional numerical methods for solving the large-scale underwater acoustic field. An efficient solution method for the parabolic equation model based on the Fourier Neural Operator was proposed in this work. This method enables efficient global feature extraction through spectral convolution, thereby effectively establishing robust correlations between physical field parameters and the target sound pressure field. A continuous mapping was constructed in this model, which ensures that this algorithm could effectively adapt to various marine scenarios through the self-adjustment function. Experimental results demonstrate that the model achieves an average coefficient of determination R2> 0.95 and a relative Root Mean Square Error (RMSE) < 0.04 dB in the predicted sound pressure field, which represents various complex ocean conditions, including the scenarios with non-uniform sound speed profiles, broadband sound sources, and sloped bathymetry, among others. Compared to the conventional RAM approach, the model proposed in this study achieves the equivalent accuracy while reducing the computational latency, with a demonstrated decrease ranging from 25% to 35%. This superior performance could be attributed to the adopted grid-independent O(nlogn) spectral convolution architecture. These results demonstrate the robustness and applicability of the framework, highlighting the potential for broader application in underwater sound field prediction in the future.