Fourier hybrid neural bathymetry network for active–passive fusion shallow water depth inversion

In this study, a shallow water inversion method based on the Fourier hybrid neural bathymetry network is proposed to address the weak representation of spatial context in active-passive fusion bathymetry. The method uses Ice, Cloud, and land Elevation Satellite-2 laser bathymetry as the reference ground truth and combines Gaofen-2 submeter pansharpened multispectral data. Spatial features (geographic coordinates) are nonlinearly mapped into a high-dimensional space through random Fourier feature mapping. A multilayer perceptron processes the high-dimensional features dimension by dimension, while a convolutional neural network extracts local spectral features, together enabling depth prediction at a submeter resolution. The experiments were conducted at Discovery Reef and Yongxing Island. Same-track validation shows strong accuracy. The root-mean-square error (RMSE) is less than 1.20 m, and the mean absolute error (MAE) is less than 0.50 m. The coefficient of determination (R²) is greater than 0.94, and the Pearson correlation coefficient (PCC) is greater than 0.97. At Discovery Reef, cross-track validation also remained accurate (RMSE = 0.31 m, MAE = 0.24 m, R²=0.90, and PCC = 0.95). Compared with the multilayer perceptron using raw coordinates and the traditional log-ratio model, our method improves accuracy in both same-track and cross-track tests.