Physics-guided deep neural networks for bathymetric mapping using Sentinel-2 multi-spectral imagery

Satellite-derived bathymetry (SDB) based on multi-spectral imagery data has been a critical tool for large-scale water depth in shallow water regions. Traditional SDB models primarily rely on known laws relating the exponential attenuation of light with the path length it traveled. In the past few years, deep computer vision models have emerged as valuable new technologies for bathymetry measurement. However, due to the black-box nature of these deep models, they may produce bathymetry results that are inconsistent with physical laws and exhibit limited generalizability across diverse areas. In this paper, we propose a novel hybrid architecture, HybridBathNet, that integrates UNet (extracting spatial and spectral feature) with a physical bathymetry network (ensuring physical relationships). By embedding physical constraints directly into the model architecture, HybridBathNet achieves improved bathymetric inversion accuracy while maintaining consistency with established optical attenuation laws. Experimental results demonstrate that the proposed model delivers high-quality bathymetric estimations across diverse island regions. Comparative evaluations against state-of-the-art methods further validate the superior accuracy and generalization capability of HybridBathNet. The code of HybridBathNet is available at https://github.com/qiushibupt/HybridBathNet .