A Physics-Informed Ensemble Learning Framework for Transferable Shallow Water Bathymetry Inversion in Data-Scarce Regions

Abstract

Satellite-derived bathymetry (SDB) is a critical technology for estimating shallow water depths. However, the extreme scarcity of field measurements in remote or inaccessible regions, such as the coral reefs of the South China Sea (SCS), poses a significant challenge for accurate bathymetric retrieval. Traditional SDB methods heavily rely on extensive in situ data for local calibration. Moreover, these methods are limited by a lack of physical constraints and the inherent instability of single models, resulting in severe performance degradation during cross-regional applications. Therefore, we propose a physics-informed ensemble learning (PIEL) method for transferable bathymetric inversion. By coupling radiative transfer (RT)-derived features with an advanced stacking ensemble strategy, the proposed method provides an efficient and reliable solution for cross-regional bathymetric mapping, particularly in data-scarce areas. Transfer experiments using Wufang Reef as the source domain demonstrated that PIEL achieved root-mean-square errors (RMSEs) of 1.25, 0.83, and 1.08 m in Houteng Reef, Zhongye East Reef, and Mengzi Reef, respectively. Compared to the best-performing single machine learning (ML) model, the proposed method improved accuracy by 10.71%–16.92%, and by 9.78%–18.80% compared to models without physical constraints. In comparison with traditional methods, our approach exhibits marked advantages in prediction accuracy, topographic fidelity, and generalization performance. Furthermore, the application of SHapley Additive exPlanations (SHAPs) quantitatively reveals the dominant contributions of physics-informed features and base learners in cross-domain transfer tasks, enhancing model transparency and reliability. The proposed method effectively mitigates the severe dependence of traditional models on extensive in situ data, demonstrating enhanced accuracy and robustness in cross-regional applications. This study expands the application potential of SDB technology, offering a promising technical pathway for filling bathymetric data gaps in remote and data-scarce regions.