Water Depth Inversion by Fusion of Active and Passive Remote Sensing Imagery With Waves Under the Super Learner–Neural ODE Framework

Most active and passive remote sensing imagery acquired over marine areas contains wave textures, presenting both challenges and opportunities for water depth retrieval. Although wave phenomena hinder water depth estimation via optical radiative transfer in passive remote sensing, they form the foundation of bathymetric methods based on wave texture analysis. The synergistic use of active and passive imagery with wave textures helps mitigate these adverse effects in certain inversion approaches. By integrating the inversion results from both data types—accounting for their distinct imaging mechanisms and depth detection theories—their complementary advantages can be effectively combined. To this end, a new fusion method based on a Super Learner-Neural ODE (SL-NODE) ensemble is proposed. This two-stage framework implements a decision-level fusion strategy: multiple classical machine learning models act as base learners in the first stage, and the Neural ODE serves as the meta-learner in the second. Outputs from the first-stage models are combined via cross-validation and subsequently refined by the Neural ODE to produce the final water depth estimates. In the 0 – 40 m depth range, the fused results exhibit reductions of over 17% in mean relative error and more than 3 m in mean absolute error compared to those from individual inversion methods. Moreover, the proposed ensemble achieves superior fusion accuracy to any single classical machine learning model. The integration of multi-source data and diverse inversion techniques significantly enhances the accuracy and utility of water depth retrieval from imagery with wave phenomena.