Physics‑aware mixed-scale Convolutional Neural Network: integrating long‑wavelength bathymetry and gravity anomalies for seafloor topography prediction

Mapping seafloor topography from gravity anomalies is a highly nonlinear inverse problem. While Convolutional Neural Networks (CNNs) are powerful nonlinear tools, their adaptive single-scale kernels fail to capture the spatially variable scales in the gravity–topography relationship. To address this, we propose a Mixed-scale Convolutional Neural Network (MLCNN) that applies mixed-scale convolution to satellite gravity anomalies, with long-wavelength bathymetry as a corrective prior and limited shipborne soundings as training and testing labels, to model the nonlinear mapping from gravity to bathymetry. We validate MLCNN across three geographically distinct regions, benchmarking against SAS, GGM, LDNN, and LCNN in both overall and depth-dependent accuracy. Systematic analysis of the truncated kernel size reveals that multi-scale kernels achieve superior generalization over single-scale counterparts. Ablation studies confirm the contributions of both long-wavelength bathymetry and mixed-scale convolution. Extrapolation experiments further demonstrate MLCNN’s enhanced regional transferability, with MLCNN outperforming the SAS and LCNN baselines. Overall, MLCNN exhibits robust, high-accuracy performance under sparse shipborne data constraints.