ARPENN: an improved deep convolutional neural network for bathymetry inversion with integrated physical constraints

SUMMARY With advancements in deep learning technology, many scholars have applied it to bathymetry inversion, gradually revealing its potential. However, most current studies focus primarily on data-driven approaches, using various gravity data combinations for bathymetry inversion, without fully exploring the models′ capabilities or understanding the relationship between gravity and bathymetry. This study proposes a novel Attention Residual Physical Enhanced Neural Network (ARPENN), an architecture integrating attention mechanisms, residual modules and physical constraints to help the model better understand the physical context, which enhances the utilization of shipborne data and effectively addresses the divergence issues faced by traditional algorithms in areas without shipborne measurements. The experimental results demonstrate that ARPENN achieves a root mean square of 77.37 m based on single-beam testing, outperforming the convolutional neural network (CNN) method by 17.21 per cent and the classical Smith and Sandwell (SAS) method by 40.11 per cent. In complex regions, multibeam evaluation shows ARPENN improves over SAS by 14.4 per cent. Further analysis reveals that the residual modules and physical constraints are identified as critical for improving accuracy, while attention mechanisms enhance robustness. ARPENN effectively reduces depth anomalies compared to gravity-geological method (GGM) and Smith and Sandwell method (SAS), achieving a reduction in anomaly rates by approximately 8.00 per cent and bringing them closer to zero. In evaluations using SIO_V25.1 as a reference, ARPENN demonstrates better stability and consistency. The ARPENN model offers promising potential for advancing global bathymetry prediction, particularly in improving depth estimation in areas surrounding continental margins.