Deep residual physics-informed neural network for underwater electric potential reconstruction

Underwater electrostatic field reconstruction is a key technology for underwater target detection, equipment electric-field diagnostics, and marine engineering measurements. Conventional numerical methods require complete boundary conditions, whereas purely data-driven neural networks may generate spurious solutions that violate physical laws and exhibit marked accuracy degradation under sparse and noisy measurements. This study proposes a deep residual physics-informed neural network (Res-PINN) for three-dimensional underwater potential reconstruction, with fully connected residual blocks, a weighted loss integrating physics, boundary and data terms, and Adam combined with OneCycleLR for dynamic phased adjustment of learning rate and weights.Numerical experiments under two-dimensional planar and three-dimensional spatial measurement scenarios are performed using COMSOL platinum-plate electrode simulation data. Reconstruction accuracy, loss weight sensitivity, and effects of measurement sparsity and noise are analyzed, with comparisons against DNN and standard PINN.The results indicate that the proposed network achieves accurate reconstruction, with favorable noise robustness and low data demand. It achieves an order-of-magnitude improvement over DNN, better generalization gap than standard PINN, and robust loss weights within certain limits. This study provides a new approach for underwater electric field reconstruction under data-scarce and incomplete boundary conditions.