Objective Approximation techniques have been widely used in hull-form optimization to reduce the high computational costs and lengthy turnaround times associated with high-fidelity numerical simulations. However, conventional approximation models typically rely on predefined hull-form parameters and specific parametric modeling methods. This reliance limits their capability to accurately represent complex three-dimensional hull geometries and hinders the development of a unified modeling framework for hull samples generated from diverse sources. Therefore, this study aims to develop a fast and accurate prediction method for the wave-resistance coefficient that directly utilizes hull geometry information without requiring predefined control parameters.
Method A graph-neural-network-based model, PB-GraphPR (Parallel-Branch Graph-based Prediction of Resistance), is proposed, which takes three-dimensional hull surface point clouds as a unified geometric representation. A total of 1,900 hull variants were generated from the Series 60 parent hull using radial basis function deformation, and their wave-resistance coefficients were calculated with Shipflow v7.0 to construct paired geometry-performance datasets. The original hull point clouds were downsampled to 1,024 points using a deterministic farthest point sampling strategy initialized from the point farthest from the geometric centroid. A DGCNN-PR regression model was first developed as a baseline by replacing the original DGCNN classification head with a continuous regression head. PB-GraphPR was subsequently developed by introducing a parallel multi-neighborhood EdgeConv structure in the first layer, allowing geometric features at multiple neighborhood scales to be extracted simultaneously and fused for subsequent feature learning. A Kriging surrogate model based on predefined RBF deformation control parameters was established for comparison. Furthermore, ablation and sensitivity analyses were performed to investigate the effects of the point-cloud sampling strategy and the neighborhood-scale configuration of the first layer.
Results The results show that PB-GraphPR can accurately predict the wave-resistance coefficients of the Series 60 hull variants. On the independent test set, PB-GraphPR achieved an R² value of 0.989, outperforming DGCNN-PR (0.946) and the conventional Kriging model (0.903), thereby demonstrating superior fitting and prediction capabilities. The sampling ablation study further revealed that the proposed deterministic FPS strategy achieved better prediction performance than random sampling and standard FPS under the given experimental conditions. Moreover, the neighborhood-scale sensitivity analysis indicated that an appropriate multi-neighborhood configuration in the first EdgeConv layer can effectively enhance prediction accuracy while maintaining a reasonable computational cost.
Conclusion PPB-GraphPR provides a parameterization-independent point-cloud-based framework for rapid prediction of the wave-resistance coefficient. By integrating deterministic point-cloud sampling with multi-neighborhood graph feature extraction, the proposed method improves prediction accuracy while preserving a unified geometric representation. The framework offers a practical approach for extending data-driven ship-performance prediction to multi-source hull datasets and, further, to diverse parent hulls and operating conditions.
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