RANS-GPINN integrating residual-gradient enhancement and KAN for unsteady flow-field prediction around subsea pipelines

This study addresses the slow convergence, limited representation of local high-gradient regions, and accumulation of boundary errors encountered by conventional physics-informed neural networks in predicting unsteady flow-fields around subsea pipelines. A RANS-GPINN model based on the RANS governing equations and integrating a residual-gradient enhancement mechanism with a Kolmogorov-Arnold Network (KAN) is developed for predicting the unsteady flow-field around subsea pipelines. The continuity equation, momentum equations, and turbulence governing equations are embedded into the training process, and residual-gradient terms are introduced in addition to the physical-residual constraints to improve the prediction accuracy for complex flow-field variations. A dataset for the flow-field around subsea pipelines is constructed from numerical simulations, and the effects of network depth, network width, and data normalization strategies are analyzed. The results show that a network with eight hidden layers and 64 neurons per layer, combined with full normalization, achieves a favorable balance among prediction accuracy, convergence performance, and computational cost. Compared with the conventional PINN-NS model, the RANS-GPINN model converges faster and provides stronger error control in complex boundary regions, reducing the maximum error from 0.0239 to 0.0111, a decrease of approximately 53.6%. Long simulations show better model stability, aiding turbulent load assessment on ocean engineering equipment.