A physics-informed Temporal–Spatial gated Kolmogorov–Arnold network for real-time response prediction of floating structures

Efficiently and effectively predicting the dynamic response of floating structures is essential for ensuring the safety and reliability of various marine equipment. Conventional numerical methods, such as OrcaFlex, are usually computationally intensive and difficult to apply for rapid assessment or real-time decision scenarios. To address this limitation, this paper develops a physics-informed hybrid deep learning architecture (P-DeepGKAN), which integrates Temporal Convolutional Networks (TCNs), Gated Recurrent Units (GRUs), and Kolmogorov–Arnold Networks (KANs) into an efficient Deep Operator Network (DeepONet) for fast response prediction of floating structures under wave and wind loads. To enhance physical consistency and generalization, a high-low frequency separation mechanism is introduced, along with several physical constraints on the loss function, including the residuals of Cummins equations, initial conditions and the frequency-domain consistency. Samples for training the proposed architecture are generated using OrcaFlex under the consideration of various wind speeds and wave forces. Ablation studies confirm the indispensable role of physics-informed constraints, GRU module and frequency separation mechanism. Furthermore, comparison of experimental test with results by baseline neural networks demonstrates that the proposed P-DeepGKAN achieves superior predictive performances in terms of computational efficiency and accuracy. It is noted that the P-DeepGKAN model greatly reduces the RMSE values in displacement and acceleration predictions, with the improved R2 value by 3% and 24%, respectively. Moreover, the proposed model demonstrates stable short-term extrapolation capabilities beyond the training window and achieves a near-real-time response prediction with inference speeds 2400 times faster than conventional numerical simulations. Overall, the developed P-DeepGKAN architecture serves as a high-precision and efficient complement to conventional numerical tools, providing a practical solution for rapid dynamic response assessment in marine engineering applications.