Physics-guided hybrid network for predicting nonlinear dynamic response of structures under bi-directional ground motions

Abstract

Seismic structural response is a critical indicator for assessing collapse resistance and ensuring post-earthquake functionality. Therefore, accurate and rapid prediction of these responses is essential, with Deep Learning (DL) models offering a robust alternative to finite element methods due to their computational efficiency and capability to model nonlinear dynamic responses of structures. However, prevailing DL approaches predominantly focus on unidirectional seismic excitations, often neglecting the complex effects of bidirectional seismic excitations on real-world structures. Furthermore, while the development of the physics-informed neural network effectively enhances interpretability under limited data, most existing approaches incorporate physical constraints solely into the loss function, potentially leading to optimization conflicts and slow convergence rates. To bridge these gaps, this study introduces a novel physics-guided hybrid deep learning framework, the Physical Residual Long Short-term Memory network-Kolmogorov–Arnold network model (Phy-RLK), for real-time bidirectional seismic structural response prediction. The proposed DL architecture embeds the Newmark-$\beta$ numerical integration scheme as a physical residual within LSTM cells. Simultaneously, the adaptive basis functions of the KAN enhance the feature extraction capability from bidirectional seismic inputs, enabling real-time correction of acceleration, velocity, and displacement predictions at each time step, thereby ensuring improved accuracy and physical consistency. The effectiveness of the proposed model is initially verified on a six-story Reinforced Concrete (RC) frame structure, determining optimal hyperparameters in the process. An ablation study further confirms the necessity of both the physics-residual LSTM cell and KAN layer. The model is subsequently implemented on a five-story RC frame structure to verify accuracy and applicability. The experimental results demonstrate that the Phy-RLK provides superior predictive accuracy and robustness, and significantly higher computational efficiency compared to finite element simulations.