A physics-informed transformer framework for seismic response modeling and fragility evaluation of soil–pile systems

To capture the complex dynamic response characteristics of soil-pile interaction systems under seismic excitation, this study proposes a physics-informed neural network (PINN) for predicting the full-length and full-time seismic responses of pile foundations and evaluating their seismic fragility. The data-driven component incorporates a multi-head attention mechanism to enhance the capture of temporal dependencies. A nondimensionalized dynamic governing equation is employed to construct physics-based constraints, and an adaptive control strategy is adopted to balance the gradients of data and physics losses. This design improves the training stability and physical consistency of the model. The results demonstrate that the proposed PINN framework significantly enhances curvature prediction accuracy along the pile length while maintaining high fidelity in seismic displacement prediction. Furthermore, by integrating the uncertainty propagation of the PINN predictions, a prediction-corrected seismic fragility analysis method is developed. Comparison with finite element results indicates that the corrected PINN-based fragility curves show generally small discrepancies in seismic risk evaluation, with errors remaining within approximately 2.3% in the New Madrid region and within about 4%–15% in the Coos Bay region, thereby confirming the reliability of the proposed method.