Seismic acceleration response prediction of rectangular tunnels via learnable spline mapping and kinematic constraints

Seismic response prediction at tunnel sites remains challenging because rapid assessment requires both computational efficiency and physically consistent results. This study proposes a physics-constrained Kolmogorov-Arnold and long short-term memory (KAN-LSTM) sequence model for predicting the acceleration time history at the tunnel key point RP1. This method took the site base ground motion acceleration time history as input and, during the training phase, introduced the joint prediction of the three states: displacement, velocity, and acceleration, to enhance the model’s learning of kinematic consistency. However, in the final engineering application, the model only output the acceleration time history at RP1. A Kolmogorov-Arnold network (KAN) was integrated into the LSTM decoder to strengthen nonlinear mapping, and a kinematic derivative-consistency constraint among response quantities was added to the loss function. This constraint improved prediction stability and physical consistency. Training and testing samples were generated from numerical simulations for three representative soils, including soft clay, silty fine sand, and medium-to-coarse sand. Comparisons with GRU, LSTM, Phy-LSTM, and KAN-LSTM show that the proposed model maintains accurate time-history fitting and reduces peak-response bias under strongly nonlinear conditions. This effect improves the consistency of the peak ground acceleration (PGA) metric and increases the 95% confidence interval (CI₉₅) coverage. Under near-linear conditions, differences among models become smaller, and the main benefit is bias control for a limited number of high-intensity records. The results indicate that the proposed approach provides an efficient and physically consistent surrogate for seismic acceleration response prediction at sites with underground structures.