Physics-Informed Long Short-Term Memory Network with Data Folding for Efficient Site Seismic Response Prediction

Accurate prediction of site seismic response is essential for earthquake engineering and seismic design. Numerical simulation methods, although physically rigorous, become computationally intensive when soils exhibit complex nonlinear behavior and are sensitive to constitutive model selection and parameter calibration. Data‑driven deep learning models can approximate nonlinear mappings efficiently, yet they lack built‑in physical constraints and risk producing predictions that violate fundamental mechanics when extrapolating beyond the training domain. This study presents a physics‑informed deep long short-term memory (LSTM) framework for efficient and accurate site seismic response prediction. The framework enforces physical consistency by adding kinematic derivative relationships as soft constraints in the loss function and improves training efficiency by using Data folding modules. A targeted data augmentation strategy addresses measurement noise and signal variability in recorded data. Comprehensive validation on numerically simulated events and on KiK‑net recordings shows the effectiveness of the methodology. On numerical data, the physics‑informed model reaches a 97.98% confidence level within ±2% normalized error and reduces training time by more than 60%. On recorded data, the enhanced model with data augmentation reaches an 88.84% confidence level and a response spectrum correlation of 0.951, which supports reliable prediction of frequency content for engineering use. The framework provides an efficient and physically consistent solution for site response prediction with implications for seismic hazard assessment and structural design.