Physics‐Based Encoder‐Only Transformer for Structural Hysteresis Prediction and Dynamic Analysis

ABSTRACT

Accurate modeling of structural hysteresis is a critical task for ensuring the safety of structures through reliable response predictions. However, conventional hysteresis models often struggle to represent diverse hysteresis characteristics observed in real‐world structures, as the manual selection of a model form may not assure validity and the associated model parameter calibration process is both challenging and uncertain. To learn diverse structural hysteresis directly from data, convolutional and recurrent neural networks have been explored; however, efficiently capturing long‐range dependencies over extended loading histories remains challenging. To address these limitations, this study proposes a hysteresis modeling approach built on a Transformer architecture for predicting diverse rate‐independent hysteretic behaviors represented by analytical hysteresis models and experimental structural data under different loading histories. The proposed Physics‐based Encoder‐only Transformer (PET) model uses encoder self‐attention to capture long‐range dependencies within the selected displacement history and maps the resulting latent representations to the restoring‐force sequence through a projection head with a linear skip connection. To address memory constraints arising from long time‐series sequences, an input selection scheme is applied. Furthermore, physics‐informed loss terms based on Drucker's postulate and the local stiffness consistency constraint are incorporated to ensure efficient and physically consistent training under data scarcity. The model is evaluated separately for six representative analytical hysteresis formulations and further validated using a steel frame experimental dataset. The results demonstrate accurate prediction under unseen loading histories, and the trained model is further embedded into numerical dynamic analysis as a step‐by‐step restoring‐force predictor. The proposed approach provides a physics‐consistent modeling strategy for structural hysteresis prediction and can serve as a basis for future extensions to broader structural response analysis and simulation tasks.