Phy-LInformers approach toward structural seismic response prediction

In order to accurately assess the dynamic and ductile properties of building structures under seismic action and to promote the construction of resilient cities and towns, in this study, we introduce a novel deep learning framework denoted as Phy-LInformers, which integrates long short-term memory (LSTM), Transformer-based model Informer, and prior physical knowledge to achieve precise prediction of nonlinear seismic responses in building structures. The central concept of Phy-LInformers lies in fusing the Encoder and Decoder architectures of Informer, while integrating LSTM within the Decoder component to forecast preceding historical states of the building. Meanwhile, the learning space of the Phy-LInformers’ training process is instructed and constrained by encoding existing physical knowledge (e.g., state dependencies between predictor variables and motion control equations, etc.) into the loss function. And at the same time, the prediction performance of the deep learning model is improved with limited training data. Subsequently, the satisfactory performance of the proposed framework is successfully demonstrated through two illustrative examples. The results demonstrate that the proposed Phy-LInformers is a nonlinear seismic response prediction method with better robustness and superior prediction performance, which can still accurately predict the dynamic response of a structure under seismic excitation even with very few training samples (e.g., only 10 samples). This feature makes PhyLInformers feasible for engineering practice and shows promising application prospects in the field of seismic performance evaluation of building structures.