Physics informed spatial-temporal neural operators for nonlinear structural system response reconstruction and identification

In recent years, deep learning-based data-driven techniques have been widely used for structural system identification and large amounts of high-quality data are required to train deep learning models. In practice, the data for damage scenarios are difficult to obtain and the observations at limited locations are obtained from limited sensors, which causes the identification of structural parameters to become difficult. To address this challenge, this paper proposes a novel physics informed spatial-temporal neural operator (PhySTN) framework for structural response reconstruction and identification from limited observations. This framework mainly consists of a spatial feature encoder and a temporal operator. The spatial feature encoder describes the spatial relationship between the full state and limited observation data. The temporal operator is based on neural ordinary differential equations (NODEs), which consists of the physical knowledge in ODEs and a neural network to describe the complex discrepancy term between the physical knowledge and real structure. The integration of the temporal operator and the spatial encoder allows a limited number of observations to reconstruct unmeasured structural responses and predict the discrepancy terms for structural identification directly. The performance of the proposed framework is evaluated through the numerical and experimental study on building structures with smart magnetorheological elastomer isolators, and practical applications on Canton Tower. Effects of measurement noise, and the observation number and locations are discussed. Numerical and experimental results show that the purposed framework can accurately identify the nonlinear structural parameters and reconstruct unmeasured responses from limited noisy observations. • A physics informed spatial-temporal neural operator is developed for structural response reconstruction and identification. • The proposed method integrates the spatial feature encoder with the temporal operator. • The proposed method increases the explainability and extendibility by embedding the physics knowledge. • Numerical and experimental studies are conducted to verify the performance of the proposed method.