Physics-informed neural networks for enhancing structural seismic response prediction with pseudo-labelling

Despite the great promise of machine learning in the structural seismic analysis, the deployment of advanced neural networks has been limited in practical applications because of the high costs of data acquisition. This paper introduces a new framework that integrates the powerful learning ability of physics-informed neural networks (PINNs) with the effectiveness of pseudo-labelling in data augmentation to improve the accuracies of seismic response predictions of structures. The architecture of PINNs consists of two blocks of gated recurrent unit-fully connected neural networks (GRU-FCNNs) and one block of ordinary differential equation (ODE) that leverages the knowledge of structural dynamics. The first block of GRU-FCNNs serves as a generator of pseudo-labels when drawing upon the input of unlabelled datasets. The second block of GRU-FCNNs in combination with the ODE block is a selector of reliable pseudo-labels. The performance of PINNs trained on limited labelled data can be significantly improved by successively selecting reliable pseudo-labels from the generator and selector to supplement training datasets. The effectiveness of pseudo-labelling in PINNs is validated and compared with PINNs without pseudo-labelling through case studies with simulation datasets and real datasets from experiment. The results show that the proposed framework is effective and robust in improving prediction accuracies of structural seismic responses with limited labelled data.