Incomplete temperature-induced strains reconstruction for high-speed railway bridges using physics-informed spatiotemporal graph neural network

Temperature-induced strains play a critical role in evaluating the long-term performance of high-speed railway bridges, which significantly influences cumulative displacement and stiffness degradation over time. However, significant data loss due to sensor degradation, transmission errors, and environmental interference compromises the accuracy of structural health assessments. This study proposes a physics-informed spatiotemporal graph neural network (PI-STGNN) for reconstructing incomplete temperature-induced strains in high-speed railway bridges. PI-STGNN embeds thermoelastic partial differential equation (PDE)-based physical constraints into a data-driven framework. The model comprises multiple physics-informed spatiotemporal blocks, each constructing dynamic graphs to capture the real-time evolution of structural responses via an adaptive spatial attention mechanism. The physics-informed graph convolutional layer enforces physical constraints by approximating the Laplacian matrix with Chebyshev polynomial expansions for spatial derivatives, while a Toeplitz matrix captures temporal evolution. A temporal attention layer learns long-term strain patterns. Experiments on a monitored high-speed railway cable-stayed bridge show that PI-STGNN outperforms six state-of-the-art models (MSGNet, Transformer, MLP, SAE, CAE, and CS) in reconstruction accuracy and computational efficiency while providing physically interpretable insights into strain spatiotemporal patterns.