Physics-informed LSTM networks for train-bridge dynamic response prediction

Predicting dynamic train-bridge interaction responses is essential for structural assessment, but it is computationally demanding when using traditional methods like finite element analysis. Among deep learning models, long short-term memory (LSTM) networks have shown good performance in handling sequential data like time series in structural dynamics. However, these data-driven models may lose accuracy under varying operational conditions. This paper proposes a physics-informed LSTM (PhyLSTM) model specifically proposed for predicting train-bridge dynamic responses efficiently and accurately. By integrating the governing equations of motion directly into the loss function, the PhyLSTM model ensures that the predictions are physically consistent. The model is validated on a simply supported beam subjected to a high-speed load model (HSLM) train. Experimental results demonstrate that PhyLSTM outperforms standard LSTMs in terms of accuracy and robustness, particularly under resonance conditions. This hybrid approach effectively combines the temporal learning power of LSTMs with fundamental mechanical principles, offering a promising solution for structural health monitoring (SHM) and digital twin applications.