Enhancing multi-step-ahead prediction of wave propagation with the CAE-LSTM model: a novel deep learning-based approach to flood dynamics

A deep understanding of the wave propagation process during flood dynamics is fundamental for hazard prediction and mitigation, wherein up-to-date Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to conventional numerical methods, offering a paradigm shift in scientific modeling. However, traditional fully connected neural network-based PINNs have shown limitations of insufficient learning ability for long-term wave propagation processes and limited generalization to various untrained scenarios. This paper introduces a novel Convolutional Autoencoder (CAE)-integrated Long Short-Term Memory (LSTM) model to address these problems. Inspired by the Finite Difference Method for solving Shallow Water Equations, the proposed CAE-LSTM model is designed to enhance the capture and prediction ability for wave propagation by integrating both spatial and temporal dimensions. The CAE component employs convolutional neural networks to extract spatial features, producing compact latent representations that simplify the complexity of wave propagation. The LSTM captures temporal dependencies within this latent space, enabling precise predictions based on time series data. Validated on four dam-break scenarios, the CAE-LSTM model generally achieves an RMSE less than 0.5 after 3,000 steps of rolling prediction, with computational efficiency approximately 200 times higher than traditional finite volume method (FVM) simulations.