Modeling the complex spatio-temporal dynamics of ocean wave parameters: A hybrid PINN-LSTM approach for accurate wave forecasting

• Our PINN-LSTM captures spatiotemporal wave dynamics using a linear equation for shallow waters. • Our model outperforms its components and other forecasting models at various depths and horizons. • PINN-LSTM shows lower forecast errors compared to existing studies that use PINN. • Linear equation in PINN loss improves accuracy over time series forecasting alone. This study introduces a hybrid model, PINN-LSTM (Physics-Informed Neural Network-Long Short-Term Memory), developed to enhance wave speed forecasting at depths of 1.5 to 11.5 m over forecast horizons of 6, 12, 24, and 48 h. The hybrid PINN-LSTM model was chosen for its unique capability to integrate the physics-based accuracy of PINNs with the temporal sequence learning strength of LSTM networks, enabling the model to capture both spatial and temporal dynamics effectively. The PINN component leverages a linear wave equation to model shallow water dynamics, while the LSTM component addresses long-term dependencies in time-series data. Comparative analyses against standalone LSTM, GRU, and PINN models, as well as methods reported in recent literature, reveal that the PINN-LSTM model achieves superior accuracy, demonstrating more than a 20% reduction in error metrics (MAE, MSE, RMSE) compared to standalone and numerical models. While attention mechanisms have been proposed for sequence modeling, our findings indicate that the original PINN-LSTM architecture performs more effectively in this context. By addressing gaps in existing approaches, this research underscores the potential of integrating physics-informed models with deep learning techniques, providing a robust solution for ocean wave spatio-temporal dynamics forecasting challenges highlighted in previous studies.