Physics and data dual-driven deep learning model for tide level forecasting

High-precision tide level forecasting is essential for the prevention of coastal disasters and ensuring the safety of marine engineering projects. Current research demonstrates that deep learning models utilizing observational data achieve high accuracy in tide level prediction, but the results lack physical consistency. To address the issue, a high-precision 1–24 h forecasting model, termed Phy-BiGRU, is proposed, integrating physics-informed constraints with bidirectional gated recurrent units. The model incorporates nonstationary harmonic analysis as a physical constraint. Bayesian optimization balances physical and data-driven loss weights to improve the model capability. Experiments were conducted at 9 tide gauge stations in the U.S. with different tidal types. Additionally, 3 tide gauge stations in Japan demonstrate the model's cross-region adaptability. By integrating the exceptional nonlinear representation capabilities of neural networks with physical constraints, the proposed model achieves the characterization of physical mechanisms while maintaining high performance in tidal level prediction tasks. The model demonstrates superior performance compared to nonstationary harmonic analysis, the National Oceanic and Atmospheric Administration (NOAA) model, and other classic deep learning models. This research provides a scientific basis and technical support for early disaster warning in coastal areas and the development and utilization of marine resources.