SMD-xLSTM-TSMixer: A deep learning framework with wave-age modulation for wave height forecasting

Accurate wave height prediction is crucial for maritime safety and coastal protection, while reliable long-term forecasts are essential for infrastructure design and energy management. Existing models primarily rely on historical wave height data as the sole input, neglecting the physical dynamics of wave generation. In this paper, a novel SMD-xLSTM-TSMixer model is proposed. Physical domain knowledge is integrated by incorporating wave age and wave steepness as auxiliary variables. To mitigate data non-stationarity, a hybrid SMD decomposition strategy is constructed, combining Seasonal-Trend Decomposition using LOESS (STL) with Variational Mode Decomposition (VMD). The decomposed sub-signals are subsequently processed by a dual-branch neural network. Specifically, long-term temporal dependencies are captured by an xLSTM, while complex inter-channel correlations are extracted by a TSMixer. Finally, features from these parallel branches are adaptively integrated via a gating mechanism. Experimental results on four buoy datasets show that, compared to effective benchmark models such as VMD-LSTM-TCN and SMD-LSTM-Informer, the proposed model reduces error metrics (RMSE, MAE, and MAPE) by more than 50% within a 24-h prediction horizon. Furthermore, in a 48-h prediction scenario, the coefficient of determination exceeds 0.92 for all datasets. This framework demonstrates stability and robustness in extreme wave events, overcoming peak-shaving and time-lag issues. © 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.