Causal Matrix Long Short-Term Memory Network for Interpretable Significant Wave Height Forecasting

This study proposes a novel causality-structured matrix long short-term memory (C-mLSTM) model for significant wave height (SWH) forecasting. The framework incorporates a two-stage causal feature selection methodology using cointegration testing and Granger causality testing to identify long-term stable causal relationships among variables. These relationships are embedded within the C-mLSTM architecture, enabling the model to effectively capture both temporal dependencies and causal information within the data. Furthermore, the model integrates Bayesian optimization (BO) and twin delayed deep deterministic policy gradient (TD3) algorithms for synergistic optimization. This combined TD3-BO approach achieves an 11.11% improvement in the mean absolute percentage error (MAPE) on average compared to the base model without optimization. For 1–24 h SWH forecasts, the proposed TD3-BO-C-mLSTM outperforms the benchmark models TD3-BO-LSTM and TD3-BO-mLSTM in prediction accuracy. Finally, a Shapley additive explanations (SHAP) analysis was conducted on the input features of the BO-C-mLSTM model, which reveals interpretability patterns consistent with the two-stage causal feature selection methodology. This research demonstrates that integrating causal modeling with optimization strategies significantly enhances time-series forecasting performance.