Multimodal Fusion of Optimized GRU–LSTM with Self-Attention Layer for Hydrological Time Series Forecasting

Accurate flow forecasting is crucial for effective basin management, regional agricultural policy development, environmental impact analysis, soil and water conservation studies, and flood protection planning. This study proposes a novel approach that integrates particle swarm optimization (PSO) with bidirectional long short-term memory (Bi-LSTM) and bidirectional gated recurrent unit (Bi-GRU) architectures, augmented by feature fusion and attention layers. Our approach consistently outperforms traditional methods across multiple datasets, including Ahmethacı, Büyükincirli, and Ersil, thereby achieving lower RMSE, MAE, and higher KGE and BF scores. Specifically, in Ahmethacı, our method yields an RMSE of 3.448, MAE of 1.224, and an R² of 0.886. In Büyükincirli, it records an RMSE of 0.085, MAE of 0.040, and an R² of 0.964. In Ersil, it achieves an RMSE of 1.495, MAE of 0.565, and R² of 0.883. These results underscore the effectiveness of the proposed approach in flow forecasting.