Enhancing hydrological time series forecasting with a hybrid Bayesian-ConvLSTM model optimized by particle swarm optimization

Hydrological time series forecasting often relies on addressing the inherent uncertainties and complex temporal dependencies embedded in the data. This study presents an innovative hybrid framework, the Bayesian-ConvLSTM-PSO model, specifically designed to tackle these challenges. The framework synergistically combines 1D convolutional neural networks (CNNs), a convolutional Bayesian network, multi-head attention, and long short-term memory (LSTM) networks, with parameters optimized through particle swarm optimization (PSO). The fusion of the convolutional Bayesian network and 1D convolutional neural networks enhances feature robustness by capturing both probabilistic uncertainties and spatial patterns effectively. The multi-head attention model further amplifies this by focusing on the most relevant features, improving the learning process and ensuring better representation of complex temporal dependencies. The proposed model is rigorously tested on daily streamflow data from three flow measurement stations (FMS): Ahullu (D14A014), Kızıllı (D14A080), and Erenkaya (D14A127). Experimental results reveal that the Bayesian-ConvLSTM-PSO model achieves significant performance gains across various evaluation metrics, including root mean square error (RMSE), mean absolute error (MAE), determination coefficient (R2), Kling–Gupta efficiency (KGE), and bias factor (BF). Notably, the model demonstrates exceptional accuracy with an R2 of 0.9950, a KGE of 0.9950, and a bias factor of 0.0003, surpassing the results of PSO-1D CNN-LSTM and benchmark models, such as DNN, DNN-LSTM, and 1D ConvLSTM. These compelling findings underscore the potential of the Bayesian-ConvLSTM-PSO framework as a robust and effective tool for applications in river engineering and hydrological time series forecasting. © The Author(s) 2025.