Combination of hybrid artificial neural networks with particle swarm optimization algorithm for SPEI forecasting

Forecasting drought is critical to mitigate its potential impacts on agriculture, water resources, and ecosystems. In this study, we focused on predicting the Standardized precipitation evapotranspiration index (SPEI), a widely used climatic water balance indicator. We developed a hybrid modeling framework that combines artificial neural networks (ANN) with particle swarm optimization (PSO) to train network weights. The study evaluated the influence of four factors on SPEI forecasting performance: the PSO variant, the number of input variables, the number of hidden-layer neurons, and the choice of objective function. A total of 150 model configurations were tested using long-term meteorological data from eight U.S. catchments from the MOPEX database. Results showed that the APartPSO variant achieved the best optimization performance, and the Nash–Sutcliffe efficiency was the most effective objective function. These findings confirm that the integration of ANN with PSO is suitable for forecasting the SPEI, and suggest that advanced PSO variants can be effectively applied to other inverse modeling problems in hydrology.