Integrated metaheuristic algorithms with extreme learning machine models for river streamflow prediction

Accurate river streamflow prediction is pivotal for effective resource planning and flood risk management. Traditional river streamflow forecasting models encounter challenges such as nonlinearity, stochastic behavior, and convergence reliability. To overcome these, we introduce novel hybrid models that combine extreme learning machines (ELM) with cutting-edge mathematical inspired metaheuristic optimization algorithms, including Pareto-like sequential sampling (PSS), weighted mean of vectors (INFO), and the Runge–Kutta optimizer (RUN). Our comparative assessment includes 20 hybrid models across eight metaheuristic categories, using streamflow data from the Aswan High Dam on the Nile River. Our findings highlight the superior performance of mathematically based models, which demonstrate enhanced predictive accuracy, robust convergence, and sustained stability. Specifically, the PSS-ELM model achieves superior performance with a root mean square error of 2.0667, a Pearson’s correlation index (R) of 0.9374, and a Nash–Sutcliffe efficiency (NSE) of 0.8642. Additionally, INFO-ELM and RUN-ELM models exhibit robust convergence with mean absolute percentage errors of 15.21% and 15.28% respectively, a mean absolute errors of 1.2145 and 1.2105, and high Kling-Gupta efficiencies values of 0.9113 and 0.9124, respectively. These findings suggest that the adoption of our proposed models significantly enhances water management strategies and reduces any risks.