This article discusses the challenges faced by traditional river streamflow forecasting models and introduces novel hybrid models that combine extreme learning machines with mathematical inspired metaheuristic optimization algorithms. The comparative assessment of 20 hybrid models highlights the superior performance of mathematically based models, specifically the PSS-ELM model, which achieved a root mean square error of 2.0667, a Pearson’s correlation index of 0.9374, and a Nash-Sutcliffe efficiency of 0.8642. These findings suggest that the adoption of these models can significantly enhance water management strategies and reduce risks.