Figure 3 displays a simple structure of the ANFIS-based model with two inputs. More details regarding the structure of this model are presented by Awan & Bae (2014). PSO was used as the optimizer. Figure 4 is a flowchart of the PSO-ANFIS approach. In brief, PSO was utilized to train the ANFIS-based model and find the optimal coefficients for connecting neurons in the network because evolutionary algorithms such as PSO can improve the predictive ability (Sedighkia et al. 2022). Table 1 displays the main characteristics of the ANFIS-based water temperature model. The water temperature depends on several factors and, hence, data-driven models are a good option to achieve a reasonable simulation of the thermal regime. This data-driven model can be directly applied to reservoir operation optimization. Two known indices – the Nash–Sutcliffe efficiency (NSE) index and root means square error (RMSE) – were applied to evaluate the goodness-of-fit of the hybrid machine-learning model (see Gupta et al. (2009) for more details).