Evaporation is one of the main components of the hydrological cycle, and its estimation is crucial and important for water resources management issues. Access to a reliable estimator tool for evaporation simulation is important in arid and semi-arid areas such as Iran, which lose more than 70% of their received precipitation by evaporation. Current research employs the Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG) algorithms for training the Multilayer Perceptron (MLP) model (as MLP-BR and MLP-SCG) and comparing their performance with the Levenberg–Marquardt (LM) algorithm (as MLP-LM). For this purpose, 16 meteorological variables were used on a daily scale; including temperature (5 variables), air pressure (4 variables), and relative humidity (6 variables) as input data sets, and pan evaporation as the target variable of the MLP model. The surveys were conducted during the period of 2006–2021 in Fars Province in Iran, which is a semi-arid region and has many natural lakes. Various combinations of input-target pairs were tested by several learning algorithms, resulting in seven input scenarios: (1) temperature-based (T), (2) pressure-based (F), (3) humidity-based (RH), (4) temperature–pressure-based (T-F), (5) temperature–humidity-based (T-RH), (6) pressure–humidity-based (F-RH) and (7) temperature–pressure–humidity-based (T-F-RH). The results indicated the relative superiority of the three-component scenario of T-F-RH, and a considerable weakness in the single-component scenario of RH compared with others. The best performance with a root mean square error (RMSE) equal to 1.629 and 1.742 mm per day and a Wilmott Index (WI) equal to 0.957 and 0.949 (respectively for validation and test periods) belonged to the MLP-BR model. Additionally, the amount of R2 (greater than 84%), Nash-Sutcliff efficiency (greater than 0.8) and normalized RMSE (less than 0.1) all indicate the reliability of the estimates provided for the daily pan evaporation. In the comparison between the studied training algorithms, two algorithms, BR and SCG, in most cases, showed better performance than the powerful and common LM algorithm. The obtained results suggest that future researchers in this field consider BR and SCG training algorithms for the supervised training of MLP for the numerical estimation of pan evaporation by the MLP model.