With soaring evaporation rates and shrinking freshwater resources, hyper-arid regions require accurate instruments to measure atmospheric water loss, making pan evaporation forecasting a crucial aspect of contemporary water resources management. This paper proposes a hybrid framework that integrates the Physics-Constrained Neural Network (PCNN) and the Bat Algorithm (BA) to predict daily pan evaporation in Kuwait. The proposed PCNN incorporates physical constraints into the loss function, including vapor pressure deficit, net radiation, and aerodynamic resistance based on surface energy balance theory, to ensure both predictive accuracy and physical plausibility, unlike traditional machine learning models. Daily meteorological data and Class A pan evaporation data from two different stations, Kuwait International Airport (KIA) and Abdaly, are used to train and test the model. The obtained results demonstrate a high accuracy and good generalizability with RMSE of 0.904 mm/day, 1.186 mm/day, and R2 of 0.953 and 0.884 at KIA and Abdaly, respectively. The model’s consistency with thermodynamic principles is also confirmed by a new metric called physics residual RMSE (PRMSE). Tests of robustness in the presence of synthetic noise show that the model is insensitive to uncertainty in its inputs. The added value of the PCNN–BA framework is demonstrated through systematic comparison with established data-driven models, showing that the proposed approach achieves competitive predictive accuracy while explicitly enforcing physical consistency. The resulting framework is computationally efficient and scalable, making it suitable for hyper-arid environments and directly applicable to desert agriculture, irrigation scheduling, and water resources management under data-limited and water-scarce conditions.
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