Next-generation intelligent framework for pan evaporation prediction: introducing Chebyshev polynomial-based Kolmogorov-Arnold networks

Pan evaporation (Epan) is one of the crucial parameters in hydrological studies, sustainable agricultural development, and water resources management. Predicting Epan remains a challenging problem among researchers worldwide because of its dependency to the diverse climate elements. Hence, it is necessary to precisely predict Epan time series through establishing reliable predictive models. A Chebyshev Polynomial-Based Kolmogorov-Arnold Network (CKAN) is proposed in this study for Epan prediction of two stations located in Australia (Perth and Sydney). Besides the CKAN, three deep learning methods comprising Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU), Transformer (TFR), and two machine learning models, namely Classification and Regression Tress (CART) and eXtreme Gradient Boosting (XGBoost) were also developed. The findings demonstrated that the proposed CKAN model performed better than other methods used for predicting Epan at both the stations. Two interpretable techniques, including Shapely Additive eXplanations (SHAP) and local interpretable model-agnostic explanations (LIME) were used to reveal the most important inputs. The outcomes for the superior CKAN model under full-input scenario indicated that solar radiation at Perth and minimum temperature at Sydney were found to show most contributions for the global SHAP method, whereas in the selected samples of LIME, mean temperature at Perth and relative humidity at Sydney were generally emerged as the influential input parameters. Finally, a K-fold cross validation technique was utilized for the superior CKAN model, denoting the effectiveness and generalizability of proposed CKAN for prediction of Epan.