Exploring Kolmogorov-Arnold neural networks for hybrid and transparent hydrological modeling

The limited interpretability of deep learning models poses challenges for their integration into process-based hydrological frameworks. To explore potential solutions, we develop K50, a hybrid model that incorporates Kolmogorov–Arnold Networks (KAN) into the Exp-Hydro model. Based on the CAMELS dataset, this study undertakes the following investigations. First, we compare the predictive performance of K50 with that of the Multilayer Perceptron (MLP)-based hybrid model. Second, we visualize the KAN's activation functions to reveal the functional relationships between key input variables and runoff generation. Third, we apply symbolic regression to these functions to derive basin-specific empirical formulas. The results indicate that K50 achieves predictive accuracy comparable to the MLP-based model, while offering an interpretable representation of internal processes. The empirical functions derived from KAN can provide simplified expressions that support physical reasoning. These findings suggest that KAN has the potential to contribute to more interpretable and transparent hybrid hydrological modeling.