Advanced streamflow forecasting for Central European Rivers: The Cutting-Edge Kolmogorov-Arnold networks compared to Transformers

Accurate streamflow forecasting is crucial for effective water resource management, flood mitigation, and maintaining ecological balance, especially in Central Europe’s major rivers. This study investigates the performance of two advanced deep learning algorithms—Kolmogorov-Arnold Network (KAN) and Transformers—using long-term hydrological data from four key rivers: the Rhine, Danube, Elbe, and Oder. These rivers, characterized by varying flow regimes and significant human and climatic impacts, serve as vital arteries for both commerce and ecosystems. The dataset comprises historical daily streamflow data, alongside derived input parameters such as moving averages and flow rate changes, used to predict short-term (1 to 7 days) river discharges. The KAN model, leveraging learnable spline-based activation functions, was developed to enhance accuracy and interpretability in capturing complex hydrological patterns. In contrast, the Transformer model uses advanced attention mechanisms, which excel in handling sequential data with long-range dependencies. Results show that the KAN model significantly outperforms the Transformer in short-term forecasts (up to 3 days). For 1-day forecasts, the KAN achieved R2 values of 0.975 for the Rhine, 0.956 for the Danube, 0.992 for the Elbe, and 0.969 for the Oder, with MAPE values ranging from 3.20 % to 8.09 %. At the 3-day horizon, the KAN’s R2 values remained high, demonstrating its robustness. However, as the forecasting horizon extends to 7 days, the performance of both models converges. These findings underscore the methodological novelty of KAN, which provides enhanced short-term predictive capabilities compared to existing methods, offering valuable insights for improving water resource management strategies in complex hydrological settings.