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<p>The establishment of an hour-by-hour runoff forecasting mechanism is of great significance for carrying out short-term scheduling of reservoirs and giving full play to their storage functions. Due to the nonlinear and nonstationary nature of the runoff series, it is difficult to accurately capture the nonlinear trend information in the existing forecasting methods. To this end, we introduce the Kolmogorov-Arnold Network (KAN) to model the nonlinear relationship between rainfall and runoff sequences, as well as within the runoff sequences, by taking advantage of its univariate activation function that can be learned. At the same time, we adopt KAN to replace Multi-Layer Perceptrons (MLP) in conventional forecasting models, evaluating their feasibility as an enhancement to improve predictive performance. The experimental results in the Three Gorges Reservoir Area show that compared with the conventional MLP model, the Nash–Sutcliffe efficiency coefficient(NSE) and Kling-Gupta Efficiency2012(KGE2012) of this method are improved by 0.0191 and 0.0242, and the Mean Squared Error(MSE) and Mean Absolute Error(MAE) are reduced by 6.92% and 1.11%, respectively. Further after replacing the linear and MLP structure with KAN in several models such as Long Short-Term Memory(LSTM) and Transformer, the forecasting performance was also significantly improved. These results indicate that KAN, as an improved method, has a wide range of applications in runoff forecasting tasks.</p>

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Kolmogorov-Arnold networks: a new approach for runoff forecasting

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Yuan Yao,
  • Xiaopeng Wang,
  • Fanwei Meng,
  • Biqiong Wu,
  • Hui Cao,
  • Haoqiang Zhang,
  • Jie Zhao

摘要

The establishment of an hour-by-hour runoff forecasting mechanism is of great significance for carrying out short-term scheduling of reservoirs and giving full play to their storage functions. Due to the nonlinear and nonstationary nature of the runoff series, it is difficult to accurately capture the nonlinear trend information in the existing forecasting methods. To this end, we introduce the Kolmogorov-Arnold Network (KAN) to model the nonlinear relationship between rainfall and runoff sequences, as well as within the runoff sequences, by taking advantage of its univariate activation function that can be learned. At the same time, we adopt KAN to replace Multi-Layer Perceptrons (MLP) in conventional forecasting models, evaluating their feasibility as an enhancement to improve predictive performance. The experimental results in the Three Gorges Reservoir Area show that compared with the conventional MLP model, the Nash–Sutcliffe efficiency coefficient(NSE) and Kling-Gupta Efficiency2012(KGE2012) of this method are improved by 0.0191 and 0.0242, and the Mean Squared Error(MSE) and Mean Absolute Error(MAE) are reduced by 6.92% and 1.11%, respectively. Further after replacing the linear and MLP structure with KAN in several models such as Long Short-Term Memory(LSTM) and Transformer, the forecasting performance was also significantly improved. These results indicate that KAN, as an improved method, has a wide range of applications in runoff forecasting tasks.