A graph Fourier Kolmogorov-Arnold Network (G-FourierKAN) and its application to spring discharge simulation

Karst spring discharge, a vital indicator of regional groundwater dynamics, is influenced by both anthropogenic activities and climate variability. It exhibits nonlinear and nonstationary behaviors, making accurate simulation challenging even with machine learning methods. To overcome this challenge, this study develops a G-FourierKAN model, which introduces the Fourier Kolmogorov-Arnold Network (FourierKAN) into Graph Neural Networks (GNNs) by replacing the conventional Multilayer Perceptrons (MLPs). This G-FourierKAN model enhances the extraction and representation of node features within GNNs. Specifically, the FourierKAN layer represents precipitation and karst spring discharge as a combination of multi-frequency features, enabling the model to automatically learn the importance of each frequency component and extract transformed node features. Subsequently, the transformed node features are aggregated with information from neighboring nodes to enable high-precision simulation of spring discharge.Following this approach, a precipitation-driven spring discharge prediction model is established using monthly precipitation and spring discharge data from 1959 to 2003 (the period of groundwater overexploitation) at Xin’an Spring, China. The data from 2004 to 2022 (the groundwater exploitation relieving period after implementation of sustainable development policies) are used to assess the model’s adaptability to policy changes.The results of this application demonstrate that the model achieves high accuracy in simulating karst spring discharge, with a Nash-Sutcliffe Efficiency (NSE) of 0.72 during the testing period (1996–2003). Moreover, the model demonstrates good adaptability in simulating spring discharge from 2004 to 2022. A comparative analysis with Graph Convolutional Network (GCN) reveals that the NSE of G-FourierKAN is 0.05 higher than that of GCN in testing period. The model shows excellent stability and accuracy in simulating spring discharge dynamics in karst terrain.