Refining Groundwater Level Prediction with Kolmogorov–Arnold Architectures: A Dual Temporal–Frequency Domain Perspective

Accurate forecasting of groundwater levels (GWL) remains a critical yet complex challenge in regions characterized by pronounced hydrogeological heterogeneity, with significant implications for sustainable water management. This study addresses a key gap in the literature by providing the first comprehensive evaluation of two advanced deep-learning architectures, Kolmogorov–Arnold Network (KAN) and Kolmogorov–Arnold Fourier Network (KAF), benchmarked against the established Long Short-Term Memory (LSTM) model. Leveraging three decades of daily GWL observations from six representative wells encompassing confined, semi-confined, and unconfined aquifers across Florida, USA, we systematically assess multi-step GWL forecasting performance over horizons ranging from one to seven days. All models demonstrate high predictive skill at short lead times (R² >0.97; MAPE < 0.4% in confined aquifers), with the KAF model, uniquely integrating Random Fourier Features with GELU-activated pathways, exhibiting robust accuracy even at extended horizons (RMSE < 0.06 m at seven days). Notably, the Wasserstein Distance (WD) is introduced as a novel evaluation metric, enabling a nuanced analysis of forecast reliability by quantifying distributional deviations often overlooked by standard pointwise metrics. The results reveal that aquifer typology exerts a more substantial influence on forecast skill than model architecture, underscoring the critical role of subsurface heterogeneity in shaping groundwater dynamics. Collectively, these findings establish the potential of next-generation deep-learning frameworks, particularly KAF, to advance both the accuracy and computational efficiency of groundwater forecasting. The rigorous methodological framework introduced here offers a robust foundation for future research integrating exogenous predictors, uncertainty quantification, and hybrid modelling, thereby supporting more resilient groundwater management under increasing hydroclimatic variability.