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<p>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 &gt;0.97; MAPE &lt; 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 &lt; 0.06&#xa0;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.</p> Graphical Abstract <p>The graphical abstract offers a visually engaging synthesis of the study’s pioneering approach to groundwater level (GWL) forecasting across Florida’s hydrogeologically diverse landscape. In the upper left, a detailed map delineates the spatial extent of the Biscayne and Floridan aquifers, highlighting the geographic distribution of the six USGS monitoring wells that underpin the empirical evaluation. Adjacent to this, the central panel presents a comparative performance assessment of two advanced deep-learning architectures—Kolmogorov–Arnold Network (KAN) and Kolmogorov–Arnold Fourier Network (KAF)—juxtaposed with the benchmark Long Short-Term Memory (LSTM) model. A representative time-series plot for well G-3676 showcases the models’ predictive trajectories versus observed GWL data over a seven-day horizon, visually attesting to the models’ high fidelity in reproducing real-world groundwater dynamics. Beneath the time-series, a tabular summary synthesizes key accuracy metrics (R², RMSE, MAPE, WI) for each model across all wells, underscoring the subtle but consistent superiority of KAF and KAN over LSTM, particularly in frequency-rich or oscillatory regimes. The bottom left features a stylized vignette: contrasting imagery of drought-impacted versus sustainably irrigated agricultural landscapes, evocatively illustrating the tangible societal and environmental benefits of accurate GWL forecasting. Collectively, the graphical abstract distills the methodological innovation, empirical rigor, and practical relevance of the study—emphasizing the transformative role of next-generation neural architectures in enabling proactive, climate-resilient groundwater management.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Francesco Granata,
  • Fabio Di Nunno,
  • Salim Heddam,
  • Senlin Zhu

摘要

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.

Graphical Abstract

The graphical abstract offers a visually engaging synthesis of the study’s pioneering approach to groundwater level (GWL) forecasting across Florida’s hydrogeologically diverse landscape. In the upper left, a detailed map delineates the spatial extent of the Biscayne and Floridan aquifers, highlighting the geographic distribution of the six USGS monitoring wells that underpin the empirical evaluation. Adjacent to this, the central panel presents a comparative performance assessment of two advanced deep-learning architectures—Kolmogorov–Arnold Network (KAN) and Kolmogorov–Arnold Fourier Network (KAF)—juxtaposed with the benchmark Long Short-Term Memory (LSTM) model. A representative time-series plot for well G-3676 showcases the models’ predictive trajectories versus observed GWL data over a seven-day horizon, visually attesting to the models’ high fidelity in reproducing real-world groundwater dynamics. Beneath the time-series, a tabular summary synthesizes key accuracy metrics (R², RMSE, MAPE, WI) for each model across all wells, underscoring the subtle but consistent superiority of KAF and KAN over LSTM, particularly in frequency-rich or oscillatory regimes. The bottom left features a stylized vignette: contrasting imagery of drought-impacted versus sustainably irrigated agricultural landscapes, evocatively illustrating the tangible societal and environmental benefits of accurate GWL forecasting. Collectively, the graphical abstract distills the methodological innovation, empirical rigor, and practical relevance of the study—emphasizing the transformative role of next-generation neural architectures in enabling proactive, climate-resilient groundwater management.