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<p>This study presents Kolmogorov-Arnold Networks (KANs) for time series forecasting (TSF) as a transformative paradigm, leveraging the Kolmogorov-Arnold theorem to decompose multivariate temporal dependencies into interpretable, spline-parameterized univariate functions. Through architectural innovations like adaptive grid refinement, gated residual mechanisms, and hybrid attention integration, KAN-based models achieve state-of-the-art performance, outperforming transformers with up to 98% lower MSE on benchmarks while offering unparalleled transparency in feature attribution. Our systematic evaluation reveals that KANs excel in modeling nonlinear dynamics across univariate, multivariate, and high-frequency regimes, with applications spanning cryptocurrency volatility prediction, hydrological forecasting, and IoT-enabled anomaly detection. However, challenges persist, including computational overhead in spline optimization and scalability in high-dimensional settings. We propose actionable solutions to enhance robustness and energy efficiency, such as meta-learned spline initialization, federated learning frameworks, and integration with graph neural networks. Beyond technical advancements, KANs bridge the gap between domain expertise and AI, enabling actionable insights in precision medicine, climate resilience, and sustainable energy systems. By aligning with ethical AI principles and global sustainability goals, this work positions KANs as a cornerstone for next-generation TSF, urging interdisciplinary collaboration to unlock their full potential in real-world decision-making.</p>

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Kolmogorov-Arnold networks for time series forecasting: a comprehensive review

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Peter Tettey Yamak,
  • Yujian Li,
  • Ting Zhang,
  • Muhammad Salman Pathan

摘要

This study presents Kolmogorov-Arnold Networks (KANs) for time series forecasting (TSF) as a transformative paradigm, leveraging the Kolmogorov-Arnold theorem to decompose multivariate temporal dependencies into interpretable, spline-parameterized univariate functions. Through architectural innovations like adaptive grid refinement, gated residual mechanisms, and hybrid attention integration, KAN-based models achieve state-of-the-art performance, outperforming transformers with up to 98% lower MSE on benchmarks while offering unparalleled transparency in feature attribution. Our systematic evaluation reveals that KANs excel in modeling nonlinear dynamics across univariate, multivariate, and high-frequency regimes, with applications spanning cryptocurrency volatility prediction, hydrological forecasting, and IoT-enabled anomaly detection. However, challenges persist, including computational overhead in spline optimization and scalability in high-dimensional settings. We propose actionable solutions to enhance robustness and energy efficiency, such as meta-learned spline initialization, federated learning frameworks, and integration with graph neural networks. Beyond technical advancements, KANs bridge the gap between domain expertise and AI, enabling actionable insights in precision medicine, climate resilience, and sustainable energy systems. By aligning with ethical AI principles and global sustainability goals, this work positions KANs as a cornerstone for next-generation TSF, urging interdisciplinary collaboration to unlock their full potential in real-world decision-making.