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<p>Accurate and timely traffic forecasting is essential for developing effective intelligent transportation systems. The complex, high-dimensional, and nonlinear nature of vehicular dynamics often limits the reliability of traditional forecasting models. This paper introduces a deep learning-based, delay-embedded Koopman operator framework for forecasting highway traffic dynamics. The proposed method employs a neural network to learn nonlinear lifting functions, enabling a linear representation of the system dynamics in a higher-dimensional latent space, while delay embedding is used to capture temporal dependencies through Hankel-structured inputs. Evaluated on NGSIM and PeMS datasets, the proposed approach consistently outperforms a Koopman-based benchmark, achieving improvements of approximately 5%–16% in forecasting accuracy. Compared to LSTM and CNN-LSTM models, it demonstrates competitive performance, with differences typically within 0.5%–3%. Unlike black-box models, this approach provides interpretability through Koopman mode decomposition, enabling the identification of underlying spatiotemporal dynamics within the traffic data. These results highlight the proposed method as an efficient and interpretable alternative for traffic forecasting, potentially suitable for computationally efficient or near-real-time forecasting applications.</p>

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Forecasting of Highway Traffic Dynamics: a Deep Learning-Based Delay-Embedded Koopman Operator Approach

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Mustapha K. Khaldi,
  • Muhammad F. Emzir,
  • Nezar M. Alyazidi,
  • Muhammad F. Mysorewala,
  • Sami El-Ferik

摘要

Accurate and timely traffic forecasting is essential for developing effective intelligent transportation systems. The complex, high-dimensional, and nonlinear nature of vehicular dynamics often limits the reliability of traditional forecasting models. This paper introduces a deep learning-based, delay-embedded Koopman operator framework for forecasting highway traffic dynamics. The proposed method employs a neural network to learn nonlinear lifting functions, enabling a linear representation of the system dynamics in a higher-dimensional latent space, while delay embedding is used to capture temporal dependencies through Hankel-structured inputs. Evaluated on NGSIM and PeMS datasets, the proposed approach consistently outperforms a Koopman-based benchmark, achieving improvements of approximately 5%–16% in forecasting accuracy. Compared to LSTM and CNN-LSTM models, it demonstrates competitive performance, with differences typically within 0.5%–3%. Unlike black-box models, this approach provides interpretability through Koopman mode decomposition, enabling the identification of underlying spatiotemporal dynamics within the traffic data. These results highlight the proposed method as an efficient and interpretable alternative for traffic forecasting, potentially suitable for computationally efficient or near-real-time forecasting applications.