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A novel framework for direct multistep prediction in complex systems

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Abstract

Multistep prediction is an open challenge in many real-world systems for a long time. Despite the advantages of previous approaches, e.g., step-by-step iteration, they have some shortcomings, such as accumulated errors, high cost, and low interpretation. To this end, Gaussian process regression and delay embedding are used to create a combination framework, namely spatial–temporal mapping (STM). Delay embedding is employed to reconstruct an isomorphic dynamical structure with the original system through a single time series, which provides the fundamental architecture for multistep predictions (interpretation). Gaussian process regression is used to achieve predictions by identifying a mapping between the reconstructed dynamical structure and the original structure. This combination framework outputs multistep ahead predictions in a single step (low cost). We test the feasibility of STM for both model systems, including the 3-species ecology system, the Lorenz chaotic system, and the Rossler chaotic system, and several real-world systems, involving energy, finance, life science, and climate. STM framework outperforms traditional iterative approaches and has the potential for many other real-world systems.

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Acknowledgements

This research is supported by the Basic Science Center Project for National Natural Science Foundation of China (No. 72088101, the Theory and Application of Resource and Environment Management in the Digital Economy Era), National Natural Science Foundation of China (Grant No.71991481, 71991485, 71991480).

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Authors and Affiliations

  1. School of Economics and Management, China University of Geosciences (Beijing), Beijing, 100083, China

    Tao Wu & Xiangyun Gao

  2. Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association, 14473, Potsdam, Germany

    Tao Wu & Jürgen Kurths

  3. School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China

    Feng An

  4. Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources, Beijing, 100083, China

    Xiangyun Gao

  5. Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing, 100037, China

    Weiqiong Zhong

  6. Research Center for Strategy of Global Mineral Resources, Chinese Academy of Geological Sciences, Beijing, 100037, China

    Weiqiong Zhong

  7. Department of Physics, Humboldt University at Berlin, 12489, Berlin, Germany

    Jürgen Kurths

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  1. Tao Wu
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Correspondence to Feng An or Xiangyun Gao.

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Wu, T., An, F., Gao, X. et al. A novel framework for direct multistep prediction in complex systems. Nonlinear Dyn 111, 9289–9304 (2023). https://doi.org/10.1007/s11071-023-08360-7

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