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Predicting multiple observations in complex systems through low-dimensional embeddings

Author

Listed:
  • Tao Wu

    (Chengdu University of Technology)

  • Xiangyun Gao

    (China University of Geosciences
    Ministry of Land and Resources)

  • Feng An

    (Beijing University of Chemical Technology)

  • Xiaotian Sun

    (China University of Geosciences)

  • Haizhong An

    (China University of Geosciences
    Ministry of Land and Resources)

  • Zhen Su

    (Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association
    Humboldt University at Berlin)

  • Shraddha Gupta

    (Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association
    Humboldt University at Berlin)

  • Jianxi Gao

    (Rensselaer Polytechnic Institute
    Rensselaer Polytechnic Institute)

  • Jürgen Kurths

    (Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association
    Humboldt University at Berlin)

Abstract

Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

Suggested Citation

  • Tao Wu & Xiangyun Gao & Feng An & Xiaotian Sun & Haizhong An & Zhen Su & Shraddha Gupta & Jianxi Gao & Jürgen Kurths, 2024. "Predicting multiple observations in complex systems through low-dimensional embeddings," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-46598-w
    DOI: 10.1038/s41467-024-46598-w
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    References listed on IDEAS

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    1. Daniel J. Gauthier & Erik Bollt & Aaron Griffith & Wendson A. S. Barbosa, 2021. "Next generation reservoir computing," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
    2. Jianxi Gao & Baruch Barzel & Albert-László Barabási, 2016. "Erratum: Universal resilience patterns in complex networks," Nature, Nature, vol. 536(7615), pages 238-238, August.
    3. Pei Chen & Rui Liu & Kazuyuki Aihara & Luonan Chen, 2020. "Autoreservoir computing for multistep ahead prediction based on the spatiotemporal information transformation," Nature Communications, Nature, vol. 11(1), pages 1-15, December.
    4. Jianxi Gao & Baruch Barzel & Albert-László Barabási, 2016. "Universal resilience patterns in complex networks," Nature, Nature, vol. 530(7590), pages 307-312, February.
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