Predicting multiple observations in complex systems through low-dimensional embeddings

Tao Wu, Xiangyun Gao (), Feng An (), Xiaotian Sun, Haizhong An, Zhen Su, Shraddha Gupta, Jianxi Gao () and Jürgen Kurths ()
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Tao Wu: Chengdu University of Technology
Xiangyun Gao: China University of Geosciences
Feng An: Beijing University of Chemical Technology
Xiaotian Sun: China University of Geosciences
Haizhong An: China University of Geosciences
Zhen Su: Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association
Shraddha Gupta: Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association
Jianxi Gao: Rensselaer Polytechnic Institute
Jürgen Kurths: Potsdam Institute for Climate Impact Research (PIK)–Member of the Leibniz Association

Nature Communications, 2024, vol. 15, issue 1, 1-12

Abstract: 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.

Date: 2024
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DOI: 10.1038/s41467-024-46598-w

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