Predicting multiple observations in complex systems through low-dimensional 
embeddings

Wu, Tao; Gao, Xiangyun; An, Feng; Sun, Xiaotian; An, Haizhong; Su, Zhen; Gupta, Shraddha; Gao, Jianxi; Kurths, Jürgen

doi:10.1038/s41467-024-46598-w

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Journal Article

Predicting multiple observations in complex systems through low-dimensional embeddings

Authors

Wu, Tao
External Organizations;

Gao, Xiangyun
External Organizations;

An, Feng
External Organizations;

Sun, Xiaotian
External Organizations;

An, Haizhong
External Organizations;

/persons/resource/zhen.su

Su, Zhen
Potsdam Institute for Climate Impact Research;

/persons/resource/shraddha.gupta

Gupta, Shraddha
Potsdam Institute for Climate Impact Research;

Gao, Jianxi
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

External Ressource

https://github.com/wt1234wt/FRMM-framework
(Supplementary material)

Fulltext (public)

Wu_s41467-024-46598-w.pdf
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There is no public supplementary material available

Citation

Wu, T., Gao, X., An, F., Sun, X., An, H., Su, Z., Gupta, S., Gao, J., Kurths, J. (2024): Predicting multiple observations in complex systems through low-dimensional embeddings. - Nature Communications, 15, 2242.
https://doi.org/10.1038/s41467-024-46598-w

Cite as: https://publications.pik-potsdam.de/pubman/item/item_30102

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.