Predicting multiple observations in complex systems through low-dimensional embeddings

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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.

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Wu, T., Gao, X., An, F., Sun, X., An, H., Su, Z., … Kurths, J. (2024). Predicting multiple observations in complex systems through low-dimensional embeddings. Nature Communications, 15(1). https://doi.org/10.1038/s41467-024-46598-w

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