Predicting multiple observations in complex systems through low-dimensional embeddings
Nature Communications(2024)
摘要
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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