Olive Cawiding, Predicting multiple observations in complex systems through low-dimensional embeddings

In this talk, we discuss the paper, “Predicting multiple observations in complex systems through low-dimensional embeddings”, by Tao Wu et. al., Nature Communications, 2024.

Zoom : https://us06web.zoom.us/j/99567630778?pwd=N2ZrUWtqZzJ0YURVTzlZT3JJR3FUQT09

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.