Data-driven modeling and forecasting of chaotic dynamics on inertial manifolds constructed as spectral submanifolds.
Chaos
; 34(3)2024 Mar 01.
Article
em En
| MEDLINE
| ID: mdl-38531092
ABSTRACT
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds containing the chaotic attractor of the underlying high-dimensional system. The reduced dynamics on the SSMs turn out to predict chaotic dynamics accurately over a few Lyapunov times and also reproduce long-term statistical features, such as the largest Lyapunov exponents and probability distributions, of the chaotic attractor. We illustrate this methodology on numerical data sets including delay-embedded Lorenz and Rössler attractors, a nine-dimensional Lorenz model, a periodically forced Duffing oscillator chain, and the Kuramoto-Sivashinsky equation. We also demonstrate the predictive power of our approach by constructing an SSM-reduced model from unforced trajectories of a buckling beam and then predicting its periodically forced chaotic response without using data from the forced beam.
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01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Chaos
Assunto da revista:
CIENCIA
Ano de publicação:
2024
Tipo de documento:
Article
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