Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable ) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear mod...

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Bibliographic Details
Published in:Nature communications 2022-02, Vol.13 (1), p.872-13, Article 872
Main Authors: Cenedese, Mattia, Axås, Joar, Bäuerlein, Bastian, Avila, Kerstin, Haller, George
Format: Article
Language:English
Subjects:
639/166/988
639/705/1046
Canonical forms
Datasets
Design optimization
Dynamical systems
Humanities and Social Sciences
Linear systems
Machine learning
Manifolds (mathematics)
multidisciplinary
Nonlinear response
Orbits
Oscillations
Prediction models
Reduction
Science
Science (multidisciplinary)
System theory
Vortex shedding
Water tanks
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Summary:We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable ) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing. Current data-driven modelling techniques perform reliably on linear systems or on those that can be linearized. Cenedese et al. develop a data-based reduced modeling method for non-linear, high-dimensional physical systems. Their models reconstruct and predict the dynamics of the full physical system.
ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-022-28518-y