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

Author

Listed:
  • Mattia Cenedese

    (Institute for Mechanical Systems, ETH Zürich)

  • Joar Axås

    (Institute for Mechanical Systems, ETH Zürich)

  • Bastian Bäuerlein

    (University of Bremen, Faculty of Production Engineering
    Leibniz Institute for Materials Engineering IWT)

  • Kerstin Avila

    (University of Bremen, Faculty of Production Engineering
    Leibniz Institute for Materials Engineering IWT)

  • George Haller

    (Institute for Mechanical Systems, ETH Zürich)

Abstract

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.

Suggested Citation

  • Mattia Cenedese & Joar Axås & Bastian Bäuerlein & Kerstin Avila & George Haller, 2022. "Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-28518-y
    DOI: 10.1038/s41467-022-28518-y
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    References listed on IDEAS

    as
    1. Bethany Lusch & J. Nathan Kutz & Steven L. Brunton, 2018. "Deep learning for universal linear embeddings of nonlinear dynamics," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
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