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

Mattia Cenedese, Joar Axås, Bastian Bäuerlein, Kerstin Avila and George Haller ()
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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
Kerstin Avila: University of Bremen, Faculty of Production Engineering
George Haller: Institute for Mechanical Systems, ETH Zürich

Nature Communications, 2022, vol. 13, issue 1, 1-13

Abstract: 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.

Date: 2022
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DOI: 10.1038/s41467-022-28518-y

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