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arXiv · 2201.04976

Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds

Mattia Cenedese·Joar Axås·Bastian Bäuerlein·Kerstin Avila·George Haller
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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.

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Mattia Cenedese, Joar Axås, Bastian Bäuerlein, Kerstin Avila, George Haller. 2022-01-13. Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds. https://doi.org/10.1038/s41467-022-28518-y

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