Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds
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.
- Publication:
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Nature Communications
- Pub Date:
- February 2022
- DOI:
- 10.1038/s41467-022-28518-y
- arXiv:
- arXiv:2201.04976
- Bibcode:
- 2022NatCo..13..872C
- Keywords:
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- Mathematics - Dynamical Systems;
- Computer Science - Machine Learning;
- Electrical Engineering and Systems Science - Systems and Control;
- Nonlinear Sciences - Chaotic Dynamics;
- 37N10;
- 37N15
- E-Print:
- Under consideration at Nature Communications