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.

Under consideration at Nature Communications

References in corpus (2)

• Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
• Nondestructive Prediction of the Buckling Load of Imperfect Shells

Cited by in corpus (1)

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