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

Current data-driven modelling techniques perform reliably on linear systems or on those that can be linearized. Cenedese et al. develop a data-based reduced modeling method for non-linear, high-dimensional physical systems. Their models reconstruct and predict the dynamics of the full physical system. 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.

Automated summary

This study develops a data-driven reduced modeling method for non-linear, high-dimensional physical systems, which reconstructs and predicts the dynamics of the full physical system. The method demonstrates accurate predictive ability on experimental data.