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

• Published in: Nature communications Vol. 13; no. 1; pp. 872 - 13
• Main Authors: Cenedese, Mattia, Axås, Joar, Bäuerlein, Bastian, Avila, Kerstin, Haller, George
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.02.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/166/988; 639/705/1046; Canonical forms; Datasets; Design optimization; Dynamical systems; Humanities and Social Sciences; Linear systems; Machine learning; Manifolds (mathematics); multidisciplinary; Nonlinear response; Orbits; Oscillations; Prediction models; Reduction; Science; Science (multidisciplinary); System theory; Vortex shedding; Water tanks
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-022-28518-y

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. 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.