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

TL;DR

This paper introduces a data-driven method to construct low-dimensional models for complex nonlinear dynamical systems using spectral submanifolds, enabling accurate prediction of responses under external forcing.

Contribution

It develops a novel spectral submanifold-based reduction technique that captures nonlinear dynamics from data, applicable to high-dimensional and experimentally measured systems.

Findings

SSM reduction accurately predicts forced responses

Method effective on numerical and experimental data

Models are sparse and extend normal forms

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.