Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
This work addresses the challenge of modeling complex nonlinear systems for applications in engineering and physics, representing an incremental improvement with a novel method for a known bottleneck.
The authors tackled the problem of predicting nonlinear dynamics in forced systems by constructing low-dimensional models from data, achieving accurate predictions of nonlinear responses under external forcing as demonstrated in beam oscillations, vortex shedding, and water sloshing experiments.
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.