Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a maximally sparse approximation to the reduced dynamics on it. The r...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Axås, Joar, Cenedese, Mattia, Haller, George
Format: Article
Language:English
Subjects:
Algorithms
Canonical forms
Dynamical systems
Manifolds (mathematics)
Model reduction
Nonlinear dynamics
Nonlinear systems
Optimization
Online Access:Get full text
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Summary:We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a maximally sparse approximation to the reduced dynamics on it. The recently released SSMLearn algorithm uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to the normal form. Here, we present two simplified algorithms, which reformulate manifold fitting and normal form computation as explicit problems under certain assumptions. We show on both numerical and experimental datasets that these algorithms yield accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics. The new algorithms are significantly simplified and provide a speedup of several orders of magnitude.
ISSN:2331-8422