Fast data-driven model reduction for nonlinear dynamical systems
| Autor: | Joar Axås, Mattia Cenedese, George Haller |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Applied Mathematics
Mechanical Engineering Aerospace Engineering Ocean Engineering Dynamical Systems (math.DS) Normal forms Control and Systems Engineering Spectral submanifolds Machine learning Reduced-order modeling FOS: Mathematics Model order reduction Spectral submanifolds (SSM) Engineering & allied operations Electrical and Electronic Engineering Mathematics - Dynamical Systems ddc:620 Invariant manifold |
| Zdroj: | Nonlinear Dynamics, 111 (9) |
| ISSN: | 0924-090X 1573-269X |
| DOI: | 10.3929/ethz-b-000581947 |
| Popis: | We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom. Nonlinear Dynamics, 111 (9) ISSN:0924-090X ISSN:1573-269X |
| Databáze: | OpenAIRE |
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