ArticlePhilosophical transactions. Series A, Mathematical, physical, and engineering sciences2022
Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems.
Article in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- Nonlinear spectral modeling and control of soft-robotic muscles from data.Nature communications · 2026Article
- Inverse problems for dynamic patterns in coupled oscillator networks: when larger networks are simpler.Nature communications · 2026Article
- Globalizing manifold-based reduced models for equations and data.Nature communications · 2025Article
- Data-driven linearization of dynamical systems.Nonlinear dynamics · 2024Article
- Data-driven prediction in dynamical systems: recent developments.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2022Article
- Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds.Nature communications · 2022Article
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5 authors.
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Abstract
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing nonlinearizable systems with multiple coexisting steady states have been unavailable. In this paper, we review such a data-driven nonlinear model reduction methodology based on spectral submanifolds. As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low-dimensional invariant manifolds. These normal forms capture amplitude-dependent properties and are accurate enough to provide predictions for nonlinearizable system response under the additions of external forcing. We illustrate these results on examples from structural vibrations, featuring both synthetic and experimental data. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.
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