Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)
| Title: | Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO) |
|---|---|
| Authors: | Baddoo, Peter J., Herrmann, Benjamin, McKeon, Beverley J., Brunton, Steven L. |
| Publication Year: | 2021 |
| Collection: | Mathematics Physics (Other) |
| Subject Terms: | Physics - Fluid Dynamics, Mathematics - Optimization and Control, Physics - Data Analysis, Statistics and Probability |
| More Details: | Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. In contrast, sparse identification of nonlinear dynamics (SINDy) learns fully nonlinear models, disambiguating the linear and nonlinear effects, but is restricted to low-dimensional systems. In this work, we present a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems. Our method performs kernel regression on a sparse dictionary of samples that appreciably contribute to the underlying dynamics. We show that this kernel method efficiently handles high-dimensional data and is flexible enough to incorporate partial knowledge of system physics. It is possible to accurately recover the linear model contribution with this approach, disambiguating the effects of the implicitly defined nonlinear terms, resulting in a DMD-like model that is robust to strongly nonlinear dynamics. We demonstrate our approach on data from a wide range of nonlinear ordinary and partial differential equations that arise in the physical sciences. This framework can be used for many practical engineering tasks such as model order reduction, diagnostics, prediction, control, and discovery of governing laws. Comment: 44 pages, 12 figures |
| Document Type: | Working Paper |
| DOI: | 10.1098/rspa.2021.0830 |
| Access URL: | http://arxiv.org/abs/2106.01510 |
| Accession Number: | edsarx.2106.01510 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO) – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Baddoo%2C+Peter+J%2E%22">Baddoo, Peter J.</searchLink><br /><searchLink fieldCode="AR" term="%22Herrmann%2C+Benjamin%22">Herrmann, Benjamin</searchLink><br /><searchLink fieldCode="AR" term="%22McKeon%2C+Beverley+J%2E%22">McKeon, Beverley J.</searchLink><br /><searchLink fieldCode="AR" term="%22Brunton%2C+Steven+L%2E%22">Brunton, Steven L.</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2021 – Name: Subset Label: Collection Group: HoldingsInfo Data: Mathematics<br />Physics (Other) – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Physics+-+Fluid+Dynamics%22">Physics - Fluid Dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+-+Optimization+and+Control%22">Mathematics - Optimization and Control</searchLink><br /><searchLink fieldCode="DE" term="%22Physics+-+Data+Analysis%2C+Statistics+and+Probability%22">Physics - Data Analysis, Statistics and Probability</searchLink> – Name: Abstract Label: Description Group: Ab Data: Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. In contrast, sparse identification of nonlinear dynamics (SINDy) learns fully nonlinear models, disambiguating the linear and nonlinear effects, but is restricted to low-dimensional systems. In this work, we present a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems. Our method performs kernel regression on a sparse dictionary of samples that appreciably contribute to the underlying dynamics. We show that this kernel method efficiently handles high-dimensional data and is flexible enough to incorporate partial knowledge of system physics. It is possible to accurately recover the linear model contribution with this approach, disambiguating the effects of the implicitly defined nonlinear terms, resulting in a DMD-like model that is robust to strongly nonlinear dynamics. We demonstrate our approach on data from a wide range of nonlinear ordinary and partial differential equations that arise in the physical sciences. This framework can be used for many practical engineering tasks such as model order reduction, diagnostics, prediction, control, and discovery of governing laws.<br />Comment: 44 pages, 12 figures – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: DOI Label: DOI Group: ID Data: 10.1098/rspa.2021.0830 – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2106.01510" linkWindow="_blank">http://arxiv.org/abs/2106.01510</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2106.01510 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1098/rspa.2021.0830 Subjects: – SubjectFull: Physics - Fluid Dynamics Type: general – SubjectFull: Mathematics - Optimization and Control Type: general – SubjectFull: Physics - Data Analysis, Statistics and Probability Type: general Titles: – TitleFull: Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO) Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Baddoo, Peter J. – PersonEntity: Name: NameFull: Herrmann, Benjamin – PersonEntity: Name: NameFull: McKeon, Beverley J. – PersonEntity: Name: NameFull: Brunton, Steven L. IsPartOfRelationships: – BibEntity: Dates: – D: 02 M: 06 Type: published Y: 2021 |
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