Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework
Bernard O Koopman proposed an alternative view of dynamical systems based on linear operator theory, in which the time evolution of a dynamical system is analogous to the linear propagation of an infinite-dimensional vector of observables. In the last few years, several works have shown that finite-...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acccd6 |
| _version_ | 1797835010839937024 |
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| author | Said Ouala Bertrand Chapron Fabrice Collard Lucile Gaultier Ronan Fablet |
| author_facet | Said Ouala Bertrand Chapron Fabrice Collard Lucile Gaultier Ronan Fablet |
| author_sort | Said Ouala |
| collection | DOAJ |
| description | Bernard O Koopman proposed an alternative view of dynamical systems based on linear operator theory, in which the time evolution of a dynamical system is analogous to the linear propagation of an infinite-dimensional vector of observables. In the last few years, several works have shown that finite-dimensional approximations of this operator can be extremely useful for several applications, such as prediction, control, and data assimilation. In particular, a Koopman representation of a dynamical system with a finite number of dimensions will avoid all the problems caused by nonlinearity in classical state-space models. In this work, the identification of finite-dimensional approximations of the Koopman operator and its associated observables is expressed through the inversion of an unknown augmented linear dynamical system. The proposed framework can be regarded as an extended dynamical mode decomposition that uses a collection of latent observables. The use of a latent dictionary applies to a large class of dynamical regimes, and it provides new means for deriving appropriate finite-dimensional linear approximations to high-dimensional nonlinear systems. |
| first_indexed | 2024-04-09T14:47:47Z |
| format | Article |
| id | doaj.art-6ab0c7abc797458d91f74c1f6fcd830d |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-04-09T14:47:47Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-6ab0c7abc797458d91f74c1f6fcd830d2023-05-02T10:51:47ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014202501810.1088/2632-2153/acccd6Extending the extended dynamic mode decomposition with latent observables: the latent EDMD frameworkSaid Ouala0https://orcid.org/0000-0003-0554-3971Bertrand Chapron1Fabrice Collard2Lucile Gaultier3Ronan Fablet4IMT Atlantique; Lab-STICC , 29200 Brest, FranceIfremer, LOPS , 29200 Brest, FranceODL , 29200 Brest, FranceODL , 29200 Brest, FranceIMT Atlantique; Lab-STICC , 29200 Brest, FranceBernard O Koopman proposed an alternative view of dynamical systems based on linear operator theory, in which the time evolution of a dynamical system is analogous to the linear propagation of an infinite-dimensional vector of observables. In the last few years, several works have shown that finite-dimensional approximations of this operator can be extremely useful for several applications, such as prediction, control, and data assimilation. In particular, a Koopman representation of a dynamical system with a finite number of dimensions will avoid all the problems caused by nonlinearity in classical state-space models. In this work, the identification of finite-dimensional approximations of the Koopman operator and its associated observables is expressed through the inversion of an unknown augmented linear dynamical system. The proposed framework can be regarded as an extended dynamical mode decomposition that uses a collection of latent observables. The use of a latent dictionary applies to a large class of dynamical regimes, and it provides new means for deriving appropriate finite-dimensional linear approximations to high-dimensional nonlinear systems.https://doi.org/10.1088/2632-2153/acccd6dynamical systemsKoopman operatorextended dynamic mode decompositionKalman filter |
| spellingShingle | Said Ouala Bertrand Chapron Fabrice Collard Lucile Gaultier Ronan Fablet Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework Machine Learning: Science and Technology dynamical systems Koopman operator extended dynamic mode decomposition Kalman filter |
| title | Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework |
| title_full | Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework |
| title_fullStr | Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework |
| title_full_unstemmed | Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework |
| title_short | Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework |
| title_sort | extending the extended dynamic mode decomposition with latent observables the latent edmd framework |
| topic | dynamical systems Koopman operator extended dynamic mode decomposition Kalman filter |
| url | https://doi.org/10.1088/2632-2153/acccd6 |
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