On Convergent Dynamic Mode Decomposition and its Equivalence with Occupation Kernel Regression
This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator...
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| Published in | IFAC-PapersOnLine Vol. 58; no. 17; pp. 103 - 108 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.01.2024
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| ISSN | 2405-8963 2405-8971 2405-8963 |
| DOI | 10.1016/j.ifacol.2024.10.121 |
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| Abstract | This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator (also known as the Koopman generator) can be made to be compact. In this paper, it is shown that by selecting appropriate collections of finite basis functions in the domain and the range, a novel finite-rank representation of the Liouville operator may be obtained. It is also shown that the model resulting from dynamic mode decomposition of the finite-rank representation is closely related to regularized regression using the so-called occupation kernels as basis functions. |
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| AbstractList | This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator (also known as the Koopman generator) can be made to be compact. In this paper, it is shown that by selecting appropriate collections of finite basis functions in the domain and the range, a novel finite-rank representation of the Liouville operator may be obtained. It is also shown that the model resulting from dynamic mode decomposition of the finite-rank representation is closely related to regularized regression using the so-called occupation kernels as basis functions. |
| Author | Abudia, Moad Kamalapurkar, Rushikesh Rosenfeld, Joel |
| Author_xml | – sequence: 1 givenname: Moad surname: Abudia fullname: Abudia, Moad email: abudia@okstate.edu organization: Oklahoma State University, Stillwater, OK, USA – sequence: 2 givenname: Joel surname: Rosenfeld fullname: Rosenfeld, Joel email: rosenfeldj@usf.edu organization: University of South Florida, Tampa, FL, USA – sequence: 3 givenname: Rushikesh surname: Kamalapurkar fullname: Kamalapurkar, Rushikesh email: rushikesh.kamalapurkar@okstate.edu organization: Oklahoma State University, Stillwater, OK, USA |
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| Cites_doi | 10.1137/19M127029X 10.1007/978-0-387-72831-5 10.1090/S0002-9947-1950-0051437-7 10.1007/s00332-021-09746-w 10.1109/TNNLS.2018.2870040 10.1007/s00332-017-9423-0 10.1016/j.tcs.2012.10.016 10.1063/1.4772195 10.1016/j.acha.2021.02.004 10.1109/LCSYS.2020.3046408 10.1137/22M1475892 10.1007/s11071-005-2824-x |
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| Keywords | System Identification Machine Learning and Control Operator Theoretic Methods in Systems Theory |
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| Title | On Convergent Dynamic Mode Decomposition and its Equivalence with Occupation Kernel Regression |
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