Sparsity Structures for Koopman and Perron-Frobenius Operators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00364895" target="_blank" >RIV/68407700:21230/22:00364895 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/21M1466608" target="_blank" >https://doi.org/10.1137/21M1466608</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1466608" target="_blank" >10.1137/21M1466608</a>
Alternative languages
Result language
angličtina
Original language name
Sparsity Structures for Koopman and Perron-Frobenius Operators
Original language description
We present a decomposition of the Koopman and Perron-Frobenius operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of the Koopman operator, we show that eigenfunctions for the subsystems induce eigenfunctions for the whole system. The use of principal eigenfunctions allows us to reverse this result. Similarly for the adjoint operator, the Perron-Frobenius operator, invariant measures for the dynamical system induce invariant measures of the subsystems, while constructing invariant measures from invariant measures of the subsystems is less straightforward. We address this question and show that under necessary compatibility as-sumptions such an invariant measure exists. Based on these results we demonstrate that the a priori knowledge of a decomposition of a dynamical system allows for a reduction of the computational cost on the examples of the dynamic mode decomposition and invariant measure computation.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
<a href="/en/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koopman operator framework for control of complex nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Siam Journal on Applied Dynamical Systems
ISSN
1536-0040
e-ISSN
—
Volume of the periodical
21
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
2187-2214
UT code for WoS article
000913566000007
EID of the result in the Scopus database
2-s2.0-85138456903