Sparsity Structures for Koopman and Perron-Frobenius Operators

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Sparsity Structures for Koopman and Perron-Frobenius Operators

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Sparsity Structures for Koopman and Perron-Frobenius Operators

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koncept Koopmanova operátoru pro řízení komplexních nelineárních dynamických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Siam Journal on Applied Dynamical Systems

ISSN

1536-0040

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

2187-2214

Kód UT WoS článku

000913566000007

EID výsledku v databázi Scopus

2-s2.0-85138456903