Clarifying the Effect of Mean Subtraction on Dynamic Mode Decomposition*

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00388359" target="_blank" >RIV/68407700:21230/25:00388359 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/23M1569940" target="_blank" >https://doi.org/10.1137/23M1569940</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/23M1569940" target="_blank" >10.1137/23M1569940</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Clarifying the Effect of Mean Subtraction on Dynamic Mode Decomposition*

Popis výsledku v původním jazyce

Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven approximation, dynamic mode decomposition (DMD), has been extensively developed and deployed across a plethora of fields. In this work, we study the effect of subtracting the temporal mean on the DMD approximation for observables possessing only a finite number of Koopman modes. Preprocessing time-sequential training data by removing the temporal mean has been a point of contention in the companion matrix formulation of DMD. This stems from the potential of said preprocessing to render DMD equivalent to a temporal discrete Fourier transform (DFT). We prove that this equivalence is impossible when the training data is linearly consistent and the order of the DMD model exceeds the number of Koopman modes. Since model order and training set size are synonymous in this variant of DMD, the parity of DMD and DFT can, therefore, be indicative of inadequate training data.

Název v anglickém jazyce

Clarifying the Effect of Mean Subtraction on Dynamic Mode Decomposition*

Popis výsledku anglicky

Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven approximation, dynamic mode decomposition (DMD), has been extensively developed and deployed across a plethora of fields. In this work, we study the effect of subtracting the temporal mean on the DMD approximation for observables possessing only a finite number of Koopman modes. Preprocessing time-sequential training data by removing the temporal mean has been a point of contention in the companion matrix formulation of DMD. This stems from the potential of said preprocessing to render DMD equivalent to a temporal discrete Fourier transform (DFT). We prove that this equivalence is impossible when the training data is linearly consistent and the order of the DMD model exceeds the number of Koopman modes. Since model order and training set size are synonymous in this variant of DMD, the parity of DMD and DFT can, therefore, be indicative of inadequate training data.

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/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotika a pokročilá průmyslová výroba</a><br>

Návaznosti

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

Rok uplatnění

2025

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

24

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

2318-2344

Kód UT WoS článku

001572373100003

EID výsledku v databázi Scopus

2-s2.0-105017591737