Clarifying the Effect of Mean Subtraction on Dynamic Mode Decomposition*
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Clarifying the Effect of Mean Subtraction on Dynamic Mode Decomposition*
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
<a href="/en/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotics and advanced industrial production</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
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
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Volume of the periodical
24
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
2318-2344
UT code for WoS article
001572373100003
EID of the result in the Scopus database
2-s2.0-105017591737