ONLINE DYNAMIC MODE DECOMPOSITION: AN ALTERNATIVE APPROACH FOR LOW RANK DATASETS

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2023-01-01 DOI:10.56082/annalsarscimath.2023.1-2.229

G.H. Nedzhibov

引用次数: 0

Abstract

In this study, we provide an alternative approach for computing the dynamic mode decomposition (DMD) in real-time for streaming datasets. It is a low-storage method that updates the DMD approximation of a given dynamic as new data becomes available. Unlike the standard online DMD method, which is applicable only to overconstrained and full-rank datasets, the new method is applicable for both overconstrained and underconstrained datasets. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations and is entirely data-driven. Several numerical examples are presented to demonstrate the performance of the method.

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在线动态模式分解:低秩数据集的替代方法

在这项研究中，我们提供了一种替代方法来实时计算流数据集的动态模式分解(DMD)。这是一种低存储方法，当新数据可用时更新给定动态的DMD近似值。与标准的在线DMD方法只适用于过度约束和全秩数据集不同，新方法既适用于过度约束数据集，也适用于欠约束数据集。该方法是无方程的，因为它不需要了解潜在的控制方程，并且完全是数据驱动的。算例验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.