G.H. Nedzhibov†
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.
MSC: 65P99, 37M02, 37L65
keywords: MDmethod, Online Dynamic mode decomposition, Koopman operator, Singular value decomposition, Equation-free.
DOI 10.56082/annalsarscimath.2023.1-2.229
†savin.treanta@upb.ro (1) Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania; (2) Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania; (3) Fundamental Sciences Applied in Engineering- Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania;
‡nita alina@yahoo.com (1) Department of Mathematical Methods and Models, University Politehnica of Bucharest, 060042 Bucharest, Romania; (2) Fundamental Sciences Applied in Engineering- Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania;
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
