Working Paper Article Version 1 This version is not peer-reviewed

Randomized Projection Learning Method for Dynamic Mode Decomposition

Version 1 : Received: 22 September 2021 / Approved: 24 September 2021 / Online: 24 September 2021 (09:14:01 CEST)

A peer-reviewed article of this Preprint also exists.

Surasinghe, S.; Bollt, E.M. Randomized Projection Learning Method for Dynamic Mode Decomposition. Mathematics 2021, 9, 2803. Surasinghe, S.; Bollt, E.M. Randomized Projection Learning Method for Dynamic Mode Decomposition. Mathematics 2021, 9, 2803.

Journal reference: Mathematics 2021, 9, 2803
DOI: 10.3390/math9212803

Abstract

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension.

Keywords

Koopman Operator; Dynamic Mode Decomposition(DMD); Johnson-Lindenstrauss Lemma; Random Projection; Data-driven method

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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