Naslov
Data Driven Modal Decompositions: Analysis and Enhancements

Autori
Drmač, Zlatko ; Mezić, Igor ; Mohr, Ryan

Izvornik
SIAM journal on scientific computing (1064-8275) 40 (2018), 4; A2253, 33

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
dynamic mode decomposition, Koopman operator, Krylov subspaces, optimal mode decomposition, proper orthogonal decomposition, Rayleigh-Ritz approximation, Schur decomposition, weighted inner product

Sažetak
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of applications in applied sciences and engineering. Its exceptional performance triggered developments of several modifications that make the DMD an attractive method in data driven framework. This work offers improvements of the DMD to make it more reliable, and to enhance its functionality. In particular, data driven formula for the residuals allows selection of the Ritz pairs, thus providing more precise spectral information of the underlying Koopman operator, and the well-known technique of refining the Ritz vectors is adapted to data driven scenarios. Further, the DMD is formulated in a more general setting of weighted inner product spaces, and the consequences for numerical computation are discussed in detail. Numerical experiments illustrate the advantages of the proposed method, designated as DDMD\_RRR (Refined Rayleigh Ritz Data Driven Modal Decomposition).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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