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Data Driven Modal Decompositions: Analysis and Enhancements (CROSBI ID 288840)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Drmač, Zlatko ; Mezić, Igor ; Mohr, Ryan Data Driven Modal Decompositions: Analysis and Enhancements // SIAM journal on scientific computing, 40 (2018), 4; A2253, 33. doi: 10.1137/17m1144155

Podaci o odgovornosti

Drmač, Zlatko ; Mezić, Igor ; Mohr, Ryan

engleski

Data Driven Modal Decompositions: Analysis and Enhancements

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).

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

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Podaci o izdanju

40 (4)

2018.

A2253

33

objavljeno

1064-8275

1095-7197

10.1137/17m1144155

Povezanost rada

Matematika

Poveznice
Indeksiranost