A dynamic mode decomposition technique for the analysis of non–uniformly sampled flow data

On Alternative Algorithms for Computing Dynamic Mode Decomposition

“…In this case, matrix Ā defined by ( 16) is in type of the Frobenius companion matrix and it relates the data sets exactly Y = X Ā, even if the data are generated by nonlinear dynamics. Moreover, in this case, the projected DMD modes (23) and exact DMD modes (22) are identical. Theorem 4.…”

“…Theorem 4. If the columns of Y are spanned by those of X the DMD modes (23) are eigenvectors of Ā defined by (17).…”

“…Since its initial introduction, along with its wide application in various fields, the DMD method has undergone various modifications and improvements. For some recent results on the topics of DMD for non-uniformly sampled data, higher order DMD method, parallel implementations of DMD and some derivative DMD techniques, we recommend to the reader [19][20][21][22][23][24][25][26]; see also [27][28][29][30][31][32][33].…”

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…Some of the available methods for formulating data-based approximations and projections include (i) the proper orthogonal decomposition (POD) (a.k.a. principle component analysis (PCA) or the Karhunen-Loève expansion) [26,27,28,29,30,31,32], (ii) the dynamic mode decomposition (DMD) [33,34,35,36,37,38], (iii) deep neural networks (DNNs) [39], (iv) the proper generalized decomposition (PGD) [40], (v) balanced truncation [41] and (vi) reduced basis methods [42].…”

Extended Online DMD and Weighted Modifications for Streaming Data Analysis

“…For a review of the DMD literature, we refer the reader to [13][14][15][16][17]. For some recent modifications of DMD for non-uniformly sampled data, the higher-order DMD method, parallel implementations of DMD, and some derivative DMD techniques, we recommend [18][19][20][21][22][23][24][25][26][27][28][29].…”