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private:writeups:dmd
Assume we start with 2D data matrix, $Z$, with dimensions R and T. (R is space, T is time).
Define $X=Z(t)$ and $X'=Z(t+dt)$
Perform SVD on X to get spatial basis functions. $U,S,V^T = \text{SVD}(X)$
Define $A=(U^T \cdot X') \cdot \left (\frac{V}{S} \right)$
Find eivenvalues and eigenvectors. $\lambda, v = \text{eig} (A)$
spatial structure. $Bt = \left(X' \cdot \frac{V}{S} \right) \cdot v$
$\omega = \frac{ \text{log} \left| \lambda \right| }{dt}$
time evolution. Vandermonde, $M = e^{\omega \otimes t}$
private/writeups/dmd.txt · Last modified: 2020/11/27 19:11 by admin
