Speaker
Description
We present two themes from a recent development of the Dynamic Mode Decomposition (DMD).
First, the DMD is presented as a data driven Rayleigh-Ritz extraction
of spectral information. This (unlike the mere regression aspect) allows
for a better connection with the Koopman operator, and provides better understanding
of the dynamics under study. Computable residuals can be used to select
physically meaningful eigenvalues and modes, and to guide sparse representation
of the snapshot in the KMD (Koopman Mode Decomposition). We believe that this
is the proper approach to the DMD as a numerical toolbox for Koopman
operator based data driven analysis of nonlinear dynamics.
Then, we discuss the problem of ill-conditioned eigenvectors in the non-normal
case and show how the recently proposed Koopman-Schur decomposition can be used
both in the operator setting and in numerical computation.
