Residual Dynamic Mode Decomposition: A very easy way to get error bounds for your DMD computations

Research Abstract by Matt Colbrook, Cambridge University

Dynamic Mode Decomposition (DMD) and computations of spectral properties of Koopman operators have several open challenges. These include spurious (unphysical) modes, verifying Koopman mode decompositions (KMDs), and dealing with continuous spectra. Residual Dynamic Mode Decomposition (ResDMD) overcomes these challenges through the data-driven computation of residuals associated with the full infinite-dimensional Koopman operator. ResDMD computes spectra of general Koopman operators with error control (thus allowing us to detect spurious modes) and computes smoothed approximations of spectral measures (including continuous spectra) with explicit high-order convergence theorems. It also allows verification of dictionaries, KMDs, and related reduced-order models. Moreover, it is straightforward to use with existing DMD-type methods. This video describes the main idea and showcases the algorithm on several challenging examples.

http://www.damtp.cam.ac.uk/user/mjc249/pdfs/RigorousKoopman.pdf [damtp.cam.ac.uk]
http://www.damtp.cam.ac.uk/user/mjc249/pdfs/ResDMD.pdf [damtp.cam.ac.uk]

Видео Residual Dynamic Mode Decomposition: A very easy way to get error bounds for your DMD computations канала Steve Brunton