130 citations · 345 across the 38 of their papers we have counts for
7 papers · 1 filter
Avoiding spectral pollution for transfer operators using residuals
April Herwig, Matthew J. Colbrook, Oliver Junge +2
Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional appro…
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Matthew J. Colbrook, Igor Mezić, Alexei Stepanenko
Many systems resist analytical modeling, making data-driven inference of dynamics important. Yet data-driven methods can fail to converge or generalize, leaving open a central ques…
Multiplicative Dynamic Mode Decomposition
Nicolas Boullé, Matthew J. Colbrook
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of…
Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators
Matthew J. Colbrook, Catherine Drysdale, Andrew Horning
We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolutio…
Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size
Matthew J. Colbrook
Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dime…
The Multiverse of Dynamic Mode Decomposition Algorithms
Matthew J. Colbrook
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dyn…