4 papers · 1 filter
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Matthew J. Colbrook, Igor MeziÄ, 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…
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…
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…