130 citations · 345 across the 38 of their papers we have counts for
6 papers · 1 filter
Computation and Verification of Spectra for Non-Hermitian Systems
Catherine Drysdale, Matthew Colbrook, Michael T. M. Woodley
We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Intro…
An Introductory Guide to Koopman Learning
Matthew J. Colbrook, Zlatko Drmač, Andrew Horning
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges.…
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…
Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces
Nicolas Boullé, Matthew J. Colbrook, Gustav Conradie
Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface t…
Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms
Sina Mohammad-Taheri, Matthew J. Colbrook, Simone Brugiapaglia
Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterativ…
Universal Methods for Nonlinear Spectral Problems
Matthew J. Colbrook, Catherine Drysdale
Nonlinear spectral problems arise across a range of fields, including mechanical vibrations, fluid-solid interactions, and photonic crystals. Discretizing infinite-dimensional nonl…