130 citations · 345 across the 38 of their papers we have counts for
9 papers · 1 filter
Computing Generalized Eigenfunctions in Rigged Hilbert Spaces
Matthew J. Colbrook, Andrew Horning, Tianyiwa Xie
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach…
Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response
Niccolò Zagli, Matthew Colbrook, Valerio Lucarini +2
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into i…
A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity
Catherine Drysdale, Matthew J. Colbrook
The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathe…
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
Matthew J. Colbrook, Mark Embree, Jake Fillman
Many structures in mathematical physics and dynamics exhibit intricate fractal geometry. Such behavior appears prominently in quantum mechanics and materials science through spectr…
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…
On the Convergence of Hermitian Dynamic Mode Decomposition
Nicolas Boullé, Matthew J. Colbrook
We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that appr…