73 citations · 398 across the 44 of their papers we have counts for
5 papers · 1 filter
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
Matthew J. Colbrook, Qin Li, Ryan V. Raut +1
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectra…
Avoiding discretization issues for nonlinear eigenvalue problems
Matthew J. Colbrook, Alex Townsend
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue…
Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling
Annan Yu, Alex Townsend
Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a…
Elliptic PDE learning is provably data-efficient
Nicolas Boullé, Diana Halikias, Alex Townsend
PDE learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data. While deep learning models traditionally re…
Are sketch-and-precondition least squares solvers numerically stable?
Maike Meier, Yuji Nakatsukasa, Alex Townsend +1
Sketch-and-precondition techniques are efficient and popular for solving large least squares (LS) problems of the form with and . This i…