2 papers
math.DS2026
PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism
Matthew J. Colbrook, April Herwig, J. Nathan Kutz
Data-driven dynamics often asks how to linearize a nonlinear system. We ask instead: which observables should be advanced, and where should their futures live? This leads to Petrov…
math.DS2025
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…