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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.DS2026
Finding Koopman Invariant Subspaces via Personalized PageRank
Hyukpyo Hong, Qin Li, Matthew J. Colbrook +1
Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploi…
math.DS2026
Weighted Birkhoff Averages Accelerate Data-Driven Methods
Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages c…