PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism

PRONE (Petrov Regression Of Nonlinear Evolution) proposes a unified framework for learning dynamical systems by asking which observables should be advanced and where their futures should live. The method employs distinct trial and test dictionaries in a Petrov-Galerkin formulation, revealing that DMD, EDMD, SINDy, Koopman regression, sparse regression, and low-rank regression are all special cases of this construction. This provides a theoretical unification of popular data-driven dynamics discovery approaches.