Dynamic mode decomposition for analytic maps
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
Abstract
Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron–Frobenius and Koopman operators defined on suitable Hardy-Hilbert spaces when the method is applied to classes of analytic maps. Our findings elucidate the interpretation of the spectra obtained by EDMD for complex dynamical systems. We illustrate our results by numerical simulations for analytic maps.
Topics & Concepts
Dynamic mode decompositionDynamical systems theoryInterpretation (philosophy)Hilbert spaceDecompositionClass (philosophy)MathematicsMode (computer interface)Applied mathematicsAnalytic functionPure mathematicsStatistical physicsMathematical analysisComputer sciencePhysicsArtificial intelligenceQuantum mechanicsMachine learningBiologyEcologyOperating systemProgramming languageModel Reduction and Neural NetworksFluid Dynamics and Turbulent FlowsFluid Dynamics and Vibration Analysis