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The kernel perspective on dynamic mode decomposition

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arxiv 2106.00106 v3 pith:QYPHZFQA submitted 2021-05-31 math.FA cs.LGcs.SYeess.SY

Efrain Gonzalez , Moad Abudia , Michael Jury , Rushikesh Kamalapurkar , Joel A. Rosenfeld This is my paper · ORCID
classification math.FAcs.LGcs.SYeess.SY
keywords koopmanoperatorsassumptionskerneldecompositiondynamiceigenfunctionsmanuscript
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This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and compactness of Koopman operators. Counterexamples that illustrate restrictiveness of the assumptions are provided for each of the assumptions. In particular, this manuscript proves that the native reproducing kernel Hilbert space (RKHS) of the Gaussian RBF kernel function only supports bounded Koopman operators if the dynamics are affine. In addition, a new framework for DMD, that requires only densely defined Koopman operators over RKHSs is introduced, and its effectiveness is demonstrated through numerical examples.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces

    math.NA 2025-06 accept novelty 8.0 of 10

    New convergent algorithms with error control and matching impossibility bounds for Koopman and Perron-Frobenius spectral computations on RKHSs.

  2. On the lattice property of the Koopman operator spectrum

    math.DS 2025-07 reject novelty 5.0 of 10

    The claimed multiplicative lattice property of the Koopman spectrum on L2 is false; the theorem is disproved by a simple example.

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