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• W3120406975 abstract "This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space (X,d <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> ). Approximations are constructed in terms of reproducing kernel bases that are centered at samples taken along the system trajectory. It is proven that when the samples are dense in a certain type of smooth manifold M ⊆ X, the derived rates of convergence depend on the fill distance of samples along the trajectory in that manifold. Error bounds for projection-based and data-dependent approximations of the Koopman operator are derived in the paper. A discussion of how these bounds are realized in intrinsic and extrinsic approximation methods is given. Finally, a numerical example that illustrates qualitatively the convergence guarantees derived in the paper is given." @default.
• W3120406975 created "2021-01-18" @default.
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• W3120406975 date "2020-12-14" @default.
• W3120406975 modified "2023-10-16" @default.
• W3120406975 title "Intrinsic and Extrinsic Approximation of Koopman Operators over Manifolds" @default.
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• W3120406975 doi "https://doi.org/10.1109/cdc42340.2020.9304383" @default.
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