We will report on two dual techniques based on Koopman operator theory for identifying nonlinear dynamical systems from (low-sampled) datasets. These methods will be illustrated with several examples and convergence properties will be derived from classic results of operator semigroups theory. The proposed techniques will also be extended to the identification of nonlinear PDEs (from low-sampled data) by considering Koopman operator semigroups acting on nonlinear functionals. Finally, the duality property of the two methods will be recovered through a two-level lifting, i.e. the “Koopman operator of the Koopman operator semigroup”.
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