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Séminaire de Mécanique d'Orsay

Le Jeudi 16 janvier 2020 à 14h00 - Salle de conférences du LIMSI

Data-driven methods in Koopman operator theory: linear identification of nonlinear ODEs and PDEs

Alexandre Mauroy
Department of Mathematics Namur Center for Complex Systems (naXys) Université de Namur Belgique

The Koopman operator provides an alternative description of nonlinear systems, which is not only linear but also amenable to data-driven analysis. In this talk, we will exploit this description in the context of nonlinear identification and parameter estimation for continuous-time systems. Since the generator of the semigroup of Koopman operators is directly connected to the underlying dynamics, identifying the linear generator is equivalent to identifying the nonlinear system. Using this systematic approach, we will report on two dual linear techniques that will be illustrated with several examples. Convergence properties will also be derived from classic results of operator semigroups theory. Finally, the proposed identification method will be extended to nonlinear PDEs by considering Koopman operator semigroups acting on a space of nonlinear functionals.

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