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Prediction capabilities of data-driven operator based algorithms on some classes of differential equations

Nowadays, the possibilities of predicting the behavior of different dynamical systems are in the focus of the research in many scientific disciplines. In this paper we consider the dynamical systems generated by chosen nonlinear and non-autonomous ordinary differential equations. These dynamical systems are approximated by using the Koopman operator based data-driven algorithms applied on the observable functions evaluated at some finite set of the system states. The learned model is then used as a prediction tool to envisage the values of the observable functions in the future system states. The aim of this work is to test and analyze the prediction capabilities of such data-driven algorithms on simple examples in order to make a foundation for understanding their behavior in the prediction task in more complex systems, even in those for which the associated differential equations modeling the system are not known.

differential equations ; Koopman operator, data-driven algorithms, DMD algorithm, prediction

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