engleski

Numerical aspects of the Koopman and the dynamic mode decomposition

The Dynamic Mode Decomposition (DMD, introduced by P. Schmid) has become a tool of trade in computational data driven analysis of complex dynamical systems, e.g. fluid flows, where it can be used to decompose the flow field into component fluid structures, called DMD modes, that describe the evolution of the flow. The DMD is deeply connected with the Koopman spectral analysis of nonlinear dynamical systems, and it can be considered as a computational device in the Koopman analysis framework. Its exceptional performance motivated developments of several modifications that make the DMD an attractive method for analysis and model reduction of nonlinear systems in data driven settings. In this talk, we will present our recent results on the numerical aspects of the DMD/Koopman analysis. We show how the state of the art numerical linear algebra can be deployed to improve the numerical performances in the cases that are usually considered notoriously ill-conditioned. Further, we show how even in the data driven setting, we can work with residual bounds, which allows error estimates for the computed modes.

Koopman mode decomposition, dynamic mode decomposition, numerical methods

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