Peter Schmid

Koopman analysis and the sparsity-promoting dynamic mode decomposition

Koopman analysis is a mathematical technique that embeds a nonlinear system into a linear framework for an infinite number of observables. This embedding is described by the spectrum (eigenvalues and eigenfunctions) of the Koopman operator. The dynamic mode decomposition is a computational method to extract these eigensolutions directly from data. The associated amplitudes for the expansion of the underlying physical process in Koopman modes are obtained from a sparsity-constrained convex optimisation problem. We will discuss the components of the full analysis and present a range of applications from fluid dynamics to illustrate the flexibility and effectiveness of Koopman spectral analysis.