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Mathematics Colloquium - Koopman analysis and dynamic modes

October 29, 2019 @ 4:00 pm - 5:00 pm MDT

Dr. Peter Schmid
Chair Professor of Applied Mathematics and Mathematical Physics Imperial College London
October 29, 2019 at 4:00-5:00pm in ILC 402

Koopman analysis and dynamic modes

Koopman analysis is a mathematical technique that embeds nonlinear dynamical systems into a linear framework
based on a sequence of observables of the state vector. Computing the proper embeddings that result in a closed
linear system requires the extraction of the eigenfunctions of the Koopman operator from data. Dynamic modes
approximate these eigenfunctions via a tailored data-matrix decomposition. The associated spectrum of this
decomposition is given by a convex optimization problem that balances data-conformity with sparsity of the
spectrum. The Koopman-dynamic-mode process will be discussed and illustrated on physical examples.


Peter Schmid is Chair Professor of Applied Mathematics and Mathematical Physics at
Imperial College London. He obtained his PhD in Mathematics from MIT and held faculty and
research positions at the University of Washington in Seattle, the French National Research
Agency (CNRS) and the Ecole Polytechnique in Paris. He is a fellow of the American Physical
Society, Gordon and Betty Moore Distinguished Scholar at Caltech, an Overseas Fellow of
Churchill College (Cambridge University), and the recipient of the French “Chaire
d’excellence” award and the Alexander von Humboldt Research Fellowship. His interests are
in computational fluid dynamics, hydrodynamic stability, flow control, model reduction,
optimization and data-based flow analysis.

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