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.
About the Speaker:
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. His interests are in computational fluid dynamics, hydrodynamic stability, flow control, model reduction, optimization and data-based flow analysis.