Summary
International Symposium on Nonlinear Theory and Its Applications
2022
Session Number:D1L-D
Session:
Number:D1L-D-02
Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition
Masih Haseli , Jorge Cort?s,
pp.622-622
Publication Date:12/12/2022
Online ISSN:2188-5079
Summary:
We provide several data-driven methods to identify Koopman eigenfunctions and invariant subspaces associated with unknown nonlinear systems. We show that by applying the well-known Extended Dynamic Mode Decomposition (EDMD) algorithm forward and backward in time, one can identify all Koopman eigenfunctions in an arbitrary finite-dimensional space of functions. Moreover, we provide an algorithm termed Symmetric Subspace Decomposition (SSD) that can identify the maximal Koopman-invariant subspace of any arbitrary finite-dimensional space of functions almost surely. In addition, we provide several extensions for the proposed algorithm to accommodate the scenario of large and streaming data sets as well as the approximation of Koopman-invariant subspaces with tunable level accuracy.