The paper proves a forward-backward EDMD condition that identifies Koopman eigenfunctions, and presents SSD and SSSD algorithms that provably find the maximal Koopman-invariant subspace in a dictionary's span.
Koopman operator framework for constrained state estimation,
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Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition
The paper proves a forward-backward EDMD condition that identifies Koopman eigenfunctions, and presents SSD and SSSD algorithms that provably find the maximal Koopman-invariant subspace in a dictionary's span.