English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a parallel data-driven strategy to identify finite-dimensionalfunctional spaces invariant under the Koopman operator associated to an unknowndynamical system. We build on the Symmetric Subspace Decomposition (SSD)algorithm, a centralized method that under mild conditions on data samplingprovably finds the maximal Koopman-invariant subspace and all Koopmaneigenfunctions in an arbitrary finite-dimensional functional space. A networkof processors, each aware of a common dictionary of functions and equipped witha local set of data snapshots, repeatedly interact over a directedcommunication graph. Each processor receives its neighbors' estimates of theinvariant dictionary and refines its estimate by applying SSD with its localdata on the intersection of the subspaces spanned by its own dictionary and theneighbors' dictionaries. We identify conditions on the network topology toensure the algorithm identifies the maximal Koopman-invariant subspace in thespan of the original dictionary, characterize its time, computational, andcommunication complexity, and establish its robustness against communicationfailures.

Parallel Learning of Koopman Eigenfunctions and Invariant Subspaces For Accurate Long-Term Prediction