Code for riggedDMD: generalized eigenfunction expansions (and spectral measures) of Koopman operators
Computation of generalized eigenfunctios and spectral measures of Koopman operators associated with discrete-time autonomous dynamical systems. The code includes "main_routines" and a gallery of examples.
For a pedagogical review of DMD methods, including code, see the repository: https://github.com/MColbrook/DMD-Multiverse
For measure-preserving EDMD, see the repository: https://github.com/MColbrook/Measure-preserving-Extended-Dynamic-Mode-Decomposition
For residual DMD, see the repository: https://github.com/MColbrook/Residual-Dynamic-Mode-Decomposition
Please cite the following papers:
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M.J. Colbrook, C. Drysdale, A. Horning "Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators".
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M.J. Colbrook, "The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems".
Paper can be found here: https://www.damtp.cam.ac.uk/user/mjc249/pdfs/mpEDMD.pdf
Please cite using the following bibtex: @article{colbrook2023mpedmd, title={The mp{EDMD} algorithm for data-driven computations of measure-preserving dynamical systems}, author={Colbrook, Matthew J.}, journal={SIAM Journal on Numerical Analysis}, volume={61}, number={3}, pages={1585--1608}, year={2023}, publisher={SIAM} } -
M.J. Colbrook, A. Townsend, "Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems".
Paper can be found here: http://www.damtp.cam.ac.uk/user/mjc249/pdfs/RigorousKoopman.pdf
Please cite using the following bibtex: @article{colbrook2024rigorous, title={Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems}, author={Colbrook, Matthew J and Townsend, Alex}, journal={Communications on Pure and Applied Mathematics}, volume={77}, number={1}, pages={221--283}, year={2024}, publisher={Wiley Online Library} }