Residual-Dynamic-Mode-Decomposition

Computation of spectral properties of Koopman operators associated with discrete-time autonomous dynamical systems. Highlights include: verified computation of spectra with error control (and avoidance of spurious modes) and computation of spectral measures with explicit high-order convergence.

This repository will grow as further papers are written and if you are interested in collaborating, please get in touch at: m.colbrook@damtp.cam.ac.uk

The code includes "main_routines" that are used across the papers (see that subfolder for the additional README file). Each paper has a gallery of examples.

To get started on a simple example, try the file "Duffing_example.m"

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

Code for the papers:

1. M.J. Colbrook, A. Townsend, "Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems" in "Examples_gallery_1". 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} }

2. M.J. Colbrook, L. Ayton, M. Szőke, "Residual Dynamic Mode Decomposition: Robust and verified Koopmanism" in "Examples_gallery_2". Paper can be found here: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/residual-dynamic-mode-decomposition-robust-and-verified-koopmanism
   Please cite using the following bibtex: @article{colbrook2023residual, title={Residual dynamic mode decomposition: robust and verified {K}oopmanism}, author={Colbrook, Matthew J and Ayton, Lorna J and Sz{\H{o}}ke, M{'a}t{'e}}, journal={Journal of Fluid Mechanics}, volume={955}, pages={A21}, year={2023}, publisher={Cambridge University Press} }

3. M.J. Colbrook, Q. Li, R.V. Raut, A. Townsend, "Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems" in "Examples_gallery_3". Paper can be found here: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/residual-dynamic-mode-decomposition-robust-and-verified-koopmanism
   Please cite using the following bibtex: @article{colbrook2024beyond, title={Beyond expectations: residual dynamic mode decomposition and variance for stochastic dynamical systems}, author={Colbrook, Matthew J and Li, Qin and Raut, Ryan V and Townsend, Alex}, journal={Nonlinear Dynamics}, volume={112}, number={3}, pages={2037--2061}, year={2024}, publisher={Springer} }

4. M.J. Colbrook, "Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size" in "Examples_gallery_4".

Datasets (needed for some of the examples) can be found here: https://www.dropbox.com/sh/xj59e5in7dfsobi/AAAfkxqa1x9WFSTgrvqoqqRqa?dl=0

Some of the code for setting up the examples makes use of Chebfun, which can be found at https://www.chebfun.org/.