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Measure-preserving-Extended-Dynamic-Mode-Decomposition

General-purpose code and examples for the mpEDMD algorithm. Data-driven computation of spectral properties of Koopman operators associated with arbitrary measure-preserving dynamical systems.

Highlights include: convergence to spectral properties of Koopman operator, measure-preserving discretization, enhanced robustness to noise, and improved prediction and qualitative behavior of the Koopman mode decomposition. The algorithm is versatile and can work with any choice of dictionary or any shape/format of the dataset.

The reference paper can be found here:
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
Please send comments and suggestions to: m.colbrook@damtp.cam.ac.uk
If you use this method, please cite with 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} }

The code includes main routines mpEDMD (old) and mpEDMDqr (latest), as well as the three examples from the paper. To get started, try the simple example in Lorenz_simple_example.m Other examples will be added in the future. If you have an example and want to add it, please get in touch!

Datasets (needed for turbulent flow example) 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/.