A Matlab library that implements the cluster-based reduced-order modeling (CROM) strategy for time series data and provides tools for its analysis. For details see Kaiser et. al (2016) [JFM, arXiv].
Apply CROM to time series data of the chaotic Lorenz system
dx/dt = sigma (y-x)
dy/dt = x (rho-z) - y
dz/dt = x y - beta z
with sigma = 10, rho=28, and beta=8/3.
This is the phase plot of the time series data. Below the clustered Lorenz attractor and the associated transition probability matrix are displayed.
| Voronoi diagram | Transition matrix |
|---|---|
 |
 |
- Run the example.
- Folder structure:
CROM
-- src : source files
-- docs : documentation
-- examples : execution files, results in 'output'
- Requirements: Matlab's Statistics and Machine Learning Toolbox for k-means algorithm
- Add source path to Matlab's search path, e.g., using
addpath('PathToCROM/matCROM/src/')
The code is published under the CiteMe OSS license. See the LICENSE file for details.
E. Kaiser, B. R. Noack, L. Cordier, A. Spohn, M. Segond, M. Abel, G. Daviller, J. Östh, S. Krajnović and R. K. Niven. Cluster-based reduced-order modelling of a mixing layer. Journal of Fluid Mechanics, 754, pp. 365-414, 2014. [JFM, arXiv]