The project includes discussion about the Koopman operator, implemention the EDMD algorithm(Neural Network as well), testing on an example in the paper by Williams et al., and on a simple example in crowd dynamics. The final discussion of the results and presentation is also included here.
Budišić, M., Mohr, R., and Mezić, I. (2012).
Applied Koopmanism.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 22:047510.
Williams, M. O., Kevrekidis, I. G., and Rowley, C. W. (2015a).
A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition.
Journal of Nonlinear Science, 25(6):1307–1346.
Williams, M. O., Rowley, C. W., and Kevrekidis, I. G. (2015b).
A kernel-based method for data-driven koopman spectral analysis.
Journal of Computational Dynamics, 2(2):247–265.
Li, Q., Dietrich, F., Bollt, E. M., and Kevrekidis, I. G. (2017).
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(10):103111.
Mauroy, A. and Goncalves, J. (2017).
Koopman-based lifting techniques for nonlinear systems identification.
arXiv.
Dietrich, F., Thiem, T. N., and Kevrekidis, I. G. (2019).
On the koopman operator of algorithms.
arXiv.