19 References
Argyris, John, Gunter Faust, Maria Haase, and Rudolf Friedrich. 2017.
Die Erforschung Des Chaos. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-54546-1.
Arthur, David, and Sergei Vassilvitskii. 2006. “K-Means++: The
Advantages of Careful Seeding.” Stanford.
Bishop, Christopher. 2006. Pattern Recognition and Machine
Learning. Springer. https://www.microsoft.com/en-us/research/publication/pattern-recognition-machine-learning/.
Boeing, Geoff. 2016. “Visual Analysis of Nonlinear Dynamical
Systems: Chaos, Fractals, Self-Similarity and the Limits of
Prediction.” Systems 4 (4): 37. https://doi.org/10.3390/systems4040037.
Brunton, Steven L, Joshua L Proctor, and J Nathan Kutz. 2016.
“Sparse Identification of Nonlinear Dynamics with Control
(SINDYc).” IFAC-PapersOnLine 49 (18): 710–15.
Brunton, Steven, and J Kutz. 2019. “Data-Driven Science and
Engineering.” Cambridge University Press. https://doi.org/10.1017/9781108380690.
Butt, Javed. 2021. “Development of a Module for Mission Analysis
for a Gradient-Based Aerodynamic Shape Optimization Process.” TU
Braunschweig. https://elib.dlr.de/144285/.
CAO, Ying, Qi-Guang MIAO, Jia-Chen LIU, and Lin GAO. 2013.
“Advance and Prospects of AdaBoost Algorithm.” Acta
Automatica Sinica 39 (6): 745–58. https://doi.org/https://doi.org/10.1016/S1874-1029(13)60052-X.
Chen, Guanrong, and Tetsushi Ueta. 1999. “Yet Another Chaotic
Attractor.” International Journal of Bifurcation and
Chaos 9 (07): 1465–66.
Devia Narvaez, Diana, German Velez, and Diego Devia Narvaez. 2018.
“Bifurcation Analysis of the van Der Pol Oscillator.”
Contemporary Engineering Sciences 11 (85): 4245–52. https://doi.org/10.12988/ces.2018.88389.
Fernex, Daniel, Bernd R. Noack, and Richard Semaan. 2021.
“Cluster-Based Network Modelingfrom Snapshots to
Complex Dynamical Systems.” Science Advances 7 (25). https://doi.org/10.1126/sciadv.abf5006.
Fernex, Daniel, Richard Semaan, and Bernd Noack. 2021.
“Generalized Cluster-Based Network Model for an Actuated Turbulent
Boundary Layer.” In AIAA Scitech 2021 Forum. American
Institute of Aeronautics; Astronautics. https://doi.org/10.2514/6.2021-1333.
Frochte, Jörg. 2020. Maschinelles Lernen. Carl Hanser Verlag
GmbH & Co. KG. https://doi.org/10.3139/9783446463554.
Gerbrands, Jan J. 1981. “On the Relationships Between SVD, KLT and
PCA.” Pattern Recognition 14 (1-6): 375–81.
Grebogi, Celso, Edward Ott, Steven Pelikan, and James A. Yorke. 1984.
“Strange Attractors That Are Not Chaotic.” Physica D:
Nonlinear Phenomena 13 (1): 261–68. https://doi.org/https://doi.org/10.1016/0167-2789(84)90282-3.
Harris, Charles R., K. Jarrod Millman, Stéfan J. van der Walt, Ralf
Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, et al. 2020.
“Array Programming with NumPy.”
Nature 585 (7825): 357–62. https://doi.org/10.1038/s41586-020-2649-2.
Hunter, J. D. 2007. “Matplotlib: A 2D Graphics
Environment.” Computing in Science & Engineering 9
(3): 90–95. https://doi.org/10.1109/MCSE.2007.55.
Inc., Plotly Technologies. 2015. “Collaborative Data
Science.” Montreal, QC: Plotly Technologies Inc. 2015. https://plot.ly.
Kaiser, Eurika, Bernd R Noack, Laurent Cordier, Andreas Spohn, Marc
Segond, Markus Abel, Guillaume Daviller, Jan Östh, Siniša Krajnović, and
Robert K Niven. 2014. “Cluster-Based Reduced-Order Modelling of a
Mixing Layer.” Journal of Fluid Mechanics 754: 365–414.
Kaptanoglu, Alan, Brian De Silva, Urban Fasel, Kadierdan Kaheman, Andy
Goldschmidt, Jared Callaham, Charles Delahunt, et al. 2022.
“PySINDy: A Comprehensive Python Package for Robust Sparse System
Identification.” Journal of Open Source Software 7 (69):
3994. https://doi.org/10.21105/joss.03994.
“K-Means Finding Set of Initial Points.” n.d. https://theory.stanford.edu/~sergei/slides/BATS-Means.pdf.
“K-Means++ Visual Explanation.” n.d. https://theory.stanford.edu/~sergei/slides/BATS-Means.pdf.
Kutz, Prof. J. Nathan. 2022. “AMATH 568Advanced Differential
Equations: Asymptotics & Perturbations.”
Lambe, Andrew B., and Joaquim R. R. A. Martins. 2012. “Extensions
to the Design Structure Matrix for the Description of Multidisciplinary
Design, Analysis, and Optimization Processes.” Structural and
Multidisciplinary Optimization 46: 273–84. https://doi.org/10.1007/s00158-012-0763-y.
Langer, Stefan, Axel Schwöppe, and Norbert Kroll. 2014. “The DLR
Flow Solver TAU - Status and Recent Algorithmic Developments.” In
52nd Aerospace Sciences Meeting. https://elib.dlr.de/90979/.
Lee, Daniel D, and H Sebastian Seung. 1999. “Learning the Parts of
Objects by Non-Negative Matrix Factorization.” Nature
401 (6755): 788–91.
Li, Chunbiao, Ihsan Pehlivan, Julien Clinton Sprott, and Akif Akgul.
2015. “A Novel Four-Wing Strange Attractor Born in
Bistablity.” IEICE Electronics Express 12 (February). https://doi.org/10.1587/elex.12.20141116.
Li, Hao, Daniel Fernex, Richard Semaan, Jianguo Tan, Marek Morzyński,
and Bernd R Noack. 2021. “Cluster-Based Network Model.”
Journal of Fluid Mechanics 906.
Lloyd, Stuart. 1982. “Least Squares Quantization in PCM.”
IEEE Transactions on Information Theory 28 (2): 129–37.
Lorenz, Edward N. 1963. “Deterministic Nonperiodic Flow.”
Journal of Atmospheric Sciences 20 (2): 130–41.
Lu, Jinhu, and Guanrong Chen. 2002. “A New Chaotic Attractor
Coined.” I. J. Bifurcation and Chaos 12 (March): 659–61.
https://doi.org/10.1142/S0218127402004620.
Pedregosa, F., G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O.
Grisel, M. Blondel, et al. 2011. “Scikit-Learn: Machine Learning
in Python.” Journal of Machine Learning
Research 12: 2825–30.
Pierzyna, Maximilian. 2021. “Control-Oriented Cluster-Basednetwork
Modeling.” Research report, TU Braunschweig.
Protas, Bartosz, Bernd R Noack, and Jan Östh. 2015. “Optimal
Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows.”
Journal of Fluid Mechanics 766: 337–67.
“pySindy’s Remark on RK45 Vs. LSODA.” 2022. https://pysindy.readthedocs.io/en/latest/examples/1_feature_overview.html.
Rasmussen, Carl Edward. 2004. “Gaussian Processes in Machine
Learning.” In Advanced Lectures on Machine Learning,
63–71. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-28650-9_4.
Rickles, D., P. Hawe, and A. Shiell. 2007. “A Simple Guide to
Chaos and Complexity.” Journal of Epidemiology
& Community Health 61 (11): 933–37. https://doi.org/10.1136/jech.2006.054254.
Rössler, O. E. 1976. “An Equation for Continuous Chaos.”
Physics Letters A 57 (5): 397–98. https://doi.org/https://doi.org/10.1016/0375-9601(76)90101-8.
Silva, Brian de, Kathleen Champion, Markus Quade, Jean-Christophe
Loiseau, J. Kutz, and Steven Brunton. 2020. “PySINDy:
A Python Package for the Sparse Identification of Nonlinear Dynamical
Systems from Data.” Journal of Open Source Software 5
(49): 2104. https://doi.org/10.21105/joss.02104.
SPROTT, Julien. 2020. “Do We Need More Chaos Examples?”
Chaos Theory and Applications 2 (2): 49–51.
Strogatz, Steven. 2019. Nonlinear Dynamics and Chaos : With
Applications to Physics, Biology, Chemistry, and Engineering. Boca
Raton: CRC Press.
Taylor, Robert LV. 2010. “Attractors: Nonstrange to
Chaotic.” Society for Industrial and Applied Mathematics,
Undergraduate Research Online, 72–80.
Tibshirani, Robert. 1996. “Regression Shrinkage and Selection via
the Lasso.” Journal of the Royal Statistical Society: Series
B (Methodological) 58 (1): 267–88.
Vaidyanathan, Sundarapandian, Aceng Sambas, Sen Zhang, Yicheng Zeng,
Mohamad Afendee Mohamed, and Mustafa Mamat. 2019. “A New
Two-Scroll Chaotic System with Two Nonlinearities: Dynamical Analysis
and Circuit Simulation.” Telkomnika 17 (5): 2465–74.
Van Rossum, Guido, and Fred L. Drake. 2009. Python 3 Reference
Manual. Scotts Valley, CA: CreateSpace.
Virtanen, Pauli, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler
Reddy, David Cournapeau, Evgeni Burovski, et al. 2020. “SciPy 1.0: Fundamental Algorithms for
Scientific Computing in Python.” Nature Methods
17: 261–72. https://doi.org/10.1038/s41592-019-0686-2.
“Wikipedia Entry on Chaos Theory.” 2021. https://en.wikipedia.org/wiki/Chaos_theory.
Zheng, Peng, Travis Askham, Steven L Brunton, J Nathan Kutz, and
Aleksandr Y Aravkin. 2018. “A Unified Framework for Sparse Relaxed
Regularized Regression: SR3.” IEEE Access 7: 1404–23.