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The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery.
Susuki, Y., & Mezic, I. (2011). Nonlinear Koopman modes and coherency identification of coupled swing dynamics. IEEE Transactions on Power Systems, 26(4), 1894-1904
1904
Earlier work this paper cites.
Koopman, B. O. (1931). Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences, 17(5), 315-318
1931
Earlier work this paper cites.
Srivastava, N., Hinton, G. E., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014). Dropout: a simple way to prevent neural networks from overfitting. Journal of machine learning research, 15(1), 1929-1958
1958
Earlier work this paper cites.
Kowalski, K., & Steeb, W. H. (1991). Nonlinear dynamical systems and Carleman linearization. World Scientific
1991
Earlier work this paper cites.
Fouad, Abdel-Azia, and Vijay Vittal. Power system transient stability analysis using the transient energy function method. Pearson Education, 1991
1991
Earlier work this paper cites.
Kundur, P. (1994). Power system stability and control (Vol. 7). N. J. Balu, & M. G. Lauby (Eds.). New York: McGraw-hill
1994
Earlier work this paper cites.
Grainger, J. J. S., Grainger, W. D. J. J., & Stevenson, W. D. (1994). Power system analysis
1994
Earlier work this paper cites.
Mezic, I., & Banaszuk, A. (2004). Comparison of systems with complex behavior. Physica D: Nonlinear Phenomena, 197(1), 101-133
2004
Earlier work this paper cites.
Mezic, I. (2005). Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics, 41(1), 309-325
2005
Earlier work this paper cites.
Gona̧lves, J., & Warnick, S. (2008). Necessary and sufficient conditions for dynamical structure reconstruction of LTI networks. IEEE Transactions on Automatic Control, 53(7), 1670-1674
2008
Cited alongside, same era.
Rowley, C. W., Mezi?, I., Bagheri, S., Schlatter, P., & Henningson, D. S. (2009). Spectral analysis of nonlinear flows. Journal of fluid mechanics, 641, 115-127
2009
Cited alongside, same era.
Huang, Z., Chen, Y., & Nieplocha, J. (2009, July). Massive contingency analysis with high performance computing. In Power & Energy Society General Meeting, 2009. PES’09. IEEE (pp. 1-8). IEEE
2009
Cited alongside, same era.
Duchi, J., Hazan, E., & Singer, Y. (2011). Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12(Jul), 2121-2159
2011
Cited alongside, same era.
Williams, M. O., & Kevrekidis, I. G., & Rowley, C. W. (2015). A data-driven approximation of the koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, 25(6), 1307-1346. Chicago
2015
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Daniels, B. C., & Nemenman, I. (2015). Efficient inference of parsimonious phenomenological models of cellular dynamics using S-systems and alternating regression. PloS one, 10(3), e0119821
2015
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Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932-3937. Chicago
2016
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Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2016). Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems, 15(1), 142-161
2016
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Bengio, Yoshua, and Olivier Delalleau. "On the expressive power of deep architectures." International Conference on Algorithmic Learning Theory. Springer Berlin Heidelberg, 2011
2011
Cited alongside, same era.
Susuki, Y., & Mezic, I. (2012). Nonlinear Koopman modes and a precursor to power system swing instabilities. IEEE Transactions on Power Systems, 27(3), 1182-1191
2012
Cited alongside, same era.
Bengio, Y., Mesnil, G., Dauphin, Y., & Rifai, S. (2013). Better Mixing via Deep Representations. In ICML (1) (pp. 552-560)
2013
Cited alongside, same era.
2014
Cited alongside, same era.
Williams, M. O., Hemati M. S., Dawson S. T., Kevrekidis I. G. & Rowley, C. W. (2016). Extending Data-Driven Koopman Analysis to Actuated Systems. IFAC-PapersOnLine, 49(18), 704-709
2016
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2016
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2016
Later among the works it cites.