Koopman Theory for Partial Differential Equations
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[1] Benjamin Peherstorfer,et al. Detecting and Adapting to Parameter Changes for Reduced Models of Dynamic Data-driven Application Systems , 2015, ICCS.
[2] Bernd R. Noack,et al. Cluster-based reduced-order modelling of a mixing layer , 2013, Journal of Fluid Mechanics.
[3] Athanasios C. Antoulas,et al. Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.
[4] B. O. Koopman,et al. Hamiltonian Systems and Transformation in Hilbert Space. , 1931, Proceedings of the National Academy of Sciences of the United States of America.
[5] Steven L. Brunton,et al. Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems , 2013, SIAM J. Appl. Dyn. Syst..
[6] S. Brunton,et al. Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.
[7] Clarence W. Rowley,et al. A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition , 2014, Journal of Nonlinear Science.
[8] I. Mezić,et al. Applied Koopmanism. , 2012, Chaos.
[9] Frank Noé,et al. A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems , 2012, Multiscale Model. Simul..
[10] Frank Noé,et al. Variational Approach to Molecular Kinetics. , 2014, Journal of chemical theory and computation.
[11] S. Frick,et al. Compressed Sensing , 2014, Computer Vision, A Reference Guide.
[12] I. Mezić,et al. Analysis of Fluid Flows via Spectral Properties of the Koopman Operator , 2013 .
[13] W. Steeb,et al. Nonlinear dynamical systems and Carleman linearization , 1991 .
[14] I. Mezić,et al. Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.
[15] Willi-Hans Steeb,et al. Non-linear autonomous systems of differential equations and Carleman linearization procedure , 1980 .
[16] Andrzej Banaszuk,et al. Comparison of systems with complex behavior , 2004 .
[17] Stefan Klus,et al. On the numerical approximation of the Perron-Frobenius and Koopman operator , 2015, 1512.05997.
[18] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[19] Charbel Farhat,et al. Real-time solution of computational problems using databases of parametric linear reduced-order models with arbitrary underlying meshes , 2015 .
[20] Clarence W. Rowley,et al. A Kernel Approach to Data-Driven Koopman Spectral Analysis , 2014 .
[21] Steven L. Brunton,et al. Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.
[22] Stephen P. Banks,et al. Infinite-dimensional Carleman linearization, the Lie series and optimal control of non-linear partial differential equations , 1992 .
[23] Matthew O. Williams,et al. A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis , 2014, 1411.2260.
[24] Steven L. Brunton,et al. Dynamic mode decomposition - data-driven modeling of complex systems , 2016 .
[25] Benjamin Peherstorfer,et al. Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates , 2015, SIAM J. Sci. Comput..
[26] I. Mezić. Spectral Properties of Dynamical Systems, Model Reduction and Decompositions , 2005 .
[27] Schuster,et al. Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.
[28] P. Schmid,et al. Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.
[29] Steven L. Brunton,et al. On dynamic mode decomposition: Theory and applications , 2013, 1312.0041.
[30] J. Nathan Kutz,et al. Mode-Locked Soliton Lasers , 2006, SIAM Rev..
[31] J. Burgers. A mathematical model illustrating the theory of turbulence , 1948 .
[32] Petros Boufounos,et al. Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows , 2015, SIAM J. Appl. Dyn. Syst..
[33] Steven L. Brunton,et al. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control , 2015, PloS one.
[34] Michael Rabadi,et al. Kernel Methods for Machine Learning , 2015 .
[35] J. Cole. On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .
[36] Bernhard Schölkopf,et al. A kernel view of the dimensionality reduction of manifolds , 2004, ICML.
[37] Hao Wu,et al. Data-Driven Model Reduction and Transfer Operator Approximation , 2017, J. Nonlinear Sci..
[38] G. Baudat,et al. Kernel-based methods and function approximation , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).
[39] B. O. Koopman,et al. Dynamical Systems of Continuous Spectra. , 1932, Proceedings of the National Academy of Sciences of the United States of America.
[40] B. R. Noack,et al. Closed-Loop Turbulence Control: Progress and Challenges , 2015 .
[41] A. Majda. Challenges in Climate Science and Contemporary Applied Mathematics , 2012 .
[42] Benjamin Peherstorfer,et al. Dynamic data-driven reduced-order models , 2015 .
[43] H. Sompolinsky,et al. Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis. , 2012, Annual review of neuroscience.
[44] Toni Giorgino,et al. Identification of slow molecular order parameters for Markov model construction. , 2013, The Journal of chemical physics.