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The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Differentiable manifolds
H. Whitney · 1936
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Detecting strange attractors in turbulence
F. Takens · 1981
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Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
J. M. Hyman, B. Nicolaenko, and S. Zaleski · 1986
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Embedology
T. Sauer, J. A. Yorke, and M. Casdagli · 1991
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Optimal prediction and the Mori-Zwanzig representation of irreversible processes
A. J. Chorin, O. H. Hald, and R. Kupferman · 2000
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A topological delay embedding theorem for infinite-dimensional dynamical systems
J.C. Robinson · 2005
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Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. S. Henningson · 2009
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
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Applied Koopmanism
M. Budišić, R. Mohr, and I. Mezić · 2012
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Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
I. Mezić · 2013
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Geodesic Convolutional Neural Networks on Riemannian Manifolds
J. Masci, D. Boscaini, M. M. Bronstein, and P. Vandergheynst · 2015
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Dynamic mode decomposition with control
J. L. Proctor, S. L. Brunton, and J. N. Kutz · 2015
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A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
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A kernel-based method for data-driven Koopman spectral analysis
M. O. Williams, C. W. Rowley, and I. G. Kevrekidis · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
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Group Equivariant Convolutional Networks
T. S. Cohen and M. Welling · 2016
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On the computation of attractors for delay differential equations
M. Dellnitz, M. Hessel-von Molo, and A. Ziessler · 2016
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On the numerical approximation of the Perron-Frobenius and Koopman operator
S. Klus, P. Koltai, and C. Schütte · 2016
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Koopman Theory for Partial Differential Equations, 2016
J. N. Kutz, J. L. Proctor, and S. L. Brunton · 2016
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Effective dynamics along given reaction coordinates, and reaction rate theory
W. Zhang, C. Hartmann, and C. Schütte · 2016
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Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the koopman operator
H. Arbabi and I. Mezić · 2017
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Geometric Deep Learning: Going beyond Euclidean data
M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst · 2017
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Chaos as an intermittently forced linear system
S. L. Brunton, B. W. Brunton, J L. Proctor, E. Kaiser, and J. N. Kutz · 2017
Cited alongside, same era.
Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics
A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, and C. Schütte · 2017
Cited alongside, same era.
Sparse learning of stochastic dynamical equations
L. Boninsegna, F. Nüske, and C. Clementi · 2018
Cited alongside, same era.
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
M. Korda and I. Mezić · 2018
Cited alongside, same era.
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
M. Korda and I. Mezić · 2018
Cited alongside, same era.
Shenfun: High performance spectral Galerkin computing platform
Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems
A. Mauroy · 2021
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Spectral Properties of Effective Dynamics from Conditional Expectations
F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi · 2021
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Data-driven model reduction of agent-based systems using the Koopman generator
J.-H. Niemann, S. Klus, and C. Schütte · 2021
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Explicit multiobjective model predictive control for nonlinear systems with symmetries
S. Ober-Blöbaum and S. Peitz · 2021
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Modern Koopman Theory for Dynamical Systems
S. L. Brunton, M. Budišić, E. Kaiser, and J. N. Kutz · 2022
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Dictionary-free Koopman model predictive control with nonlinear input transformation
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M. Mortensen · 2018
Cited alongside, same era.
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach
J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott · 2018
Cited alongside, same era.
Koopman analysis of Burgers equation
J. Page and R. R. Kerswell · 2018
Cited alongside, same era.
Data-driven forecasting of high-dimensional chaotic systems with long short-Term memory networks
P. R. Vlachas, W. Byeon, Z. Y. Wan, T. P. Sapsis, and P. Koumoutsakos · 2018
Cited alongside, same era.
Linearly Recurrent Autoencoder Networks for Learning Dynamics
S. E. Otto and C. W. Rowley · 2019
Cited alongside, same era.
Koopman operator-based model reduction for switched-system control of PDEs
S. Peitz and S. Klus · 2019
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Cited alongside, same era.
V. Cibulka, M. Korda, and T. Haniš · 2022
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On Numerical Approximations of the Koopman Operator
I. Mezić · 2022
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Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics
M. Weissenbacher, S. Abbott, A. Garg, and Y. Kawahara · 2022
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Koopman kernel regression
P. Bevanda, M. Beier, A. Lederer, S. Sosnowski, E. Hüllermeier, and S. Hirche · 2023
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Finite-data error bounds for Koopman-based prediction and control
F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann · 2023
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Towards reliable data-based optimal and predictive control using extended DMD
M. Schaller, K. Worthmann, F. Philipp, S. Peitz, and F. Nüske · 2023
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Effective control of two-dimensional Rayleigh-Bénard convection: Invariant multi-agent reinforcement learning is all you need
C. Vignon, J. Rabault, J. Vasanth, F. Alcántara-Ávila, M. Mortensen, and R. Vinuesa · 2023
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A quantitative analysis of Koopman operator methods for system identification and predictions
C. Zhang and E. Zuazua · 2023
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Data-driven MPC with stability guarantees using extended dynamic mode decomposition
L. Bold, L. Grüne, M. Schaller, and K. Worthmann · 2024
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Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches, 2024
C. R. Constante-Amores, A. J. Linot, and M. D. Graham · 2024
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Group Convolutional Extended Dynamic Mode Decomposition
H. Harder, S. Peitz, F. Nüske, F. M. Philipp, M. Schaller, and K. Worthmann · 2024
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Solving Partial Differential Equations with Equivariant Extreme Learning Machines
H. Harder, J. Rabault, R. Vinuesa, M. Mortensen, and S. Peitz · 2024
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L ∞ {L}^{\infty} -error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition
F. Köhne, F. M. Philipp, M. Schaller, A. Schiela, and K. Worthmann · 2024
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Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories
S. E. Otto, S. Peitz, and C. W. Rowley · 2024
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Variance representations and convergence rates for data-driven approximations of Koopman operators
F. M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, and K. Worthmann · 2024
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Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S. L. Brunton, and K. Taira · 2024
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Error bounds for kernel-based approximations of the Koopman operator
F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske · 2024
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