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Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity.
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W. Liu, J. C. Príncipe, and S. Haykin, · 2010
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A. Monokrousos, E. Åkervik, L. Brandt, and D. S. Henningson, “Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers,”
2010
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2017
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2017
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2017
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2017
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K. K. Chen, J. H. Tu, and C. W. Rowley, “Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses,”
2012
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I. Mezić, “Analysis of fluid flows via spectral properties of the Koopman operator,”
2013
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JHU Press, 2013
G. H. Golub and C. F. Van Loan, · 2013
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J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, “On dynamic mode decomposition: Theory and applications,”
2014
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2014
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2014
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C. Wehmeyer and F. Noé, “Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics,”
2018
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S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, and F. Noé, “Data-Driven Model Reduction and Transfer Operator Approximation,”
2018
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A. Towne, O. T. Schmidt, and T. Colonius, “Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis,”
2018
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T. Askham and J. N. Kutz, “Variable projection methods for an optimized dynamic mode decomposition,”
2018
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J. C. Loiseau and S. L. Brunton, “Constrained sparse Galerkin regression,”
2018
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E. Kaiser, J. N. Kutz, and S. L. Brunton, “Sparse identification of nonlinear dynamics for model predictive control in the low-data limit,”
2018
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Cambridge University Press, 2019
S. L. Brunton and J. N. Kutz, · 2019
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M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,”
2019
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K. Taira, M. S. Hemati, S. L. Brunton, Y. Sun, K. Duraisamy, S. Bagheri, S. T. M. Dawson, and C.-A. Yeh, “Modal Analysis of Fluid Flows: Applications and Outlook,”
2019
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O. Azencot, W. Yin, and A. Bertozzi, “Consistent dynamic mode decomposition,”
2019
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H. Owhadi and G. R. Yoo, “Kernel Flows: From learning kernels from data into the abyss,”
2019
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D. Giannakis, “Data-driven spectral decomposition and forecasting of ergodic dynamical systems,”
2019
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I. Abraham and T. D. Murphey, “Active learning of dynamics for data-driven control using Koopman operators,”
2019
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D. Bruder, B. Gillespie, C. David Remy, and R. Vasudevan, “Modeling and control of soft robots using the Koopman operator and model predictive control,” in
2019
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X. T. G Mamakoukas, M Castano and T. Murphey, “Local Koopman operators for data-driven control of robotic systems,” in
2019
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P. Gelß, S. Klus, J. Eisert, and C. Schütte, “Multidimensional Approximation of Nonlinear Dynamical Systems,”
2019
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2019
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J.-C. Loiseau, M. A. Bucci, S. Cherubini, and J.-C. Robinet, “Time-stepping and Krylov methods for large-scale instability problems,” in
2019
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H. Zhang, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, “Online dynamic mode decomposition for time-varying systems,”
2019
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C.-A. Yeh and K. Taira, “Resolvent-analysis-based design of airfoil separation control,”
2019
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M. Raissi, A. Yazdani, and G. E. Karniadakis, “Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations,”
2020
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2020
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E. Qian, B. Kramer, B. Peherstorfer, and K. Willcox, “Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems,”
2020
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2020
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2020
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2020
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2020
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2020
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A. A. Kaptanoglu, K. D. Morgan, C. J. Hansen, and S. L. Brunton, “Characterizing magnetized plasmas with dynamic mode decomposition,”
2020
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P. Benner, P. Goyal, B. Kramer, B. Peherstorfer, and K. Willcox, “Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms,”
2020
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H. Montanelli and N. Bootland, “Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators,”
2020
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J. H. M. Ribeiro, C.-A. Yeh, and K. Taira, “Randomized resolvent analysis,”
2020
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S. L. Brunton, M. Budišić, E. Kaiser, and J. N. Kutz, “Modern Koopman Theory for Dynamical Systems,”
2021
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M. R. Jovanović, “From bypass transition to flow control and data-driven turbulence modeling: An input–output viewpoint,”
2021
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B. Herrmann, P. J. Baddoo, R. Semaan, S. L. Brunton, and B. J. McKeon, “Data-driven resolvent analysis,”
2021
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S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” 2021
2021
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