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Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior.
P. J. Morrison and J. M. Greene, Noncanonical hamiltonian density formulation of hydrodynamics and ideal magnetohydrodynamics, Physical Review Letters 45
1980
Earlier work this paper cites.
T. Dudok de Wit, A.-L. Pecquet, J.-C. Vallet, and R. Lima, The biorthogonal decomposition as a tool for investigating fluctuations in plasmas, Physics of Plasmas 1
1994
Earlier work this paper cites.
G. H. Golub et al. , Matrix computations, The Johns Hopkins (1996)
1996
Earlier work this paper cites.
I. Furno, Fast transient transport phenomena measured by soft x-ray emission in TCV tokamak plasmas , Tech. Rep. (2001)
2001
Earlier work this paper cites.
J. Candy and R. E. Waltz, Anomalous transport scaling in the DIII-D tokamak matched by supercomputer simulation, Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
2004
Earlier work this paper cites.
C. W. Rowley, T. Colonius, and R. M. Murray, Model reduction for compressible flows using POD and Galerkin projection, Physica D: Nonlinear Phenomena 189
2004
Earlier work this paper cites.
A. Frieze, R. Kannan, and S. Vempala, Fast Monte-Carlo algorithms for finding low-rank approximations, Journal of the ACM (JACM) 51
2004
Earlier work this paper cites.
P. Benner, V. Mehrmann, and D. C. Sorensen, Dimension reduction of large-scale systems , Vol. 45 (Springer, 2005)
2005
Earlier work this paper cites.
D. D. Schnack, D. C. Barnes, D. P. Brennan, C. C. Hegna, E. Held, C. C. Kim, S. E. Kruger, A. Y. Pankin, and C. R. Sovinec, Computational modeling of fully ionized magnetized plasmas using the fluid approximation, Physics of Plasmas 13
2006
Earlier work this paper cites.
T. Jarboe, W. Hamp, G. Marklin, B. Nelson, R. O’Neill, A. Redd, P. Sieck, R. Smith, and J. Wrobel, Spheromak formation by steady inductive helicity injection, Physical review letters 97
2006
Earlier work this paper cites.
K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Computers & Fluids 35
2006
Earlier work this paper cites.
R. Jiménez-Gómez, E. Ascasíbar, T. Estrada, I. García-Cortés, B. Van Milligen, A. López-Fraguas, I. Pastor, and D. López-Bruna, Analysis of magnetohydrodynamic instabilities in TJ-II plasmas, Fusion science and technology 51
2007
Earlier work this paper cites.
E. Liberty, F. Woolfe, P.-G. Martinsson, V. Rokhlin, and M. Tygert, Randomized algorithms for the low-rank approximation of matrices, Proceedings of the National Academy of Sciences 104
2007
Earlier work this paper cites.
F. Woolfe, E. Liberty, V. Rokhlin, and M. Tygert, A fast randomized algorithm for the approximation of matrices, Applied and Computational Harmonic Analysis 25
2008
Earlier work this paper cites.
P. Astrid, S. Weiland, K. Willcox, and T. Backx, Missing point estimation in models described by proper orthogonal decomposition, IEEE Transactions on Automatic Control 53
2008
Earlier work this paper cites.
S. Chaturantabut and D. C. Sorensen, Discrete empirical interpolation for nonlinear model reduction, in Proceedings of the 48th IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference (IEEE, 2009) pp. 4316–4321
2009
Cited alongside, same era.
B. R. Noack, M. Schlegel, M. Morzynski, and G. Tadmor, Galerkin method for nonlinear dynamics (Springer, 2011)
2011
Cited alongside, same era.
F. Ebrahimi, B. Lefebvre, C. B. Forest, and A. Bhattacharjee, Global Hall-MHD simulations of magnetorotational instability in a plasma Couette flow experiment, Physics of Plasmas 18
2011
Cited alongside, same era.
O. Ohia, J. Egedal, V. S. Lukin, W. Daughton, and A. Le, Demonstration of anisotropic fluid closure capturing the kinetic structure of magnetic reconnection, Phys. Rev. Lett. 109
2012
Cited alongside, same era.
H. M. Abdelhamid, Y. Kawazura, and Z. Yoshida, Hamiltonian formalism of extended magnetohydrodynamics, Journal of Physics A: Mathematical and Theoretical 48
2015
Later among the works it cites.
M. Pandya, Low edge safety factor disruptions in the Compact Toroidal Hybrid: Operation in the low-q regime, passive disruption avoidance and the nature of MHD precursors , Ph.D. thesis, Auburn University (2016)
2016
Later among the works it cites.
E. Strait, J. King, J. Hanson, and N. Logan, Spatial and temporal analysis of DIII-D 3D magnetic diagnostic data, Review of Scientific Instruments 87
2016
Later among the works it cites.
S. Galtier, Introduction to modern magnetohydrodynamics (Cambridge University Press, 2016)
2016
Later among the works it cites.
Z. Drmac and S. Gugercin, A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions, SIAM Journal on Scientific Computing 38
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2012
Cited alongside, same era.
M. J. Balajewicz, E. H. Dowell, and B. R. Noack, Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation, Journal of Fluid Mechanics 729
2013
Cited alongside, same era.
J. Levesque, N. Rath, D. Shiraki, S. Angelini, J. Bialek, P. Byrne, B. DeBono, P. Hughes, M. Mauel, G. Navratil, et al. , Multimode observations and 3D magnetic control of the boundary of a tokamak plasma, Nuclear Fusion 53
2013
Cited alongside, same era.
K. Carlberg, C. Farhat, J. Cortial, and D. Amsallem, The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows, Journal of Computational Physics 242
2013
Cited alongside, same era.
Z. Yoshida and E. Hameiri, Canonical hamiltonian mechanics of hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics, Journal of Physics A: Mathematical and Theoretical 46
2013
Cited alongside, same era.
B. P. van Milligen, E. Sánchez, A. Alonso, M. A. Pedrosa, C. Hidalgo, A. M. de Aguilera, and A. L. Fraguas, The use of the biorthogonal decomposition for the identification of zonal flows at TJ-II, Plasma Physics and Controlled Fusion 57
2014
Cited alongside, same era.
C. Galperti, C. Marchetto, E. Alessi, D. Minelli, M. Mosconi, F. Belli, L. Boncagni, A. Botrugno, P. Buratti, B. Esposito, et al. , Development of real-time MHD markers based on biorthogonal decomposition of signals from Mirnov coils, Plasma Physics and Controlled Fusion 56
2014
Cited alongside, same era.
B. P. Van Milligen, E. Sánchez, A. Alonso, M. Pedrosa, C. Hidalgo, A. M. De Aguilera, and A. L. Fraguas, The use of the biorthogonal decomposition for the identification of zonal flows at TJ-II, Plasma Physics and Controlled Fusion 57
2014
Cited alongside, same era.
2016
Later among the works it cites.
S. L. Brunton, J. L. Proctor, and J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences 113
2016
Later among the works it cites.
K. Taira, S. L. Brunton, S. Dawson, C. W. Rowley, T. Colonius, B. J. McKeon, O. T. Schmidt, S. Gordeyev, V. Theofilis, and L. S. Ukeiley, Modal analysis of fluid flows: An overview, AIAA Journal 55
2017
Later among the works it cites.
P. J. Byrne, Study of External Kink Modes in Shaped HBT-EP Plasmas , Ph.D. thesis, Columbia University (2017)
2017
Later among the works it cites.
P. Benner, M. Ohlberger, A. Cohen, and K. Willcox, Model reduction and approximation: theory and algorithms (SIAM, 2017)
2017
Later among the works it cites.
K. Carlberg, M. Barone, and H. Antil, Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction, Journal of Computational Physics 330
2017
Later among the works it cites.
D. Grošelj, A. Mallet, N. F. Loureiro, and F. Jenko, Fully kinetic simulation of 3D kinetic Alfvén turbulence, Phys. Rev. Lett. 120
2018
Later among the works it cites.
J.-C. Loiseau, B. R. Noack, and S. L. Brunton, Sparse reduced-order modeling: sensor-based dynamics to full-state estimation, Journal of Fluid Mechanics 844
2018
Later among the works it cites.
S. Gu, B. Wan, Y. Sun, N. Chu, Y. Liu, T. Shi, H. Wang, M. Jia, and K. He, A new criterion for controlling edge localized modes based on a multi-mode plasma response, Nuclear Fusion 59
2019
Later among the works it cites.
S. L. Brunton and J. N. Kutz, Data-driven science and engineering: Machine learning, dynamical systems, and control (Cambridge University Press, 2019)
2019
Later among the works it cites.