Fetching the paper…
Reading the bibliography…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior.
B. O. Koopman, Hamiltonian systems and transformation in Hilbert space, Proceedings of the National Academy of Sciences 17
1931
Earlier work this paper cites.
E. N. Lorenz, Deterministic nonperiodic flow, Journal of the atmospheric sciences 20
1963
Earlier work this paper cites.
S. Braginskii and M. Leontovich, Reviews of plasma physics (1965)
1965
Earlier work this paper cites.
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.
D. Rempfer and H. F. Fasel, Dynamics of three-dimensional coherent structures in a flat-plate boundary layer, Journal of Fluid Mechanics 275
1994
Earlier work this paper cites.
D. Biskamp, Cascade models for magnetohydrodynamic turbulence, Physical Review E 50
1994
Earlier work this paper cites.
G. H. Golub et al. , Matrix computations, The Johns Hopkins (1996)
1996
Earlier work this paper cites.
R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological) , 267 (1996)
1996
Earlier work this paper cites.
F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings, and S. J. Wright, Nonlinear predictive control and moving horizon estimation—an introductory overview, in Advances in control (Springer, 1999) pp. 391–449
1999
Earlier work this paper cites.
J. R. Roth, Industrial plasma engineering: Volume 2: Applications to nonthermal plasma processing , Vol. 2 (CRC press, 2001)
2001
Earlier work this paper cites.
Z. Ma and A. Bhattacharjee, Hall magnetohydrodynamic reconnection: The geospace environment modeling challenge, Journal of Geophysical Research: Space Physics 106
2001
Earlier work this paper cites.
K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA journal 40
2002
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.
B. R. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele, A hierarchy of low-dimensional models for the transient and post-transient cylinder wake, Journal of Fluid Mechanics 497
2003
Earlier work this paper cites.
M. Couplet, P. Sagaut, and C. Basdevant, Intermodal energy transfers in a proper orthogonal decomposition-Galerkin representation of a turbulent separated flow, Journal of Fluid Mechanics 491
2003
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 189
2004
Earlier work this paper cites.
V. Krishan and S. Mahajan, Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind, Journal of Geophysical Research: Space Physics 109
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.
2004
Earlier work this paper cites.
C. Sovinec, A. Glasser, T. Gianakon, D. Barnes, R. Nebel, S. Kruger, D. Schnack, S. Plimpton, A. Tarditi, M.-S. Chu, et al. , Nonlinear magnetohydrodynamics simulation using high-order finite elements, Journal of Computational Physics 195
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.
S. Ravindran, Real-time computational algorithm for optimal control of an MHD flow system, SIAM Journal on Scientific Computing 26
2005
Earlier work this paper cites.
C. W. Rowley, Model reduction for fluids, using balanced proper orthogonal decomposition, International Journal of Bifurcation and Chaos 15
2005
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.
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.
L. Spitzer, Physics of fully ionized gases (Courier Corporation, 2006)
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.
A. Loarte, B. Lipschultz, A. Kukushkin, G. Matthews, P. Stangeby, N. Asakura, G. Counsell, G. Federici, A. Kallenbach, K. Krieger, et al. , Power and particle control, Nuclear Fusion 47
2007
Earlier work this paper cites.
J. Bongard and H. Lipson, Automated reverse engineering of nonlinear dynamical systems, Proceedings of the National Academy of Sciences 104
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.
C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D. Henningson, Spectral analysis of nonlinear flows, J. Fluid Mech. 645
2009
Earlier work this paper cites.
M. Schmidt and H. Lipson, Distilling free-form natural laws from experimental data, Science 324
2009
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
Earlier work this paper cites.
P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics 656
2010
Earlier work this paper cites.
B. McKeon and A. Sharma, A critical-layer framework for turbulent pipe flow, Journal of Fluid Mechanics 658
2010
Earlier work this paper cites.
B. R. Noack, M. Schlegel, M. Morzynski, and G. Tadmor, Galerkin method for nonlinear dynamics (Springer, 2011)
2011
Earlier work this paper cites.
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
Earlier work this paper cites.
J. S. Wrobel, A study of HIT-SI plasma dynamics using surface magnetic field measurements (University of Washington, 2011)
2011
Earlier work this paper cites.
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
Earlier work this paper cites.
P. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, Turbulence, coherent structures, dynamical systems and symmetry (Cambridge university press, 2012)
2012
Cited alongside, same era.
N. M. Ferraro, Calculations of two-fluid linear response to non-axisymmetric fields in tokamaks, Physics of Plasmas 19
2012
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.
I. Mezic, Analysis of fluid flows via spectral properties of the Koopman operator, Annual Review of Fluid Mechanics 45
2013
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
B. Lusch, J. N. Kutz, and S. L. Brunton, Deep learning for universal linear embeddings of nonlinear dynamics, Nature communications 9
2018
Later among the works it cites.
S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, and F. Noé, Data-driven model reduction and transfer operator approximation, Journal of Nonlinear Science (2018)
2018
Later among the works it cites.
C. Wehmeyer and F. Noé, Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics, The Journal of Chemical Physics 148
2018
Later among the works it cites.
A. Mardt, L. Pasquali, H. Wu, and F. Noé, VAMPnets: Deep learning of molecular kinetics, Nature Communications 9
2018
Later among the works it cites.
J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach, Physical review letters 120
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2013
Cited alongside, same era.
F. Plunian, R. Stepanov, and P. Frick, Shell models of magnetohydrodynamic turbulence, Physics Reports 523
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.
C. Akcay, Extended magnetohydrodynamic simulations of the helicity injected torus (HIT-SI) spheromak experiment with the NIMROD code , Ph.D. thesis, University of Washington, Seattle (2013)
2013
Cited alongside, same era.
C. Akcay, C. C. Kim, B. S. Victor, and T. R. Jarboe, Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code, Physics of Plasmas 20
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.
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, On dynamic mode decomposition: theory and applications, Journal of Computational Dynamics 1
2014
Cited alongside, same era.
2018
Later among the works it cites.
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.
L. Boninsegna, F. Nüske, and C. Clementi, Sparse learning of stochastic dynamical equations, The Journal of Chemical Physics 148
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.
K. D. Humbird, J. L. Peterson, B. Spears, and R. McClarren, Transfer learning to model inertial confinement fusion experiments, IEEE Transactions on Plasma Science 48
2019
Later among the works it cites.
K. Champion, B. Lusch, J. N. Kutz, and S. L. Brunton, Data-driven discovery of coordinates and governing equations, Proceedings of the National Academy of Sciences 116
2019
Later among the works it cites.
K. Duraisamy, G. Iaccarino, and H. Xiao, Turbulence modeling in the age of data, Annual Reviews of Fluid Mechanics 51
2019
Later among the works it cites.
F. Noé, S. Olsson, J. Köhler, and H. Wu, Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning, Science 365
2019
Later among the works it cites.
Y. Bar-Sinai, S. Hoyer, J. Hickey, and M. P. Brenner, Learning data-driven discretizations for partial differential equations, Proceedings of the National Academy of Sciences 116
2019
Later among the works it cites.
2019
Later among the works it cites.
M. Mohebujjaman, L. G. Rebholz, and T. Iliescu, Physically constrained data-driven correction for reduced-order modeling of fluid flows, International Journal for Numerical Methods in Fluids 89
2019
Later among the works it cites.
A. Pouquet, D. Rosenberg, J. E. Stawarz, and R. Marino, Helicity dynamics, inverse, and bidirectional cascades in fluid and magnetohydrodynamic turbulence: a brief review, Earth and Space Science 6
2019
Later among the works it cites.
P. Zheng, T. Askham, S. L. Brunton, J. N. Kutz, and A. Y. Aravkin, A unified framework for sparse relaxed regularized regression: SR3, IEEE Access 7
2019
Later among the works it cites.
P. Gelß, S. Klus, J. Eisert, and C. Schütte, Multidimensional approximation of nonlinear dynamical systems, Journal of Computational and Nonlinear Dynamics 14
2019
Later among the works it cites.
J. Z. Kolter and G. Manek, Learning stable deep dynamics models, in Advances in Neural Information Processing Systems , Vol. 32 (2019) pp. 11128–11136
2019
Later among the works it cites.
S. L. Brunton, B. R. Noack, and P. Koumoutsakos, Machine learning for fluid mechanics, Annual Review of Fluid Mechanics 52
2020
Closest in time.
2020
Closest in time.
M. G. Kapteyn, D. J. Knezevic, and K. Willcox, Toward predictive digital twins via component-based reduced-order models and interpretable machine learning, in AIAA Scitech 2020 Forum (2020) p. 0418
2020
Closest in time.
L. Wang, X. Xu, B. Zhu, C. Ma, and Y.-a. Lei, Deep learning surrogate model for kinetic Landau-fluid closure with collision, AIP Advances 10
2020
Closest in time.
K. L. van de Plassche, J. Citrin, C. Bourdelle, Y. Camenen, F. J. Casson, V. I. Dagnelie, F. Felici, A. Ho, S. Van Mulders, and J. Contributors, Fast modeling of turbulent transport in fusion plasmas using neural networks, Physics of Plasmas 27
2020
Closest in time.
J.-C. Loiseau, Data-driven modeling of the chaotic thermal convection in an annular thermosyphon, Theoretical and Computational Fluid Dynamics 34
2020
Closest in time.
2020
Closest in time.
K. Lee and K. T. Carlberg, Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders, Journal of Computational Physics 404
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
K. Kaheman, J. N. Kutz, and S. L. Brunton, SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics, Proceedings of the Royal Society A 476
2020
Closest in time.
D. B. Brückner, P. Ronceray, and C. P. Broedersz, Inferring the dynamics of underdamped stochastic systems, Physical review letters 125
2020
Closest in time.
S. Beetham and J. Capecelatro, Formulating turbulence closures using sparse regression with embedded form invariance, Physical Review Fluids 5
2020
Closest in time.
S. Pan and K. Duraisamy, Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability, SIAM Journal on Applied Dynamical Systems 19
2020
Closest in time.
2020
Closest in time.
2021
Closest in time.
D. Kochkov, J. A. Smith, A. Alieva, Q. Wang, M. P. Brenner, and S. Hoyer, Machine learning–accelerated computational fluid dynamics, Proceedings of the National Academy of Sciences 118
2021
Closest in time.
2021
Closest in time.
A. Cortiella, K.-C. Park, and A. Doostan, Sparse identification of nonlinear dynamical systems via reweighted l 1 l_{1} -regularized least squares, Computer Methods in Applied Mechanics and Engineering 376
2021
Closest in time.