Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Kaptanoglu, Alan A.; Morgan, Kyle D.; Hansen, Chris J.; Brunton, Steven L.

doi:10.1103/physreve.104.015206

Title: Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Journal Article · 12 July 2021 · Physical Review. E

DOI: https://doi.org/10.1103/physreve.104.015206 · OSTI ID:1848364

^[1];

^[2];

^[3];

^[2]

Univ. of Washington, Seattle, WA (United States); OSTI
Univ. of Washington, Seattle, WA (United States)
Univ. of Washington, Seattle, WA (United States); Columbia Univ., New York, NY (United States)

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. Finally, this manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: CTFusion, Inc., Seattle, WA (United States); Univ. of California, Oakland, CA (United States); Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); USDOE Advanced Research Projects Agency - Energy (ARPA-E)

Grant/Contract Number:: AC02-05CH11231; AR0001098; SC0016256

OSTI ID:: 1848364

Journal Information:: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 1 Vol. 104; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (104)

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows Mohebujjaman, M.; Rebholz, L. G.; Iliescu, T. International Journal for Numerical Methods in Fluids, Vol. 89, Issue 3 https://doi.org/10.1002/fld.4684	journal	October 2018
Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models Kapteyn, M. G.; Knezevic, D. J.; Huynh, D. B. P. International Journal for Numerical Methods in Engineering https://doi.org/10.1002/nme.6423	journal	June 2020
Data-driven modeling of the chaotic thermal convection in an annular thermosyphon Loiseau, Jean-Christophe Theoretical and Computational Fluid Dynamics, Vol. 34, Issue 4 https://doi.org/10.1007/s00162-020-00536-w	journal	July 2020
Data-Driven Model Reduction and Transfer Operator Approximation Klus, Stefan; Nüske, Feliks; Koltai, Péter Journal of Nonlinear Science, Vol. 28, Issue 3 https://doi.org/10.1007/s00332-017-9437-7	journal	January 2018
A fast randomized algorithm for the approximation of matrices Woolfe, Franco; Liberty, Edo; Rokhlin, Vladimir Applied and Computational Harmonic Analysis, Vol. 25, Issue 3 https://doi.org/10.1016/j.acha.2007.12.002	journal	November 2008
Sparse identification of nonlinear dynamical systems via reweighted ℓ 1 -regularized least squares Cortiella, Alexandre; Park, Kwang-Chun; Doostan, Alireza Computer Methods in Applied Mechanics and Engineering, Vol. 376 https://doi.org/10.1016/j.cma.2020.113620	journal	April 2021
Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition Willcox, K. Computers & Fluids, Vol. 35, Issue 2 https://doi.org/10.1016/j.compfluid.2004.11.006	journal	February 2006
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows Carlberg, Kevin; Farhat, Charbel; Cortial, Julien Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.028	journal	June 2013
Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction Carlberg, Kevin; Barone, Matthew; Antil, Harbir Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.10.033	journal	February 2017
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders Lee, Kookjin; Carlberg, Kevin T. Journal of Computational Physics https://doi.org/10.1016/j.jcp.2019.108973	journal	November 2019
Model reduction for compressible flows using POD and Galerkin projection Rowley, Clarence W.; Colonius, Tim; Murray, Richard M. Physica D: Nonlinear Phenomena, Vol. 189, Issue 1-2 https://doi.org/10.1016/j.physd.2003.03.001	journal	February 2004
Shell models of magnetohydrodynamic turbulence Plunian, Franck; Stepanov, Rodion; Frick, Peter Physics Reports, Vol. 523, Issue 1 https://doi.org/10.1016/j.physrep.2012.09.001	journal	February 2013
Data-Driven Science and Engineering Brunton, Steven L.; Kutz, J. Nathan https://doi.org/10.1017/9781108380690	book	February 2019
Turbulence, Coherent Structures, Dynamical Systems and Symmetry Holmes, Philip; Lumley, John L.; Berkooz, Gahl Cambridge University Press https://doi.org/10.1017/CBO9780511919701	book	January 2012
Intermodal energy transfers in a proper orthogonal decomposition–Galerkin representation of a turbulent separated flow Couplet, M.; Sagaut, P.; Basdevant, C. Journal of Fluid Mechanics, Vol. 491 https://doi.org/10.1017/S0022112003005615	journal	September 2003
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake Noack, Bernd R.; Afanasiev, Konstantin; MorzyŃSki, Marek Journal of Fluid Mechanics, Vol. 497 https://doi.org/10.1017/S0022112003006694	journal	December 2003
Spectral analysis of nonlinear flows Rowley, Clarence W.; MeziĆ, Igor; Bagheri, Shervin Journal of Fluid Mechanics, Vol. 641 https://doi.org/10.1017/S0022112009992059	journal	November 2009
Dynamic mode decomposition of numerical and experimental data Schmid, Peter J. Journal of Fluid Mechanics, Vol. 656 https://doi.org/10.1017/S0022112010001217	journal	July 2010
A critical-layer framework for turbulent pipe flow McKEON, B. J.; Sharma, A. S. Journal of Fluid Mechanics, Vol. 658 https://doi.org/10.1017/S002211201000176X	journal	July 2010
Dynamics of three-dimensional coherent structures in a flat-plate boundary layer Rempfer, Dietmar; Fasel, Hermann F. Journal of Fluid Mechanics, Vol. 275 https://doi.org/10.1017/S0022112094002351	journal	September 1994
Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation Balajewicz, Maciej J.; Dowell, Earl H.; Noack, Bernd R. Journal of Fluid Mechanics, Vol. 729 https://doi.org/10.1017/jfm.2013.278	journal	July 2013
Opposition control within the resolvent analysis framework Luhar, M.; Sharma, A. S.; McKeon, B. J. Journal of Fluid Mechanics, Vol. 749 https://doi.org/10.1017/jfm.2014.209	journal	May 2014
On long-term boundedness of Galerkin models Schlegel, Michael; Noack, Bernd R. Journal of Fluid Mechanics, Vol. 765 https://doi.org/10.1017/jfm.2014.736	journal	January 2015
Recursive dynamic mode decomposition of transient and post-transient wake flows Noack, Bernd R.; Stankiewicz, Witold; Morzyński, Marek Journal of Fluid Mechanics, Vol. 809 https://doi.org/10.1017/jfm.2016.678	journal	November 2016
Constrained sparse Galerkin regression Loiseau, Jean-Christophe; Brunton, Steven L. Journal of Fluid Mechanics, Vol. 838 https://doi.org/10.1017/jfm.2017.823	journal	January 2018
Sparse reduced-order modelling: sensor-based dynamics to full-state estimation Loiseau, Jean-Christophe; Noack, Bernd R.; Brunton, Steven L. Journal of Fluid Mechanics, Vol. 844 https://doi.org/10.1017/jfm.2018.147	journal	April 2018
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis Towne, Aaron; Schmidt, Oliver T.; Colonius, Tim Journal of Fluid Mechanics, Vol. 847 https://doi.org/10.1017/jfm.2018.283	journal	May 2018
Hall magnetohydrodynamic reconnection: The Geospace Environment Modeling challenge Ma, Z. W.; Bhattacharjee, A. Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3 https://doi.org/10.1029/1999JA001004	journal	March 2001
Magnetic fluctuations and Hall magnetohydrodynamic turbulence in the solar wind Krishan, V. Journal of Geophysical Research, Vol. 109, Issue A11 https://doi.org/10.1029/2004JA010496	journal	January 2004
Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review Pouquet, A.; Rosenberg, D.; Stawarz, J. E. Earth and Space Science, Vol. 6, Issue 3 https://doi.org/10.1029/2018EA000432	journal	March 2019
VAMPnets for deep learning of molecular kinetics Mardt, Andreas; Pasquali, Luca; Wu, Hao Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-017-02388-1	journal	January 2018
Deep learning for universal linear embeddings of nonlinear dynamics Lusch, Bethany; Kutz, J. Nathan; Brunton, Steven L. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07210-0	journal	November 2018
Computational modeling of fully ionized magnetized plasmas using the fluid approximation Schnack, D. D.; Barnes, D. C.; Brennan, D. P. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2183738	journal	May 2006
Global Hall-MHD simulations of magnetorotational instability in a plasma Couette flow experiment Ebrahimi, F.; Lefebvre, B.; Forest, C. B. Physics of Plasmas, Vol. 18, Issue 6 https://doi.org/10.1063/1.3598481	journal	June 2011
Calculations of two-fluid linear response to non-axisymmetric fields in tokamaks Ferraro, N. M. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3694657	journal	May 2012
Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code Akcay, Cihan; Kim, Charlson C.; Victor, Brian S. Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4817951	journal	August 2013
Sustained spheromaks with ideal n = 1 kink stability and pressure confinement Victor, B. S.; Jarboe, T. R.; Hansen, C. J. Physics of Plasmas, Vol. 21, Issue 8, Article No. 082504 https://doi.org/10.1063/1.4892261	journal	August 2014
Numerical studies and metric development for validation of magnetohydrodynamic models on the HIT-SI experimenta) Hansen, C.; Victor, B.; Morgan, K. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4919277	journal	May 2015
Direct identification of predator-prey dynamics in gyrokinetic simulations Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4930127	journal	September 2015
Spatial and temporal analysis of DIII-D 3D magnetic diagnostic data Strait, E. J.; King, J. D.; Hanson, J. M. Review of Scientific Instruments, Vol. 87, Issue 11 https://doi.org/10.1063/1.4960419	journal	August 2016
Sparse identification of a predator-prey system from simulation data of a convection model Dam, Magnus; Brøns, Morten; Juul Rasmussen, Jens Physics of Plasmas, Vol. 24, Issue 2 https://doi.org/10.1063/1.4977057	journal	February 2017
Validation of extended magnetohydrodynamic simulations of the HIT-SI3 experiment using the NIMROD code Morgan, K. D.; Jarboe, T. R.; Hossack, A. C. Physics of Plasmas, Vol. 24, Issue 12 https://doi.org/10.1063/1.4997944	journal	December 2017
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics Wehmeyer, Christoph; Noé, Frank The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5011399	journal	June 2018
Sparse learning of stochastic dynamical equations Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5018409	journal	June 2018
Fast modeling of turbulent transport in fusion plasmas using neural networks van de Plassche, K. L.; Citrin, J.; Bourdelle, C. Physics of Plasmas, Vol. 27, Issue 2 https://doi.org/10.1063/1.5134126	journal	February 2020
Characterizing magnetized plasmas with dynamic mode decomposition Kaptanoglu, A. A.; Morgan, K. D.; Hansen, C. J. Physics of Plasmas, Vol. 27, Issue 3 https://doi.org/10.1063/1.5138932	journal	March 2020
The biorthogonal decomposition as a tool for investigating fluctuations in plasmas Dudok de Wit, T.; Pecquet, A. ‐L.; Vallet, J. ‐C. Physics of Plasmas, Vol. 1, Issue 10 https://doi.org/10.1063/1.870481	journal	October 1994
Two-temperature effects in Hall-MHD simulations of the HIT-SI experiment Kaptanoglu, A. A.; Benedett, T. E.; Morgan, K. D. Physics of Plasmas, Vol. 27, Issue 7 https://doi.org/10.1063/5.0006311	journal	July 2020
Deep learning surrogate model for kinetic Landau-fluid closure with collision Wang, Libo; Xu, X. Q.; Zhu, Ben AIP Advances, Vol. 10, Issue 7 https://doi.org/10.1063/5.0010917	journal	July 2020
Automated reverse engineering of nonlinear dynamical systems Bongard, J.; Lipson, H. Proceedings of the National Academy of Sciences, Vol. 104, Issue 24 https://doi.org/10.1073/pnas.0609476104	journal	June 2007
Randomized algorithms for the low-rank approximation of matrices Liberty, E.; Woolfe, F.; Martinsson, P. -G. Proceedings of the National Academy of Sciences, Vol. 104, Issue 51 https://doi.org/10.1073/pnas.0709640104	journal	December 2007
Discovering governing equations from data by sparse identification of nonlinear dynamical systems Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan Proceedings of the National Academy of Sciences, Vol. 113, Issue 15 https://doi.org/10.1073/pnas.1517384113	journal	March 2016
Reconstruction of normal forms by learning informed observation geometries from data Yair, Or; Talmon, Ronen; Coifman, Ronald R. Proceedings of the National Academy of Sciences, Vol. 114, Issue 38 https://doi.org/10.1073/pnas.1620045114	journal	August 2017
Hamiltonian Systems and Transformation in Hilbert Space Koopman, B. O. Proceedings of the National Academy of Sciences, Vol. 17, Issue 5 https://doi.org/10.1073/pnas.17.5.315	journal	May 1931
Learning data-driven discretizations for partial differential equations Bar-Sinai, Yohai; Hoyer, Stephan; Hickey, Jason Proceedings of the National Academy of Sciences, Vol. 116, Issue 31 https://doi.org/10.1073/pnas.1814058116	journal	July 2019
Data-driven discovery of coordinates and governing equations Champion, Kathleen; Lusch, Bethany; Kutz, J. Nathan Proceedings of the National Academy of Sciences, Vol. 116, Issue 45 https://doi.org/10.1073/pnas.1906995116	journal	October 2019
Machine learning–accelerated computational fluid dynamics Kochkov, Dmitrii; Smith, Jamie A.; Alieva, Ayya Proceedings of the National Academy of Sciences, Vol. 118, Issue 21 https://doi.org/10.1073/pnas.2101784118	journal	May 2021
Chapter 4: Power and particle control Loarte, A.; Lipschultz, B.; Kukushkin, A. S. Nuclear Fusion, Vol. 47, Issue 6 https://doi.org/10.1088/0029-5515/47/6/S04	journal	June 2007
Multimode observations and 3D magnetic control of the boundary of a tokamak plasma Levesque, J. P.; Rath, N.; Shiraki, D. Nuclear Fusion, Vol. 53, Issue 7 https://doi.org/10.1088/0029-5515/53/7/073037	journal	June 2013
Real-time capable first principle based modelling of tokamak turbulent transport Citrin, J.; Breton, S.; Felici, F. Nuclear Fusion, Vol. 55, Issue 9 https://doi.org/10.1088/0029-5515/55/9/092001	journal	July 2015
Development of real-time MHD markers based on biorthogonal decomposition of signals from Mirnov coils Galperti, C.; Marchetto, C.; Alessi, E. Plasma Physics and Controlled Fusion, Vol. 56, Issue 11 https://doi.org/10.1088/0741-3335/56/11/114012	journal	October 2014
The use of the biorthogonal decomposition for the identification of zonal flows at TJ-II van Milligen, B. Ph; Sánchez, E.; Alonso, A. Plasma Physics and Controlled Fusion, Vol. 57, Issue 2 https://doi.org/10.1088/0741-3335/57/2/025005	journal	December 2014
Development of validation metrics using biorthogonal decomposition for the comparison of magnetic field measurements Victor, B. S.; Akcay, C.; Hansen, C. J. Plasma Physics and Controlled Fusion, Vol. 57, Issue 4 https://doi.org/10.1088/0741-3335/57/4/045010	journal	March 2015
A new criterion for controlling edge localized modes based on a multi-mode plasma response Gu, S.; Wan, B.; Sun, Y. Nuclear Fusion, Vol. 59, Issue 12 https://doi.org/10.1088/1741-4326/ab4566	journal	October 2019
Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics Yoshida, Z.; Hameiri, E. Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 33 https://doi.org/10.1088/1751-8113/46/33/335502	journal	July 2013
Hamiltonian formalism of extended magnetohydrodynamics Abdelhamid, H. M.; Kawazura, Y.; Yoshida, Z. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 23 https://doi.org/10.1088/1751-8113/48/23/235502	journal	May 2015
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics Kaheman, Kadierdan; Kutz, J. Nathan; Brunton, Steven L. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2242 https://doi.org/10.1098/rspa.2020.0279	journal	October 2020
Nonlinear stochastic modelling with Langevin regression Callaham, J. L.; Loiseau, J. -C.; Rigas, G. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 477, Issue 2250 https://doi.org/10.1098/rspa.2021.0092	journal	June 2021
Sparse identification of slow timescale dynamics Bramburger, Jason J.; Dylewsky, Daniel; Kutz, J. Nathan Physical Review E, Vol. 102, Issue 2 https://doi.org/10.1103/PhysRevE.102.022204	journal	August 2020
Cascade models for magnetohydrodynamic turbulence Biskamp, D. Physical Review E, Vol. 50, Issue 4 https://doi.org/10.1103/PhysRevE.50.2702	journal	October 1994
Formulating turbulence closures using sparse regression with embedded form invariance Beetham, S.; Capecelatro, J. Physical Review Fluids, Vol. 5, Issue 8 https://doi.org/10.1103/PhysRevFluids.5.084611	journal	August 2020
Demonstration of Anisotropic Fluid Closure Capturing the Kinetic Structure of Magnetic Reconnection Ohia, O.; Egedal, J.; Lukin, V. S. Physical Review Letters, Vol. 109, Issue 11 https://doi.org/10.1103/PhysRevLett.109.115004	journal	September 2012
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach Pathak, Jaideep; Hunt, Brian; Girvan, Michelle Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.024102	journal	January 2018
Fully Kinetic Simulation of 3D Kinetic Alfvén Turbulence Grošelj, Daniel; Mallet, Alfred; Loureiro, Nuno F. Physical Review Letters, Vol. 120, Issue 10 https://doi.org/10.1103/PhysRevLett.120.105101	journal	March 2018
Inferring the Dynamics of Underdamped Stochastic Systems Brückner, David B.; Ronceray, Pierre; Broedersz, Chase P. Physical Review Letters, Vol. 125, Issue 5 https://doi.org/10.1103/PhysRevLett.125.058103	journal	July 2020
Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics Morrison, Philip J.; Greene, John M. Physical Review Letters, Vol. 45, Issue 10 https://doi.org/10.1103/PhysRevLett.45.790	journal	September 1980
Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation Candy, J.; Waltz, R. E. Physical Review Letters, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevLett.91.045001	journal	July 2003
Spheromak Formation by Steady Inductive Helicity Injection Jarboe, T. R.; Hamp, W. T.; Marklin, G. J. Physical Review Letters, Vol. 97, Issue 11, Article No. 115003 https://doi.org/10.1103/PhysRevLett.97.115003	journal	September 2006
A Unified Framework for Sparse Relaxed Regularized Regression: SR3 Zheng, Peng; Askham, Travis; Brunton, Steven L. IEEE Access, Vol. 7 https://doi.org/10.1109/ACCESS.2018.2886528	journal	January 2019
Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian Chu, Hoang K.; Hayashibe, Mitsuhiro IEEE Robotics and Automation Letters, Vol. 5, Issue 2 https://doi.org/10.1109/LRA.2020.2970626	journal	April 2020
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition Astrid, Patricia; Weiland, Siep; Willcox, Karen IEEE Transactions on Automatic Control, Vol. 53, Issue 10 https://doi.org/10.1109/TAC.2008.2006102	journal	November 2008
Integration of a Real-Time Node for Magnetic Perturbations Signal Analysis in the Distributed Digital Control System of the TCV Tokamak Galperti, C.; Coda, S.; Duval, B. P. IEEE Transactions on Nuclear Science, Vol. 64, Issue 6 https://doi.org/10.1109/TNS.2017.2711625	journal	June 2017
Transfer Learning to Model Inertial Confinement Fusion Experiments Humbird, K. D.; Peterson, J. L.; Spears, B. K. IEEE Transactions on Plasma Science, Vol. 48, Issue 1 https://doi.org/10.1109/TPS.2019.2955098	journal	January 2020
Regression Shrinkage and Selection Via the Lasso Tibshirani, Robert Journal of the Royal Statistical Society: Series B (Methodological), Vol. 58, Issue 1 https://doi.org/10.1111/j.2517-6161.1996.tb02080.x	journal	January 1996
Multidimensional Approximation of Nonlinear Dynamical Systems Gelß, Patrick; Klus, Stefan; Eisert, Jens Journal of Computational and Nonlinear Dynamics, Vol. 14, Issue 6 https://doi.org/10.1115/1.4043148	journal	April 2019
Distilling Free-Form Natural Laws from Experimental Data Schmidt, Michael; Lipson, Hod Science, Vol. 324, Issue 5923 https://doi.org/10.1126/science.1165893	journal	April 2009
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning Noé, Frank; Olsson, Simon; Köhler, Jonas Science, Vol. 365, Issue 6457 https://doi.org/10.1126/science.aaw1147	journal	September 2019
Model Reduction and Approximation Benner, Peter; Ohlberger, Mario; Cohen, Albert https://doi.org/10.1137/1.9781611974829	journal	January 2017
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems Benner, Peter; Gugercin, Serkan; Willcox, Karen SIAM Review, Vol. 57, Issue 4 https://doi.org/10.1137/130932715	journal	January 2015
A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions Drmač, Zlatko; Gugercin, Serkan SIAM Journal on Scientific Computing, Vol. 38, Issue 2 https://doi.org/10.1137/15M1019271	journal	January 2016
Physics-Informed Probabilistic Learning of Linear Embeddings of Nonlinear Dynamics with Guaranteed Stability Pan, Shaowu; Duraisamy, Karthik SIAM Journal on Applied Dynamical Systems, Vol. 19, Issue 1 https://doi.org/10.1137/19M1267246	journal	January 2020
Real-Time Computational Algorithm for Optimal Control of an MHD Flow System Ravindran, S. S. SIAM Journal on Scientific Computing, Vol. 26, Issue 4 https://doi.org/10.1137/S1064827502400534	journal	January 2005
Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition Rowley, C. W. International Journal of Bifurcation and Chaos, Vol. 15, Issue 03 https://doi.org/10.1142/S0218127405012429	journal	March 2005
Fast monte-carlo algorithms for finding low-rank approximations Frieze, Alan; Kannan, Ravi; Vempala, Santosh Journal of the ACM, Vol. 51, Issue 6 https://doi.org/10.1145/1039488.1039494	journal	November 2004
Turbulence Modeling in the Age of Data Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng Annual Review of Fluid Mechanics, Vol. 51, Issue 1 https://doi.org/10.1146/annurev-fluid-010518-040547	journal	January 2019
Machine Learning for Fluid Mechanics Brunton, Steven L.; Noack, Bernd R.; Koumoutsakos, Petros Annual Review of Fluid Mechanics, Vol. 52, Issue 1 https://doi.org/10.1146/annurev-fluid-010719-060214	journal	September 2019
Model Reduction for Flow Analysis and Control Rowley, Clarence W.; Dawson, Scott T. M. Annual Review of Fluid Mechanics, Vol. 49, Issue 1 https://doi.org/10.1146/annurev-fluid-010816-060042	journal	January 2017
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator Mezić, Igor Annual Review of Fluid Mechanics, Vol. 45, Issue 1 https://doi.org/10.1146/annurev-fluid-011212-140652	journal	January 2013
Deterministic Nonperiodic Flow Lorenz, Edward N. Journal of the Atmospheric Sciences, Vol. 20, Issue 2 https://doi.org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2	journal	March 1963
Analysis of Magnetohydrodynamic Instabilities in TJ-II Plasmas Jiménez-Gómez, R.; Ascasíbar, E.; Estrada, T. Fusion Science and Technology, Vol. 51, Issue 1 https://doi.org/10.13182/FST07-A1283	journal	January 2007
Modal Analysis of Fluid Flows: An Overview Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M. AIAA Journal, Vol. 55, Issue 12 https://doi.org/10.2514/1.J056060	journal	December 2017
Balanced Model Reduction via the Proper Orthogonal Decomposition Willcox, K.; Peraire, J. AIAA Journal, Vol. 40, Issue 11 https://doi.org/10.2514/2.1570	journal	November 2002
On dynamic mode decomposition: Theory and applications Kutz, J. Nathan; Brunton, Steven L.; Luchtenburg, Dirk M. Journal of Computational Dynamics, Vol. 1, Issue 2 https://doi.org/10.3934/jcd.2014.1.391	journal	December 2014

Cited By (1)

Greedy permanent magnet optimization Kaptanoglu, Alan A.; Conlin, Rory; Landreman, Matt arXiv https://doi.org/10.48550/arxiv.2208.10620	text	January 2022

Similar Records

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Journal Article · 2022 · Scientific Reports · OSTI ID:1894703

San, Omer; Pawar, Suraj; Rasheed, Adil

An artificial neural network framework for reduced order modeling of transient flows

Journal Article · 2019 · Communications in Nonlinear Science and Numerical Simulation · OSTI ID:1593569

San, Omer; Maulik, Romit; Ahmed, Mansoor

Reduced order modeling of fluid/structure interaction.

Technical Report · 2009 · OSTI ID:974411

Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph; +1 more

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Hall magnetohydrodynamics
first-principles calculations in plasma physics
magnetohydrodynamic techniques
magnetohydrodynamics
mathematical physics
physics

Title: Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Citation Formats

References (104)

Cited By (1)

Similar Records

Related Subjects