Edit Profile (opens in new tab) Kutz, J. Nathan Co-Author Distance Author ID: kutz.j-nathan Published as: Kutz, J. Nathan; Kutz, J. N.; Nathan Kutz, J. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 143 Publications since 1996, including 4 Books and 58 Additional arXiv Preprints 1 Further Contribution Co-Authors: 133 Co-Authors with 138 Joint Publications 2,220 Co-Co-Authors all top 5 Co-Authors 6 single-authored 82 Brunton, Steven L. 16 Proctor, Joshua L. 14 Brunton, Bingni Wen 12 Kaiser, Eurika 8 Manohar, Krithika 7 Bramburger, Jason J. 7 Deconinck, Bernard 6 Aravkin, Aleksandr Y. 5 Askham, Travis 5 Fasel, Urban 5 Williams, Matthew O. 4 Hirsh, Seth M. 4 Kaheman, Kadierdan 4 Morrison, Megan 4 Shlizerman, Eli 3 Alla, Alessandro 3 Bright, Ido 3 Champion, Kathleen P. 3 Clark, Emily 3 de Silva, Brian M. 3 Ebers, Megan R. 3 Erichson, N. Benjamin 3 Maia, Pedro D. 3 Mangan, Niall M. 3 Mendible, Ariana 3 Rudy, Samuel H. 3 Tu, Jonathan H. 3 Williams, Jan P. 3 Zheng, Peng 2 Baddoo, Peter Jonathan 2 Bakarji, Joseph 2 Frigyik, Béla A. 2 Fu, Xing 2 Holmes, Philip J. 2 Ichinaga, Sara M. 2 Klishin, Andrei A. 2 Koch, James V. 2 Lange, Henning 2 Lin, Guang 2 Liu, Yuying 2 Lusch, Bethany 2 Mathelin, Lionel 2 Rahman, Aminur 2 Rozza, Gianluigi 2 Sargsyan, Syuzanna 2 Schmid, Peter Joseph 2 Shea, Daniel E. 2 Steele, Katherine M. 2 Wilkening, Jon A. 2 Zahn, Olivia 2 Zolman, Nicholas 1 Andreuzzi, Francesco 1 Bai, Zhe 1 Barajas-Solano, David A. 1 Barreiro, Andrea K. 1 Bieker, Katharina 1 Blom-Schieber, Agnes 1 Bradley, R. Mark 1 Bronski, Jared C. 1 Brune, Christoph 1 Budišić, Marko 1 Bush, John W. M. 1 Buttrick, James 1 Callaham, Jared L. 1 Carter, John D. 1 Conti, Paolo 1 Daviller, Guillaume 1 Dellnitz, Michael 1 Demo, Nicola 1 Dorabiala, Olga 1 Dylewsky, Daniel 1 Falcone, Maurizio 1 Fehr, Jörg 1 Fieseler, Charles 1 Frangi, Attilio 1 Gao, L. Mars 1 Gin, Craig R. 1 Ginger, David S. 1 Giridharagopal, Rajiv 1 Goebel, Nicholas 1 Guo, Mengwu 1 Harris, Kameron Decker 1 Herrmann, Benjamin 1 Hewitt, Sarah E. 1 Hinze, Michael 1 Johnson, Mikala C. 1 Kalia, Manu 1 Kamb, Mason 1 Kaptanoglu, Alan A. 1 Kath, William L. 1 Kiyak, Firat 1 Klemisch, Jennifer 1 Kneifl, Jonas 1 Kundtz, Nathan B. 1 Lapo, Karl 1 Li, Bian 1 Loiseau, Jean-Christophe 1 Lowrie, Wes 1 Lowrie, Weston 1 Luchtenburg, Dirk M. ...and 37 more Co-Authors all top 5 Serials 17 SIAM Journal on Applied Dynamical Systems 7 Physica D 5 Journal of Computational Physics 5 SIAM Journal on Applied Mathematics 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Multiscale Modeling & Simulation 2 Nonlinearity 2 Physics Letters. A 2 Mathematics and Computers in Simulation 2 Journal of Physics A: Mathematical and General 2 SIAM Review 2 SIAM Journal on Scientific Computing 2 Journal of Computational Neuroscience 2 Journal of Computational Dynamics 1 Journal of Fluid Mechanics 1 Wave Motion 1 IEEE Transactions on Automatic Control 1 European Journal of Applied Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Journal of Nonlinear Science 1 Physics of Fluids 1 Applied and Computational Harmonic Analysis 1 Advances in Computational Mathematics 1 Complexity 1 Nonlinear Dynamics 1 IEEE Transactions on Antennas and Propagation 1 Quantitative Finance 1 Journal of Machine Learning Research (JMLR) 1 Lecture Notes in Mathematics 1 Computational & Mathematical Methods in Medicine 1 Numerical Mathematics: Theory, Methods and Applications 1 The Journal of Mathematical Neuroscience 1 Other Titles in Applied Mathematics 1 IEEE Control Systems all top 5 Fields 43 Dynamical systems and ergodic theory (37-XX) 34 Numerical analysis (65-XX) 21 Partial differential equations (35-XX) 16 Computer science (68-XX) 16 Systems theory; control (93-XX) 15 Statistics (62-XX) 14 Optics, electromagnetic theory (78-XX) 10 Ordinary differential equations (34-XX) 9 Fluid mechanics (76-XX) 9 Biology and other natural sciences (92-XX) 9 Information and communication theory, circuits (94-XX) 5 Operator theory (47-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Approximations and expansions (41-XX) 4 Mechanics of particles and systems (70-XX) 3 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Quantum theory (81-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 69 Publications have been cited 1,938 times in 1,025 Documents Cited by ▼ Year ▼ Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Zbl 1355.94013 Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan 422 2016 On dynamic mode decomposition: theory and applications. Zbl 1346.37064 Tu, Jonathan H.; Rowley, Clarence W.; Luchtenburg, Dirk M.; Brunton, Steven L.; Kutz, J. Nathan 201 2014 Dynamic mode decomposition. Data-driven modeling of complex systems. Zbl 1365.65009 Kutz, J. Nathan; Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L. 185 2016 Data-driven science and engineering. Machine learning, dynamical systems, and control. Zbl 1407.68002 Brunton, Steven L.; Kutz, J. Nathan 106 2019 Dynamic mode decomposition with control. Zbl 1334.65199 Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 97 2016 Deep learning in fluid dynamics. Zbl 1383.76380 Kutz, J. Nathan 65 2017 Computing spectra of linear operators using the Floquet-Fourier-Hill method. Zbl 1105.65119 Deconinck, Bernard; Kutz, J. Nathan 65 2006 Data-driven identification of parametric partial differential equations. Zbl 1456.65096 Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 51 2019 Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Zbl 1425.93175 Kaiser, E.; Kutz, J. N.; Brunton, S. L. 51 2018 Multiresolution dynamic mode decomposition. Zbl 1338.37121 Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 51 2016 Model selection for dynamical systems via sparse regression and information criteria. Zbl 1404.65308 Mangan, N. M.; Kutz, J. N.; Brunton, S. L.; Proctor, J. L. 43 2017 Data-driven modeling and scientific computation. Methods for complex systems and big data. Zbl 1280.65002 Kutz, J. Nathan 43 2013 Deep learning of dynamics and signal-noise decomposition with time-stepping constraints. Zbl 1452.68170 Rudy, Samuel H.; Nathan Kutz, J.; Brunton, Steven L. 36 2019 Variable projection methods for an optimized dynamic mode decomposition. Zbl 1384.37122 Askham, Travis; Kutz, J. Nathan 33 2018 Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems. Zbl 1354.37078 Brunton, Steven L.; Tu, Jonathan H.; Bright, Ido; Kutz, J. Nathan 30 2014 Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Zbl 1320.76003 Bright, Ido; Lin, Guang; Kutz, J. Nathan 29 2013 Sparse sensor placement optimization for classification. Zbl 1350.49037 Brunton, B. W.; Brunton, S. L.; Proctor, J. L.; Kutz, J. N. 28 2016 Data-driven sparse sensor placement for reconstruction: demonstrating the benefits of exploiting known patterns. Zbl 1477.93128 Manohar, Krithika; Brunton, Bingni W.; Kutz, J. Nathan; Brunton, Steven L. 28 2018 Compressed sensing and dynamic mode decomposition. Zbl 1347.94012 Kutz, J. Nathan; Tu, Jonathan H.; Proctor, Joshua L.; Brunton, Steven L. 27 2015 Generalizing Koopman theory to allow for inputs and control. Zbl 1390.93226 Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 23 2018 Nonlinear model order reduction via dynamic mode decomposition. Zbl 1373.65090 Alla, Alessandro; Kutz, J. Nathan 19 2017 Mode-locked soliton lasers. Zbl 1121.35130 Kutz, J. Nathan 18 2006 Modern Koopman theory for dynamical systems. Zbl 1497.37105 Brunton, Steven L.; Budišić, Marko; Kaiser, Eurika; Kutz, J. Nathan 18 2022 Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems. Zbl 1409.37029 Nathan Kutz, J.; Proctor, J. L.; Brunton, S. L. 16 2018 SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics. Zbl 1473.93007 Kaheman, Kadierdan; Kutz, J. Nathan; Brunton, Steven L. 16 2020 Discovery of nonlinear multiscale systems: sampling strategies and embeddings. Zbl 1474.65476 Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan 15 2019 Randomized dynamic mode decomposition. Zbl 1427.65410 Erichson, N. Benjamin; Mathelin, Lionel; Kutz, J. Nathan; Brunton, Steven L. 15 2019 SpectrUW: a laboratory for the numerical exploration of spectra of linear operators. Zbl 1113.65058 Deconinck, Bernard; Kiyak, Firat; Carter, John D.; Kutz, J. Nathan 15 2007 Dynamic mode decomposition for financial trading strategies. Zbl 1400.91558 Mann, Jordan; Kutz, J. Nathan 14 2016 Dynamics and stability of Bose-Einstein condensates: the nonlinear Schrödinger equation with periodic potential. Zbl 1009.35078 Deconinck, B.; Frigyik, B. A.; Kutz, J. N. 13 2002 Model selection for hybrid dynamical systems via sparse regression. Zbl 1427.93253 Mangan, N. M.; Askham, T.; Brunton, S. L.; Kutz, J. N.; Proctor, J. L. 13 2019 Time-delay observables for Koopman: theory and applications. Zbl 1441.37090 Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 12 2020 Sparse principal component analysis via variable projection. Zbl 1440.62231 Erichson, N. Benjamin; Zheng, Peng; Manohar, Krithika; Brunton, Steven L.; Kutz, J. Nathan; Aravkin, Aleksandr Y. 11 2020 Data-driven science and engineering. Machine learning, dynamical systems, and control. 2nd edition. Zbl 1487.68001 Brunton, Steven L.; Kutz, J. Nathan 10 2022 Dynamics of periodic multi-component Bose-Einstein condensates. Zbl 1038.82056 Deconinck, Bernard; Kutz, J. Nathan; Patterson, Matthew S.; Warner, Brandon W. 9 2003 Randomized model order reduction. Zbl 1418.65193 Alla, Alessandro; Kutz, J. Nathan 8 2019 Hybrid reduced-order integration with proper orthogonal decomposition and dynamic mode decomposition. Zbl 1293.65136 Williams, Matthew O.; Schmid, Peter J.; Kutz, J. Nathan 8 2013 Shallow neural networks for fluid flow reconstruction with limited sensors. Zbl 1472.68172 Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei; Brunton, Steven L.; Mahoney, Michael W.; Kutz, J. Nathan 8 2020 Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator. Zbl 0973.78026 Promislow, Keith; Kutz, J. Nathan 7 2000 Stability of exact solutions of the defocusing nonlinear Schrödinger equation with periodic potential in two dimensions. Zbl 0984.81028 Deconinck, B.; Frigyik, B. A.; Kutz, J. N. 6 2001 Centering data improves the dynamic mode decomposition. Zbl 1465.37092 Hirsh, Seth M.; Harris, Kameron Decker; Kutz, J. Nathan; Brunton, Bingni W. 6 2020 Exact nonstationary solutions to the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials. Zbl 1136.82339 Bradley, R. Mark; Deconinck, Bernard; Kutz, J. Nathan 5 2005 Deep learning models for global coordinate transformations that linearise PDEs. Zbl 1479.35021 Gin, Craig; Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan 5 2021 From Fourier to Koopman: spectral methods for long-term time series prediction. Zbl 07370558 Lange, Henning; Brunton, Steven L.; Kutz, J. Nathan 5 2021 Compromised axonal functionality after neurodegeneration, concussion and/or traumatic brain injury. Zbl 1409.92050 Maia, Pedro D.; Kutz, J. Nathan 4 2014 Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers. Zbl 0851.35124 Kutz, J. Nathan; Kath, William L. 4 1996 Sparsity enabled cluster reduced-order models for control. Zbl 1375.76075 Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L. 4 2018 Asymptotic behavior of the nonlinear Schrödinger equation with rapidly varying, mean-zero dispersion. Zbl 0938.35178 Bronski, Jared C.; Kutz, J. Nathan 3 1997 Continuation of periodic solutions in the waveguide array mode-locked laser. Zbl 1235.78034 Williams, Matthew O.; Wilkening, Jon; Shlizerman, Eli; Kutz, J. Nathan 3 2011 Optimal sensor and actuator selection using balanced model reduction. Zbl 07564832 Manohar, Krithika; Kutz, J. Nathan; Brunton, Steven L. 3 2022 Data-driven approximations of dynamical systems operators for control. Zbl 1453.93047 Kaiser, Eurika; Kutz, J. Nathan; Brunton, Steven L. 3 2020 Adaptive dimensionality-reduction for time-stepping in differential and partial differential equations. Zbl 1413.65302 Fu, Xing; Kutz, J. Nathan 2 2017 Optimized sampling for multiscale dynamics. Zbl 07033871 Manohar, Krithika; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 2 2019 Mode-locking of fiber lasers via nonlinear mode-coupling. Zbl 1080.35142 Kutz, J. N. 2 2005 Deep learning of conjugate mappings. Zbl 1491.37074 Bramburger, Jason J.; Brunton, Steven L.; Nathan Kutz, J. 2 2021 Poincaré maps for multiscale physics discovery and nonlinear Floquet theory. Zbl 1493.37096 Bramburger, Jason J.; Kutz, J. Nathan 2 2020 Classification of spatiotemporal data via asynchronous sparse sampling: application to flow around a cylinder. Zbl 1381.37101 Bright, Ido; Lin, Guang; Kutz, J. Nathan 2 2016 Averaged models for passive mode-locking using nonlinear mode-coupling. Zbl 1110.78008 Proctor, J.; Kutz, J. Nathan 2 2007 Singular instability of exact stationary solutions of the non-local Gross-Pitaevskii equation. Zbl 1045.35077 Deconinck, Bernard; Kutz, J. Nathan 2 2003 Neural activity measures and their dynamics. Zbl 1318.92008 Shlizerman, Eli; Schroder, Konrad; Kutz, J. Nathan 2 2012 Parsimony as the ultimate regularizer for physics-informed machine learning. Zbl 1517.68337 Kutz, J. Nathan; Brunton, Steven L. 2 2022 Online interpolation point refinement for reduced-order models using a genetic algorithm. Zbl 1383.65123 Sargsyan, Syuzanna; Brunton, Steven L.; Kutz, J. Nathan 1 2018 Symmetries constrain dynamics in a family of balanced neural networks. Zbl 1395.92029 Barreiro, Andrea K.; Kutz, J. Nathan; Shlizerman, Eli 1 2017 Global existence and uniqueness for an optical fibre laser model. Zbl 0913.35018 Mielke, Alexander; Holmes, Philip; Kutz, J. Nathan 1 1998 Dynamics and bifurcations of a planar map modeling dispersion managed breathers. Zbl 0936.34030 Holmes, Philip; Kutz, J. Nathan 1 1999 Mode-locked matter waves in Bose-Einstein condensates. Zbl 1167.82328 Kutz, J. Nathan 1 2009 Robust and scalable methods for the dynamic mode decomposition. Zbl 1490.37100 Askham, Travis; Zheng, Peng; Aravkin, Aleksandr; Kutz, J. Nathan 1 2022 Smoothing and parameter estimation by soft-adherence to governing equations. Zbl 1453.62399 Rudy, Samuel H.; Brunton, Steven L.; Kutz, J. Nathan 1 2019 The low dimensionality of time-periodic standing waves in water of finite and infinite depth. Zbl 1263.37084 Williams, Matthew O.; Shlizerman, Eli; Wilkening, Jon; Kutz, J. Nathan 1 2012 Modern Koopman theory for dynamical systems. Zbl 1497.37105 Brunton, Steven L.; Budišić, Marko; Kaiser, Eurika; Kutz, J. Nathan 18 2022 Data-driven science and engineering. Machine learning, dynamical systems, and control. 2nd edition. Zbl 1487.68001 Brunton, Steven L.; Kutz, J. Nathan 10 2022 Optimal sensor and actuator selection using balanced model reduction. Zbl 07564832 Manohar, Krithika; Kutz, J. Nathan; Brunton, Steven L. 3 2022 Parsimony as the ultimate regularizer for physics-informed machine learning. Zbl 1517.68337 Kutz, J. Nathan; Brunton, Steven L. 2 2022 Robust and scalable methods for the dynamic mode decomposition. Zbl 1490.37100 Askham, Travis; Zheng, Peng; Aravkin, Aleksandr; Kutz, J. Nathan 1 2022 Deep learning models for global coordinate transformations that linearise PDEs. Zbl 1479.35021 Gin, Craig; Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan 5 2021 From Fourier to Koopman: spectral methods for long-term time series prediction. Zbl 07370558 Lange, Henning; Brunton, Steven L.; Kutz, J. Nathan 5 2021 Deep learning of conjugate mappings. Zbl 1491.37074 Bramburger, Jason J.; Brunton, Steven L.; Nathan Kutz, J. 2 2021 SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics. Zbl 1473.93007 Kaheman, Kadierdan; Kutz, J. Nathan; Brunton, Steven L. 16 2020 Time-delay observables for Koopman: theory and applications. Zbl 1441.37090 Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 12 2020 Sparse principal component analysis via variable projection. Zbl 1440.62231 Erichson, N. Benjamin; Zheng, Peng; Manohar, Krithika; Brunton, Steven L.; Kutz, J. Nathan; Aravkin, Aleksandr Y. 11 2020 Shallow neural networks for fluid flow reconstruction with limited sensors. Zbl 1472.68172 Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei; Brunton, Steven L.; Mahoney, Michael W.; Kutz, J. Nathan 8 2020 Centering data improves the dynamic mode decomposition. Zbl 1465.37092 Hirsh, Seth M.; Harris, Kameron Decker; Kutz, J. Nathan; Brunton, Bingni W. 6 2020 Data-driven approximations of dynamical systems operators for control. Zbl 1453.93047 Kaiser, Eurika; Kutz, J. Nathan; Brunton, Steven L. 3 2020 Poincaré maps for multiscale physics discovery and nonlinear Floquet theory. Zbl 1493.37096 Bramburger, Jason J.; Kutz, J. Nathan 2 2020 Data-driven science and engineering. Machine learning, dynamical systems, and control. Zbl 1407.68002 Brunton, Steven L.; Kutz, J. Nathan 106 2019 Data-driven identification of parametric partial differential equations. Zbl 1456.65096 Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 51 2019 Deep learning of dynamics and signal-noise decomposition with time-stepping constraints. Zbl 1452.68170 Rudy, Samuel H.; Nathan Kutz, J.; Brunton, Steven L. 36 2019 Discovery of nonlinear multiscale systems: sampling strategies and embeddings. Zbl 1474.65476 Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan 15 2019 Randomized dynamic mode decomposition. Zbl 1427.65410 Erichson, N. Benjamin; Mathelin, Lionel; Kutz, J. Nathan; Brunton, Steven L. 15 2019 Model selection for hybrid dynamical systems via sparse regression. Zbl 1427.93253 Mangan, N. M.; Askham, T.; Brunton, S. L.; Kutz, J. N.; Proctor, J. L. 13 2019 Randomized model order reduction. Zbl 1418.65193 Alla, Alessandro; Kutz, J. Nathan 8 2019 Optimized sampling for multiscale dynamics. Zbl 07033871 Manohar, Krithika; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 2 2019 Smoothing and parameter estimation by soft-adherence to governing equations. Zbl 1453.62399 Rudy, Samuel H.; Brunton, Steven L.; Kutz, J. Nathan 1 2019 Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Zbl 1425.93175 Kaiser, E.; Kutz, J. N.; Brunton, S. L. 51 2018 Variable projection methods for an optimized dynamic mode decomposition. Zbl 1384.37122 Askham, Travis; Kutz, J. Nathan 33 2018 Data-driven sparse sensor placement for reconstruction: demonstrating the benefits of exploiting known patterns. Zbl 1477.93128 Manohar, Krithika; Brunton, Bingni W.; Kutz, J. Nathan; Brunton, Steven L. 28 2018 Generalizing Koopman theory to allow for inputs and control. Zbl 1390.93226 Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 23 2018 Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems. Zbl 1409.37029 Nathan Kutz, J.; Proctor, J. L.; Brunton, S. L. 16 2018 Sparsity enabled cluster reduced-order models for control. Zbl 1375.76075 Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L. 4 2018 Online interpolation point refinement for reduced-order models using a genetic algorithm. Zbl 1383.65123 Sargsyan, Syuzanna; Brunton, Steven L.; Kutz, J. Nathan 1 2018 Deep learning in fluid dynamics. Zbl 1383.76380 Kutz, J. Nathan 65 2017 Model selection for dynamical systems via sparse regression and information criteria. Zbl 1404.65308 Mangan, N. M.; Kutz, J. N.; Brunton, S. L.; Proctor, J. L. 43 2017 Nonlinear model order reduction via dynamic mode decomposition. Zbl 1373.65090 Alla, Alessandro; Kutz, J. Nathan 19 2017 Adaptive dimensionality-reduction for time-stepping in differential and partial differential equations. Zbl 1413.65302 Fu, Xing; Kutz, J. Nathan 2 2017 Symmetries constrain dynamics in a family of balanced neural networks. Zbl 1395.92029 Barreiro, Andrea K.; Kutz, J. Nathan; Shlizerman, Eli 1 2017 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Zbl 1355.94013 Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan 422 2016 Dynamic mode decomposition. Data-driven modeling of complex systems. Zbl 1365.65009 Kutz, J. Nathan; Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L. 185 2016 Dynamic mode decomposition with control. Zbl 1334.65199 Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 97 2016 Multiresolution dynamic mode decomposition. Zbl 1338.37121 Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 51 2016 Sparse sensor placement optimization for classification. Zbl 1350.49037 Brunton, B. W.; Brunton, S. L.; Proctor, J. L.; Kutz, J. N. 28 2016 Dynamic mode decomposition for financial trading strategies. Zbl 1400.91558 Mann, Jordan; Kutz, J. Nathan 14 2016 Classification of spatiotemporal data via asynchronous sparse sampling: application to flow around a cylinder. Zbl 1381.37101 Bright, Ido; Lin, Guang; Kutz, J. Nathan 2 2016 Compressed sensing and dynamic mode decomposition. Zbl 1347.94012 Kutz, J. Nathan; Tu, Jonathan H.; Proctor, Joshua L.; Brunton, Steven L. 27 2015 On dynamic mode decomposition: theory and applications. Zbl 1346.37064 Tu, Jonathan H.; Rowley, Clarence W.; Luchtenburg, Dirk M.; Brunton, Steven L.; Kutz, J. Nathan 201 2014 Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems. Zbl 1354.37078 Brunton, Steven L.; Tu, Jonathan H.; Bright, Ido; Kutz, J. Nathan 30 2014 Compromised axonal functionality after neurodegeneration, concussion and/or traumatic brain injury. Zbl 1409.92050 Maia, Pedro D.; Kutz, J. Nathan 4 2014 Data-driven modeling and scientific computation. Methods for complex systems and big data. Zbl 1280.65002 Kutz, J. Nathan 43 2013 Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Zbl 1320.76003 Bright, Ido; Lin, Guang; Kutz, J. Nathan 29 2013 Hybrid reduced-order integration with proper orthogonal decomposition and dynamic mode decomposition. Zbl 1293.65136 Williams, Matthew O.; Schmid, Peter J.; Kutz, J. Nathan 8 2013 Neural activity measures and their dynamics. Zbl 1318.92008 Shlizerman, Eli; Schroder, Konrad; Kutz, J. Nathan 2 2012 The low dimensionality of time-periodic standing waves in water of finite and infinite depth. Zbl 1263.37084 Williams, Matthew O.; Shlizerman, Eli; Wilkening, Jon; Kutz, J. Nathan 1 2012 Continuation of periodic solutions in the waveguide array mode-locked laser. Zbl 1235.78034 Williams, Matthew O.; Wilkening, Jon; Shlizerman, Eli; Kutz, J. Nathan 3 2011 Mode-locked matter waves in Bose-Einstein condensates. Zbl 1167.82328 Kutz, J. Nathan 1 2009 SpectrUW: a laboratory for the numerical exploration of spectra of linear operators. Zbl 1113.65058 Deconinck, Bernard; Kiyak, Firat; Carter, John D.; Kutz, J. Nathan 15 2007 Averaged models for passive mode-locking using nonlinear mode-coupling. Zbl 1110.78008 Proctor, J.; Kutz, J. Nathan 2 2007 Computing spectra of linear operators using the Floquet-Fourier-Hill method. Zbl 1105.65119 Deconinck, Bernard; Kutz, J. Nathan 65 2006 Mode-locked soliton lasers. Zbl 1121.35130 Kutz, J. Nathan 18 2006 Exact nonstationary solutions to the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials. Zbl 1136.82339 Bradley, R. Mark; Deconinck, Bernard; Kutz, J. Nathan 5 2005 Mode-locking of fiber lasers via nonlinear mode-coupling. Zbl 1080.35142 Kutz, J. N. 2 2005 Dynamics of periodic multi-component Bose-Einstein condensates. Zbl 1038.82056 Deconinck, Bernard; Kutz, J. Nathan; Patterson, Matthew S.; Warner, Brandon W. 9 2003 Singular instability of exact stationary solutions of the non-local Gross-Pitaevskii equation. Zbl 1045.35077 Deconinck, Bernard; Kutz, J. Nathan 2 2003 Dynamics and stability of Bose-Einstein condensates: the nonlinear Schrödinger equation with periodic potential. Zbl 1009.35078 Deconinck, B.; Frigyik, B. A.; Kutz, J. N. 13 2002 Stability of exact solutions of the defocusing nonlinear Schrödinger equation with periodic potential in two dimensions. Zbl 0984.81028 Deconinck, B.; Frigyik, B. A.; Kutz, J. N. 6 2001 Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator. Zbl 0973.78026 Promislow, Keith; Kutz, J. Nathan 7 2000 Dynamics and bifurcations of a planar map modeling dispersion managed breathers. Zbl 0936.34030 Holmes, Philip; Kutz, J. Nathan 1 1999 Global existence and uniqueness for an optical fibre laser model. Zbl 0913.35018 Mielke, Alexander; Holmes, Philip; Kutz, J. Nathan 1 1998 Asymptotic behavior of the nonlinear Schrödinger equation with rapidly varying, mean-zero dispersion. Zbl 0938.35178 Bronski, Jared C.; Kutz, J. Nathan 3 1997 Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers. Zbl 0851.35124 Kutz, J. Nathan; Kath, William L. 4 1996 all cited Publications top 5 cited Publications all top 5 Cited by 2,054 Authors 52 Kutz, J. Nathan 42 Brunton, Steven L. 20 Deconinck, Bernard 16 Peherstorfer, Benjamin 15 Rozza, Gianluigi 13 Kevrekidis, Ioannis George 12 Karniadakis, George Em 12 Mezić, Igor 12 Noack, Bernd R. 12 Willcox, Karen E. 10 Peitz, Sebastian 10 San, Omer 10 Xiu, Dongbin 9 Chinesta, Francisco 9 Duan, Jinqiao 9 Hesthaven, Jan S. 9 Iliescu, Traian 9 Klus, Stefan 9 Proctor, Joshua L. 9 Trichtchenko, Olga 8 Le Clainche, Soledad 8 Maulik, Romit 8 Schaeffer, Hayden 7 Alla, Alessandro 7 Benner, Peter 7 Cueto, Elias 7 Giannakis, Dimitrios 7 Kaiser, Eurika 7 Krämer, Boris 7 Lermusiaux, Pierre F. J. 7 Lin, Guang 7 Rowley, Clarence Worth 7 Schütte, Christof 7 Wu, Kailiang 6 Barker, Blake 6 Bollt, Erik M. 6 Brunton, Bingni Wen 6 Carter, John D. 6 Johnson, Mathew A. 6 Kang, Sung Ha 6 Kevrekidis, Panayotis G. 6 Perdikaris, Paris G. 6 Raissi, Maziar 6 Tran, Giang N. 6 Vega, José Manuel 6 Wilson, Dan D. 6 Zhang, Dongxiao 6 Zumbrun, Kevin R. 5 Chen, Zhen 5 Das, Suddhasattwa 5 Dietrich, Felix 5 Duraisamy, Karthik 5 Kapitula, Todd M. 5 Li, Yang 5 Liao, Wenjing 5 Loiseau, Jean-Christophe 5 Malomed, Boris A. 5 Morzyński, Marek 5 Mou, Changhong 5 Nüske, Feliks 5 Pan, Shaowu 5 Sapsis, Themistoklis P. 5 Stabile, Giovanni 5 Tartakovsky, Daniel M. 4 Abisset-Chavanne, Emmanuelle 4 Adams, Nikolaus A. 4 Ahmed, Shady E. 4 Babaee, Hessam 4 Biondini, Gino 4 Bortz, David M. 4 Chakraborty, Souvik 4 Chang, Haibin 4 Deng, Nan 4 Drmač, Zlatko 4 Erichson, N. Benjamin 4 Fukagata, Koji 4 Fukami, Kai 4 He, Yuchen 4 Huang, Juntao 4 Ibañez, Ruben 4 Jiang, Lijian 4 Karasözen, Bülent 4 Kawahara, Yoshinobu 4 Koltai, Péter 4 Koutsourelakis, Phaedon-Stelios 4 Kumar, Siddhant 4 Liu, Yingjie 4 Livescu, Daniel 4 Lu, Hannah 4 Maggioni, Mauro 4 Marzuola, Jeremy Louis 4 Mathelin, Lionel 4 Mauroy, Alexandre 4 Messenger, Daniel A. 4 Nicholls, David P. 4 Quaini, Annalisa 4 Rasheed, Adil 4 Rodrigues, Luis Miguel 4 Rudy, Samuel H. 4 Sherratt, Jonathan A. ...and 1,954 more Authors all top 5 Cited in 178 Serials 137 Journal of Computational Physics 98 Journal of Fluid Mechanics 74 Physica D 71 Computer Methods in Applied Mechanics and Engineering 64 SIAM Journal on Applied Dynamical Systems 37 SIAM Journal on Scientific Computing 29 Chaos 24 Computers and Fluids 22 Journal of Nonlinear Science 15 Journal of Scientific Computing 13 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 11 Automatica 11 Computational Mechanics 11 Advances in Computational Mathematics 11 Communications in Nonlinear Science and Numerical Simulation 10 Computers & Mathematics with Applications 10 Nonlinear Dynamics 9 Physica A 9 Journal of Computational Dynamics 8 Mathematics and Computers in Simulation 8 SIAM/ASA Journal on Uncertainty Quantification 7 SIAM Review 7 International Journal of Computational Fluid Dynamics 7 European Journal of Mechanics. B. Fluids 7 Multiscale Modeling & Simulation 7 Communications in Computational Physics 6 Inverse Problems 6 Applied Mathematics and Computation 6 Studies in Applied Mathematics 6 SIAM Journal on Applied Mathematics 6 International Journal of Robust and Nonlinear Control 5 International Journal for Numerical Methods in Engineering 5 Journal of Computational and Applied Mathematics 5 Journal of Differential Equations 5 Applied and Computational Harmonic Analysis 5 ETNA. Electronic Transactions on Numerical Analysis 5 Journal of Machine Learning Research (JMLR) 5 GAMM-Mitteilungen 4 Computer Physics Communications 4 Journal of Statistical Physics 4 Physics Letters. A 4 Wave Motion 4 Bulletin of Mathematical Biology 4 SIAM Journal on Mathematical Analysis 4 Computational Geosciences 3 Biological Cybernetics 3 Journal of the Franklin Institute 3 Journal of Mathematical Biology 3 Journal of Mathematical Physics 3 Nonlinearity 3 SIAM Journal on Numerical Analysis 3 Applied Numerical Mathematics 3 Neural Networks 3 Computational and Applied Mathematics 3 Complexity 3 Discrete and Continuous Dynamical Systems 3 Stochastics and Dynamics 3 Acta Numerica 3 Journal of Statistical Mechanics: Theory and Experiment 3 Journal of Physics A: Mathematical and Theoretical 2 Acta Mechanica 2 Archive for Rational Mechanics and Analysis 2 International Journal of Control 2 Journal of Mathematical Analysis and Applications 2 Mathematical Methods in the Applied Sciences 2 Mathematics of Computation 2 Chaos, Solitons and Fractals 2 Advances in Mathematics 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Matrix Analysis and Applications 2 European Journal of Applied Mathematics 2 Machine Learning 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Global Optimization 2 Applied Mathematical Modelling 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Computational Neuroscience 2 Engineering Analysis with Boundary Elements 2 Multibody System Dynamics 2 European Journal of Mechanics. A. Solids 2 Archives of Computational Methods in Engineering 2 Analysis and Applications (Singapore) 2 International Journal of Computational Methods 2 Oberwolfach Reports 2 Advances in Data Analysis and Classification. ADAC 2 SIAM Journal on Imaging Sciences 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Mathematics in Industry 2 SIAM Journal on Mathematics of Data Science 2 Sampling Theory, Signal Processing, and Data Analysis 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 European Journal of Physics 1 International Journal of Theoretical Physics 1 Applied Mathematics and Optimization 1 Calcolo 1 Computing 1 Information Sciences 1 International Journal of Mathematics and Mathematical Sciences ...and 78 more Serials all top 5 Cited in 44 Fields 354 Numerical analysis (65-XX) 287 Fluid mechanics (76-XX) 250 Dynamical systems and ergodic theory (37-XX) 250 Computer science (68-XX) 221 Partial differential equations (35-XX) 127 Systems theory; control (93-XX) 120 Statistics (62-XX) 72 Biology and other natural sciences (92-XX) 53 Mechanics of deformable solids (74-XX) 45 Probability theory and stochastic processes (60-XX) 44 Statistical mechanics, structure of matter (82-XX) 39 Ordinary differential equations (34-XX) 38 Operator theory (47-XX) 34 Operations research, mathematical programming (90-XX) 29 Mechanics of particles and systems (70-XX) 28 Geophysics (86-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 22 Information and communication theory, circuits (94-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 Optics, electromagnetic theory (78-XX) 17 Quantum theory (81-XX) 15 Classical thermodynamics, heat transfer (80-XX) 7 Approximations and expansions (41-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Functional analysis (46-XX) 5 General and overarching topics; collections (00-XX) 5 Differential geometry (53-XX) 4 Combinatorics (05-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Astronomy and astrophysics (85-XX) 3 Integral equations (45-XX) 2 Mathematical logic and foundations (03-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Relativity and gravitational theory (83-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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