References
Published online by Cambridge University Press: 12 January 2023
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Data-Driven Fluid MechanicsCombining First Principles and Machine Learning, pp. 409 - 448Publisher: Cambridge University PressPrint publication year: 2023
References
Abdi, H. (2003), ‘Factor rotations in factor analyses’, Encyclopedia for Research Methods for the Social Sciences, Sage, Thousand Oaks, CA, pp. 792–795.Google Scholar
Abraham, R., Marsden, J. E., and Marsden, J. E. (1978), Foundations of Mechanics, Benjam-in/Cummings Publishing Company, Reading, MA.Google Scholar
Abraham, R., Marsden, J. E., and Ratiu, T. (1988), Manifolds, Tensor Analysis, and Applications, Vol. 75 of Applied Mathematical Sciences, Springer-Verlag, New York.CrossRefGoogle Scholar
Abu-Mostafa, Y. S., Magndon-Ismail, M., and Lin, H.-T. (2012), Learning from Data: A Short Course, https://amlbook.com/.Google Scholar
Abu-Zurayk, M., Ilic, C., Schuster, A., and Liepelt, R. (2017), Effect of gradient approximations on aero-structural gradient-based wing optimization, in ‘EUROGEN 2017’, September 13–15, 2017, Madrid, Spain.Google Scholar
Adrian, R. J. (1975), On the role of conditional averages in turbulence theory, in ‘Proceedings of the 4th Biennial Symposium on Turbulence in Liquids, University of Missouri-Rolla, 1975’, Science Press, Princeton, NJ.Google Scholar
Adrian, R. J. (1991), ‘Particle-imaging techniques for experimental fluid mechanics’, Annual Review of Fluid Mechanics 23(1), 261–304.CrossRefGoogle Scholar
Adrian, R. J. (2007), ‘Hairpin vortex organization in wall turbulence’, Physics of Fluids 19, 041301.Google Scholar
Adrian, R. J., Jones, B., Chung, M., Hassan, Y., Nithianandan, C., and Tung, A.-C. (1989), ‘Approximation of turbulent conditional averages by stochastic estimation’, Physics of Fluids A: Fluid Dynamics 1(6), 992–998.Google Scholar
Ahuja, S. and Rowley, C. W. (2010), ‘Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators’, Journal of Fluid Mechanics 645, 447–478.Google Scholar
Albers, M., Meysonnat, P. S., Fernex, D., Semaan, R., Noack, B. R., and Schröder, W. (2020), ‘Drag reduction and energy saving by spanwise traveling transversal surface waves for flat plate flow’, Flow, Turbulence and Combustion 105, 125–157.CrossRefGoogle Scholar
Aleksic, K., Luchtenburg, D. M., King, R., Noack, B. R., and Pfeiffer, J. (2010), Robust nonlinear control versus linear model predictive control of a bluff body wake, in ‘5th AIAA Flow Control Conference’, June 28–July 1, 2010, Chicago, AIAA-Paper 2010-4833, pp. 1–18.Google Scholar
Allaire, G. and Schoenauer, M. (2007), Conception optimale de structures, Vol. 58 of Mathématiques et Applications, Springer, Berlin.Google Scholar
Alsalman, M., Colvert, B., and Kanso, E. (2018), ‘Training bioinspired sensors to classify flows’, Bioinspiration & Biomimetics 14(1), 016009.Google Scholar
Amsallem, D., Zahr, M. J., and Farhat, C. (2012), ‘Nonlinear model order reduction based on local reduced-order bases’, International Journal for Numerical Methods in Engineering 92(10), 891–916.Google Scholar
Antoranz, A., Gonzalo, A., Flores, O., and Garcia-Villalba, M. (2015), ‘Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions’, International Journal of Heat and Fluid Flow 55, 45–51.CrossRefGoogle Scholar
Antoranz, A., Ianiro, A., Flores, O., and García-Villalba, M. (2018), ‘Extended proper orthogonal decomposition of non-homogeneous thermal fields in a turbulent pipe flow’, International Journal of Heat and Mass Transfer 118, 1264–1275.Google Scholar
Antoulas, A. C. (2005), Approximation of Large-Scale Dynamical Systems, Society for Indus-trial and Applied Mathematics, Philadelphia.Google Scholar
Arbabi, H. and Mezić, I. (2017), ‘Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator’, SIAM Journal on Applied Dynamical Systems 16(4), 2096–2126.Google Scholar
Armstrong, E. and Sutherland, J. C. (2021), ‘A technique for characterizing feature size and quality of manifolds’, Combustion Theory and Modelling, 25, 646–668.CrossRefGoogle Scholar
Arthur, D. and Vassilvitskii, S. (2007), k-means++: The advantages of careful seeding, in ‘Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms’, Society for Industrial and Applied Mathematics, Philadelphia, pp. 1027–1035.Google Scholar
Ashurst, W. T. and Meiburg, E. (1988), ‘Three-dimensional shear layers via vortex dynamics’, Journal of Fluid Mechanics 189, 87–116.Google Scholar
Aström, K. J. and Murray, R. M. (2010), Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, Princeton, NJ.Google Scholar
Aubry, N., Holmes, P., Lumley, J. L., and Stone, E. (1988), ‘The dynamics of coherent structures in the wall region of a turbulent boundary layer’, Journal of Fluid Mechanics 192(1), 115–173.Google Scholar
Baars, W. J. and Tinney, C. E. (2014), ‘Proper orthogonal decomposition-based spectral higher-order stochastic estimation’, Physics of Fluids 26(5), 055112.Google Scholar
Babaee, H. and Sapsis, T. P. (2016), ‘A variational principle for the description of time-dependent modes associated with transient instabilities’, Philosophical Transactions of the Royal Society of London 472, 20150779.Google Scholar
Bagheri, S., Brandt, L., and Henningson, D. (2009), ‘Input–output analysis, model reduction and control of the flat-plate boundary layer’, Journal of Fluid Mechanics 620, 263–298.Google Scholar
Bagheri, S., Hoepffner, J., Schmid, P. J., and Henningson, D. S. (2009), ‘Input–output analysis and control design applied to a linear model of spatially developing flows’, Applied Mechanics Reviews 62(2), 020803-1–020803-27.CrossRefGoogle Scholar
Balajewicz, M., Dowell, E. H., and Noack, B. R. (2013), ‘Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation’, Journal of Fluid Mechanics 729, 285–308.Google Scholar
Baldi, P. and Hornik, K. (1989), ‘Neural networks and principal component analysis: Learning from examples without local minima’, Neural Networks 2(1), 53–58.Google Scholar
Banerjee, I. and Ierapetritou, M. (2006), ‘An adaptive reduction scheme to model reactive flow’, Combustion and Flame 144(3), 619–633.Google Scholar
Baraniuk, R. G. (2007), ‘Compressive sensing’, IEEE Signal Processing Magazine 24(4), 118–120.CrossRefGoogle Scholar
Barbagallo, A., Sipp, D., and Schmid, P. J. (2009), ‘Closed-loop control of an open cavity flow using reduced-order models’, Journal of Fluid Mechanics 641, 1–50.Google Scholar
Barkley, D. and Henderson, R. (1996), ‘Three-dimensional Floquet stability analysis of the wake of a circular cylinder’, Journal of Fluid Mechanics 322, 215–241.Google Scholar
Barlow, R. S. and Frank, J. H. (1998), ‘Effects of turbulence on species mass fractions in methane/air jet flames’, Symposium (International) on Combustion 27, 1087–1095.CrossRefGoogle Scholar
Batchelor, G. K. (1969), ‘Computation of the energy spectrum in homogeneous two dimensional turbulence’, Physics of Fluids 12 (Suppl. II), 233–239.Google Scholar
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R. Gulcehre, C., Song, F., Ballard, A., Gilmer, J., Dahl, G., Vaswani, A., Allen, K., Nash, C., Langston, V., Dyer, C., Heess, N., Wierstra, D., Kohli, P., Botvinick, M., Vinyals, O., Li, Y., and Pascanu, R. (2018), ‘Relational inductive biases, deep learning, and graph networks’, arXiv preprint arXiv:1806.01261.Google Scholar
Beerends, R. J., ter Morsche, H. G., Van den Berg, J. C., and van de Vrie, E. M. (2003), Fourier and Laplace Transforms, Cambridge University Press, New York.Google Scholar
Beetham, S. and Capecelatro, J. (2020), ‘Formulating turbulence closures using sparse regres-sion with embedded form invariance’, arXiv preprint arXiv:2003.12884.Google Scholar
Beintema, G., Corbetta, A., Biferale, L., and Toschi, F. (2020), ‘Controlling Rayleigh–Bénard convection via reinforcement learning’, Journal of Turbulence 21(9–10), 585–605.Google Scholar
Bekemeyer, P., Ripepi, M., Heinrich, R., and Görtz, S. (2019), ‘Nonlinear unsteady reduced-order modeling for gust-load predictions’, AIAA Journal 57(5), 1839–1850.Google Scholar
Bekemeyer, P., Wunderlich, T., Görtz, S., and Dähne, D. (2019), Effect of gradient approx-imations on aero-structural gradient-based wing optimization, in ‘International Forum on Aeroelasticity and Structural Dynamics (IFASD-2019)’, June 9–13, 2019, Savannah, GA.Google Scholar
Bekemeyer, P., Bertram, A., Chaves, D. A. H., Ribeiro, M. D., Garbo, A., Kiener, A., Sabater, C., Stradtner, M., Wassing, S., Widhalm, M., Goertz, S., Jaeckel, F., Hoppe, R. & Hoffmann, N. (2022), ‘Data-driven aerodynamic modeling using the DLR SMARTy toolbox’.CrossRefGoogle Scholar
Bellemans, A., Aversano, G., Coussement, A., and Parente, A. (2018), ‘Feature extraction and reduced-order modelling of nitrogen plasma models using principal component analysis’, Computers & Chemical Engineering 115, 504–514.CrossRefGoogle Scholar
Bellemare, M. G., Dabney, W., and Munos, R. (2017), A distributional perspective on reinforcement learning, in ‘Proceedings of the 34th International Conference on Machine Learning – Volume 70’, ICML 17, JMLR.org, pp. 449–458.Google Scholar
Bellman, R. (1957), ‘A Markovian decision process’, Journal of Mathematics and Mechanics 6(5), 679–684.Google Scholar
Belson, B. A., Semeraro, O., Rowley, C. W., and Henningson, D. S. (2013), ‘Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators’, Physics of Fluids (1994–present) 25(5), 054106.Google Scholar
Belson, B. A., Tu, J. H., and Rowley, C. W. (2014), ‘Algorithm 945: Modred – A parallelized model reduction library’, ACM Transactions on Mathematical Software (TOMS) 40(4), 30.Google Scholar
Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., and Reglade, U. (2019), ‘Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film’, AIP Advances 9(12), 125014.CrossRefGoogle Scholar
Bence, J. R. (1995), ‘Analysis of short time series: Correcting for autocorrelation’, Ecology 76(2), 628–639.Google Scholar
Benner, P., Gugercin, S., and Willcox, K. (2015), ‘A survey of projection-based model reduction methods for parametric dynamical systems’, SIAM Review 57(4), 483–531.Google Scholar
Bergmann, M., Cordier, L., and Brancher, J.-P. (2005), ‘Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model’, Physics of Fluids (1994–present) 17(9), 097101.Google Scholar
Berkooz, G., Holmes, P., and Lumley, J. L. (1993), ‘The proper orthogonal decomposition in the analysis of turbulent flows’, Annual Review of Fluid Mechanics 23, 539–575.Google Scholar
Bernal, L. P. (1981), The coherent structure of turbulent mixing layers, PhD thesis, California Institute of Technology, Pasadena.Google Scholar
Berry, M. W., Browne, M., Langville, A. N., Pauca, V. P., and Plemmons, R. J. (2007), ‘Algo-rithms and applications for approximate nonnegative matrix factorization’, Computational Statistics & Data Analysis 52(1), 155–173.CrossRefGoogle Scholar
Bertolotti, F., Herbert, T., and Spalart, P. (1992), ‘Linear and nonlinear stability of the Blasius boundary layer’, Journal of Fluid Mechanics 242, 441–474.Google Scholar
Betchov, R. (1956), ‘An inequality concerning the production of vorticity in isotropic turbulence’, Journal of Fluid Mechanics 1, 497–504.Google Scholar
Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., and Dellnitz, M. (2019), ‘Deep model predictive control with online learning for complex physical systems’, arXiv preprint arXiv:1905.10094.Google Scholar
Biglari, A. and Sutherland, J. C. (2012), ‘A filter-independent model identification technique for turbulent combustion modeling’, Combustion and Flame 159(5), 1960–1970.Google Scholar
Biglari, A. and Sutherland, J. C. (2015), ‘An a-posteriori evaluation of principal component analysis-based models for turbulent combustion simulations’, Combustion and Flame 162(10), 4025–4035.Google Scholar
Bilger, R., Starner, S., and Kee, R. (1990), ‘On reduced mechanisms for methane-air combustion in nonpremixed flames’, Combustion and Flame 80, 135–149.Google Scholar
Billings, S. A. (2013), Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, John Wiley & Sons, Hoboken, NJ.Google Scholar
Bistrian, D. and Navon, I. (2016), ‘Randomized dynamic mode decomposition for non-intrusive reduced order modelling’, International Journal for Numerical Methods in Engineering 112, 3–25.Google Scholar
Black, F., Schulze, P., and Unger, B. (2019), ‘Nonlinear Galerkin model reduction for systems with multiple transport velocities’, arXiv preprint arXiv:1912.11138.Google Scholar
Boffetta, G. and Ecke, R. E. (2012), ‘Two-dimensional turbulence’, The Annual Review of Fluid Mechanics 44, 427–451.Google Scholar
Bohn, E., Coates, E. M., Moe, S., and Johansen, T. A. (2019), Deep reinforcement learning attitude control of fixed-wing UAVs using proximal policy optimization, in ‘2019 International Conference on Unmanned Aircraft Systems (ICUAS)’, June 11–14, 2019, Atlanta, GA, IEEE, pp. 523–533.Google Scholar
Bongard, J. and Lipson, H. (2007), ‘Automated reverse engineering of nonlinear dynamical systems’, Proceedings of the National Academy of Sciences 104(24), 9943–9948.Google Scholar
Borée, J. (2003), ‘Extended proper orthogonal decomposition: A tool to analyse correlated events in turbulent flows’, Experiments in Fluids 35(2), 188–192.Google Scholar
Bourgeois, J. A., Martinuzzi, R. J., and Noack, B. R. (2013), ‘Generalised phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake’, Journal of Fluid Mechanics 736, 316–350.Google Scholar
Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M. (2015), Time Series Analysis: Forecasting and Control, John Wiley & Sons, Hoboken, NJ.Google Scholar
Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2011), ‘Distributed optimization and statistical learning via the alternating direction method of multipliers’, Foundations and Trends in Machine Learning 3, 1–122.Google Scholar
Brackston, R., De La Cruz, J. G., Wynn, A., Rigas, G., and Morrison, J. (2016), ‘Stochastic modelling and feedback control of bistability in a turbulent bluff body wake’, Journal of Fluid Mechanics 802, 726–749.CrossRefGoogle Scholar
Brenner, M., Eldredge, J., and Freund, J. (2019a), ‘Perspective on machine learning for advancing fluid mechanics’, Physical Review Fluids 4(10), 100501.Google Scholar
Bright, I., Lin, G., and Kutz, J. N. (2013), ‘Compressive sensing and machine learning strategies for characterizing the flow around a cylinder with limited pressure measurements’, Physics of Fluids 25(127102), 1–15.Google Scholar
Brockwell, P. J. and Davis, R. A. (2010), Introduction to Time Series and Forecasting (Springer Texts in Statistics), Springer, New York.Google Scholar
Brooks, R. (1990), ‘Elephants don’t play chess’, Robotics and Autonomous Systems 6, 3–15.Google Scholar
Brown, G. L. and Roshko, A. (1974), ‘On the density effects and large structure in turbulent mixing layers’, Journal of Fluid Mechanics 64, 775–816.Google Scholar
Brunton, B. W., Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016a), ‘Sparse sensor placement optimization for classification’, SIAM Journal on Applied Mathematics 76(5), 2099–2122.Google Scholar
Brunton, S., Brunton, B., Proctor, J., Kaiser, E., and Kutz, J. (2017), ‘Chaos as an intermittently forced linear system’, Nature Communication 8(19), 1–9.Google Scholar
Brunton, S. L., Brunton, B. W., Proctor, J. L., and Kutz, J. N. (2016b), ‘Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control’, PLoS ONE 11(2), e0150171.Google Scholar
Brunton, S. L., Dawson, S. T. M., and Rowley, C. W. (2014), ‘State-space model identification and feedback control of unsteady aerodynamic forces’, Journal of Fluids and Structures 50, 253–270.Google Scholar
Brunton, S. L., Hemati, M. S., and Taira, K. (2020), ‘Special issue on machine learning and data-driven methods in fluid dynamics’, Theoretical and Computational Fluid Dynamics 34, 333–337.CrossRefGoogle Scholar
Brunton, S. L. and Kutz, J. N. (2019), Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge University Press, Cambridge.Google Scholar
Brunton, S. L. and Noack, B. R. (2015), ‘Closed-loop turbulence control: Progress and challenges’, Applied Mechanics Reviews 67(5), 050801:01–48.Google Scholar
Brunton, S. L., Noack, B. R., and Koumoutsakos, P. (2020), ‘Machine learning for fluid mechanics’, Annual Review of Fluid Mechanics 52, 477–508.Google Scholar
Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016a), ‘Discovering governing equations from data by sparse identification of nonlinear dynamical systems’, Proceedings of the National Academy of Sciences 113(15), 3932–3937.Google Scholar
Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016b), ‘Sparse identification of nonlinear dynamics with control (SINDYc)’, IFAC NOLCOS 49(18), 710–715.Google Scholar
Bucci, M. A., Semeraro, O., Allauzen, A., Wisniewski, G., Cordier, L., and Mathelin, L. (2019), ‘Control of chaotic systems by deep reinforcement learning’, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475(2231), 20190351.Google Scholar
Budišić, M. and Mezić, I. (2009), An approximate parametrization of the ergodic partition using time averaged observables, in ‘Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. December 15–18, 2009, Shanghai, China, IEEE, Piscataway, NJ, pp. 3162–3168.Google Scholar
Budišić, M. and Mezić, I. (2012), ‘Geometry of the ergodic quotient reveals coherent structures in flows’, Physica D: Nonlinear Phenomena 241(15), 1255–1269.Google Scholar
Budišić, M., Mohr, R. and Mezić, I. (2012), ‘Applied Koopmanism’, Chaos: An Interdisci-plinary Journal of Nonlinear Science 22(4), 047510.Google Scholar
Burda, Y., Edwards, H., Storkey, A. J., and Klimov, O. (2019), Exploration by random network distillation, in ‘7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6–9, 2019’, OpenReview.net.Google Scholar
Burkardt, J., Gunzburger, M., and Lee, H.-C. (2006), ‘POD and CVT-based reduced-order mod-eling of Navier–Stokes flows’, Computer Methods in Applied Mechanics and Engineering 196(1–3), 337–355.Google Scholar
Busse, F. (1991), ‘Numerical analysis of secondary and tertiary states of fluid flow and their stability properties’, Applied Scientific Research 48(3), 341–351.Google Scholar
Butler, K. and Farrell, B. (1992), ‘Three-dimensional optimal perturbations in viscous shear flow’, Physics of Fluids 4, 1637–1650.Google Scholar
Butler, K. M. and Farrell, B. F. (1993), ‘Optimal perturbations and streak spacing in wall-bounded shear flow’, Physics of Fluids A 5, 774–777.Google Scholar
Callaham, J., Maeda, K., and Brunton, S. L. (2019), ‘Robust reconstruction of flow fields from limited measurements’, Physical Review Fluids 4, 103907.Google Scholar
Cammilleri, A., Gueniat, F., Carlier, J., Pastur, L., Memin, E., Lusseyran, F., and Artana, G. (2013), ‘POD-spectral decomposition for fluid flow analysis and model reduction’, Theoretical and Computational Fluid Dynamics 27(6), 787–815.Google Scholar
Candès, E. J. (2006), Compressive sensing, in ‘Proceedings of the International Congress of Mathematics, August 22–30, 2006’, European Mathematical Society, Zurich.Google Scholar
Candès, E. J., Romberg, J., and Tao, T. (2006a), ‘Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information’, IEEE Transactions on Information Theory 52(2), 489–509.Google Scholar
Candès, E. J., Romberg, J., and Tao, T. (2006b), ‘Stable signal recovery from incomplete and inaccurate measurements’, Communications in Pure and Applied Mathematics 8, 1207–1223.Google Scholar
Candès, E. J. and Tao, T. (2006), ‘Near optimal signal recovery from random projections: Universal encoding strategies?’, IEEE Transactions on Information Theory 52(12), 5406–5425.Google Scholar
Cardesa, J. I., Vela-Martín, A., and Jiménez, J. (2017), ‘The turbulent cascade in five dimensions’, Science 357, 782–784.Google Scholar
Carlberg, K., Barone, M., and Antil, H. (2017), ‘Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction’, Journal of Computational Physics 330, 693–734.Google Scholar
Carlberg, K., Bou-Mosleh, C., and Farhat, C. (2011), ‘Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations’, International Journal for Numerical Methods in Engineering 86(2), 155–181.Google Scholar
Carlberg, K., Tuminaro, R., and Boggs, P. (2015), ‘Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamics’, SIAM Journal on Scientific Computing 37(2), B153–B184.Google Scholar
Carleman, T. (1932), ‘Application de la théorie des équations intégrales linéaires aux systémes d’équations différentielles non linéaires’, Acta Mathematica 59(1), 63–87.Google Scholar
Carnevale, G. F., McWilliams, J. C., Pomeau, Y., Weiss, J. B., and Young, W. R. (1991), ‘Evolution of vortex statistics in two-dimensional turbulence’, Physical Review Letters 66, 2735–2737.Google Scholar
Cassel, K. (2013), Variational Methods with Applications in Science and Engineering, Cambridge University Press, Cambridge.Google Scholar
Cattafesta, L. N. III and Sheplak, M. (2011), ‘Actuators for active flow control’, Annual Review of Fluid Mechanics 43, 247–272.Google Scholar
Cattell, R. B. (1966), ‘The scree test for the number of factors’, Multivariate Behavioral Research 1(2), 245–276.Google Scholar
Cavaliere, A. and de Joannon, M. (2004), ‘Mild combustion’, Progress in Energy and Combustion Science 30, 329–366.Google Scholar
Champion, K., Lusch, B., Kutz, J. N., and Brunton, S. L. (2019), ‘Data-driven discovery of coordinates and governing equations’, Proceedings of the National Academy of Sciences 116(45), 22445–22451.Google Scholar
Champion, K., Zheng, P., Aravkin, A. Y., Brunton, S. L., and Kutz, J. N. (2020), ‘A unified sparse optimization framework to learn parsimonious physics-informed models from data’, IEEE Access 8, 169259–169271.Google Scholar
Chang, H., Yeung, D.-Y., and Xiong, Y. (2004), Super-resolution through neighbor embedding, in ‘Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004.’, Vol. 1, IEEE, pp. I–I.Google Scholar
Chartrand, R. (2011), ‘Numerical differentiation of noisy, nonsmooth data’, ISRN Applied Mathematics 2011, article ID 164564.Google Scholar
Chen, K. K. and Rowley, C. W. (2011), ‘H2 optimal actuator and sensor placement in the linearised complex Ginzburg-Landau system’, Journal of Fluid Mechanics 681, 241–260.Google Scholar
Chen, K. K., Tu, J. H., and Rowley, C. W. (2012), ‘Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses’, Journal of Nonlinear Science 22(6), 887–915.Google Scholar
Choi, H., Moin, P., and Kim, J. (1994), ‘Active turbulence control for drag reduction in wall-bounded flows’, Journal of Fluid Mechanics 262, 75–110.Google Scholar
Cimbala, J. M., Nagib, H. M., and Roshko, A. (1988), ‘Large structure in the far wakes of two-dimensional bluff bodies’, Journal of Fluid Mechanics 190, 265–298.Google Scholar
Citriniti, J. H. and George, W. K. (2000), ‘Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition’, Journal of Fluid Mechanics 418, 137–166.Google Scholar
Colabrese, S., Gustavsson, K., Celani, A., and Biferale, L. (2017), ‘Flow navigation by smart microswimmers via reinforcement learning’, Physical Review Letters 118(15), 158004.Google Scholar
Colvert, B., Alsalman, M., and Kanso, E. (2018), ‘Classifying vortex wakes using neural networks’, Bioinspiration & Biomimetics 13(2), 025003.Google Scholar
Cooley, J. W. and Tukey, J. W. (1965), ‘An algorithm for the machine calculation of complex Fourier series’, Mathematics of Computation 19(90), 297–301.Google Scholar
Cordier, L., El Majd, B. A., and Favier, J. (2010), ‘Calibration of POD reduced-order models using Tikhonov regularization’, International Journal for Numerical Methods in Fluids 63(2), 269–296.Google Scholar
Cordier, L., Noack, B. R., Daviller, G., Delvile, J., Lehnasch, G., Tissot, G., Balajewicz, M., and Niven, R. (2013), ‘Control-oriented model identification strategy’, Experiments in Fluids 54, Article 1580.Google Scholar
Corino, E. R. and Brodkey, R. S. (1969), ‘A visual investigation of the wall region in turbulent flow’, Journal of Fluid Mechanics 37, 1.Google Scholar
Cornejo Maceda, G. Y., Li, Y., Lusseyran, F., Morzyński, M., and Noack, B. R. (2021), ‘Stabilization of the fluidic pinball with gradient-based machine learning control’, Journal of Fluid Mechanics 917, A42, 1–43.Google Scholar
Cornejo Maceda, G., Noack, Bernd R., Lusseyran, F., Deng, N., Pastur, L., and Morzyński, M. (2019), ‘Artificial intelligence control applied to drag reduction of the fluidic pinball’, Proceedings in Applied Mathematics and Mechanics 19(1), e201900268:1–2.Google Scholar
Corrsin, S. (1958), Local isotropy in turbulent shear flow, Res. Memo 58B11, National Advisory Committee for Aeronautics, Washington, DC.Google Scholar
Coussement, A., Gicquel, O., and Parente, A. (2013), ‘MG-local-PCA method for reduced order combustion modeling’, Proceedings of the Combustion Institute 34(1), 1117–1123.Google Scholar
Coussement, A., Isaac, B. J., Gicquel, O., and Parente, A. (2016), ‘Assessment of different chemistry reduction methods based on principal component analysis: Comparison of the MG-PCA and score-PCA approaches’, Combustion and Flame 168, 83–97.Google Scholar
Coveney, P. V., Dougherty, E. R., and Highfield, R. R. (2016), ‘Big data need big theory too’, Philosophical Transactions of the Royal Society A 374, 20160153.Google Scholar
Cox, T. F. and Cox, M. A. A. (2000), Multidimensional Scaling, Vol. 88 of Monographs on Statistics and Applied Probability, 2nd ed., Chapman & Hall, London.CrossRefGoogle Scholar
Cranmer, M. D., Xu, R., Battaglia, P., and Ho, S. (2019), ‘Learning symbolic physics with graph networks’, arXiv preprint arXiv:1909.05862.Google Scholar
Cranmer, M., Greydanus, S., Hoyer, S., Battaglia, P., Spergel, D., and Ho, S. (2020), ‘Lagrangian neural networks’, arXiv preprint arXiv:2003.04630.Google Scholar
Cristianini, N. and Shawe–Taylor, J. (2000), An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Cambridge University Press, Cambridge.Google Scholar
Cuoci, A., Frassoldati, A., Faravelli, T., and Ranzi, E. (2013), ‘Numerical modeling of laminar flames with detailed kinetics based on the operator-splitting method’, Energy & Fuels 27(12), 7730–7753.Google Scholar
Cuoci, A., Frassoldati, A., Faravelli, T., and Ranzi, E. (2015), ‘OpenSMOKE++: An object-oriented frame-work for the numerical modeling of reactive systems with detailed kinetic mechanisms’, Computer Physics Communications 192, 237–264.Google Scholar
Dalakoti, D. K., Wehrfritz, A., Savard, B., Day, M. S., Bell, J. B., and Hawkes, E. R. (2020), ‘An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions’, Proceedings of the Combustion Institute 38, 2701–2709.Google Scholar
D’Alessio, G., Attili, A., Cuoci, A., Pitsch, H., and Parente, A. (2020a), Analysis of turbulent reacting jets via principal component analysis, in ‘Data Analysis for Direct Numerical Simulations of Turbulent Combustion’, Springer, Cham, pp. 233–251.Google Scholar
D’Alessio, G., Attili, A., Cuoci, A., Pitsch, H., and Parente, A. (2020b), Unsupervised data analysis of direct numerical simulation of a turbulent flame via local principal component analysis and procustes analysis, in ‘15th International Workshop on Soft Computing Models in Industrial and Environmental Applications’, September 16–18, 2020, Burgos, Spain, Springer Nature, Switzerland, pp. 460–469.Google Scholar
D’Alessio, G., Cuoci, A., Aversano, G., Bracconi, M., Stagni, A., and Parente, A. (2020), ‘Impact of the partitioning method on multidimensional adaptive-chemistry simulations’, Energies 13(10), 2567.Google Scholar
D’Alessio, G., Cuoci, A., and Parente, A. (2020), ‘OpenMORe: A Python framework for reduction, clustering and analysis of reacting flow data’, SoftwareX 12, 100630.Google Scholar
D’Alessio, G., Parente, A., Stagni, A., and Cuoci, A. (2020), ‘Adaptive chemistry via pre-partitioning of composition space and mechanism reduction’, Combustion and Flame 211, 68–82.Google Scholar
Dam, M., Brøns, M., Juul Rasmussen, J., Naulin, V., and Hesthaven, J. S. (2017), ‘Sparse identification of a predator-prey system from simulation data of a convection model’, Physics of Plasmas 24(2), 022310.Google Scholar
Daubechies, I. (1990), ‘The wavelet transform, time-frequency localization and signal analysis’, IEEE Transactions on Information Theory 36(5), 961–1005.Google Scholar
Daubechies, I. (1992), Ten Lectures on Wavelets, Vol. 61, Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Daubechies, I., Devore, R., Fornasier, M., and Güntürk, C. (2010), ‘Iteratively reweighted least squares minimization for sparse recovery’, Communications on Pure and Applied Mathematics 63, 1–38.Google Scholar
de Silva, B., Higdon, D. M., Brunton, S. L., and Kutz, J. N. (2019), ‘Discovery of physics from data: Universal laws and discrepancy models’, arXiv preprint arXiv:1906.07906.Google Scholar
Deane, A. E., Kevrekidis, I. G., Karniadakis, G. E., and Orszag, S. A. (1991), ‘Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders’, Physics of Fluids A 3, 2337–2354.CrossRefGoogle Scholar
Deb, K. and Gupta, H. (2006), ‘Introducing robustness in multi-objective optimization’, Evolutionary Computation 14, 463–494.Google Scholar
Debien, A., von Krbek, K. A., Mazellier, N., Duriez, T., Cordier, L., Noack, B. R., Abel, M. W., and Kourta, A. (2016), ‘Closed-loop separation control over a sharp edge ramp using genetic programming’, Experiments in Fluids 57(3), 40.Google Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P., and Moser, R. D. (2006), ‘Self-similar vortex clusters in the logarithmic region’, Journal of Fluid Mechanics 561, 329–358.Google Scholar
Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. (2009), Imagenet: A large-scale hierarchical image database, in ‘2009 IEEE Conference on Computer Vision and Pattern Recognition’, June 20–25, 2009, Miami, FL, IEEE, pp. 248–255.Google Scholar
Deng, N., Noack, B. R., Morzyński, M., and Pastur, L. R. (2020), ‘Low-order model for successive bifurcations of the fluidic pinball’, Journal of Fluid Mechanics 884, A37.Google Scholar
Discetti, S., Bellani, G., Örlü, R., Serpieri, J., Vila, C. S., Raiola, M., Zheng, X., Mascotelli, L., Talamelli, A., and Ianiro, A. (2019), ‘Characterization of very-large-scale motions in high-Re pipe flows’, Experimental Thermal and Fluid Science 104, 1–8.Google Scholar
Discetti, S. and Ianiro, A. (2017), Experimental Aerodynamics, CRC Press, Boca Raton, FL.Google Scholar
Discetti, S., Raiola, M., and Ianiro, A. (2018), ‘Estimation of time-resolved turbulent fields through correlation of non-time-resolved field measurements and time-resolved point measurements’, Experimental Thermal and Fluid Science 93, 119–130.Google Scholar
Distefano, J. (2013), Schaum’s Outline of Feedback and Control Systems, McGraw-Hill Education, New York.Google Scholar
Dong, C., Loy, C. C., He, K., and Tang, X. (2014), Learning a deep convolutional network for image super-resolution, in ‘European Conference on Computer Vision’, September 6–12, 2014, Zurich, Switzerland, Springer, Cham, pp. 184–199.Google Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A., and Jiménez, J. (2017), ‘Coherent structures in statistically stationary homogeneous shear turbulence’, Journal of Fluid Mechanics 816, 167–208.CrossRefGoogle Scholar
Donoho, D. L. (1995), ‘De-noising by soft-thresholding’, IEEE Transactions on Information Theory 41(3), 613–627.Google Scholar
Donoho, D. L. (2006), ‘Compressed sensing’, IEEE Transactions on Information Theory 52(4), 1289–1306.Google Scholar
Donoho, D. L. and Johnstone, J. M. (1994), ‘Ideal spatial adaptation by wavelet shrinkage’, Biometrika 81(3), 425–455.Google Scholar
Dracopoulos, D. C. (1997), Evolutionary Learning Algorithms for Neural Adaptive Control, Perspectives in Neural Computing, Springer-Verlag, London.Google Scholar
Drazin, P. and Reid, W. (1981), Hydrodynamic Stability, Cambridge University Press, Cambridge, UK.Google Scholar
Dullerud, G. E. and Paganini, F. (2000), A Course in Robust Control Theory: A Convex Approach, Texts in Applied Mathematics, Springer, Berlin, Heidelberg.Google Scholar
Duraisamy, K., Iaccarino, G., and Xiao, H. (2019), ‘Turbulence modeling in the age of data’, Annual Reviews of Fluid Mechanics 51, 357–377.Google Scholar
Duriez, T., Brunton, S. L., and Noack, B. R. (2017), Machine Learning Control: Taming Nonlinear Dynamics and Turbulence, Springer, Cham.CrossRefGoogle Scholar
Duwig, C. and Iudiciani, P. (2010), ‘Extended proper orthogonal decomposition for analysis of unsteady flames’, Flow, Turbulence and Combustion 84(1), 25.Google Scholar
Echekki, T., Kerstein, A. R., and Sutherland, J. C. (2011), The one-dimensional-turbulence model, in Echekki, T. & Mastorakos, E., eds., ‘Turbulent Combustion Modeling’, Springer, Dordrecht, pp. 249–276.Google Scholar
Echekki, T. and Mirgolbabaei, H. (2015), ‘Principal component transport in turbulent combustion: A posteriori analysis’, Combustion and Flame 162(5), 1919–1933.Google Scholar
Eckart, C. and Young, G. (1936), ‘The approximation of one matrix by another of lower rank’, Psychometrika 1(3), 211–218.Google Scholar
Ehlert, A., Nayeri, C. N., Morzyński, M., and Noack, B. R. (2020), ‘Locally linear embedding for transient cylinder wakes’. arXiv manuscript 1906.07822 [physics.flu-dyn].Google Scholar
El Sayed, M. Y., Semaan, R., and Radespiel, R. (2018), Sparse modeling of the lift gains of a high-lift configuration with periodic coanda blowing, in ‘2018 AIAA Aerospace Sciences Meeting’, January 8–12, 2018, Kissimmee, FL, p. 1054.Google Scholar
Encinar, M. P. and Jiménez, J. (2020), ‘Momentum transfer by linearised eddies in turbulent channel flows’, arXiv e-prints p. 1911.06096.Google Scholar
Engstrom, L., Ilyas, A., Santurkar, S., Tsipras, D., Janoos, F., Rudolph, L., and Madry, A. (2020), Implementation matters in deep RL: A case study on PPO and TRPO, in ‘International Conference on Learning Representations’ April 26–30, 2020, Addis Ababa, Ethiopia.Google Scholar
Epps, B. P. and Krivitzky, E. M. (2019), ‘Singular value decomposition of noisy data: Noise filtering’, Experiments in Fluids 60(8), 126.Google Scholar
Erichson, N. B., Mathelin, L., Kutz, J. N., and Brunton, S. L. (2019), ‘Randomized dynamic mode decomposition’, SIAM Journal on Applied Dynamical Systems 18(4), 1867–1891.Google Scholar
Erichson, N. B., Mathelin, L., Yao, Z., Brunton, S. L., Mahoney, M. W., and Kutz, J. N. (2020), ‘Shallow neural networks for fluid flow reconstruction with limited sensors’, Proceedings of the Royal Society A 476(2238), 20200097.Google Scholar
Espeholt, L., Soyer, H., Munos, R., Simonyan, K., Mnih, V., Ward, T., Doron, Y., Firoiu, V., Harley, T., Dunning, I., Legg, S., and Kavukcuoglu, K. (2018), IMPALA: Scalable distributed deep-RL with importance weighted actor-learner architectures, in Dy, J. and Krause, A., eds., ‘Proceedings of the 35th International Conference on Machine Learning’, Vol. 80 of Proceedings of Machine Learning Research, PMLR, Stockholmsmassan, Stock-holm, Sweden, pp. 1407–1416.Google Scholar
Esposito, C., Mendez, M., Gouriet, J., Steelant, J., and Vetrano, M. (2021), ‘Spectral and modal analysis of a cavitating flow through an orifice’, Experimental Thermal and Fluid Science 121, 110251.Google Scholar
Evans, W. R. (1948), ‘Graphical analysis of control systems’, Transactions of the American Institute of Electrical Engineers 67(1), 547–551.Google Scholar
Everitt, B. and Skrondal, A. (2002), The Cambridge Dictionary of Statistics, Vol. 106, Cambridge University Press, Cambridge.Google Scholar
Ewing, D. and Citriniti, J. H. (1999), Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer, in ‘IUTAM Symposium on Simulation and Identification of Organized Structures in Flows’, May 25–29, 1997, Lyngby, Denmark, Springer, Dordrecht, pp. 375–384.Google Scholar
Fabbiane, N., Semeraro, O., Bagheri, S., and Henningson, D. S. (2014), ‘Adaptive and model-based control theory applied to convectively unstable flows’, Applied Mechanics Reviews 66(6), 060801-1–060801-20.Google Scholar
Farge, M. (1992), ‘Wavelet transforms and their applications to turbulence’, Annual Review of Fluid Mechanics 24(1), 395–458.Google Scholar
Fernex, D., Noack, B. R., and Semaan, R. (2021), ‘Cluster-based network models – From snapshots to complex dynamical systems’, Science Advances 7(25).Google Scholar
Fernex, D., Semann, R., Albers, M., Meysonnat, P. S., Schröder, W., Ishar, R., Kaiser, E., and Noack, B. R. (2019), ‘Cluster-based network model for drag reduction mechanisms of an actuated turbulent boundary layer’, Proceedings in Applied Mathematics and Mechanics 19(1), 1–2.Google Scholar
Ferziger, J. H., Perić, M., and Street, R. L. (2002), Computational Methods for Fluid Dynamics, Vol. 3, Springer, Berlin.Google Scholar
Feynman, R. P., Leighton, R. B., and Sands, M. (2013), The Feynman Lectures on Physics, Vol. 2, Basic Books, New York.Google Scholar
Finzi, M., Wang, K. A., and Wilson, A. G. (2020), ‘Simplifying Hamiltonian and Lagrangian neural networks via explicit constraints’, Advances in Neural Information Processing Systems 33, 17605–17616.Google Scholar
Fleming, P. J. and Purshouse, R. C. (2002), ‘Evolutionary algorithms in control systems engineering: A survey’, Control Engineering Practice 10, 1223–1241.Google Scholar
Fletcher, C. A. J. (1984), Computational Galerkin Methods, 1st ed., Springer, New York.Google Scholar
Flierl, G. R., Larichev, V. D., McWilliams, J. C., and Reznik, G. M. (1980), ‘The dynamics of baroclinic and barotropic solitary eddies’, Dynamics of Atmospheres and Oceans 5, 1–41.Google Scholar
Flinois, T. L. and Morgans, A. S. (2016), ‘Feedback control of unstable flows: A direct mod-elling approach using the eigensystem realisation algorithm’, Journal of Fluid Mechanics 793, 41–78.Google Scholar
Flores, O. and Jiménez, J. (2010), ‘Hierarchy of minimal flow units in the logarithmic layer’, Physics of Fluids 22, 071704.Google Scholar
Floryan, D. and Graham, M. D. (2021), ‘Discovering multiscale and self-similar structure with data-driven wavelets’, Proceedings of the National Academy of Sciences 118(1), e2021299118.Google Scholar
Föppl, L. (1913), ‘Wirbelbewegung hinter einem kreiszylinder (Vortex movement behind a circular cylinder)’, Bayerische Akademie der Wissenschaften, Munich.Google Scholar
Fornberg, B. (1977), ‘A numerical study of 2-D turbulence’, Journal of Computational Physics 25, 1–31.Google Scholar
Fosas de Pando, M., Schmid, P., and Sipp, D. (2014), ‘A global analysis of tonal noise in flows around aerofoils’, Journal of Fluid Mechanics 754, 5–38.Google Scholar
Fosas de Pando, M., Schmid, P., and Sipp, D. (2017), ‘On the receptivity of aerofoil tonal noise: An adjoint analysis’, Journal of Fluid Mechanics 812, 771–791.Google Scholar
Fosas de Pando, M., Sipp, D., and Schmid, P. (2012), ‘Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers’, Journal of Computational Physics 231(23), 7739–7755.Google Scholar
Franklin, G. F., Powell, J. D., and Emami-Naeini, A. (1994), Feedback Control of Dynamic Systems, Vol. 3, Addison-Wesley, Reading, MA.Google Scholar
Franz, T. and Held, M. (2017), Data fusion of CFD solutions and experimental aerodynamic data, in ‘Proceedings Onera-DLR Aerospace Symposium (ODAS)’ June 7–9, 2017, Aussois, France.Google Scholar
Franz, T., Zimmermann, R., and Görtz, S. (2017), Adaptive sampling for nonlinear dimension-ality reduction based on manifold learning, in Benner, P., Ohlberger, M., Patera, A., Rozza, G., and Urban, K., eds., Model Reduction of Parametrized Systems, Springer, Cham, pp. 255–269.Google Scholar
Franz, T., Zimmermann, R., Görtz, S., and Karcher, N. (2014), ‘Interpolation-based reduced-order modelling for steady transonic flows via manifold learning’, International Journal of Computational Fluid Dynamics 28(3–4), 106–121.Google Scholar
Frassoldati, A., Faravelli, T., and Ranzi, E. (2003), ‘Kinetic modeling of the interactions between NO and hydrocarbons at high temperature’, Combustion and Flame 135, 97–112.Google Scholar
Freeman, W. T., Jones, T. R., and Pasztor, E. C. (2002), ‘Example-based super-resolution’, IEEE Computer Graphics and Applications 22(2), 56–65.Google Scholar
Freymuth, P. (1966), ‘On transition in a separated laminar boundary layer’, Journal of Fluid Mechanics 25, 683–704.Google Scholar
Friedman, J. (1991), ‘Multivariate adaptive regression splines’, The Annals of Statistics 19(1), 1–67.Google Scholar
Fu, J., Luo, K., and Levine, S. (2018), Learning robust rewards with adverserial inverse reinforcement learning, in ‘6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30–May 3, 2018, Conference Track Proceedings’, OpenReview.net.Google Scholar
Fukami, K., Fukagata, K., and Taira, K. (2018), ‘Super-resolution reconstruction of turbulent flows with machine learning’, arXiv preprint arXiv:1811.11328.Google Scholar
Gabor, D. (1946), ‘Theory of communication. Part 1: The analysis of information’, Journal of the Institution of Electrical Engineers-Part III: Radio and Communication Engineering 93(26), 429–441.Google Scholar
Gad-el Hak, M. (2007), Flow Control: Passive, Active, and Reactive Flow Management, Cambridge University Press, Cambridge.Google Scholar
Galerkin, B. G. (1915), ‘Rods and plates: Series occuring in various questions regarding the elastic equilibrium of rods and plates (translated)’, Vestn. Inzhen. 19, 897—908.Google Scholar
Galletti, G., Bruneau, C. H., Zannetti, L., and Iollo, A. (2004), ‘Low-order modelling of laminar flow regimes past a confined square cylinder’, Journal of Fluid Mechanics 503, 161–170.Google Scholar
Gardiner, W. C., Lissianski, V. V., Qin, Z., Smith, G. P., Golden, D. M., Frenklach, M., Moriarty, N. W., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R. K., and Song, S. Jr. (2012), ‘Gri-mech 3.0’.Google Scholar
Gardner, E. (1988), ‘The space of interactions in neural network models’, Journal of Physics A: Mathematical and General 21(1), 257.Google Scholar
Garnier, P., Viquerat, J., Rabault, J., Larcher, A., Kuhnle, A., and Hachem, E. (2019), ‘A review on deep reinforcement learning for fluid mechanics’, arXiv preprint arXiv:1908.04127.Google Scholar
Gaster, M., Kit, E., and Wygnanski, I. (1985), ‘Large-scale structures in a forced turbulent mixing layer’, Journal of Fluid Mechanics 150, 23–39.Google Scholar
Gautier, N., Aider, J.-L., Duriez, T., Noack, B., Segond, M., and Abel, M. (2015), ‘Closed-loop separation control using machine learning’, Journal of Fluid Mechanics 770, 442–457.Google Scholar
Gazzola, M., Hejazialhosseini, B., and Koumoutsakos, P. (2014), ‘Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers’, SIAM Journal on Scientific Computing 36(3), B622–B639.Google Scholar
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A., and Koumoutsakos, P. (2016), ‘Learning to school in the presence of hydrodynamic interactions’, Journal of Fluid Mechanics 789, 726–749.CrossRefGoogle Scholar
Gerhard, J., Pastoor, M., King, R., Noack, B. R., Dillmann, A., Morzyński, M., and Tadmor, G. (2003), Model-based control of vortex shedding using low-dimensional Galerkin models, in ‘33rd AIAA Fluids Conference and Exhibit’, Orlando, FL, June 23–26, 2003. Paper 2003-4262.Google Scholar
Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. (1991), ‘A dynamic subgrid-scale eddy viscosity model’, Physics of Fluids A: Fluid Dynamics 3(7), 1760–1765.Google Scholar
Giannetti, F. and Luchini, P. (2007), ‘Structural sensitivity of the first instability of the cylinder wake’, Journal of Fluid Mechanics 581, 167–197.Google Scholar
Glaz, B., Liu, L., and Friedmann, P. P. (2010), ‘Reduced-order nonlinear unsteady aerodynamic modeling using a surrogate-based recurrence framework’, AIAA Journal 48(10), 2418–2429.Google Scholar
Goldstein, T. and Osher, S. (2009), ‘The split Bregman method for L1-regularized problems’, SIAM Journal on Imaging Sciences 2(2), 323–343.Google Scholar
Gonzalez-Garcia, R., Rico-Martinez, R., and Kevrekidis, I. (1998), ‘Identification of distributed parameter systems: A neural net based approach’, Computers & Chemical Engineering 22, S965–S968.Google Scholar
Gonzalez, R. C. and Woods, R. E. (2017), Digital Image Processing, 4th ed., Pearson, New York.Google Scholar
Goodfellow, I., Bengio, Y., and Courville, A. (2016), Deep Learning, MIT Press, Cambridge, MA.Google Scholar
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014), Generative adversarial nets, in ‘Advances in Neural Information Processing Systems’, December 8–13, 2014, Montreal, Canada, pp. 2672–2680.Google Scholar
Görtz, S., Ilic, C., Abu-Zurayk, M., Liepelt, R., Jepsen, J., Führer, T., Becker, R., Scherer, J., Kier, T., and Siggel, M. (2016), Collaborative multi-level MDO process development and application to long-range transport aircraft, in ‘Proceedings of the 30th Congress of the International Council of the Aeronautical Sciences (ICAS)’, September 25–30, 2016, Daejeon, Korea.Google Scholar
Gray, R. M. (2005), ‘Toeplitz and circulant matrices: A review’, Foundations and TrendsR in Communications and Information Theory 2(3), 155–239.Google Scholar
Greydanus, S., Dzamba, M., and Yosinski, J. (2019), ‘Hamiltonian neural networks’, Advances in Neural Information Processing Systems 32, 15379–15389.Google Scholar
Griewank, A. and Walther, A. (2000), ‘Algorithm 799: Revolve: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation’, ACM Transactions on Mathematical Software 26(1), 19–45.Google Scholar
Grossmann, A. and Morlet, J. (1984), ‘Decomposition of hardy functions into square integrable wavelets of constant shape’, SIAM Journal on Mathematical Analysis 15(4), 723–736.Google Scholar
Gu, S., Lillicrap, T., Sutskever, I., and Levine, S. (2016), Continuous deep Q-learning with model-based acceleration, Vol. 48 of Proceedings of Machine Learning Research, PMLR, New York, pp. 2829–2838.Google Scholar
Guan, Y., Brunton, S. L., and Novosselov, I. (2020), ‘Sparse nonlinear models of chaotic electroconvection’, arXiv preprint arXiv:2009.11862.Google Scholar
Guastoni, L., Güemes, A., Ianiro, A., Discetti, S., Schlatter, P., Azizpour, H., and Vinuesa, R. (2020), ‘Convolutional-network models to predict wall-bounded turbulence from wall quantities’, arXiv preprint arXiv:2006.12483.Google Scholar
Guckenheimer, J. and Holmes, P. (1983), Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Verlag, New York.Google Scholar
Güemes, A., Discetti, S., and Ianiro, A. (2019), ‘Sensing the turbulent large-scale motions with their wall signature’, Physics of Fluids 31(12), 125112.Google Scholar
Guidorzi, R. (2003), Multivariable System Identification. From Observations to Models, Bononia University Press, Bologna.Google Scholar
Gunzburger, M. (2003), Perspectives in Flow Control and Optimization, Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Haar, A. (1911), ‘Zur theorie der orthogonalen funktionensysteme’, Mathematische Annalen 71(1), 38–53.Google Scholar
Haarnoja, T., Zhou, A., Abbeel, P., and Levine, S. (2018), Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor, in Dy, J. and Krause, A., eds, ‘Proceedings of the 35th International Conference on Machine Learning’, Vol. 80 of Proceedings of Machine Learning Research, PMLR, Stockholmsmassan, Stockholm, Sweden, pp. 1861–1870.Google Scholar
Halko, N., Martinsson, P.-G., Shkolnisky, Y., and Tygert, M. (2011), ‘An algorithm for the principal component analysis of large data sets’, SIAM Journal on Scientific Computing 33, 2580–2594.Google Scholar
Halko, N., Martinsson, P.-G., and Tropp, J. A. (2011), ‘Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions’, SIAM Review 53(2), 217–288.Google Scholar
Hama, F. R. (1962), ‘Streaklines in a perturbed shear flow’, The Physics of Fluids 5(6), 644–650.Google Scholar
Hamilton, J. M., Kim, J., and Waleffe, F. (1995), ‘Regeneration mechanisms of near-wall turbulence structures’, Journal of Fluid Mechanics 287, 317–348.Google Scholar
Han, Z.-H., Abu-Zurayk, M., Görtz, S., and Ilic, C. (2018), Surrogate-based aerodynamic shape optimization of a wing-body transport aircraft configuration, in ‘Notes on Numerical Fluid Mechanics and Multidisciplinary Design’, October 13–14, 2015, Braunschweig, Germany, Springer, Berlin, pp. 257–282.Google Scholar
Han, Z.-H. and Görtz, S. (2012a), ‘Alternative cokriging method for variable-fidelity surrogate modeling’, AIAA Journal 50(5), 1205–1210.Google Scholar
Han, Z.-H. and Görtz, S. (2012b), ‘Hierarchical kriging model for variable-fidelity surrogate modeling’, AIAA Journal 50(9), 1885–1896.Google Scholar
Han, Z.-H., Görtz, S., and Zimmermann, R. (2013), ‘Improving variable-fidelity surrogate mod-eling via gradient-enhanced kriging and a generalized hybrid bridge function’, Aerospace Science and Technology 25(1), 177–189.Google Scholar
Hansen, N., Niederberger, A. S., Guzzella, L., and Koumoutsakos, P. (2009), ‘A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion’, IEEE Transactions on Evolutionary Computation 13(1), 180–197.Google Scholar
Harris, F. (1978), ‘On the use of windows for harmonic analysis with the discrete Fourier transform’, Proceedings of the IEEE 66(1), 51–83.Google Scholar
Hasselmann, K. (1988), ‘PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns’, Journal of Geophysical Research 93(D9), 11015.Google Scholar
Hasselt, H. V., Guez, A., and Silver, D. (2016), Deep reinforcement learning with double Q-learning, in ‘Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence’, AAAI 16, February 12–17, 2016, Phoenix, AZ, AAAI Press, Palo Alto, CA, pp. 2094–2100.Google Scholar
Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning, Vol. 2, Springer, New York.Google Scholar
Hayes, M. (2011), Schaums Outline of Digital Signal Processing, McGraw-Hill Education, New York.Google Scholar
Hemati, M., Rowley, C., Deem, E., and Cattafesta, L. (2017), ‘De-biasing the dynamic mode decomposition for applied Koopman spectral analysis’, Theoretical and Computational Fluid Dynamics 31(4), 349–368.Google Scholar
Henderson, P., Islam, R., Bachman, P., Pineau, J., Precup, D., and Meger, D. (2018), Deep reinforcement learning that matters, in McIlraith, S. A. and Weinberger, K. Q., eds., ‘Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI-18), the 30th Innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2–7, 2018’, AAAI Press, Palo Alto, CA., pp. 3207–3214.Google Scholar
Henningson, D. (2010), ‘Description of complex flow behaviour using global and dynamic modes’, Journal of Fluid Mechanics 656, 1–4.Google Scholar
Herbert, T. (1988), ‘Secondary instability of boundary layers’, Annual Review of Fluid Mechanics 20, 487–526.Google Scholar
Hernán, M. A. and Jiménez, J. (1982), ‘Computer analysis of a high-speed film of the plane turbulent mixing layer’, Journal of Fluid Mechanics 119, 323–345.Google Scholar
Hervé, A., Sipp, D., Schmid, P. J. and Samuelides, M. (2012), ‘A physics-based approach to flow control using system identification’, Journal of Fluid Mechanics 702, 26–58.Google Scholar
Hill, D. (1995), ‘Adjoint systems and their role in the receptivity problem for boundary layers’, Journal of Fluid Mechanics 292, 183–204.Google Scholar
Hinton, G. E. (2006), ‘Reducing the dimensionality of data with neural networks’, Science 313(5786), 504–507.Google Scholar
Hinton, G. E. and Sejnowski, T. J. (1986), ‘Learning and releaming in Boltzmann machines’, Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1(282–317), 2.Google Scholar
Hinze, M. and Kunisch, K. (2000), ‘Three control methods for time-dependent fluid flow’, Flow, Turbulence and Combustion 65, 273–298.Google Scholar
Ho, B. L. and Kalman, R. E. (1965), Effective construction of linear state-variable models from input/output data, in ‘Proceedings of the 3rd Annual Allerton Conference on Circuit and System Theory’, October 20–22, 1965, Monticello, IL, pp. 449–459.Google Scholar
Ho, J. and Ermon, S. (2016), Generative adversarial imitation learning, in Lee, D. D., Sugiyama, M., Luxburg, U. V., Guyon, I., and Garnett, R., eds., ‘Advances in Neural Information Processing Systems 29’, December 5–10, 2016, Barcelona, Spain, Curran Associates, Red Hook, NY, pp. 4565–4573.Google Scholar
Hochbruck, M. and Ostermann, A. (2010), ‘Exponential integrators’, Acta Numerica 19, 209–286.Google Scholar
Hochreiter, S. and Schmidhuber, J. (1997), ‘Long short-term memory’, Neural Computation 9(8), 1735–1780.Google Scholar
Hof, B., Van Doorne, C. W., Westerweel, J., Nieuwstadt, F. T., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R., and Waleffe, F. (2004), ‘Experimental observation of nonlinear traveling waves in turbulent pipe flow’, Science 305(5690), 1594–1598.Google Scholar
Hoffmann, M., Fröhner, C., and Noé, F. (2019), ‘Reactive SINDy: Discovering governing reactions from concentration data’, Journal of Chemical Physics 150, 025101.Google Scholar
Holland, J. H. (1975), Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor.Google Scholar
Holmes, P., Lumley, J. L., Berkooz, G., and Rowley, C. W. (2012), Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd paperback ed., Cambridge University Press, Cambridge.Google Scholar
Hopf, E. (1948), ‘A mathematical example displaying features of turbulence’, Communications on Pure and Applied Mathematics 1(4), 303–322.Google Scholar
Hopfield, J. J. (1982), ‘Neural networks and physical systems with emergent collective computational abilities’, Proceedings of the National Academy of Sciences 79(8), 2554–2558.Google Scholar
Horn, R. A. and Johnson, C. R. (2012), Matrix Analysis, Cambridge University Press, Cambridge.Google Scholar
Hornik, K., Stinchcombe, M., and White, H. (1989), ‘Multilayer feedforward networks are universal approximators’, Neural Networks 2(5), 359–366.Google Scholar
Hosseini, Z., Martinuzzi, R. J., and Noack, B. R. (2015), ‘Sensor-based estimation of the velocity in the wake of a low-aspect-ratio pyramid’, Experiments in Fluids 56(1), 13.Google Scholar
Hou, W., Darakananda, D., and Eldredge, J. (2019), Machine learning based detection of flow disturbances using surface pressure measurements, in ‘AIAA Scitech 2019 Forum’, January 7–11, 2019, San Diego, CA, p. 1148.Google Scholar
Hoyas, S. and Jiménez, J. (2006), ‘Scaling of the velocity fluctuations in turbulent channels up to Reτ = 2003’, Physics of Fluids 18, 011702.Google Scholar
Hsu, H. (2013), Schaum’s Outline of Signals and Systems, 3rd ed. (Schaum’s Outlines), McGraw-Hill Education, New York.Google Scholar
Huang, Z., Du, W., and Chen, B. (2005), Deriving private information from randomized data, in ‘Proceedings of the 2005 ACM SIGMOD International Conference on Management of Data’, June 14–16, 2005, Baltimore, MD, pp. 37–48.Google Scholar
Hwangbo, J., Lee, J., Dosovitskiy, A., Bellicoso, D., Tsounis, V., Koltun, V., and Hutter, M. (2019), ‘Learning agile and dynamic motor skills for legged robots’, arXiv preprint arXiv:1901.08652.Google Scholar
Illingworth, S. J. (2016), ‘Model-based control of vortex shedding at low Reynolds numbers’, Theoretical and Computational Fluid Dynamics 30(5), 1–20.Google Scholar
Illingworth, S. J., Morgans, A. S., and Rowley, C. W. (2010), ‘Feedback control of flow reso-nances using balanced reduced-order models’, Journal of Sound and Vibration 330(8), 1567–1581.Google Scholar
Illingworth, S. J., Morgans, A. S., and Rowley, C. W. (2012), ‘Feedback control of cavity flow oscillations using simple linear models’, Journal of Fluid Mechanics 709, 223–248.Google Scholar
Illingworth, S. J., Naito, H., and Fukagata, K. (2014), ‘Active control of vortex shedding: An explanation of the gain window’, Physical Review E 90(4), 043014.Google Scholar
Ingle, V. K. and Proakis, J. G. (2011), Digital Signal Processing Using MATLAB, Cengage Learning, Boston.Google Scholar
Isaac, B. J., Coussement, A., Gicquel, O., Smith, P. J., and Parente, A. (2014), ‘Reduced-order PCA models for chemical reacting flows’, Combustion and Flame 161(11), 2785–2800.Google Scholar
Isaac, B. J., Thornock, J. N., Sutherland, J., Smith, P. J., and Parente, A. (2015), ‘Advanced regression methods for combustion modelling using principal components’, Combustion and Flame 162(6), 2592–2601.Google Scholar
Jackson, C. P. (1987), ‘A finite-element study of the onset of vortex shedding in flow past variously shaped bodies’, Journal of Fluid Mechanics 182, 23–45.Google Scholar
Jaderberg, M., Mnih, V., Czarnecki, W. M., Schaul, T., Leibo, J. Z., Silver, D., and Kavukcuoglu, K. (2017), Reinforcement learning with unsupervised auxiliary tasks, in ‘5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24–26, 2017, Conference Track Proceedings’, OpenReview.net.Google Scholar
James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013), An Introduction to Statistical Learning, Springer, New York.Google Scholar
Jho, H. (2018), ‘Beautiful physics: Re-vision of aesthetic features of science through the literature review’, The Journal of the Korean Physical Society 73, 401–413.Google Scholar
Jiménez, J. (2002), Turbulence in ‘Perspectives in Fluid Dynamics’, Cambridge University Press, Cambridge.Google Scholar
Jiménez, J. (2013), ‘How linear is wall-bounded turbulence?’, Physics of Fluids 25, 110814.Google Scholar
Jiménez, J. (2018a), ‘Coherent structures in wall-bounded turbulence’, Journal of Fluid Mechanics 842, P1.Google Scholar
Jiménez, J. (2018b), ‘Machine-aided turbulence theory’, Journal of Fluid Mechanics 854, R1.Google Scholar
Jiménez, J. (2020a), ‘Computers and turbulence’, The European Journal of Mechanics - B/Fluids 79, 1–11.Google Scholar
Jiménez, J., Kawahara, G., Simens, M. P., Nagata, M., and Shiba, M. (2005), ‘Characterization of near-wall turbulence in terms of equilibrium and “bursting” solutions’, Physics of Fluids 17, 015105.Google Scholar
Jiménez, J. and Moin, P. (1991), ‘The minimal flow unit in near-wall turbulence’, Journal of Fluid Mechanics 225, 213–240.Google Scholar
Jiménez, J. and Pinelli, A. (1999), ‘The autonomous cycle of near-wall turbulence’, Journal of Fluid Mechanics 389, 335–359. Google Scholar
Jiménez, J. and Simens, M. P. (2001), ‘Low-dimensional dynamics of a turbulent wall flow’, Journal of Fluid Mechanics 435, 81–91.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G., and Rogallo, R. S. (1993), ‘The structure of intense vorticity in isotropic turbulence’, Journal of Fluid Mechanics 255, 65–90.Google Scholar
Johannink, T., Bahl, S., Nair, A., Luo, J., Kumar, A., Loskyll, M., Ojea, J. A., Solowjow, E., and Levine, S. (2019), Residual reinforcement learning for robot control, in ‘2019 International Conference on Robotics and Automation (ICRA)’, May 20–24, 2019, Montreal, Canada, IEEE, pp. 6023–6029.Google Scholar
Jordan, D. and Smith, P. (1988), Nonlinear Ordinary Differential Equations, Clarendon Press, Oxford.Google Scholar
Joseph, D. and Carmi, S. (1969), ‘Stability of Poiseuille flow in pipes, annuli and channels’, Quarterly of Applied Mathematics 26, 575–599.Google Scholar
Jovanović, M. R., Schmid, P. J., and Nichols, J. W. (2014), ‘Sparsity-promoting dynamic mode decomposition’, Physics of Fluids 26(2), 024103.Google Scholar
Juang, J. N. (1994), Applied System Identification, Prentice Hall PTR, Upper Saddle River. 426 Data-Driven Fluid MechanicsGoogle Scholar
Juang, J. N. and Pappa, R. S. (1985), ‘An eigensystem realization algorithm for modal parameter identification and model reduction’, Journal of Guidance, Control, and Dynamics 8(5), 620–627.Google Scholar
Juang, J. N., Phan, M., Horta, L. G., and Longman, R. W. (1991), Identification of observer/Kalman filter Markov parameters: Theory and experiments, Technical Memoran-dum 104069, NASA.Google Scholar
Kaiser, E., Kutz, J. N., and Brunton, S. L. (2018), ‘Sparse identification of nonlinear dynamics for model predictive control in the low-data limit’, Proceedings of the Royal Society of London A 474(2219), 20180335.Google Scholar
Kaiser, E., Li, R., and Noack, B. R. (2017), On the control landscape topology, in ‘The 20th World Congress of the International Federation of Automatic Control (IFAC)’, Toulouse, France, pp. 1–4.Google Scholar
Kaiser, E., Noack, B. R., Cordier, L., Spohn, A., Segond, M., Abel, M., Daviller, G., Osth, J., Krajnovic, S., and Niven, R. K. (2014), ‘Cluster-based reduced-order modelling of a mixing layer’, Journal of Fluid Mechanics 754, 365–414.Google Scholar
Kaiser, E., Noack, B. R., Spohn, A., Cattafesta, L. N., and Morzyński, M. (2017a), ‘Cluster-based control of a separating flow over a smoothly contoured ramp’, Theoretical and Computational Fluid Dynamics 31(5–6), 579–593.Google Scholar
Kaiser, E., Noack, B. R., Spohn, A., Cattafesta, L. N., and Morzyński, M. (2017b), ‘Cluster-based control of nonlinear dynamics’, Theoretical and Computational Fluid Dynamics 31(5–6), 1579–593.Google Scholar
Kaiser, G. (2010), A Friendly Guide to Wavelets, Springer Science & Business Media, Boston.Google Scholar
Kaiser, H. F. (1958), ‘The varimax criterion for analytic rotation in factor analysis’, Psychome-trika 23(3), 187–200.Google Scholar
Kambhatla, N. and Leen, T. K. (1997), ‘Dimension reduction by local principal component analysis’, Neural Computation 9(7), 1493–1516.Google Scholar
Kaptanoglu, A. A., Morgan, K. D., Hansen, C. J., and Brunton, S. L. (2020), ‘Physics-constrained, low-dimensional models for MHD: First-principles and data-driven approaches’, arXiv preprint arXiv:2004.10389.Google Scholar
Kawahara, G. (2005), ‘Laminarization of minimal plane Couette flow: Going beyond the basin of attraction of turbulence’, Physics of Fluids 17, 041702.Google Scholar
Kawahara, G., Uhlmann, M., and van Veen, L. (2012), ‘The significance of simple invariant solutions in turbulent flows’, Annual Review of Fluid Mechanics 44, 203–225.Google Scholar
Kee, R. J., Coltrin, M. E., and Glarborg, P. (2005), Chemically Reacting Flow: Theory and Practice, John Wiley & Sons, Hoboken, NJ.Google Scholar
Keefe, L., Moin, P., and Kim, J. (1992), ‘The dimension of attractors underlying periodic turbulent Poiseuille flow’, Journal of Fluid Mechanics 242, 1–29.Google Scholar
Kenney, J. and Keeping, E. (1951), Mathematics of Statistics, Vol. II, D. Van Nostrand Co., New York.Google Scholar
Kerhervé, F., Roux, S., and Mathis, R. (2017), ‘Combining time-resolved multi-point and spatially-resolved measurements for the recovering of very-large-scale motions in high Reynolds number turbulent boundary layer’, Experimental Thermal and Fluid Science 82, 102–115.Google Scholar
Kerstein, A. R. (1999), ‘One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows’, Journal of Fluid Mechanics 392, 277–334.Google Scholar
Kerstens, W., Pfeiffer, J., Williams, D., King, R., and Colonius, T. (2011), ‘Closed-loop control of lift for longitudinal gust suppression at low Reynolds numbers’, AIAA Journal 49(8), 1721–1728.Google Scholar
Khalil, H. K. and Grizzle, J. W. (2002), Nonlinear Systems, Vol. 3, Prentice Hall, Upper Saddle River, NJ.Google Scholar
Kim, H. J., Jordan, M. I., Sastry, S., and Ng, A. Y. (2004), Autonomous helicopter flight via reinforcement learning, in ‘Advances in Neural Information Processing Systems’, December 8–13, 2003, Vancouver and Whistler, British Columbia, Canada, pp. 799–806.Google Scholar
Kim, H. T., Kline, S. J., and Reynolds, W. C. (1971), ‘The production of turbulence near a smooth wall in a turbulent boundary layer’, Journal of Fluid Mechanics 50, 133–160.Google Scholar
Kim, J. (2011), ‘Physics and control of wall turbulence for drag reduction’, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369(1940), 1396–1411.Google Scholar
Kim, J. and Bewley, T. (2007), ‘A linear systems approach to flow control’, Annual Review of Fluid Mechanics 39, 383–417.Google Scholar
King, P., Rowland, J., Aubrey, W., Liakata, M., Markham, M., Soldatova, L. N., Whelan, K. E., Clare, A., Young, M., Sparkes, A., Oliver, S. G., and Pir, P. (2009), ‘The robot scientist Adam’, Computer 42(7), 46–54.Google Scholar
Kingma, D. P. and Ba, J. (2014), ‘Adam: A method for stochastic optimization’, arXiv preprint arXiv:1412.6980.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A., and Runstadler, P. W. (1967), ‘Structure of turbulent boundary layers’, Journal of Fluid Mechanics 30, 741–773.Google Scholar
Knaak, M., Rothlubbers, C. and Orglmeister, R. (1997), A Hopfield neural network for flow field computation based on particle image velocimetry/particle tracking velocimetry image sequences, in ‘International Conference on Neural Networks, 1997’, Vol. 1, October 8–10, 1997, Lausanne, Switzerland, IEEE, pp. 48–52.Google Scholar
Knight, W. (2018), ‘Google just gave control over data center cooling to an AI’, *****.Google Scholar
Koch, W., Bertolotti, F., Stolte, A., and Hein, S. (2000), ‘Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability’, Journal of Fluid Mechanics 406, 131–174.Google Scholar
Kochenderfer, M. and Wheeler, T. (2019), Algorithms for Optimization, MIT Press, Cambridge, MA.Google Scholar
Kolmogorov, A. N. (1941), ‘The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers’, Doklady Akademii Nauk SSSR 30, 209–303.Google Scholar
Kot, M. (2015), A First Course in the Calculus of Variations, American Mathematical Society, Providence, RI.Google Scholar
Koza, J. R. (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, The MIT Press, Boston.Google Scholar
Kraichnan, R. H. (1967), ‘Inertial ranges in two-dimensional turbulence’, Physics of Fluids 10, 1417–1423.Google Scholar
Kraichnan, R. H. (1971), ‘Inertial range transfer in two- and three-dimensional turbulence’, Journal of Fluid Mechanics 47, 525–535.Google Scholar
Kraichnan, R. H. and Montgomery, D. (1980), ‘Two-dimensional turbulence’, Reports on Progress in Physics 43, 547–619.Google Scholar
Kramer, B., Grover, P., Boufounos, P., Benosman, M., and Nabi, S. (2015), ‘Sparse sensing and DMD based identification of flow regimes and bifurcations in complex flows’, arXiv preprint arXiv:1510.02831.Google Scholar
Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012), Imagenet classification with deep convolutional neural networks, in ‘Advances in Neural Information Processing Systems’, December 3–6, 2012, Lake Tahoe, NV, pp. 1097–1105.Google Scholar
Kroll, N., Abu-Zurayk, M., Dimitrov, D., Franz, T., Führer, T., Gerhold, T., Görtz, S., Heinrich, R., Ilic, C., Jepsen, J., Jägersküpper, J., Kruse, M., Krumbein, A., Langer, S., Liu, D., Liepelt, R., Reimer, L., Ritter, M., Schwöppe, A., Scherer, J., Spiering, F., Thormann, R., Togiti, V., Vollmer, D., and Wendisch, J.-H. (2015), ‘DLR project digital-x: Towards virtual aircraft design and flight testing based on high-fidelity methods’, CEAS Aeronautical Journal 7(1), 3–27.Google Scholar
Kroll, N., Langer, S., and Schwöppe, A. (2014), The DLR flow solver TAU – Status and recent algorithmic developments, in ‘52nd Aerospace Sciences Meeting’, January 3–17, 2014, National Harbor, MD, American Institute of Aeronautics and Astronautics, Reston, VA.Google Scholar
Kuhn, T. S. (1970), The Structure of Scientific Revolutions, 2nd ed., Chicago University Press, Chicago.Google Scholar
Kuhnle, A., Schaarschmidt, M., and Fricke, K. (2017), ‘Tensorforce: a TensorFlow library for applied reinforcement learning’, https://tensorforce.readthedocs.io/en/latest/#.Google Scholar
Kuipers, L. and Niederreiter, H. (2005), Uniform Distribution of Sequences, Dover, Mineola, NY, p. 129.Google Scholar
Kuo, K. and Acharya, R. (2012), Fundamentals of Turbulent and Multi-Phase Combustion, Wiley, New York.Google Scholar
Kutz, J., Brunton, S., Brunton, B., and Proctor, J. (2016), Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Kutz, J. N. (2017), ‘Deep learning in fluid dynamics’, Journal of Fluid Mechanics 814, 1–4.Google Scholar
Kutz, J. N., Fu, X., and Brunton, S. L. (2016), ‘Multiresolution dynamic mode decomposition’, SIAM Journal on Applied Dynamical Systems 15(2), 713–735.Google Scholar
Labonté, G. (1999), ‘A new neural network for particle-tracking velocimetry’, Experiments in Fluids 26(4), 340–346.Google Scholar
Lagaris, I. E., Likas, A., and Fotiadis, D. I. (1998), ‘Artificial neural networks for solving ordinary and partial differential equations’, IEEE Transactions on Neural Networks 9(5), 987–1000.Google Scholar
Lai, Z. and Nagarajaiah, S. (2019), ‘Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior’, Mechanical Systems and Signal Processing 117, 813–842.Google Scholar
Lall, S., Marsden, J. E., and Glavaški, S. (1999), ‘Empirical model reduction of controlled nonlinear systems,’ International Federation of Automatic Control 32(2), 2598–2603.Google Scholar
Lall, S., Marsden, J. E., and Glavaški, S. (2002), ‘A subspace approach to balanced truncation for model reduction of nonlinear control systems’, International Journal of Robust and Nonlinear Control 12(6), 519–535.Google Scholar
Lan, Y. and Mezić, I. (2013), ‘Linearization in the large of nonlinear systems and Koopman operator spectrum’, Physica D: Nonlinear Phenomena 242(1), 42–53.Google Scholar
Landau, L. D. (1944), ‘On the problem of turbulence,’ C.R. Acad. Sci. USSR 44, 311–314.Google Scholar
Landau, L. D. and Lifshitz, E. M. (1987), Fluid Mechanics, Vol. 6 in Course of Theoretical Physics, 2nd English ed., Pergamon Press, Oxford.Google Scholar
Lasota, A. and Mackey, M. (1994), Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, Springer Verlag, New York.Google Scholar
Le Clainche, S. and Vega, J. M. (2017), ‘Higher order dynamic mode decomposition to identify and extrapolate flow patterns’, Physics of Fluids 29(8), 084102.Google Scholar
Leclercq, C., Demourant, F., Poussot-Vassal, C., and Sipp, D. (2019), ‘Linear iterative method for closed-loop control of quasiperiodic flows’, Journal of Fluid Mechanics 868, 26–65.Google Scholar
LeCun, Y., Bengio, Y., and Hinton, G. (2015), ‘Deep learning’, Nature 521(7553), 436–444.Google Scholar
Lee, C., Kim, J., Babcock, D., and Goodman, R. (1997), ‘Application of neural networks to turbulence control for drag reduction’, Physics of Fluids 9(6), 1740–1747.Google Scholar
Lee, J.-H. and Sung, H. J. (2013), ‘Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations’, Physics of Fluids 25, 045103.Google Scholar
Lee, Y., Yang, H., and Yin, Z. (2017), ‘PIV-DCNN: Cascaded deep convolutional neural networks for particle image velocimetry’, Experiments in Fluids 58(12), 171.Google Scholar
Leonard, A. (1980), ‘Vortex methods for flow simulation’, Journal of Computational Physics 37(3), 289–335.Google Scholar
Li, H., Fernex, D., Semaan, R., Tan, J., Morzyński, M., and Noack, B. R. (2021), ‘Cluster-based network model’, Journal of Fluid Mechanics 906, A21:1–41.Google Scholar
Li, Q., Dietrich, F., Bollt, E. M., and Kevrekidis, I. G. (2017), ‘Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator’, Chaos: An Interdisciplinary Journal of Nonlinear Science 27(10), 103111.Google Scholar
Li, R., Noack, B. R., Cordier, L., Borée, J., Kaiser, E., and Harambat, F. (2018), ‘Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk’, Archives of Mechanics 70(6), 505–534.Google Scholar
Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A., and Eyink, G. (2008), ‘A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence’, Journal of Turbulence 9, N31.Google Scholar
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., and Tygert, M. (2007), ‘Randomized algorithms for the low-rank approximation of matrices’, Proceedings of the National Academy of Sciences 104(51), 20167–20172.Google Scholar
Lin, C.-J. (2007), ‘Projected gradient methods for nonnegative matrix factorization’, Neural Computation 19(10), 2756–2779.Google Scholar
Ling, J., Jones, R., and Templeton, J. (2016), ‘Machine learning strategies for systems with invariance properties’, Journal of Computational Physics 318, 22–35.Google Scholar
Ling, J., Kurzawski, A., and Templeton, J. (2016), ‘Reynolds averaged turbulence modelling using deep neural networks with embedded invariance’, Journal of Fluid Mechanics 807, 155–166.Google Scholar
Ling, J. and Templeton, J. (2015), ‘Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty’, Physics of Fluids 27(8), 085103.Google Scholar
Liu, J. T. C. (1989), ‘Coherent structures in transitional and turbulent free shear flows’, Annual Review of Fluid Mechanics 21(1), 285–315.Google Scholar
Ljung, L. (1999), System Identification: Theory for the User, Prentice Hall, Upper Saddle River, NJ.Google Scholar
Ljung, L. (2008), ‘Perspectives on system identification’, IFAC Proceedings Volumes 41(2), 7172–7184.Google Scholar
Ljung, L. and Glad, T. (1994), Modeling of Dynamic Systems, Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Loan, C. V. (1992), Computational Frameworks for the Fast Fourier Transform, Society for Industrial and Applied Mathematics (SIAM), Philadelphia.Google Scholar
Loiseau, J.-C. (2019), ‘Data-driven modeling of the chaotic thermal convection in an annular thermosyphon’, arXiv preprint arXiv:1911.07920.Google Scholar
Loiseau, J.-C. and Brunton, S. L. (2018), ‘Constrained sparse Galerkin regression’, Journal of Fluid Mechanics 838, 42–67.Google Scholar
Loiseau, J.-C., Brunton, S. L., and Noack, B. R. (2021), From the POD-Galerkin method to sparse manifold models, in Benner, P., Grivet-Talocaia, S., Quarteroni, A., Schilders, R. G. W., and Silveria, L. M., eds., Handbook of Model-Order Reduction. Volume 3: Applications, De Gruyter, Berlin, pp. 279–320.Google Scholar
Loiseau, J.-C., Noack, B. R., and Brunton, S. L. (2018), ‘Sparse reduced-order modeling: Sensor-based dynamics to full-state estimation’, Journal of Fluid Mechanics 844, 459–490.Google Scholar
Lorenz, E. (1956), Empirical orthogonal functions and statistical weather prediction, Statistical forecasting project, Scientific Report No. 1, MIT, Department of Meteorology, Cambridge, MA.Google Scholar
Lorenz, E. N. (1963), ‘Deterministic nonperiodic flow’, Journal of the Atmospheric Sciences 20(2), 130–141.Google Scholar
Lozano-Durán, A., Flores, O., and Jiménez, J. (2012), ‘The three-dimensional structure of momentum transfer in turbulent channels’, Journal of Fluid Mechanics 694, 100–130.Google Scholar
Lozano-Durán, A. and Jiménez, J. (2014), ‘Time-resolved evolution of coherent structures in turbulent channels: Characterization of eddies and cascades’, Journal of Fluid Mechanics 759, 432–471.Google Scholar
Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E. (2019), ‘Deepxde: A deep learning library for solving differential equations’, arXiv preprint arXiv:1907.04502.Google Scholar
Lu, S. S. and Willmarth, W. W. (1973), ‘Measurements of the structure of the Reynolds stress in a turbulent boundary layer’, Journal of Fluid Mechanics 60, 481–511.Google Scholar
Lu, T. and Law, C. K. (2009), ‘Toward accommodating realistic fuel chemistry in large-scale computations’, Progress in Energy and Combustion Science 35(2), 192–215.Google Scholar
Luchtenburg, D. M., Günter, B., Noack, B. R., King, R., and Tadmor, G. (2009), ‘A generalized mean-field model of the natural and actuated flows around a high-lift configuration’, Journal of Fluid Mechanics 623, 283–316.Google Scholar
Luchtenburg, D. M. and Rowley, C. W. (2011), ‘Model reduction using snapshot-based realizations’, Bulletin of the American Physical Society 56(18), 37pp.Google Scholar
Luchtenburg, D. M., Schlegel, M., Noack, B. R., Aleksić, K., King, R., Tadmor, G., and Günther, B. (2010), Turbulence control based on reduced-order models and nonlinear control design, in King, R., ed., Active Flow Control II, Vol. 108 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, May 26–28, 2010, Springer-Verlag, Berlin, pp. 341–356.Google Scholar
Luhar, M., Sharma, A. S., and McKeon, B. J. (2014), ‘Opposition control within the resolvent analysis framework’, Journal of Fluid Mechanics 749, 597–626.Google Scholar
Lumley, J. L. (1967), The structure of inhomogeneous turbulent flows, in Yaglam, A. M. and Tatarsky, V. I., eds., ‘Proceedings of the International Colloquium on the Fine Scale Structure of the Atmosphere and Its Influence on Radio Wave Propagation’, Doklady Akademii Nauk SSSR, Moscow, Nauka.Google Scholar
Lumley, J. L. and Poje, A. (1997), ‘Low-dimensional models for flows with density fluctuations’, Physics of Fluids 9(7), 2023–2031.Google Scholar
Lusch, B., Kutz, J. N., and Brunton, S. L. (2018), ‘Deep learning for universal linear embeddings of nonlinear dynamics’, Nature Communications 9(1), 4950.Google Scholar
Lyapunov, A. (1892), The General Problem of the Stability of Motion, The Kharkov Mathematical Society, Kharkov, 251pp.Google Scholar
Ma, Z., Ahuja, S., and Rowley, C. W. (2011), ‘Reduced order models for control of fluids using the eigensystem realization algorithm’, Theoretical and Computational Fluid Dynamics 25(1), 233–247.Google Scholar
Mackie, J. (1974), The Cement of the Universe: A Study of Causation, Oxford University Press, New York.Google Scholar
MacQueen, J. (1967), Some methods for classification and analysis of multivariate observations, in ‘Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability’, Vol. 1, Oakland, CA, pp. 281–297.Google Scholar
Magill, J., Bachmann, M., and Rixon, G. (2003), ‘Dynamic stall control using a model-based observer.’, Journal of Aircraft 40(2), 355–362.Google Scholar
Magnussen, B. F. (1981), On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow, in ‘19th AIAA Aerospace Science Meeting’, May 21–24, 2007, Williamsburg, VA.Google Scholar
Magri, L. (2019), ‘Adjoint methods as design tools in thermoacoustics’, Applied Mechanics Reviews 71(2), 020801.Google Scholar
Mahoney, M. W. (2011), ‘Randomized algorithms for matrices and data’, Foundations and Trends in Machine Learning 3, 123–224.Google Scholar
Majda, A. J. and Harlim, J. (2012), ‘Physics constrained nonlinear regression models for time series’, Nonlinearity 26(1), 201.Google Scholar
Malik, M. R., Isaac, B. J., Coussement, A., Smith, P. J., and Parente, A. (2018), ‘Principal component analysis coupled with nonlinear regression for chemistry reduction’, Combustion and Flame 187, 30–41.Google Scholar
Malik, M. R., Obando Vega, P., Coussement, A., and Parente, A. (2020), ‘Combustion modeling using Principal Component Analysis: A posteriori validation on Sandia flames D, E and F’, Proceedings of the Combustion Institute 38(2), 2635–2643.Google Scholar
Mallat, S. G. (1989), ‘Multiresolution approximations and wavelet orthonormal bases of L2(R)’, Transactions of the American Mathematical Society 315(1), 69–87.Google Scholar
Mallor, F., Raiola, M., Vila, C. S., Örlü, R., Discetti, S., and Ianiro, A. (2019), ‘Modal decomposition of flow fields and convective heat transfer maps: An application to wall-proximity square ribs’, Experimental Thermal and Fluid Science 102, 517–527.Google Scholar
Maltrud, M. E. and Vallis, G. K. (1991), ‘Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence’, Journal of Fluid Mechanics 228, 321–342.Google Scholar
Mangan, N. M., Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016), ‘Inferring biological networks by sparse identification of nonlinear dynamics’, IEEE Transactions on Molecular, Biological, and Multi-Scale Communications 2(1), 52–63.Google Scholar
Mangan, N. M., Kutz, J. N., Brunton, S. L., and Proctor, J. L. (2017), ‘Model selection for dynamical systems via sparse regression and information criteria’, Proceedings of the Royal Society A 473(2204), 1–16.Google Scholar
Manohar, K., Brunton, B. W., Kutz, J. N., and Brunton, S. L. (2018), ‘Data-driven sparse sensor placement: Demonstrating the benefits of exploiting known patterns’, IEEE Control Systems Magazine 38(3), 63–86.Google Scholar
Marčenko, V. A. and Pastur, L. A. (1967), ‘Distribution of eigenvalues for some sets of random matrices’, Mathematics of the USSR-Sbornik 1(4), 457.Google Scholar
Mardt, A., Pasquali, L., Wu, H., and Noé, F. (2018), ‘VAMPnets: Deep learning of molecular kinetics’, Nature Communications 9, 5.Google Scholar
Marsden, J. E. and Ratiu, T. S. (1999), Introduction to Mechanics and Symmetry, 2nd ed., Springer-Verlag, New York.Google Scholar
Maulik, R., San, O., Rasheed, A., and Vedula, P. (2019), ‘Subgrid modelling for two-dimensional turbulence using neural networks’, Journal of Fluid Mechanics 858, 122–144.Google Scholar
Maurel, S., Borée, J., and Lumley, J. (2001), ‘Extended proper orthogonal decomposition: Application to jet/vortex interaction’, Flow, Turbulence and Combustion 67(2), 125–136.Google Scholar
McKeon, B. and Sharma, A. (2010), ‘A critical-layer framework for turbulent pipe flow’, Journal of Fluid Mechanics 658, 336–382.Google Scholar
McWilliams, J. C. (1980), ‘An application of equivalent modons to atmospheric blocking’, Dynamics of Atmospheres and Oceans 5, 43–66.Google Scholar
McWilliams, J. C. (1984), ‘The emergence of isolated coherent vortices in turbulent flow’, Journal of Fluid Mechanics 146, 21–43.Google Scholar
McWilliams, J. C. (1990a), ‘A demonstration of the suppression of turbulent cascades by coherent vortices in two-dimensional turbulence’, Physics of Fluids A 2, 547–552.Google Scholar
McWilliams, J. C. (1990b), ‘The vortices of two-dimensional turbulence’, Journal of Fluid Mechanics 219, 361–385.Google Scholar
Meena, M. G., Nair, A. G., and Taira, K. (2018), ‘Network community-based model reduction for vortical flows’, Physical Review E 97(6), 063103.Google Scholar
Mendez, M. A., Hess, D., Watz, B. B., and Buchlin, J.-M. (2020), ‘Multiscale proper orthogonal decomposition (MPOD) of TR-PIV data- A case study on stationary and transient cylinder wake flows’, Measurement Science and Technology 80, 981–1002.Google Scholar
Mendez, M. A. and Buchlin, J.-M. (2016), ‘Notes on 2D pulsatile Poiseuille flows: An introduction to eigenfunctions and complex variables using MATLAB’, Technical Report TN 215, von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium.Google Scholar
Mendez, M. A., Scelzo, M., and Buchlin, J.-M. (2018), ‘Multiscale modal analysis of an oscillating impinging gas jet’, Experimental Thermal and Fluid Science 91, 256–276.Google Scholar
Mendez, M., Balabane, M., and Buchlin, J.-M. (2019), ‘Multi-scale proper orthogonal decom-position of complex fluid flows’, Journal of Fluid Mechanics 870, 988–1036.Google Scholar
Mendez, M., Gosset, A., and Buchlin, J.-M. (2019), ‘Experimental analysis of the stability of the jet wiping process, part II: Multiscale modal analysis of the gas jet-liquid film interaction’, Experimental Thermal and Fluid Science 106, 48–67.Google Scholar
Mendez, M., Raiola, M., Masullo, A., Discetti, S., Ianiro, A., Theunissen, R., and Buchlin, J.-M. (2017), ‘POD-based background removal for particle image velocimetry’, Experimental Thermal and Fluid Science 80, 181–192.Google Scholar
Mendible, A., Brunton, S. L., Aravkin, A. Y., Lowrie, W., and Kutz, J. N. (2020), ‘Dimension-ality reduction and reduced-order modeling for traveling wave physics’, Theoretical and Computational Fluid Dynamics 34(4), 385–400.Google Scholar
Meneveau, C. (1991), ‘Analysis of turbulence in the orthonormal wavelet representation’, Journal of Fluid Mechanics 232, 469–520.Google Scholar
Meneveau, C. and Katz, J. (2000), ‘Scale-invariance and turbulence models for large-eddy simulation’, Annual Review of Fluid Mechanics 32(1), 1–32.Google Scholar
Meunier, P., Le Dizès, S., and Leweke, T. (2005), ‘Physics of vortex merging’, C. R. Physique 6, 431–450.Google Scholar
Meyers, S. D., Kelly, B. G., and O’Brien, J. J. (1993), ‘An introduction to wavelet analysis in oceanography and meteorology: With application to the dispersion of Yanai waves’, Monthly Weather Review 121(10), 2858–2866.Google Scholar
Mezić, I. (2005), ‘Spectral properties of dynamical systems, model reduction and decompositions’, Nonlinear Dynamics 41(1–3), 309–325.Google Scholar
Mezić, I. (2013), ‘Analysis of fluid flows via spectral properties of the Koopman operator’, Annual Review of Fluid Mechanics 45, 357–378.Google Scholar
Mezić, I. and Banaszuk, A. (2004), ‘Comparison of systems with complex behavior’, Physica D: Nonlinear Phenomena 197(1), 101–133.Google Scholar
Mifsud, M., Vendl, A., Hansen, L.-U., and Görtz, S. (2019), ‘Fusing wind-tunnel measurements and CFD data using constrained gappy proper orthogonal decomposition’, Aerospace Science and Technology 86, 312–326.Google Scholar
Mifsud, M., Zimmermann, R., and Görtz, S. (2014), ‘Speeding-up the computation of high-lift aerodynamics using a residual-based reduced-order model’, CEAS Aeronautical Journal 6(1), 3–16.Google Scholar
Milano, M. and Koumoutsakos, P. (2002), ‘Neural network modeling for near wall turbulent flow’, Journal of Computational Physics 182(1), 1–26.Google Scholar
Min, C. and Choi, H. (1999), ‘Suboptimal feedback control of vortex shedding at low reynolds numbers’, Journal of Fluid Mechanics 401, 123–156.Google Scholar
Minelli, G., Dong, T., Noack, B. R., and Krajnović, S. (2020), ‘Upstream actuation for bluff-body wake control driven by a genetically inspired optimization’, Journal of Fluid Mechanics 893, A1.Google Scholar
Mizuno, Y. and Jiménez, J. (2013), ‘Wall turbulence without walls’, Journal of Fluid Mechanics 723, 429–455.Google Scholar
Mnih, V., Badia, A. P., Mirza, M., Graves, A., Lillicrap, T., Harley, T., Silver, D., and Kavukcuoglu, K. (2016), Asynchronous methods for deep reinforcement learning, in Balcan, M. F. and Weinberger, K. Q., eds., ‘Proceedings of the 33rd International Conference on Machine Learning’, Vol. 48 of Proceedings of Machine Learning Research, PMLR, New York, pp. 1928–1937.Google Scholar
Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidjeland, A. K., Ostrovski, G., Petersen, S., Beattie, C., Sadik, A., Antonoglou, I., King, H., Kumaran, D., Wierstra, D., Legg, S., and Hassabis, D. (2015), ‘Human-level control through deep reinforcement learning’, Nature 518(7540), 529–533.Google Scholar
Moarref, R., Jovanovic, M., Tropp, J., Sharma, A., and McKeon, B. (2014), ‘A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization’, Physics Fluids 26, 051701.Google Scholar
Mohammed, R., Tanoff, M., Smooke, M., Schaffer, A., and Long, M. (1998), ‘Computational and experimental study of a forced, time-varying, axisymmetric, laminar diffusion flame’, Symposium (International) on Combustion 27(1), 693–702.Google Scholar
Moisy, F. and Jiménez, J. (2004), ‘Geometry and clustering of intense structures in isotropic turbulence’, Journal of Fluid Mechanics 513, 111–133.Google Scholar
Mojgani, R. and Balajewicz, M. (2017), ‘Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows’, arXiv preprint arXiv:1701.04343.Google Scholar
Moore, B. C. (1981), ‘Principal component analysis in linear systems: Controllability, observ-ability, and model reduction’, IEEE Transactions on Automatic Control AC-26(1), 17–32.Google Scholar
Morzyński, M., Afanasiev, K., and Thiele, F. (1999), ‘Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis’, Computer Methods in Applied Mechanics and Engineering 169, 161–176.Google Scholar
Morzyński, M., Noack, B. R., and Tadmor, G. (2007), ‘Global stability analysis and reduced order modeling for bluff-body flow control’, Journal of Theoretical and Applied Mechanics 45, 621–642.Google Scholar
Morzyński, M., Stankiewicz, W., Noack, B. R., Thiele, F., and Tadmor, G. (2006), Generalized mean-field model for flow control using continuous mode interpolation, in ‘3rd AIAA Flow Control Conference’, June 5–8, 2006, San Francisco, CA, Invited AIAA-Paper 2006-3488.Google Scholar
Mowlavi, S. and Sapsis, T. P. (2018), ‘Model order reduction for stochastic dynamical systems with continuous symmetries’, SIAM Journal on Scientific Computing 40(3), A1669–A1695.Google Scholar
Murata, T., Fukami, K., and Fukagata, K. (2019), CNN-SINDY based reduced order modeling of unsteady flow fields, in ‘Fluids Engineering Division Summer Meeting’, July–August 2019, San Francisco, CA, Vol. 59032, American Society of Mechanical Engineers, New York, p. V002T02A074.Google Scholar
Nagata, M. (1990), ‘Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity’, Journal of Fluid Mechanics 217, 519–527.Google Scholar
Nair, A. G., Brunton, S. L., and Taira, K. (2018), ‘Networked-oscillator-based modeling and control of unsteady wake flows’, Physical Review E 97(6), 063107.Google Scholar
Nair, A. G. and Taira, K. (2015), ‘Network-theoretic approach to sparsified discrete vortex dynamics’, Journal of Fluid Mechanics 768, 549–571.Google Scholar
Nair, A. G., Yeh, C.-A., Kaiser, E., Noack, B. R., Brunton, S. L., and Taira, K. (2019), ‘Cluster-based feedback control of turbulent post-stall separated flows’, Journal of Fluid Mechanics 875, 345–375.Google Scholar
Narasingam, A. and Kwon, J. S.-I. (2018), ‘Data-driven identification of interpretable reduced-order models using sparse regression’, Computers & Chemical Engineering 119, 101–111.Google Scholar
Neely, T. W., Samson, E. C., Bradley, A. S., Davis, M. J., and Anderson, B. P. (2010), ‘Observation of vortex dipoles in an oblate Bose–Einstein condensate’, Physical Review Letters 104, 160401.Google Scholar
Newell, A. and Simon, H. A. (1976), ‘Computer science as empirical inquiry: Symbols and search’, Communication of ACM 19(3), 113–126.Google Scholar
Ng, A. Y., Harada, D., and Russell, S. J. (1999), Policy invariance under reward transformations: Theory and application to reward shaping, in ‘Proceedings of the Sixteenth International Conference on Machine Learning’, ICML 99, Morgan Kaufmann, San Francisco, CA, pp. 278–287.Google Scholar
Ng, A. Y., Jordan, M. I., and Weiss, Y. (2002), On spectral clustering: Analysis and an algorithm, in ‘Advances in Neural Information Processing Systems’, December 3–8, 2001, Vancouver, British Columbia, Canada, pp. 849–856.Google Scholar
Nilsson, N. (1998), Artificial Intelligence: A New Synthesis, Morgan Kaufmann, San Francisco, CA.Google Scholar
Ninni, D. and Mendez, M. A. (2021), ‘Modulo: A software for multiscale proper orthogonal decomposition of data’, SoftwareX 12, 100622.Google Scholar
Noack, B. R. (2019), Closed-loop turbulence control – From human to machine learning (and retour), in Zhou, Y., Kimura, M., Peng, G., Lucey, A. D., and Hung, L., eds., ‘Fluid-Structure-Sound Interactions and Control. Proceedings of the 4th Symposium on Fluid-Structure-Sound Interactions and Control’, Springer, Berlin, pp. 23–32.Google Scholar
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G., and Thiele, F. (2003), ‘A hierarchy of low-dimensional models for the transient and post-transient cylinder wake’, Journal of Fluid Mechanics 497, 335–363.Google Scholar
Noack, B. R. and Eckelmann, H. (1994), ‘A global stability analysis of the steady and periodic cylinder wake’, Journal of Fluid Mechanics 270, 297–330.Google Scholar
Noack, B. R., Mezić, I., Tadmor, G., and Banaszuk, A. (2004), ‘Optimal mixing in recirculation zones’, Physics of Fluids 16(4), 867–888.Google Scholar
Noack, B. R., Morzynski, M., and Tadmor, G. (2011), Reduced-Order Modelling for Flow Control, Vol. 528 of International Centre for Mechanical Sciences: Courses and Lectures, Springer Science & Business Media, Dordrecht.Google Scholar
Noack, B. R., Papas, P., and Monkewitz, P. A. (2005), ‘The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows’, Journal of Fluid Mechanics 523, 339.Google Scholar
Noack, B. R., Pelivan, I., Tadmor, G., Morzyński, M., and Comte, P. (2004), Robust low-dimensional Galerkin models of natural and actuated flows, in ‘Fourth Aeroacoustics Workshop’, RWTH, Aachen, February 26–27, 2004, pp. 0001–0012.Google Scholar
Noack, B. R., Schlegel, M., Ahlborn, B., Mutschke, G., Morzyński, M., Comte, P., and Tadmor, G. (2008), ‘A finite-time thermodynamics of unsteady fluid flows’, Journal of Non-Equilibrium Thermodynamics 33(2), 103–148.Google Scholar
Noack, B. R., Stankiewicz, W., Morzynski, M., and Schmid, P. J. (2016), ‘Recursive dynamic mode decomposition of a transient cylinder wake’, Journal of Fluid Mechanics 809, 843–872.Google Scholar
Noé, F. and Nuske, F. (2013), ‘A variational approach to modeling slow processes in stochastic dynamical systems’, Multiscale Modeling Simulation 11(2), 635–655.Google Scholar
Noé, F., Olsson, S., Köhler, J., and Wu, H. (2019), ‘Boltzmann generators: Sampling equilib-rium states of many-body systems with deep learning’, Science 365(6457), eaaw1147.Google Scholar
Noether, E. (1918), ‘Invariante Variationsprobleme’, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 1918, 235–257. English Reprint: physics/0503066, http://dx.doi.org/10.1080/00411457108231446, p. 57Google Scholar
Novati, G., Mahadevan, L., and Koumoutsakos, P. (2019), ‘Controlled gliding and perching through deep-reinforcement-learning’, Physical Review Fluids 4(9), 093902.Google Scholar
Novati, G., Verma, S., Alexeev, D., Rossinelli, D., Van Rees, W. M., and Koumoutsakos, P. (2017), ‘Synchronisation through learning for two self-propelled swimmers’, Bioinspiration & Biomimetics 12(3), aa6311.Google Scholar
Nüske, F., Schneider, R., Vitalini, F., and Noé, F. (2016), ‘Variational tensor approach for approximating the rare-event kinetics of macromolecular systems’, The Journal of Chemical Physics 144(5), 054105.Google Scholar
Obukhov, A. M. (1941), ‘On the distribution of energy in the spectrum of turbulent flow’, Doklady Akademii Nauk SSSR 32, 22–24.Google Scholar
Ogata, K. (2009), Modern Control Engineering, 5th ed., Pearson, Upper Saddle River, NJ.Google Scholar
Oppenheim, A. V. and Schafer, R. W. (2009), Discrete-Time Signal Processing, 3rd ed. (Prentice-Hall Signal Processing Series), Pearson, Harlow.Google Scholar
Oppenheim, A. V., Willsky, A. S., and with Hamid, S. (1996), Signals and Systems, 2nd ed., Prentice-Hall, Upper Saddle River, NJ.Google Scholar
Orr, W. (1907a), ‘The stability or instability of the steady motions of a perfect liquid and of a viscous liquid’, Proceedings of the Royal Irish Academy 27, 9–138.Google Scholar
Orr, W. M. (1907b), ‘The stability or instability of the steady motions of a perfect liquid, and of a viscous liquid. Part I: A perfect liquid’, Proceedings of the Royal Irish Academy 27, 9–68.Google Scholar
Orszag, S. (1971), ‘Accurate solution of the Orr-Sommerfeld stability equation’, Journal of Fluid Mechanics 50, 689–703.Google Scholar
Orszag, S. A. and Patera, A. T. (1983), ‘Secondary instability of wall-bounded shear flows’, Journal of Fluid Mechanics 128, 347–385.Google Scholar
Östh, J., Noack, B. R., and Krajnović, S. (2014), ‘On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body’, Journal of Fluid Mechanics 747, 518–544.Google Scholar
Otto, S. E. and Rowley, C. W. (2019), ‘Linearly-recurrent autoencoder networks for learning dynamics’, SIAM Journal on Applied Dynamical Systems 18(1), 558–593.Google Scholar
Ouellette, N. T., Xu, H., and Bodenschatz, E. (2006), ‘A quantitative study of three-dimensional Lagrangian particle tracking algorithms’, Experiments in Fluids 40(2), 301–313.Google Scholar
Paatero, P. and Tapper, U. (1994), ‘Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values’, Environmetrics 5(2), 111–126.Google Scholar
Pan, S., Arnold-Medabalimi, N., and Duraisamy, K. (2020), ‘Sparsity-promoting algo-rithms for the discovery of informative Koopman invariant subspaces’, arXiv preprint arXiv:2002.10637.Google Scholar
Pao, H.-T. (2008), ‘A comparison of neural network and multiple regression analysis in modeling capital structure’, Expert Systems with Applications 35, 720–727.Google Scholar
Parente, A. and Sutherland, J. C. (2013), ‘Principal component analysis of turbulent combustion data: Data pre-processing and manifold sensitivity’, Combustion and Flame 160(2), 340–350.Google Scholar
Parente, A., Sutherland, J., Dally, B., Tognotti, L., and Smith, P. (2011), ‘Investigation of the MILD combustion regime via Principal Component Analysis’, Proceedings of the Combustion Institute 33(2), 3333–3341.Google Scholar
Parente, A., Sutherland, J., Tognotti, L., and Smith, P. (2009), ‘Identification of low-dimensional manifolds in turbulent flames’, Proceedings of the Combustion Institute 32(1), 1579–1586.Google Scholar
Parezanovic, V., Cordier, L., Spohn, A., Duriez, T., Noack, B. R., Bonnet, J.-P., Segond, M., Abel, M., and Brunton, S. L. (2016), ‘Frequency selection by feedback control in a turbulent shear flow’, Journal of Fluid Mechanics 797, 247–283.Google Scholar
Parish, E. J. and Duraisamy, K. (2016), ‘A paradigm for data-driven predictive modeling using field inversion and machine learning’, Journal of Computational Physics 305, 758–774.Google Scholar
Pastoor, M. (2008), Niederdimensionale Wirbelmodelle zur Kontrolle von Scherund Nach-laufströmungen, PhD thesis, Berlin Institute of Technology, Germany.Google Scholar
Pastoor, M., Henning, L., Noack, B. R., King, R., and Tadmor, G. (2008), ‘Feedback shear layer control for bluff body drag reduction’, Journal of Fluid Mechanics 608, 161–196.Google Scholar
Pathak, D., Agrawal, P., Efros, A. A. and Darrell, T. (2017), Curiosity-driven exploration by self-supervised prediction, in Precup, D. and Teh, Y. W., eds., ‘Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6–11 August 2017’, Vol. 70 of Proceedings of Machine Learning Research, PMLR, pp. 2778–2787.Google Scholar
Peerenboom, K., Parente, A., Kozák, T., Bogaerts, A., and Degrez, G. (2015), ‘Dimension reduction of non-equilibrium plasma kinetic models using principal component analysis’, Plasma Sources Science and Technology 24(2), 025004.Google Scholar
Penland, C. (1996), ‘A stochastic model of IndoPacific sea surface temperature anomalies’, Physica D: Nonlinear Phenomena 98(2–4), 534–558.Google Scholar
Penland, C. and Magorian, T. (1993), ‘Prediction of Niño 3 sea surface temperatures using linear inverse modeling’, Journal of Climate 6(6), 1067–1076.Google Scholar
Pepiot-Desjardins, P. and Pitsch, H. (2008), ‘An efficient error-propagation-based reduction method for large chemical kinetic mechanisms’, Combustion and Flame 154(1–2), 67–81.Google Scholar
Perko, L. (2013), Differential Equations and Dynamical Systems, Vol. 7 of Texts in Applied Mathematics, Springer Science & Business Media, New York.Google Scholar
Perlman, E., Burns, R., Li, Y., and Meneveau, C. (2007), Data exploration of turbulence simulations using a database cluster, in ‘Proceedings of the SC07’, ACM, New York, pp. 23.1–23.11.Google Scholar
Perrin, R., Braza, M., Cid, E., Cazin, S., Barthet, A., Sevrain, A., Mockett, C., and Thiele, F. (2007), ‘Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD’, Experiments in Fluids 43(2–3), 341–355.Google Scholar
Peters, N. (1984), ‘Laminar diffusion flamelet models in non-premixed turbulent combustion’, Progress in Energy and Combustion Science 10(3), 319–339.Google Scholar
Phan, M. Q., Juang, J.-N., and Hyland, D. C. (1995), ‘On neural networks in identification and control of dynamic systems,’ in Guran, Ardéshir and Inman, Daniel J, eds., ‘Wave Motion, Intelligent Structures and Nonlinear Mechanics’, World Scientific, Singapore, pp. 194–225.Google Scholar
Picard, C. and Delville, J. (2000), ‘Pressure velocity coupling in a subsonic round jet’, International Journal of Heat and Fluid Flow 21(3), 359–364.Google Scholar
Poincaré, H. (1920), Science et méthode, Flammarion, Paris. English translation in Dover books, 1952.Google Scholar
Pope, S. B. (2013), ‘Small scales, many species and the manifold challenges of turbulent combustion’, Proceedings of the Combustion Institute 34(1), 1–31.Google Scholar
Proctor, J. L., Brunton, S. L., and Kutz, J. N. (2016), ‘Dynamic mode decomposition with control’, SIAM Journal on Applied Dynamical Systems 15(1), 142–161.Google Scholar
Protas, B. (2004), ‘Linear feedback stabilization of laminar vortex shedding based on a point vortex model’, Physics of Fluids 16(12), 4473–4488.Google Scholar
Quarteroni, A. and Rozza, G. (2013), Reduced Order Methods for Modeling and Computational Reduction, Vol. 9 of MS&A – Modeling, Simulation & Appplications, Springer, New York.Google Scholar
Rabault, J. (2019), ‘Deep reinforcement learning applied to fluid mechanics: Materials from the 2019 Flow/Interface School on Machine Learning and Data Driven Methods’, DOI:10.13140/RG.2.2.11533.90086.Google Scholar
Rabault, J., Belus, V., Viquerat, J., Che, Z., Hachem, E., Reglade, U., and Jensen, A. (2019), Exploiting locality and physical invariants to design effective deep reinforcement learning control of the unstable falling liquid film, in ‘The 1st Graduate Forum of CSAA and the 7th International Academic Conference for Graduates’, NUAA, November 21–22, 2019, Nanjing, China.Google Scholar
Rabault, J., Kuchta, M., Jensen, A., Reglade, U., and Cerardi, N. (2019), ‘Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control’, Journal of Fluid Mechanics 865, 281–302.Google Scholar
Rabault, J. and Kuhnle, A. (2019), ‘Accelerating deep reinforcement learning strategies of flow control through a multi-environment approach’, Physics of Fluids 31(9), 094105.Google Scholar
Rabault, J. and Kuhnle, A. (2020), ‘Deep reinforcement learning applied to active flow control’, Research Gate Preprint https://doi.org/10.13140/RG2.Google Scholar
Rabault, J., Ren, F., Zhang, W., Tang, H., and Xu, H. (2020), ‘Deep reinforcement learning in fluid mechanics: A promising method for both active flow control and shape optimization’, Journal of Hydrodynamics 32(2), 234–246.Google Scholar
Raibaudo, C., Zhong, P., Noack, B. R., and Martinuzzi, R. J. (2020), ‘Machine learning strategies applied to the control of a fluidic pinball’, Physics of Fluids 32(1), 015108.Google Scholar
Raiola, M., Discetti, S., and Ianiro, A. (2015), ‘On PIV random error minimization with optimal POD-based low-order reconstruction’, Experiments in Fluids 56(4), 75.Google Scholar
Raiola, M., Ianiro, A., and Discetti, S. (2016), ‘Wake of tandem cylinders near a wall’, Experimental Thermal and Fluid Science 78, 354–369.Google Scholar
Raissi, M. and Karniadakis, G. E. (2018), ‘Hidden physics models: Machine learning of nonlinear partial differential equations’, Journal of Computational Physics 357, 125–141.Google Scholar
Raissi, M., Perdikaris, P., and Karniadakis, G. (2019), ‘Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations’, Journal of Computational Physics 378, 686–707.Google Scholar
Raissi, M., Yazdani, A., and Karniadakis, G. E. (2020), ‘Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations’, Science 367(6481), 1026–1030.CrossRefGoogle ScholarPubMed
Ranzi, E., Frassoldati, A., Stagni, A., Pelucchi, M., Cuoci, A., and Faravelli, T. (2014), ‘Reduced kinetic schemes of complex reaction systems: fossil and biomass-derived transportation fuels’, International Journal of Chemical Kinetics 46(9), 512–542.Google Scholar
Rasmussen, C. (2006), Gaussian Processes for Machine Learning, MIT Press, Cambridge, MA.Google Scholar
Rayleigh, L. (1887), ‘On the stability of certain fluid motions’, The Proceedings of the London Mathematical Society 19, 67–74.CrossRefGoogle Scholar
Recht, B. (2019), ‘A tour of reinforcement learning: The view from continuous control’, Annual Review of Control, Robotics, and Autonomous Systems 2, 253–279.Google Scholar
Reddy, G., Celani, A., Sejnowski, T. J., and Vergassola, M. (2016), ‘Learning to soar in turbulent environments’, Proceedings of the National Academy of Sciences of the United States of America 113(33), E4877–E4884.Google Scholar
Reddy, G., Wong-Ng, J., Celani, A., Sejnowski, T. J., and Vergassola, M. (2018), ‘Glider soaring via reinforcement learning in the field’, Nature 562(7726), 236–239.Google Scholar
Reddy, S. and Henningson, D. (1993), ‘Energy growth in viscous channel flows’, Journal of Fluid Mechanics 252, 209–238.Google Scholar
Reimer, L., Heinrich, R., and Ritter, M. (2019), Towards higher-precision maneuver and gust loads computations of aircraft: Status of related features in the CFD-based multidisciplinary simulation environment FlowSimulator, in ‘Notes on Numerical Fluid Mechanics and Multidisciplinary Design’, Springer, Cham, pp. 597–607.Google Scholar
Reiss, J., Schulze, P., Sesterhenn, J., and Mehrmann, V. (2018), ‘The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena’, SIAM Journal on Scientific Computing 40(3), A1322–A1344.Google Scholar
Rempfer, D. (1995), Empirische Eigenfunktionen und Galerkin-Projektionen zur Beschreibung des laminar-turbulenten Grenzschichtumschlags (transl.: Empirical eigenfunctions and Galerkin projection for the description of the laminar-turbulent boundary-layer transition), Habilitationsschrift, Fakultät für Luftund Raumfahrttechnik, Universität Stuttgart.Google Scholar
Rempfer, D. (2000), ‘On low-dimensional Galerkin models for fluid flow’, Theoretical and Computational Fluid Dynamics 14(2), 75–88.Google Scholar
Rempfer, D. and Fasel, F. H. (1994a), ‘Dynamics of three-dimensional coherent structures in a flat-plate boundary-layer’, Journal of Fluid Mechanics 275, 257–283.CrossRefGoogle Scholar
Rempfer, D. and Fasel, F. H. (1994b), ‘Evolution of three-dimensional coherent structures in a flat-plate boundary-layer’, Journal of Fluid Mechanics 260, 351–375.Google Scholar
Ren, F., Hu, H.-b., and Tang, H. (2020), ‘Active flow control using machine learning: A brief review’, Journal of Hydrodynamics 32(2), 247–253.Google Scholar
Ren, F., Rabault, J., and Tang, H. (2020), ‘Applying deep reinforcement learning to active flow control in turbulent conditions’, arxiv preprint arXiv:2006.10683.Google Scholar
Ren, Z. and Pope, S. (2008), ‘Second-order splitting schemes for a class of reactive systems’, Journal of Computational Physics 227(17), 8165–8176.CrossRefGoogle Scholar
Reynolds, O. (1883), ‘An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels’, Proceedings of the Royal Society of London 35, 84–99.Google Scholar
Reynolds, O. (1894), ‘On the dynamical theory of incompressible viscous fluids and the determination of the criterion’, Proceedings of the Royal Society of London 56, 40–45.Google Scholar
Reynolds, W. C. and Tiederman, W. G. (1967), ‘Stability of turbulent channel flow, with application to Malkus’ theory’, Journal of Fluid Mechanics 27, 253–272.Google Scholar
Richards, J. I. and Youn, H. K. (1990), The Theory of Distributions, Cambridge University Press, Cambridge.Google Scholar
Richardson, L. F. (1920), ‘The supply of energy from and to atmospheric eddies’, Proceedings of the Royal Society A 97, 354–373.Google Scholar
Ripepi, M., Verveld, M. J., Karcher, N. W., Franz, T., Abu-Zurayk, M., Görtz, S., and Kier, T. M. (2018), ‘Reduced-order models for aerodynamic applications, loads and MDO’, CEAS Aeronautical Journal 9(1), 171–193.Google Scholar
Robinson, S. K. (1991), ‘Coherent motions in the turbulent boundary layer’, Annual Review Fluid Mechanics 23, 601–639.Google Scholar
Rokhlin, V., Szlam, A., and Tygert, M. (2009), ‘A randomized algorithm for principal component analysis’, SIAM Journal on Matrix Analysis and Applications 31, 1100–1124.Google Scholar
Rosenblatt, F. (1958), ‘The perceptron: A probabilistic model for information storage and organization in the brain’, Psychological Review 65(6), 386.Google Scholar
Roussopoulos, K. (1993), ‘Feedback control of vortex shedding at low Reynolds numbers’, Journal of Fluid Mechanics 248, 267–296.Google Scholar
Roweis, S. and Lawrence, S. (2000), ‘Nonlinear dimensionality reduction by locally linear embedding’, Science 290(5500), 2323–2326.Google Scholar
Rowley, C. W. (2005), ‘Model reduction for fluids using balanced proper orthogonal decompo-sition.’, International Journal of Bifurcation and Chaos 15(3), 997–1013.CrossRefGoogle Scholar
Rowley, C. W., Colonius, T., and Murray, R. M. (2004), ‘Model reduction for compressible flows using POD and Galerkin projection’, Physica D: Nonlinear Phenomena 189(1–2), 115–129.Google Scholar
Rowley, C. W. and Dawson, S. T. M. (2017), ‘Model reduction for flow analysis and control’, Annual Review of Fluid Mechanics 49(1), 387–417.Google Scholar
Rowley, C. W., Kevrekidis, I. G., Marsden, J. E., and Lust, K. (2003), ‘Reduction and reconstruction for self-similar dynamical systems’, Nonlinearity 16(4), 1257.Google Scholar
Rowley, C. W. and Marsden, J. E. (2000), ‘Reconstruction equations and the Karhunen–Loève expansion for systems with symmetry’, Physica D: Nonlinear Phenomena 142(1), 1–19.Google Scholar
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P., and Henningson, D. (2009), ‘Spectral analysis of nonlinear flows’, Journal of Fluid Mechanics 645, 115–127.Google Scholar
Rowley, C. W. and Williams, D. R. (2006), ‘Dynamics and control of high-Reynolds-number flow over open cavities’, Annual Review of Fluid Mechanics 38, 251–276.Google Scholar
Rudy, S. H., Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2017), ‘Data-driven discovery of partial differential equations’, Science Advances 3, e1602614.CrossRefGoogle ScholarPubMed
Rumelhart, D. E., Hinton, G. E., Williams, R. J. (1986), ‘Learning representations by back-propagating errors’, Nature 323(6088), 533–536.Google Scholar
Russell, B. (1912), ‘On the notion of cause’, The Proceedings of the Aristotelian Society 13, 1–26.Google Scholar
Sabater, C., Bekemeyer, P., and Görtz, S. (2020), ‘Efficient bilevel surrogate approach for optimization under uncertainty of shock control bumps’, AIAA Journal 58(12), 5228–5242.Google Scholar
Salimans, T. and Chen, R. (2018), ‘Learning Montezuma’s Revenge from a single demonstration’, arXiv preprint arXiv:1812.03381.Google Scholar
Salimans, T., Ho, J., Chen, X., and Sutskever, I. (2017), ‘Evolution strategies as a scalable alternative to reinforcement learning’, CoRR, arXiv:1703.03864.Google Scholar
Saltzman, B. (1962), ‘Finite amplitude free convection as an initial value problem – I’, Journal of Atmospheric Sciences 19(4), 329–341.Google Scholar
Sarlos, T. (2006), Improved approximation algorithms for large matrices via random projections, in ‘47th Annual IEEE Symposium on Foundations of Computer Science’, October 21–24, 2006, Washington, DC, pp. 143–152.Google Scholar
Savinov, N., Raichuk, A., Marinier, R., Vincent, D., Pollefeys, M., Lillicrap, T., and Gelly, S. (2018), ‘Episodic curiosity through reachability’, arXiv preprint 1810.02274.Google Scholar
Schaeffer, H. (2017), Learning partial differential equations via data discovery and sparse optimization, ‘Proceedings of the Royal Society A’, 473, 20160446.Google Scholar
Schaeffer, H. and McCalla, S. G. (2017), ‘Sparse model selection via integral terms’, Physical Review E 96(2), 023302.Google Scholar
Schäfer, M., Turek, S., Durst, F., Krause, E., and Rannacher, R. (1996), Benchmark com-putations of laminar flow around a cylinder, in ‘Flow Simulation with High-Performance Computers II’, Springer, Berlin, pp. 547–566.Google Scholar
Schaffer, S. (1994), Making up discovery, in Boden, M. A., ed., ‘Dimensions of creativity’, MIT Press, Cambridge, pp. 13–51.Google Scholar
Scherl, I., Strom, B., Shang, J. K., Williams, O., Polagye, B. L., and Brunton, S. L. (2020), ‘Robust principal component analysis for particle image velocimetry’, Physical Review Fluids 5, 054401.Google Scholar
Schlegel, M. and Noack, B. R. (2015), ‘On long-term boundedness of Galerkin models’, Journal of Fluid Mechanics 765, 325–352.Google Scholar
Schlegel, M., Noack, B. R., and Tadmor, G. (2004), Low-dimensional Galerkin models and control of transitional channel flow, Technical Report 01/2004, Hermann-Föttinger-Institut für Strömungsmechanik, Technische Universität Berlin, Germany.Google Scholar
Schmelzer, M., Dwight, R. P., and Cinnella, P. (2020), ‘Discovery of algebraic Reynolds-stress models using sparse symbolic regression’, Flow, Turbulence and Combustion 104(2), 579–603.Google Scholar
Schmid, P. (2007), ‘Nonmodal stability theory’, Annual Review of Fluid Mechanics 39, 129–162.Google Scholar
Schmid, P. and Henningson, D. (2001), Stability and Transition in Shear Flows, Springer Verlag, New York.Google Scholar
Schmid, P. J. (2010), ‘Dynamic mode decomposition of numerical and experimental data’, Journal of Fluid Mechanics 656, 5–28.Google Scholar
Schmid, P., Li, L., Juniper, M., and Pust, O. (2011), ‘Applications of the dynamic mode decomposition’, Theoretical and Computational Fluid Dynamics 25(1–4), 249–259.Google Scholar
Schmid, P., Violato, D., and Scarano, F. (2012), ‘Decomposition of time-resolved tomographic PIV’, Experiments in Fluids 52(6), 1567–1579.Google Scholar
Schmidt, M. and Lipson, H. (2009), ‘Distilling free-form natural laws from experimental data’, Science 324(5923), 81–85.Google Scholar
Schmidt, O. T. and Towne, A. (2019), ‘An efficient streaming algorithm for spectral proper orthogonal decomposition’, Computer Physics Communications 237, 98–109.Google Scholar
Schneider, K. and Vasilyev, O. V. (2010), ‘Wavelet methods in computational fluid dynamics’, Annual Review of Fluid Mechanics 42, 473–503.Google Scholar
Schölkopf, B. and Smola, A. J. (2002), Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, Cambridge.Google Scholar
Schoppa, W. and Hussain, F. (2002), ‘Coherent structure generation in near-wall turbulence’, Journal of Fluid Mechanics 453, 57–108.Google Scholar
Schulman, J., Levine, S., Abbeel, P., Jordan, M., and Moritz, P. (2015), Trust region policy optimization, in Bach, F. and Blei, D., eds., ‘Proceedings of the 32nd International Conference on Machine Learning’, Vol. 37 of Proceedings of Machine Learning Research, PMLR, Lille, France, pp. 1889–1897.Google Scholar
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. (2017), ‘Proximal policy optimization algorithms’, CoRR, arXiv:1707.06347.Google Scholar
Schulze, J., Schmid, P., and Sesterhenn, J. (2009), ‘Exponential time integration using Krylov subspaces’, The International Journal for Numerical Methods in Fluids 60(6), 591–609.Google Scholar
Schumm, M., Berger, E., and Monkewitz, P. A. (1994), ‘Self-excited oscillations in the wake of two-dimensional bluff bodies and their control’, Journal of Fluid Mechanics 271, 17–53.Google Scholar
Schwer, D., Lu, P. and Green, W. Jr. (2003), ‘An adaptive chemistry approach to modeling complex kinetics in reacting flows’, Combustion and Flame 133(4), 451–465.Google Scholar
Semaan, R., Fernex, D., Weiner, A., and Noack, B. R. (2020), xROM – A Toolkit for Reduced-Order Modeling of Fluid Flows, Vol. 1 of Machine Learning Tools for Fluid Mechanics, Technische Universität Braunschweig, Braunschweig.Google Scholar
Semaan, R., Kumar, P., Burnazzi, M., Tissot, G., Cordier, L. and Noack, B. R. (2015), ‘Reduced-order modelling of the flow around a high-lift configuration with unsteady Coanda blowing’, Journal of Fluid Mechanics 800, 72–110.Google Scholar
Semeraro, O., Bagheri, S., Brandt, L., and Henningson, D. S. (2011), ‘Feedback control of three-dimensional optimal disturbances using reduced-order models’, Journal of Fluid Mechanics 677, 63–102.Google Scholar
Semeraro, O., Bagheri, S., Brandt, L., and Henningson, D. S. (2013), ‘Transition delay in a boundary layer flow using active control’, Journal of Fluid Mechanics 731, 288–311.Google Scholar
Semeraro, O., Lusseyran, F., Pastur, L. and Jordan, P. (2017), ‘Qualitative dynamics of wave packets in turbulent jets’, Physical Review Fluids 2(9), 094605.Google Scholar
Semeraro, O. and Mathelin, L. (2016), ‘An open-source toolbox for data-driven linear system identification’, Technical report, LIMSI-CNRS, Orsay, France.Google Scholar
Sharma, A. S., Mezić, I., and McKeon, B. J. (2016), ‘Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations’, Physical Review Fluids 1(3), 032402.Google Scholar
Sieber, M., Paschereit, C. O., and Oberleithner, K. (2016), ‘Spectral proper orthogonal decomposition’, Journal of Fluid Mechanics 792, 798–828.Google Scholar
Siegel, S. G., Seidel, J., Fagley, C., Luchtenburg, D. M., Cohen, K., and McLaughlin, T. (2008), ‘Low dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition’, Journal of Fluid Mechanics 610, 1–42.Google Scholar
Sigurd Skogestad, I. P. (2005), Multivariable Feedback Control, John Wiley & Sons, Hoboken, NJ.Google Scholar
Sillero, J. A. (2014), High Reynolds numbers turbulent boundary layers, PhD thesis, Aeronautics, Universidad Politécnica, Madrid. https://tesis.biblioteca.upm.es/tesis/7538.Google Scholar
Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., Van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M. Sander, D., Dominik, G., John, N., Nal, K., Ilya, S., Timothy, L., Madeleine, L., Koray, K., Thore, G., and Demis, H. (2016), ‘Mastering the game of Go with deep neural networks and tree search’, Nature 529(7587), 484–489.Google Scholar
Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Graepel, T., Lillicrap, T., Simonyan, K., and Hassabis, D. (2018), ‘A general reinforcement learning algorithm that masters Chess, Shogi, and Go through self-play’, Science 362(6419), 1140–1144.Google Scholar
Silver, D., Lever, G., Heess, N., Degris, T., Wierstra, D., and Riedmiller, M. (2014), Deter-ministic policy gradient algorithms, in Xing, E. P. and Jebara, T., eds., ‘Proceedings of the 31st International Conference on Machine Learning’, Vol. 32 of Proceedings of Machine Learning Research, PMLR, Bejing, China, pp. 387–395.Google Scholar
Silver, D., Schrittwieser, J., Simonyan, K., Antonoglou, I., Huang, A., Guez, A., Hubert, T., Baker, L., Lai, M., and Bolton, A. (2017), ‘Mastering the game of Go without human knowledge’, Nature 550(7676), 354.Google Scholar
Singh, A. P., Medida, S., and Duraisamy, K. (2017), ‘Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils’, AIAA Journal 55, 2215–2227.Google Scholar
Sirovich, L. (1987), ‘Turbulence and the dynamics of coherent structures. I–Coherent structures. II–Symmetries and transformations. III–Dynamics and scaling’, Quarterly of Applied Mathematics 45, 561–571.Google Scholar
Sirovich, L. and Kirby, M. (1987), ‘A low-dimensional procedure for the characterization of human faces’, Journal of the Optical Society of America A 4(3), 519–524.Google Scholar
Skene, C., Eggl, M., and Schmid, P. (2020), ‘A parallel-in-time approach for accelerating direct-adjoint studies’, Journal of Computational Physics 429(2), 110033.Google Scholar
Skogestad, S. and Postlethwaite, I. (2005), Multivariable Feedback Control: Analysis and Design, 2 ed., John Wiley & Sons, Hoboken, NJ.Google Scholar
Skogestad, S. and Postlethwaite, I. (2007), Multivariable Feedback Control: Analysis and Design, Vol. 2, Wiley, New York.Google Scholar
Smith, J. O. (2007a), Introduction to Digital Filters: With Audio Applications, W3K Publishing, http://books.w3k.org/.Google Scholar
Smith, J. O. (2007b), Mathematics of the Discrete Fourier Transform (DFT): With Audio Applications, W3K Publishing, http://books.w3k.org/.Google Scholar
Smith, S. W. (1997), The Scientist & Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, www.dspguide.com/.Google Scholar
Sommerfeld, A. (1908), ‘Ein Beitrag zur hydrodynamischen Erklärung der turbulenten Flüssigkeitsbewegungen’, Atti. del 4 Congr. Int. dei Mat. III, pp. 116–124.Google Scholar
Sorokina, M., Sygletos, S., and Turitsyn, S. (2016), ‘Sparse identification for nonlinear optical communication systems: SINO method’, Optics Express 24(26), 30433–30443.Google Scholar
Spalart, P. R. (1988), ‘Direct simulation of a turbulent boundary layer up to Reθ = 1410’, Journal of Fluid Mechanics 187, 61–98.Google Scholar
Strang, G. (1968), ‘On the construction and comparison of difference schemes’, SIAM Journal on Numerical Analysis 5(3), 506–517.Google Scholar
Strang, G. (1988), Linear Algebra and Its Applications, Harcourt Brace Jovanovich College Publishers, San Diego, CA.Google Scholar
Strang, G. (1989), ‘Wavelets and dilation equations: A brief introduction’, SIAM Review 31(4), 614–627.Google Scholar
Strang, G. (1996), Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA.Google Scholar
Strang, G. (2007), Computational Science and Engineering, Wellesley-Cambridge Press, Wellesley, MA.Google Scholar
Strom, B., Brunton, S. L., and Polagye, B. (2017), ‘Intracycle angular velocity control of cross-flow turbines’, Nature Energy 2(17103), 1–9.Google Scholar
Stuart, J. (1958), ‘On the non-linear mechanics of hydrodynamic stability’, Journal of Fluid Mechanics 4, 1–21.Google Scholar
Stuart, J. T. (1971), ‘Nonlinear stability theory’, Annual Review of Fluid Mechanics 3, 347–370.Google Scholar
Succi, S. and Coveney, P. V. (2018), ‘Big data: the end of the scientific method’, Philosophical Transactions of the Royal Society A 377, 20180145.Google Scholar
Suh, Y. K. (1993), ‘Periodic motion of a point vortex in a corner subject to a potential flow’, Journal of the Physical Society of Japan 62(10), 3441–3445.CrossRefGoogle Scholar
Sundqvist, B. (1991), ‘Thermal diffusivity measurements by Ångström method in a fluid environment’, International Journal of Thermophysics 12(1), 191–206.Google Scholar
Sutherland, J. C. and Parente, A. (2009), ‘Combustion modeling using principal component analysis’, Proceedings of the Combustion Institute 32(1), 1563–1570.Google Scholar
Sutherland, J. C., Smith, P. J., and Chen, J. H. (2007), ‘A quantitative method for a priori evaluation of combustion reaction models’, Combustion Theory and Modelling 11(2), 287–303.Google Scholar
Sutton, R. S. and Barto, A. G. (2018), Reinforcement Learning: An Introduction, 2nd ed., MIT Press, Cambridge, MA.Google Scholar
Szegedy, C., Ioffe, S., Vanhoucke, V., and Alemi, A. A. (2017), Inception-v4, inception-resnet and the impact of residual connections on learning, in ‘Thirty-First AAAI Conference on Artificial Intelligence’, February 4–9, 2017, San Francisco, CA.Google Scholar
Tadmor, G., Lehmann, O., Noack, B. R., Cordier, L., Delville, J., Bonnet, J.-P., and Morzyński, M. (2011), ‘Reduced order models for closed-loop wake control’, Philosophical Transactions of the Royal Society A 369(1940), 1513–1524.Google Scholar
Tadmor, G. and Noack, B. R. (2004), Dynamic estimation for reduced Galerkin models of fluid flows, in ‘The 2004 American Control Conference’, Boston, MA, June 30–July 2, 2004, pp. 0001–0006. Paper WeM18.1.Google Scholar
Taira, K., Brunton, S., Dawson, S., Rowley, C., Colonius, T., McKeon, B., Schmidt, O., Gordeyev, S., Theofilis, V., and Ukeiley, S. (2017), ‘Modal analysis of fluid flows: An overview’, AIAA Journal 55(12), 4013–4041.Google Scholar
Taira, K., Hemati, M. S., Brunton, S. L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S., and Yeh, C.-A. (2019), ‘Modal analysis of fluid flows: Applications and outlook’, arXiv preprint arXiv:1903.05750.Google Scholar
Takeishi, N., Kawahara, Y., and Yairi, T. (2017), Learning Koopman invariant subspaces for dynamic mode decomposition, in ‘Advances in Neural Information Processing Systems’, December 4–9, 2017, Long Beach, CA, pp. 1130–1140.Google Scholar
Takens, F. (1981), Detecting strange attractors in turbulence, in ‘Dynamical systems and turbulence, Warwick 1980’, Vol. 898 in Lecture Notes in Math., Springer, Heidelberg and New York, pp. 366–381.Google Scholar
Talamelli, A., Persiani, F., Fransson, J. H., Alfredsson, P. H., Johansson, A. V., Nagib, H. M., Rüedi, J.-D., Sreenivasan, K. R., and Monkewitz, P. A. (2009), ‘CICLoPE — A response to the need for high Reynolds number experiments’, Fluid Dynamics Research 41(2), 021407.Google Scholar
Tanahashi, M., Kang, S., Miyamoto, T., and Shiokawa, S. (2004), ‘Scaling law of fine scale eddies in turbulent channel flows up to Reτ = 800’, International Journal of Heat and Fluid Flow 25, 331–341.Google Scholar
Tang, H., Rabault, J., Kuhnle, A., Wang, Y., and Wang, T. (2020), ‘Robust active flow control over a range of reynolds numbers using an artificial neural network trained through deep reinforcement learning’, Physics of Fluids 32(5), 053605.Google Scholar
Tedrake, R., Jackowski, Z., Cory, R., Roberts, J. W., and Hoburg, W. (2009), Learning to fly like a bird, in ‘14th International Symposium on Robotics Research’, Lucerne, Switzerland.Google Scholar
Tenenbaum, J. B. (2000), ‘A global geometric framework for nonlinear dimensionality reduction’, Science 290(5500), 2319–2323.Google Scholar
Tennekes, H. and Lumley, J. L. (1972), A First Course in Turbulence, MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Thaler, S., Paehler, L., and Adams, N. A. (2019), ‘Sparse identification of truncation errors’, Journal of Computational Physics 397, 108851.Google Scholar
Theofilis, V. (2011), ‘Global linear instability’, Annual Review of Fluid Mechanics 43, 319–352.Google Scholar
Thiria, B., Goujon-Durand, S., and Wesfreid, J. E. (2006), ‘The wake of a cylinder performing rotary oscillations’, Journal of Fluid Mechanics 560, 123–147.Google Scholar
Thormann, R. and Widhalm, M. (2013), ‘Linear-frequency-domain predictions of dynamic-response data for viscous transonic flows’, AIAA Journal 51(11), 2540–2557.Google Scholar
Tibshirani, R. (1996), ‘Regression shrinkage and selection via the lasso’, Journal of the Royal Statistical Society. Series B (Methodological) 58(1), 267–288.Google Scholar
Tinney, C. E., Ukeiley, L., and Glauser, M. N. (2008), ‘Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction’, Journal of Fluid Mechanics 615, 53–92.Google Scholar
Toedtli, S. S., Luhar, M., and McKeon, B. J. (2019), ‘Predicting the response of turbulent channel flow to varying-phase opposition control: Resolvent analysis as a tool for flow control design’, Physical Review Fluids 4(7), 073905.CrossRefGoogle Scholar
Torrence, C. and Compo, G. P. (1998), ‘A practical guide to wavelet analysis’, Bulletin of the American Meteorological Society 79(1), 61–78.Google Scholar
Towne, A., Schmidt, O. T., and Colonius, T. (2018), ‘Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis’, Journal of Fluid Mechanics 847, 821–867.Google Scholar
Townsend, A. A. (1976), The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge.Google Scholar
Tran, G. and Ward, R. (2016), ‘Exact recovery of chaotic systems from highly corrupted data’, arXiv preprint arXiv:1607.01067.Google Scholar
Trefethen, L. and Bau, D. (1997), Numerical Linear Algebra, Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Trefethen, L., Trefethen, A., Reddy, S., and Driscoll, T. (1993), ‘Hydrodynamic stability without eigenvalues’, Science 261, 578–584.Google Scholar
Tropp, J. A. and Gilbert, A. C. (2007), ‘Signal recovery from random measurements via orthogonal matching pursuit’, IEEE Transactions on Information Theory 53(12), 4655–4666.Google Scholar
Tu, J. H. and Rowley, C. W. (2012), ‘An improved algorithm for balanced POD through an ana-lytic treatment of impulse response tails’, Journal of Computational Physics 231(16), 5317–5333.Google Scholar
Tu, J. H., Rowley, C. W., Kutz, J. N., and Shang, J. K. (2014), ‘Spectral analysis of fluid flows using sub-Nyquist-rate PIV data’, Experiments in Fluids 55(9), 1–13.Google Scholar
Tu, J., Rowley, C., Luchtenburg, D., Brunton, S., and Kutz, J. (2014), ‘On dynamic mode decomposition: theory and applications’, Journal of Computational Dynamics 1(2), 391–421.Google Scholar
Turns, S. R. (1996), Introduction to Combustion, Vol. 287, McGraw-Hill Companies, New York.Google Scholar
Uruba, V. (2012), ‘Decomposition methods in turbulence research’, EPJ Web of Conferences 25, 01095.Google Scholar
Van Loan, C. F. and Golub, G. H. (1983), Matrix Computations, Johns Hopkins University Press, Baltimore.Google Scholar
Vassberg, J., Dehaan, M., Rivers, M., and Wahls, R. (2008), Development of a common research model for applied CFD validation studies, in ‘26th AIAA Applied Aerodynamics Conference’, August 18-21, 2008, Honolulu, HI, American Institute of Aeronautics and Astronautics, Reston, VA.Google Scholar
Venturi, D. (2006), ‘On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate’, Journal of Fluid Mechanics 559, 215–254.Google Scholar
Verma, S., Novati, G., and Koumoutsakos, P. (2018), ‘Efficient collective swimming by harnessing vortices through deep reinforcement learning’, Proceedings of the National Academy of Sciences 115(23), 5849–5854.Google Scholar
Vincent, A. and Meneguzzi, M. (1991), ‘The spatial structure and statistical properties of homogeneous turbulence’, Journal of Fluid Mechanics 225, 1–20.Google Scholar
Viquerat, J., Rabault, J., Kuhnle, A., Ghraieb, H., and Hachem, E. (2019), ‘Direct shape optimization through deep reinforcement learning’, arXiv preprint arXiv:1908.09885.Google Scholar
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P., and Koumoutsakos, P. (2018), ‘Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks’, Proceedings of the Royal Society A 474(2213), 20170844.Google Scholar
Vladimir Cherkassky, F. M. M. (2008), Learning from Data, John Wiley & Sons, New York.Google Scholar
Voit, E. O. (2019), ‘Perspective: dimensions of the scientific method’, PLoS: Computational Biology 15(9), e1007279.Google Scholar
Voltaire, F. (1764), Dictionnaire Philosophique: Atomes, Oxford University Press, 1994.Google Scholar
von Helmholtz, H. (1858), ‘Über integrale der hydrodynamischen gleichungen, welche den wirbelbewegungen entsprechen’, J. für die reine und angewandte Mathematik 55, 25–55.Google Scholar
von Kármán, T. (1911), ‘über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt’, Nachrichten der Kaiserlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 509–517.Google Scholar
von Storch, H. and Xu, J. (1990), ‘Principal oscillation pattern analysis of the 30-to 60-day oscillation in the tropical troposphere’, Climate Dynamics 4(3), 175–190.Google Scholar
Voropayev, S. I., Afanasyev, Y. D., and Filippov, I. A. (1991), ‘Horizontal jets and vortex dipoles in a stratified fluid’, Journal of Fluid Mechanics 227, 543–566.Google Scholar
Voss, R., Tichy, L., and Thormann, R. (2011), A ROM based flutter prediction process and its validation with a new reference model, in ‘International Forum on Aeroelasticity and Structural Dynamics (IFASD-2011)’, June 26–30, 2011, Paris, France.Google Scholar
Vukasonivic, B., Rusak, Z., and Glezer, A. (2010), ‘Dissipative small-scale actuation of a turbulent shear layer’, Journal of Fluid Mechanics 656, 51–81.Google Scholar
Wahde, M. (2008), Biologically Inspired Optimization Methods: An Introduction, WIT Press, Southampton.Google Scholar
Wan, Z. Y., Vlachas, P., Koumoutsakos, P., and Sapsis, T. (2018), ‘Data-assisted reduced-order modeling of extreme events in complex dynamical systems’, PloS One 13(5), e0197704.Google Scholar
Wang, J.-X., Wu, J.-L., and Xiao, H. (2017), ‘Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on DNS data’, Physical Review Fluids 2(3), 034603.Google Scholar
Wang, M. and Hemati, M. S. (2017), ‘Detecting exotic wakes with hydrodynamic sensors’, arXiv preprint arXiv:1711.10576.Google Scholar
Wang, Q., Moin, P., and Iaccarino, G. (2009), ‘Minimal repetition dynamic checkpointing algo-rithm for unsteady adjoint calculation’, SIAM Journal of Scientific Computing 31(4), 2549–2567.Google Scholar
Wang, R. (2009), Introduction to Orthogonal Transforms, Cambridge University Press, New York.Google Scholar
Wang, W. X., Yang, R., Lai, Y. C., Kovanis, V., and Grebogi, C. (2011), ‘Predicting catas-trophes in nonlinear dynamical systems by compressive sensing’, Physical Review Letters 106, 154101-1–154101-4.Google Scholar
Wang, Y., Yao, H., and Zhao, S. (2016), ‘Auto-encoder based dimensionality reduction’, Neuro-Computing 184, 232–242.Google Scholar
Wang, Z., Akhtar, I., Borggaard, J., and Iliescu, T. (2012), ‘Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison’, Computer Methods in Applied Mechanics and Engineering 237, 10–26.Google Scholar
Wang, Z., Bapst, V., Heess, N., Mnih, V., Munos, R., Kavukcuoglu, K., and de Freitas, N. (2017), Sample efficient actor-critic with experience replay, in ‘5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24–26, 2017, Conference Track Proceedings’, OpenReview.net.Google Scholar
Wang, Z., Schaul, T., Hessel, M., Van Hasselt, H., Lanctot, M., and De Freitas, N. (2016), Dueling network architectures for deep reinforcement learning, in ‘Proceedings of the 33rd International Conference on International Conference on Machine Learning – Volume 48’, ICML 16, JMLR.org, pp. 1995–2003.Google Scholar
Watkins, C. J. C. H. (1989), Learning from Delayed Rewards, PhD thesis, King’s College, Cambridge, UK.Google Scholar
Wehmeyer, C. and Noé, F. (2018), ‘Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics’, The Journal of Chemical Physics 148(241703), 1–9.Google Scholar
Welch, P. (1967), ‘The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms’, IEEE Transactions on Audio and Electroacoustics 15(2), 70–73.Google Scholar
Weller, J., Camarri, S., and Iollo, A. (2009), ‘Feedback control by low-order modelling of the laminar flow past a bluff body’, Journal of Fluid Mechanics 634, 405.Google Scholar
White, A. P., Zhu, G., and Choi, J. (2013), Linear Parameter-Varying Control for Engineering Applications, Springer, London.Google Scholar
Whittle, P. (1951), Hypothesis Testing in Time Series Analysis, Almqvist & Wiksells, Uppsala.Google Scholar
Wiener, N. (1948), Cybernetics: Control and Communication in the Animal and the Machine, Wiley, New York.Google Scholar
Wigner, E. P. (1960), ‘The unreasonable effectiveness of mathematics in the natural sciences’, Communications on Pure and Applied Mathematics 13, 1–14.Google Scholar
Willcox, K. and Peraire, J. (2002), ‘Balanced model reduction via the proper orthogonal decomposition’, AIAA Journal 40(11), 2323–2330.Google Scholar
Willert, C. E. and Gharib, M. (1991), ‘Digital particle image velocimetry’, Experiments in Fluids 10(4), 181–193.Google Scholar
Williams, M., Kevrekidis, I., and Rowley, C. (2015), ‘A data-driven approximation of the Koopman operator: extending dynamic mode decomposition’, Journal of Nonlinear Science 6, 1307–1346.Google Scholar
Williams, M., Rowley, C., and Kevrekidis, I. (2015), ‘A kernel approach to data-driven Koopman spectral analysis’, Journal of Computational Dynamics 2(2), 247–265.Google Scholar
Williams, R. J. (1992), ‘Simple statistical gradient-following algorithms for connectionist reinforcement learning’, Machine Learning 8(3–4), 229–256.Google Scholar
Wright, J., Yang, A., Ganesh, A., Sastry, S., and Ma, Y. (2009), ‘Robust face recognition via sparse representation’, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 31(2), 210–227.Google Scholar
Wünning, J. and Wünning, J. (1997), ‘Flameless oxidation to reduce thermal no-formation’, Progress in Energy and Combustion Science 23(1), 81–94.Google Scholar
Xiao, H., Wu, J.-L., Wang, J.-X., Sun, R., and Roy, C. (2016), ‘Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach’, Journal of Computational Physics 324, 115–136.Google Scholar
Xu, H., Zhang, W., Deng, J., and Rabault, J. (2020), ‘Active flow control with rotating cylinders by an artificial neural network trained by deep reinforcement learning’, Journal of Hydrodynamics 32(2), 254–258.Google Scholar
Yan, X., Zhu, J., Kuang, M., and Wang, X. (2019), ‘Aerodynamic shape optimization using a novel optimizer based on machine learning techniques’, Aerospace Science and Technology 86, 826–835.Google Scholar
Yang, J., Wright, J., Huang, T. S., and Ma, Y. (2010), ‘Image super-resolution via sparse representation’, IEEE Transactions on Image Processing 19(11), 2861–2873.Google Scholar
Yang, Y., Pope, S. B., and Chen, J. H. (2013), ‘Empirical low-dimensional manifolds in composition space’, Combustion and Flame 160(10), 1967–1980.Google Scholar
Yeh, C.-A. and Taira, K. (2019), ‘Resolvent-analysis-based design of airfoil separation control’, Journal of Fluid Mechanics 867, 572–610.Google Scholar
Yetter, R. A., Dryer, F., and Rabitz, H. (1991), ‘A comprehensive reaction mechanism for carbon monoxide/hydrogen/oxygen kinetics’, Combustion Science and Technology 79(1–3), 97–128.Google Scholar
Yeung, E., Kundu, S. and Hodas, N. (2017), ‘Learning deep neural network representations for Koopman operators of nonlinear dynamical systems’, arXiv preprint arXiv:1708.06850.Google Scholar
Zdravkovich, M. (1987), ‘The effects of interference between circular cylinders in cross flow’, Journal of Fluids and Structures 1(2), 239–261.Google Scholar
Zdybał, K., Armstrong, E., Parente, A., and Sutherland, J. C. (2020), ‘PCAfold: Python software to generate, analyze and improve PCA-derived low-dimensional manifolds’, SoftwareX 12, 100630.Google Scholar
Zdybał, K., Sutherland, J. C., Armstrong, E., and Parente, A. (2021), ‘State-space informed data sampling on combustion manifolds’, Combustion and Flame (manuscript in preparation).Google Scholar
Zdybał, K., Sutherland, J. C. & Parente, A. (2022), ‘Manifold-informed state vector subset for reduced-order modeling’, Proceedings of the Combustion Institute.Google Scholar
Zdybał, K., Armstrong, E., Sutherland, J. C. & Parente, A. (2022), ‘Cost function for low-dimensional manifold topology assessment’, Scientific Reports 12(1), 1–19.Google Scholar
Zebib, A. (1987), ‘Stability of viscous flow past a circular cylinder’, Journal of Engineering Mathematics 21, 155–165.Google Scholar
Zhang, H.-Q., Fey, U., Noack, B. R., König, M., and Eckelmann, H. (1995), ‘On the transition of the cylinder wake’, Physics of Fluids 7(4), 779–795.Google Scholar
Zhang, W., Wang, B., Ye, Z., and Quan, J. (2012), ‘Efficient method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models’, AIAA Journal 50(5), 1019–1028.Google Scholar
Zheng, P., Askham, T., Brunton, S. L., Kutz, J. N., and Aravkin, A. Y. (2019), ‘Sparse relaxed regularized regression: SR3’, IEEE Access 7(1), 1404–1423.Google Scholar
Zhong, Y. D. and Leonard, N. (2020), ‘Unsupervised learning of lagrangian dynamics from images for prediction and control’, Advances in Neural Information Processing Systems 33.Google Scholar
Zhou, K. and Doyle, J. C. (1998), Essentials of Robust Control, Prentice Hall, Upper Saddle River, NJ.Google Scholar
Zhou, Y., Fan, D., Zhang, B., Li, R., and Noack, B. R. (2020), ‘Artificial intelligence control of a turbulent jet’, Journal of Fluid Mechanics 897, 1–46.Google Scholar
Zimmermann, R. and Görtz, S. (2010), ‘Non-linear reduced order models for steady aerody-namics’, Procedia Computer Science 1(1), 165–174.Google Scholar
Zimmermann, R. and Görtz, S. (2012), ‘Improved extrapolation of steady turbulent aerody-namics using a non-linear POD-based reduced order model’, The Aeronautical Journal 116(1184), 1079–1100.Google Scholar
Zimmermann, R., Vendl, A., and Görtz, S. (2014), ‘Reduced-order modeling of steady flows subject to aerodynamic constraints’, AIAA Journal 52(2), 255–266.Google Scholar
Zou, H. and Hastie, T. (2005), ‘Regularization and variable selection via the elastic net’, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2), 301–320.Google Scholar