Machine Learning for Fluid Mechanics

Literature Cited

1. Adrian RJ 1991. Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23:261–304
   [Google Scholar]
2. Alsalman M, Colvert B, Kanso E 2018. Training bioinspired sensors to classify flows. Bioinspiration Biomim. 14:016009
   [Google Scholar]
3. Amsallem D, Zahr MJ, Farhat C 2012. Nonlinear model order reduction based on local reduced-order bases. Int. J. Numer. Meth. Eng. 92:891–916
   [Google Scholar]
4. Bai Z, Wimalajeewa T, Berger Z, Wang G, Glauser M, Varshney PK 2014. Low-dimensional approach for reconstruction of airfoil data via compressive sensing. AIAA J. 53:920–33
   [Google Scholar]
5. Baldi P, Hornik K 1989. Neural networks and principal component analysis: learning from examples without local minima. Neural Netw. 2:53–58
   [Google Scholar]
6. Barber D 2012. Bayesian Reasoning and Machine Learning Cambridge, UK: Cambridge Univ. Press
7. Barber RF, Candes EJ 2015. Controlling the false discovery rate via knock-offs. Ann. Stat. 43:2055–85Reproducible science: a framework.
   [Google Scholar]
8. Battaglia PW, Hamrick JB, Bapst V, Sanchez-Gonzalez A, Zambaldi V et al. 2018. Relational inductive biases, deep learning, and graph networks. arXiv:1806.01261 [cs.LG]
   [Google Scholar]
9. Bellman R 1952. On the theory of dynamic programming. PNAS 38:716–19
   [Google Scholar]
10. Benard N, Pons-Prats J, Periaux J, Bugeda G, Braud P et al. 2016. Turbulent separated shear flow control by surface plasma actuator: experimental optimization by genetic algorithm approach. Exp. Fluids 57:22
    [Google Scholar]
11. Bewley TR, Moin P, Temam R 2001. DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447:179–225
    [Google Scholar]
12. Bishop CM, James GD 1993. Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nucl. Instrum. Methods Phys. Res. 327:580–93
    [Google Scholar]
13. Bölcskei H, Grohs P, Kutyniok G, Petersen P 2019. Optimal approximation with sparsely connected deep neural networks. SIAM J. Math. Data Sci. 1:8–45Theoretical analysis of the approximation properties of deep neural networks.
    [Google Scholar]
14. Bourguignon JL, Tropp JA, Sharma AS, McKeon BJ 2014. Compact representation of wall-bounded turbulence using compressive sampling. Phys. Fluids 26:015109
    [Google Scholar]
15. Bousmalis K, Irpan A, Wohlhart P, Bai Y, Kelcey M et al. 2017. Using simulation and domain adaptation to improve efficiency of deep robotic grasping. arXiv:1709.07857 [cs.LG]
    [Google Scholar]
16. Breiman L 2001. Random forests. Mach. Learn. 45:5–32
    [Google Scholar]
17. Bright I, Lin G, Kutz JN 2013. Compressive sensing based machine learning strategies for characterizing the flow around a cylinder with limited pressure measurements. Phys. Fluids 25:127102
    [Google Scholar]
18. Brunton SL, Kutz JN 2019. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control New York: Cambridge Univ. Press
19. Brunton SL, Noack BR 2015. Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67:050801
    [Google Scholar]
20. Brunton SL, Proctor JL, Kutz JN 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS 113:3932–37
    [Google Scholar]
21. Bueche D, Stoll P, Dornberger R, Koumoutsakos P 2002. Multi-objective evolutionary algorithm for the optimization of noisy combustion problems. IEEE Trans. Syst. Man Cybern. C 32:460–73
    [Google Scholar]
22. Chen TQ, Rubanova Y, Bettencourt J, Duvenaud DK 2018. Neural ordinary differential equations. Advances in Neural Information Processing Systems 31 ed. S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi, R Garnett 6571–83 Red Hook, NY: Curran Assoc.
    [Google Scholar]
23. Cherkassky V, Mulier FM 2007. Learning from Data: Concepts, Theory, and Methods Hoboken, NJ: John Wiley & Sons
24. Colabrese S, Gustavsson K, Celani A, Biferale L 2017. Flow navigation by smart microswimmers via reinforcement learning. Phys. Rev. Lett. 118:158004
    [Google Scholar]
25. Colabrese S, Gustavsson K, Celani A, Biferale L 2018. Smart inertial particles. Phys. Rev. Fluids 3:084301
    [Google Scholar]
26. Colvert B, Alsalman M, Kanso E 2018. Classifying vortex wakes using neural networks. Bioinspiration Biomim. 13:025003
    [Google Scholar]
27. Dissanayake M, Phan-Thien N 1994. Neural-network-based approximations for solving partial differential equations. Comm. Numer. Meth. Eng. 10:195–201
    [Google Scholar]
28. Dong C, Loy CC, He K, Tang X 2014. Learning a deep convolutional network for image super-resolution. Computer Vision—ECCV 2014 ed. D Fleet, T Pajdla, B Schiele, T Tuytelaars 184–99 Cham, Switz.: Springer
    [Google Scholar]
29. Donoho DL 2006. Compressed sensing. IEEE Trans. Inf. Theory 52:1289–306
    [Google Scholar]
30. Dracopoulos DC 1997. Evolutionary Learning Algorithms for Neural Adaptive Control London: Springer-Verlag
31. Duraisamy K, Iaccarino G, Xiao H 2019. Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51:357–77
    [Google Scholar]
32. Duriez T, Brunton SL, Noack BR 2016. Machine Learning Control: Taming Nonlinear Dynamics and Turbulence Cham, Switz.: Springer
33. Faller WE, Schreck SJ 1996. Neural networks: applications and opportunities in aeronautics. Prog. Aerosp. Sci. 32:433–56
    [Google Scholar]
34. Fleming PJ, Purshouse RC 2002. Evolutionary algorithms in control systems engineering: a survey. Control Eng. Pract. 10:1223–41
    [Google Scholar]
35. Freeman WT, Jones TR, Pasztor EC 2002. Example-based super-resolution. IEEE Comput. Graph. 22:56–65
    [Google Scholar]
36. Fukami K, Fukagata K, Taira K 2018. Super-resolution reconstruction of turbulent flows with machine learning. arXiv:1811.11328 [physics.flu-dyn]
    [Google Scholar]
37. Gardner E 1988. The space of interactions in neural network models. J. Phys. A 21:257
    [Google Scholar]
38. Gazzola M, Hejazialhosseini B, Koumoutsakos P 2014. Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36:B622–39
    [Google Scholar]
39. Gazzola M, Tchieu A, Alexeev D, De Brauer A, Koumoutsakos P 2016. Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789:726–49
    [Google Scholar]
40. Gazzola M, Van Rees WM, Koumoutsakos P 2012. C-start: optimal start of larval fish. J. Fluid Mech. 698:5–18
    [Google Scholar]
41. Germano M, Piomelli U, Moin P, Cabot WH 1991. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3:1760–65
    [Google Scholar]
42. Giannakoglou K, Papadimitriou D, Kampolis I 2006. Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels. Comput. Methods Appl. Mech. Eng. 195:6312–29
    [Google Scholar]
43. Glaz B, Liu L, Friedmann PP 2010. Reduced-order nonlinear unsteady aerodynamic modeling using a surrogate-based recurrence framework. AIAA J. 48:2418–29
    [Google Scholar]
44. Gonzalez-Garcia R, Rico-Martinez R, Kevrekidis I 1998. Identification of distributed parameter systems: a neural net based approach. Comput. Chem. Eng. 22:S965–68
    [Google Scholar]
45. Goodfellow I, Bengio Y, Courville A 2016. Deep Learning Cambridge, MA: MIT Press
46. Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D et al. 2014. Generative adversarial nets. Advances in Neural Information Processing Systems 27 ed. Z Ghahramani, M Welling, C Cortes, ND Lawrence, KQ Weinberger 2672–80 Red Hook, NY: Curran Assoc.Powerful deep learning architecture that learns through a game between a network that can generate new data and a network that is an expert classifier.
    [Google Scholar]
47. Grant I, Pan X 1995. An investigation of the performance of multi layer, neural networks applied to the analysis of PIV images. Exp. Fluids 19:159–66
    [Google Scholar]
48. Graves A, Fernández S, Schmidhuber J 2007. Multi-dimensional recurrent neural networks. Artificial Neural Networks—ICANN 2007 ed. JM de Sa, LA Alexandre, W Duch, D Mandic 549–58 Berlin: Springer
    [Google Scholar]
49. Grossberg S 1976. Adaptive pattern classification and universal recoding, I: parallel development and coding of neural feature detectors.. Biol. Cybernet. 23121–34
    [Google Scholar]
50. Grossberg S 1988. Nonlinear neural networks: Principles, mechanisms, and architectures. Neural Netw. 117–61
    [Google Scholar]
51. Guéniat F, Mathelin L, Hussaini MY 2016. A statistical learning strategy for closed-loop control of fluid flows. Theor. Comput. Fluid Dyn. 30:497–510
    [Google Scholar]
52. Halko N, Martinsson PG, Tropp JA 2011. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. 53:217–88
    [Google Scholar]
53. Hamdaoui M, Chaskalovic J, Doncieux S, Sagaut P 2010. Using multiobjective evolutionary algorithms and data-mining methods to optimize ornithopters’ kinematics. J. Aircraft 47:1504–16
    [Google Scholar]
54. Hansen N, Müller SD, Koumoutsakos P 2003. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11:1–18
    [Google Scholar]
55. Hansen N, Niederberger AS, Guzzella L, Koumoutsakos P 2009. A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion. IEEE Trans. Evol. Comput. 13:180–97
    [Google Scholar]
56. Hastie T, Tibshirani R, Friedman J, Hastie T, Friedman J, Tibshirani R 2009. The Elements of Statistical Learning 2 New York: Springer
57. Hinton GE, Sejnowski TJ 1986. Learning and relearning in Boltzmann machines. Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1 ed. DE Rumelhart, J McClelland 282–317 Cambridge, MA: MIT Press
    [Google Scholar]
58. Hochreiter S, Schmidhuber J 1997. Long short-term memory. Neural Comput. 9:1735–80Regularization of recurrent neural networks and major contributor to the success of Google Translate.
    [Google Scholar]
59. Holland JH 1975. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence Ann Arbor: Univ. Mich. Press
60. Hopfield JJ 1982. Neural networks and physical systems with emergent collective computational abilities. PNAS 79:2554–58
    [Google Scholar]
61. Hornik K, Stinchcombe M, White H 1989. Multilayer feedforward networks are universal approximators. Neural Netw. 2:359–66
    [Google Scholar]
62. Hou W, Darakananda D, Eldredge J 2019. Machine learning based detection of flow disturbances using surface pressure measurements Paper presented at AIAA Atmospheric Flight Mechanics Conference 2019 San Diego, Calif.: AIAA Pap. 2019-1148
63. Jambunathan K, Hartle S, Ashforth-Frost S, Fontama V 1996. Evaluating convective heat transfer coefficients using neural networks. Int. J. Heat Mass Transf. 39:2329–32
    [Google Scholar]
64. Kaiser E, Noack BR, Cordier L, Spohn A, Segond M et al. 2014. Cluster-based reduced-order modelling of a mixing layer. J. Fluid Mech. 754:365–414
    [Google Scholar]
65. Kern S, Müller SD, Hansen N, Büche D, Ocenasek J, Koumoutsakos P 2004. Learning probability distributions in continuous evolutionary algorithms—a comparative review. Nat. Comput. 3:77–112
    [Google Scholar]
66. Kim B, Azevedo VC, Thuerey N, Kim T, Gross M, Solenthaler B 2018. Deep fluids: a generative network for parameterized fluid simulations. arXiv:1806.02071 [cs.LG]
    [Google Scholar]
67. Kim HJ, Jordan MI, Sastry S, Ng AY 2004. Autonomous helicopter flight via reinforcement learning. Advances in Neural Information Processing Systems 17 ed. B Scholkopf, Y Vis, JC Platt 799–806 Cambridge, MA: MIT Press
    [Google Scholar]
68. Knaak M, Rothlubbers C, Orglmeister R 1997. A Hopfield neural network for flow field computation based on particle image velocimetry/particle tracking velocimetry image sequences. IEEE Int. Conf. Neural Netw. 1:48–52
    [Google Scholar]
69. Kohonen T 1995. Self-Organizing Maps Berlin: Springer-Verlag
70. Kolmogorov A 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Cr. Acad. Sci. USSR 30:301–5
    [Google Scholar]
71. Koza JR 1992. Genetic Programming: On the Programming of Computers by Means of Natural Selection Boston: MIT Press
72. Krizhevsky A, Sutskever I, Hinton GE 2012. Imagenet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems 25 ed. F Pereira, CJC Burges, L Bottou, KQ Weinberger 1097–105 Red Hook, NY: Curran Assoc.
    [Google Scholar]
73. Kutz JN, Brunton SL, Brunton BW, Proctor JL 2016. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems Philadelphia: SIAM
74. Labonté G 1999. A new neural network for particle-tracking velocimetry. Exp. Fluids 26:340–46
    [Google Scholar]
75. Lagaris IE, Likas A, Fotiadis DI 1998. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9:987–1000
    [Google Scholar]
76. LeCun Y, Bengio Y, Hinton G 2015. Deep learning. Nature 521:436–44
    [Google Scholar]
77. Lee C, Kim J, Babcock D, Goodman R 1997. Application of neural networks to turbulence control for drag reduction. Phys. Fluids 9:1740–47
    [Google Scholar]
78. Lee Y, Yang H, Yin Z 2017. PIV-DCNN: cascaded deep convolutional neural networks for particle image velocimetry. Exp. Fluids 58:171
    [Google Scholar]
79. Li Q, Dietrich F, Bollt EM, Kevrekidis IG 2017. Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator. Chaos 27:103111
    [Google Scholar]
80. Liang D, Jiang C, Li Y 2003. Cellular neural network to detect spurious vectors in PIV data. Exp. Fluids 34:52–62
    [Google Scholar]
81. Ling J, Jones R, Templeton J 2016a. Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318:22–35
    [Google Scholar]
82. Ling J, Kurzawski A, Templeton J 2016b. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807:155–66
    [Google Scholar]
83. Ling J, Templeton J 2015. Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty. Phys. Fluids 27:085103
    [Google Scholar]
84. Loiseau JC, Brunton SL 2018. Constrained sparse Galerkin regression. J. Fluid Mech. 838:42–67
    [Google Scholar]
85. Loucks D, van Beek E, Stedinger J, Dijkman J, Villars M 2005. Water Resources Systems Planning and Management: An Introduction to Methods 2 Cham, Switz.: Springer
86. Lumley J 1970. Stochastic Tools in Turbulence New York: Academic
87. Lusch B, Kutz JN, Brunton SL 2018. Deep learning for universal linear embeddings of nonlinear dynamics. Nat. Commun. 9:4950
    [Google Scholar]
88. Mahoney MW 2011. Randomized algorithms for matrices and data. Found. Trends Mach. Learn. 3:123–224
    [Google Scholar]
89. Manohar K, Brunton BW, Kutz JN, Brunton SL 2018. Data-driven sparse sensor placement for reconstruction: demonstrating the benefits of exploiting known patterns. IEEE Control Syst. Mag. 38:63–86
    [Google Scholar]
90. Mardt A, Pasquali L, Wu H, Noé F 2018. VAMPnets for deep learning of molecular kinetics. Nat. Commun. 9:5
    [Google Scholar]
91. Martin N, Gharib M 2018. Experimental trajectory optimization of a flapping fin propulsor using an evolutionary strategy. Bioinspiration Biomim. 14:016010
    [Google Scholar]
92. Maulik R, San O, Rasheed A, Vedula P 2019. Subgrid modelling for two-dimensional turbulence using neural networks. J. Fluid Mech. 858:122–44
    [Google Scholar]
93. Meena MG, Nair AG, Taira K 2018. Network community-based model reduction for vortical flows. Phys. Rev. E 97:063103
    [Google Scholar]
94. Mehta UB, Kutler P 1984. Computational aerodynamics and artificial intelligence NASA Tech. Rep. NASA-TM-85994 Ames Res. Cent. Moffett Field, CA:
95. Meijering E 2002. A chronology of interpolation: from ancient astronomy to modern signal and image processing. Proc. IEEE 90:319–42
    [Google Scholar]
96. Meneveau C, Katz J 2000. Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32:1–32
    [Google Scholar]
97. Mezic I 2013. Analysis of fluid flows via spectral properties of the Koopman operator. Annu. Rev. Fluid Mech. 45:357–78
    [Google Scholar]
98. Milano M, Koumoutsakos P 2002. Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182:1–26
    [Google Scholar]
99. Minsky M, Papert SA 1969. Perceptrons: An Introduction to Computational Geometry Cambridge, MA: MIT Press
100. Mnih V, Kavukcuoglu K, Silver D, Rusu AA, Veness J et al. 2015. Human-level control through deep reinforcement learning. Nature 518:529–33
     [Google Scholar]
101. Nair AG, Taira K 2015. Network-theoretic approach to sparsified discrete vortex dynamics. J. Fluid Mech. 768:549–71
     [Google Scholar]
102. Noack BR 2018. Closed-loop turbulence control—from human to machine learning (and retour). Fluid-Structure-Sound Interactions and Control: Proceedings of the 4th Symposium on Fluid-Structure-Sound Interactions and Control ed. Y Zhou, M Kimura, G Peng, AD Lucey, L Hung 23–32 Singapore: Springer
     [Google Scholar]
103. Noé F, Nüske F 2013. A variational approach to modeling slow processes in stochastic dynamical systems. SIAM Multiscale Model Simul. 11:635–55
     [Google Scholar]
104. Novati G, Mahadevan L, Koumoutsakos P 2019. Controlled gliding and perching through deep-reinforcement-learning. Phys. Rev. Fluids 4:093902
     [Google Scholar]
105. Novati G, Verma S, Alexeev D, Rossinelli D, Van Rees WM, Koumoutsakos P 2017. Synchronisation through learning for two self-propelled swimmers. Bioinspiration Biomim. 12:aa6311
     [Google Scholar]
106. Nüske F, Schneider R, Vitalini F, Noé F 2016. Variational tensor approach for approximating the rare-event kinetics of macromolecular systems. J. Chem. Phys. 144:054105
     [Google Scholar]
107. Ollivier Y, Arnold L, Auger A, Hansen N 2017. Information-geometric optimization algorithms: a unifying picture via invariance principles. J. Mach. Learn. Res. 18:564–628
     [Google Scholar]
108. Ostermeier A, Gawelczyk A, Hansen N 1994. Step-size adaptation based on non-local use of selection information. International Conference on Parallel Problem Solving from Nature 1994 Oct 9189–98 Berlin: Springer
     [Google Scholar]
109. Ouellette NT, Xu H, Bodenschatz E 2006. A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 40:301–13
     [Google Scholar]
110. Papadimitriou DI, Papadimitriou C 2015. Optimal sensor placement for the estimation of turbulent model parameters in CFD. Int. J. Uncert. Quant. 5:545–68
     [Google Scholar]
111. Parish EJ, Duraisamy K 2016. A paradigm for data-driven predictive modeling using field inversion and machine learning. J. Comput. Phys. 305:758–74
     [Google Scholar]
112. Pathak J, Hunt B, Girvan M, Lu Z, Ott E 2018. Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. Phys. Rev. Lett. 120:024102
     [Google Scholar]
113. Pelikan M, Ocenasek J, Trebst S, Troyer M, Alet F 2004. Computational complexity and simulation of rare events of Ising spin glasses. Genetic and Evolutionary Computation—GECCO 200436–47 Berlin: Springer
     [Google Scholar]
114. Perdikaris P, Venturi D, Karniadakis G 2016. Multifidelity information fusion algorithms for high-dimensional systems and massive data sets. SIAM J. Sci. Comput. 38:B521–38
     [Google Scholar]
115. Perlman E, Burns R, Li Y, Meneveau C 2007. Data exploration of turbulence simulations using a database cluster. Proceedings of the 2007 ACM/IEEE Conference on Supercomputingp23 New York: ACM
     [Google Scholar]
116. Phan MQ, Juang JN, Hyland DC 1995. On neural networks in identification and control of dynamic systems. Wave Motion, Intelligent Structures and Nonlinear Mechanics ed. A Guran, DJ Inman 194–225 Singapore: World Sci.
     [Google Scholar]
117. Pierret S, Van den Braembussche R 1999. Turbomachinery blade design using a Navier-Stokes solver and artificial neural network. J. Turbomach. 121:326–32
     [Google Scholar]
118. Pollard A, Castillo L, Danaila L, Glauser M 2016. Whither Turbulence and Big Data in the 21st Century? Cham., Switz.: Springer
119. Rabault J, Kuchta M, Jensen A, Réglade U, Cerardi N 2019. Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J. Fluid Mech. 865:281–302
     [Google Scholar]
120. Raissi M, Karniadakis GE 2018. Hidden physics models: machine learning of nonlinear partial differential equations. J. Comput. Phys. 357:125–41
     [Google Scholar]
121. Raissi M, Perdikaris P, Karniadakis G 2019. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378:686–707
     [Google Scholar]
122. Rechenberg I 1964. Kybernetische lösungsansteuerung einer experimentellen forschungsaufgabe. Annual Conference of the WGLR at Berlin in September 3533
     [Google Scholar]
123. Rechenberg I 1973. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der Biologischen Evolution Stuttgart, Ger.: Frommann-Holzboog
124. Reddy G, Celani A, Sejnowski TJ, Vergassola M 2016. Learning to soar in turbulent environments. PNAS 113:E4877–84
     [Google Scholar]
125. Reddy G, Wong-Ng J, Celani A, Sejnowski TJ, Vergassola M 2018. Glider soaring via reinforcement learning in the field. Nature 562:236–39
     [Google Scholar]
126. Richter SR, Vineet V, Roth S, Koltun V 2016. Playing for data: ground truth from computer games. European Conference on Computer Vision 2016 ed. B Leibe, J Matas, N Sebe, M Welling 102–18 Cham, Switz.: Springer
     [Google Scholar]
127. Rico-Martinez R, Krischer K, Kevrekidis IG, Kube MC, Hudson JL 1992. Discrete- vs. continuous-time nonlinear signal processing of Cu electrodissolution data. Chem. Eng. Commun. 118:25–48
     [Google Scholar]
128. Rokhlin V, Szlam A, Tygert M 2009. A randomized algorithm for principal component analysis. SIAM J. Matrix Anal. Appl. 31:1100–24
     [Google Scholar]
129. Rosenblatt F 1958. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65:386–408First example of a simple binary network with learning capabilities.
     [Google Scholar]
130. Rowley CW, Dawson S 2016. Model reduction for flow analysis and control. Annu. Rev. Fluid Mech. 49:387–417
     [Google Scholar]
131. Rowley CW, Mezić I, Bagheri S, Schlatter P, Henningson D 2009. Spectral analysis of nonlinear flows. J. Fluid Mech. 645:115–27
     [Google Scholar]
132. Rudy SH, Brunton SL, Proctor JL, Kutz JN 2017. Data-driven discovery of partial differential equations. Sci. Adv. 3:e1602614
     [Google Scholar]
133. Rumelhart DE, Hinton GE, Williams RJ 1986. Learning representations by back-propagating errors. Nature 323:533–36
     [Google Scholar]
134. Salimans T, Ho J, Chen X, Sutskever I 2017. Evolution strategies as a scalable alternative to reinforcement learning. arXiv:1703.03864 [stat.ML]
     [Google Scholar]
135. Schaeffer H 2017. Learning partial differential equations via data discovery and sparse optimization. Proc. R. Soc. A 473:20160446
     [Google Scholar]
136. Schaul T, Horgan D, Gregor K, Silver D 2015. Universal value function approximators. Proceedings of the 32nd International Conference on Machine Learning ed. F Bach, DM Blei 1312–20 Red Hook, NY: Curran Assoc.
     [Google Scholar]
137. Schmid PJ 2010. Dynamic mode decomposition for numerical and experimental data. J. Fluid Mech. 656:5–28
     [Google Scholar]
138. Schmidt M, Lipson H 2009. Distilling free-form natural laws from experimental data. Science 324:81–85
     [Google Scholar]
139. Schölkopf B, Smola AJ 2002. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond Cambridge, MA: MIT Press
140. Schwefel HP 1977. Numerische Optimierung von Computer-Modellen Mittels der Evolutionsstrategie Basel, Switz.: Birkhäuser
141. Semeraro O, Lusseyran F, Pastur L, Jordan P 2016. Qualitative dynamics of wavepackets in turbulent jets. arXiv:1608.06750 [physics.flu-dyn]
     [Google Scholar]
142. Silver D, Huang A, Maddison CJ, Guez A, Sifre L et al. 2016. Mastering the game of Go with deep neural networks and tree search. Nature 529:484–89
     [Google Scholar]
143. Singh AP, Medida S, Duraisamy K 2017. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils. AIAA J. 55:2215–27
     [Google Scholar]
144. Sirovich L 1987. Turbulence and the dynamics of coherent structures, parts I–III. Q. Appl. Math. 45:561–90
     [Google Scholar]
145. Sirovich L, Kirby M 1987. A low-dimensional procedure for the characterization of human faces. J. Opt. Soc. Am. A 4:519–24
     [Google Scholar]
146. Skinner SN, Zare-Behtash H 2018. State-of-the-art in aerodynamic shape optimisation methods. Appl. Soft. Comput. 62:933–62
     [Google Scholar]
147. Strom B, Brunton SL, Polagye B 2017. Intracycle angular velocity control of cross-flow turbines. Nat. Energy 2:17103
     [Google Scholar]
148. Sutton RS, Barto AG 2018. Reinforcement Learning: An Introduction Cambridge, MA: MIT Press. 2nd ed.The classic book on reinforcement learning.
149. Taira K, Brunton SL, Dawson S, Rowley CW, Colonius T et al. 2017. Modal analysis of fluid flows: an overview. AIAA J. 55:4013–41
     [Google Scholar]
150. Takeishi N, Kawahara Y, Yairi T 2017. Learning Koopman invariant subspaces for dynamic mode decomposition. Advances in Neural Information Processing Systems 30 ed. I Guyon, UV Luxburg, S Bengio, H Wallach, R Fergus, et al. 1130–40 Red Hook, NY: Curran Assoc.
     [Google Scholar]
151. Tedrake R, Jackowski Z, Cory R, Roberts JW, Hoburg W 2009. Learning to fly like a bird Paper presented at the 14th International Symposium on Robotics Research Lucerne, Switz.:
152. Teo C, Lim K, Hong G, Yeo M 1991. A neural net approach in analysing photographs in PIV. IEEE Trans. Syst. Man Cybern. 3:1535–38
     [Google Scholar]
153. Tesauro G 1992. Practical issues in temporal difference learning. Mach. Learn. 8:257–77
     [Google Scholar]
154. Theodoridis S 2015. Machine Learning: A Bayesian and Optimization Perspective San Diego, CA: AcademicA monograph linking machine learning and Bayesian inference algorithms.
155. Tsiotras P, Mesbahi M 2017. Toward an algorithmic control theory. J. Guid. Control Dyn. 40:194–96
     [Google Scholar]
156. Van Rees WM, Gazzola M, Koumoutsakos P 2015. Optimal morphokinematics for undulatory swimmers at intermediate reynolds numbers. J. Fluid Mech. 775:178–88
     [Google Scholar]
157. Verma S, Novati G, Koumoutsakos P 2018. Efficient collective swimming by harnessing vortices through deep reinforcement learning. PNAS 115:5849–54
     [Google Scholar]
158. Vlachas PR, Byeon W, Wan ZY, Sapsis TP, Koumoutsakos P 2018. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc. R. Soc. A 474:20170844
     [Google Scholar]
159. Wan ZY, Vlachas P, Koumoutsakos P, Sapsis T 2018. Data-assisted reduced-order modeling of extreme events in complex dynamical systems. PLOS ONE 13:e0197704
     [Google Scholar]
160. Wang JX, Wu JL, Xiao H 2017. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Phys. Rev. Fluids 2:034603
     [Google Scholar]
161. Wang M, Hemati MS 2017. Detecting exotic wakes with hydrodynamic sensors. arXiv:1711.10576
     [Google Scholar]
162. Wehmeyer C, Noé F 2018. Time-lagged autoencoders: deep learning of slow collective variables for molecular kinetics. J. Chem. Phys. 148:241703
     [Google Scholar]
163. Wiener N 1965. Cybernetics or Control and Communication in the Animal and the Machine 25 Cambridge, MA: MIT Press
164. Willert CE, Gharib M 1991. Digital particle image velocimetry. Exp. Fluids 10:181–93
     [Google Scholar]
165. Williams MO, Rowley CW, Kevrekidis IG 2015. A kernel approach to data-driven Koopman spectral analysis. J. Comput. Dyn. 2:247–65
     [Google Scholar]
166. Wright J, Yang A, Ganesh A, Sastry S, Ma Y 2009. Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31:210–27
     [Google Scholar]
167. Wu H, Mardt A, Pasquali L, Noe F 2018. Deep generative Markov State Models. Adv. Neural Inf. Process. Syst. 31:3975–84
     [Google Scholar]
168. Wu X, Moin P 2008. A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608:81–112
     [Google Scholar]
169. Xiao H, Wu JL, Wang JX, Sun R, Roy C 2016. Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: a data-driven, physics-informed Bayesian approach. J. Comp. Phys. 324:115–36
     [Google Scholar]
170. Xie Y, Franz E, Chu M, Thuerey N 2018. tempoGAN: a temporally coherent, volumetric GAN for super-resolution fluid flow. ACM Trans. Graph. 37:95
     [Google Scholar]
171. Yang J, Wright J, Huang TS, Ma Y 2010. Image super-resolution via sparse representation. IEEE Trans. Image Process. 19:2861–73
     [Google Scholar]