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  • Perspective
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The transformative potential of machine learning for experiments in fluid mechanics

Nature Reviews Physics volume 5, pages 536–545 (2023)Cite this article

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Abstract

The field of machine learning (ML) has rapidly advanced the state of the art in many fields of science and engineering, including experimental fluid dynamics, which is one of the original big-data disciplines. This Perspective article highlights several aspects of experimental fluid mechanics that stand to benefit from progress in ML, including augmenting the fidelity and quality of measurement techniques, improving experimental design and surrogate digital-twin models and enabling real-time estimation and control. In each case, we discuss recent success stories and ongoing challenges, along with caveats and limitations, and outline the potential for new avenues of ML-augmented and ML-enabled experimental fluid mechanics.

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Fig. 1: Summary of machine learning impact on experimental fluid mechanics.
Fig. 2: Process of particle image velocimetry analysis based on machine learning.
Fig. 3: Schematic representation of a digital twin.
Fig. 4: Schematic representation of the process for sensing and control.

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References

  1. Taira, K. et al. Modal analysis of fluid flows: an overview. AIAA J. 55, 4013–4041 (2017).

    Article  ADS  Google Scholar 

  2. Brunton, S. L., Noack, B. R. & Koumoutsakos, P. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52, 477–508 (2020).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Brenner, M., Eldredge, J. & Freund, J. Perspective on machine learning for advancing fluid mechanics. Phys. Rev. Fluids 4, 100501 (2019).

    Article  ADS  Google Scholar 

  4. Vinuesa, R. & Brunton, S. L. Enhancing computational fluid dynamics with machine learning. Nat. Comput. Sci. 2, 358–366 (2022).

    Article  Google Scholar 

  5. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

    Article  ADS  Google Scholar 

  6. Bailey, S. C. C. et al. Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using pitot tubes. J. Fluid Mech. 715, 642–670 (2013).

    Article  ADS  MATH  Google Scholar 

  7. Tavoularis, S. Measurement in Fluid Mechanics (Cambridge Univ. Press, 2005).

  8. McKeon, B. J., Li, J., Jiang, W., Morrison, J. F. & Smits, A. J. Pitot probe corrections in fully developed turbulent pipe flow. Meas. Sci. Technol. 14, 1449–1458 (2003).

    Article  ADS  Google Scholar 

  9. Vinuesa, R. & Nagib, H. M. Enhancing the accuracy of measurement techniques in high Reynolds number turbulent boundary layers for more representative comparison to their canonical representations. Eur. J. Mech. B/Fluids 55, 300–312 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Örlü, R., Fransson, J. H. M. & Alfredsson, P. H. On near wall measurements of wall bounded flows: the necessity of an accurate determination of the wall position. Prog. Aerosp. Sci. 46, 353–387 (2010).

    Article  Google Scholar 

  11. Vinuesa, R., Schlatter, P. & Nagib, H. M. Role of data uncertainties in identifying the logarithmic region of turbulent boundary layers. Exp. Fluids 55, 1751 (2014).

    Article  Google Scholar 

  12. Ashok, A., Bailey, S. C. C., Hultmark, M. & Smits, A. J. Hot-wire spatial resolution effects in measurements of grid-generated turbulence. Exp. Fluids 53, 1713–1722 (2012).

    Article  Google Scholar 

  13. Chin, C., Hutchins, N., Ooi, A. & Marusic, I. Spatial resolution correction for hot-wire anemometry in wall turbulence. Exp. Fluids 50, 1443–1453 (2011).

    Article  Google Scholar 

  14. Monkewitz, P. A., Duncan, R. D. & Nagib, H. M. Correcting hot-wire measurements of stream-wise turbulence intensity in boundary layers. Phys. Fluids 22, 091701 (2010).

    Article  ADS  Google Scholar 

  15. Koza, J. R. Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, 1992).

  16. Brunton, S. L., Proctor, J. L. & Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 113, 3932–3937 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Lu, L., Jin, P., Pang, G., Zhang, Z. & Karniadakis, G. E. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3, 218–229 (2021).

    Article  Google Scholar 

  18. Li, Z. et al. Neural operator: graph kernel network for partial differential equations. Preprint at https://arxiv.org/abs/2003.03485 (2020).

  19. Batill, S. M. & Mueller, T. J. Visualization of transition in the flow over an airfoil using the smoke-wire technique. AIAA J. 19, 340–345 (1981).

    Article  ADS  Google Scholar 

  20. Cardona, J. L., Howland, M. F. & Dabiri, J. O. Seeing the wind: visual wind speed prediction with a coupled convolutional and recurrent neural network. In Advances in Neural Information Processing Systems 1130–1140 (Curran Associates, Inc., 2017).

  21. Guastoni, L. et al. Convolutional-network models to predict wall-bounded turbulence from wall quantities. J. Fluid Mech. 928, A27 (2021).

    Article  MathSciNet  Google Scholar 

  22. Güemes, A. et al. From coarse wall measurements to turbulent velocity fields through deep learning. Phys. Fluids 33, 075121 (2021).

    Article  ADS  Google Scholar 

  23. Liu, B., Tang, J., Huang, H. & Lu, X. Y. Deep learning methods for super-resolution reconstruction of turbulent flows. Phys. Fluids 32, 025105 (2020).

    Article  ADS  Google Scholar 

  24. Fukami, K., Maulik, R., Ramachandra, N., Fukagata, K. & Taira, K. Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning. Nat. Mach. Intell. 3, 945–951 (2021).

    Article  Google Scholar 

  25. Adrian, R. J. Twenty years of particle image velocimetry. Exp. Fluids 39, 159–169 (2005).

    Article  Google Scholar 

  26. Scarano, F. Tomographic PIV: principles and practice. Meas. Sci. Technol. 24, 012001 (2013).

    Article  ADS  Google Scholar 

  27. Atkinson, C. & Soria, J. An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp. Fluids 47, 553–568 (2009).

    Article  Google Scholar 

  28. Lumley, J. L. The structure of inhomogeneous turbulence. In Atmospheric Turbulence and Wave Propagation (eds Yaglom, A. M. & Tatarski, V. I.) 166–178 (Nauka, 1967).

  29. Méndez, M. A. et al. POD-based background removal for particle image velocimetry. Exp. Therm. Fluid Sci. 80, 181–192 (2017).

    Article  Google Scholar 

  30. Scherl, I. et al. Robust principal component analysis for modal decomposition of corrupt fluid flows. Phys. Rev. Fluids 5, 054401 (2020).

    Article  ADS  Google Scholar 

  31. Rabault, J., Kolaas, J. & Jensen, A. Performing particle image velocimetry using artificial neural networks: a proof-of-concept. Meas. Sci. Technol. 28, 125301 (2017).

    Article  ADS  Google Scholar 

  32. Fukami, K., Fukagata, K. & Taira, K. Super-resolution reconstruction of turbulent flows with machine learning. J. Fluid Mech. 870, 106–120 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Morimoto, M., Fukami, K. & Fukagata, K. Experimental velocity data estimation for imperfect particle image using machine learning. Phys. Fluids 33, 087121 (2021).

    Article  ADS  Google Scholar 

  34. Lee, Y., Yang, H. & Yin, Z. PIV-DCNN: cascaded deep convolutional neural networks for particle image velocimetry. Exp. Fluids 58, 171 (2017).

    Article  Google Scholar 

  35. Raissi, M., Perdikaris, P. & Karniadakis, G. E. 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 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Raissi, M., Yazdani, A. & Karniadakis, G. E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. Science 367, 1026–1030 (2020).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Arzani, A., Cassel, K. W. & D’Souza, R. M. Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation. J. Comput. Phys. 473, 111768 (2023).

    Article  MathSciNet  MATH  Google Scholar 

  38. Eivazi, H. & Vinuesa, R. Physics-informed deep-learning applications to experimental fluid mechanics. Preprint at https://arxiv.org/abs/2203.15402 (2022).

  39. Zhou, K., Li, J., Hong, J. & Grauer, S. J. Stochastic particle advection velocimetry (SPAV): theory, simulations, and proof-of-concept experiments. Meas. Sci. Technol. 34, 065302 (2023).

    Article  ADS  Google Scholar 

  40. Christiansen, J. P. Numerical simulation of hydrodynamics by the method of point vortices. J. Comput. Phys. 13, 363–379 (1973).

    Article  ADS  MATH  Google Scholar 

  41. Schneiders, J., Dwight, R. & Scarano, F. Time-supersampling of 3D-PIV measurements with vortex-in-cell simulation. Exp. Fluids 55, 1692 (2014).

    Article  Google Scholar 

  42. Doan, N. A. K., Polifke, W. & Magri, L. Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach. Proc. R. Soc. A 477, 20210135 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  43. Discetti, S. & Liu, Y. Machine learning for flow field measurements: a perspective. Meas. Sci. Technol. 34, 021001 (2023).

    Article  ADS  Google Scholar 

  44. Rezaeiravesh, S., Vinuesa, R., Liefvendahl, M. & Schlatter, P. Assessment of uncertainties in hot-wire anemometry and oil-film interferometry measurements for wall-bounded turbulent flows. Eur. J. Mech. B/Fluids 72, 57–73 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Kapteyn, M. G., Pretorius, J. V. R. & Willcox, K. E. A probabilistic graphical model foundation for enabling predictive digital twins at scale. Nat. Comput. Sci. 1, 337–347 (2021).

    Article  Google Scholar 

  46. Niederer, S. A., Sacks, M. S., Girolami, M. & Willcox, K. Scaling digital twins from the artisanal to the industrial. Nat. Comput. Sci. 1, 313–320 (2021).

    Article  Google Scholar 

  47. Brunton, S. L. et al. Data-driven aerospace engineering: reframing the industry with machine learning. AIAA J. 59, 2820–2847 (2021).

    Google Scholar 

  48. Herriot, J. G. Blockage Corrections for Three-Dimensional-Flow Closed-Throat Wind Tunnels, with Consideration of the Effect of Compressibility. Technical Report NACA-RM-A7B28 (National Advisory Committee for Aeronautics, 1947).

  49. Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631–655 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Tabatabaei, N. et al. RANS modelling of a NACA4412 wake using wind tunnel measurements. Fluids 7, 153 (2022).

    Article  ADS  Google Scholar 

  51. Morita, Y. et al. Applying Bayesian optimization with Gaussian-process regression to computational fluid dynamics problems. J. Comput. Phys. 449, 110788 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  52. Nocedal, J. & Wright, S. Numerical Optimization (Springer, 2006).

  53. Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. Spectral analysis of nonlinear flows. J. Fluid Mech. 645, 115–127 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. Schmid, P. J. Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. Kutz, J. N., Brunton, S. L., Brunton, B. W. & Proctor, J. L. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems (SIAM, 2016).

  56. Rowley, C. W. & Dawson, S. T. Model reduction for flow analysis and control. Annu. Rev. Fluid Mech. 49, 387–417 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. Le Clainche, S. & Vega, J. M. Higher order dynamic mode decomposition. SIAM J. Appl. Dyn. Syst. 16, 882–925 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  58. Rudy, S. H., Brunton, S. L., Proctor, J. L. & Kutz, J. N. Data-driven discovery of partial differential equations. Sci. Adv. 3, e1602614 (2017).

    Article  ADS  Google Scholar 

  59. Bongard, J. & Lipson, H. Automated reverse engineering of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 104, 9943–9948 (2007).

    Article  ADS  MATH  Google Scholar 

  60. Schmidt, M. & Lipson, H. Distilling free-form natural laws from experimental data. Science 324, 81–85 (2009).

    Article  ADS  Google Scholar 

  61. Cranmer, M., Xu, R., Battaglia, P. & Ho, S. Learning symbolic physics with graph networks. Preprint at https://arxiv.org/abs/1909.05862 (2019).

  62. Cranmer, M. et al. Discovering symbolic models from deep learning with inductive biases. Advances in Neural Information Processing Systems (NeurIPS 2020) (Curran Associates, Inc., 2020).

  63. Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P. & Koumoutsakos, P. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc. R. Soc. A 474, 20170844 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. Pathak, J., Hunt, B., Girvan, M., Lu, Z. & Ott, E. Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. Phys. Rev. Lett. 120, 024102 (2018).

    Article  ADS  Google Scholar 

  65. Cranmer, M. et al. Lagrangian neural networks. Preprint at https://arxiv.org/abs/2003.04630 (2020).

  66. Chen, R. T., Rubanova, Y., Bettencourt, J. & Duvenaud, D. Neural ordinary differential equations. Preprint at https://arxiv.org/abs/1806.07366 (2018).

  67. Reinbold, P. A., Kageorge, L. M., Schatz, M. F. & Grigoriev, R. O. Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression. Nat. Commun. 12, 3219 (2021).

    Article  ADS  Google Scholar 

  68. Callaham, J. L., Rigas, G., Loiseau, J.-C. & Brunton, S. L. An empirical mean-field model of symmetry-breaking in a turbulent wake. Sci. Adv. 8, eabm4786 (2022).

    Article  Google Scholar 

  69. Supekar, R. et al. Learning hydrodynamic equations for active matter from particle simulations and experiments. Proc. Natl Acad. Sci. USA 120, e2206994120 (2023).

    Article  MathSciNet  Google Scholar 

  70. Zanna, L. & Bolton, T. Data-driven equation discovery of ocean mesoscale closures. Geophys. Res. Lett. 47, e2020GL088376 (2020).

    Article  ADS  Google Scholar 

  71. Schmelzer, M., Dwight, R. P. & Cinnella, P. Discovery of algebraic Reynolds-stress models using sparse symbolic regression. Flow Turbul. Combust. 104, 579–603 (2020).

    Article  Google Scholar 

  72. Beetham, S. & Capecelatro, J. Formulating turbulence closures using sparse regression with embedded form invariance. Phys. Rev. Fluids 5, 084611 (2020).

    Article  ADS  Google Scholar 

  73. Beetham, S., Fox, R. O. & Capecelatro, J. Sparse identification of multiphase turbulence closures for coupled fluid–particle flows. J. Fluid Mech. 914, A11 (2021).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. Wang, M. & Zaki, T. A. Synchronization of turbulence in channel flow. J. Fluid Mech. 943, A4 (2022).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. Herrmann, B., Oswald, P., Semaan, R. & Brunton, S. L. Modeling synchronization in forced turbulent oscillator flows. Commun. Phys. 3, 195 (2020).

    Article  Google Scholar 

  76. Nóvoa, A. & Magri, L. Real-time thermoacoustic data assimilation. J. Fluid Mech. 948, A35 (2022).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  77. Jahanbakhshi, R. & Zaki, T. A. Nonlinearly most dangerous disturbance for high-speed boundary-layer transition. J. Fluid Mech. 876, 87–121 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  78. da Silva, A. F. C. & Colonius, T. Flow state estimation in the presence of discretization errors. J. Fluid Mech. 890, A10 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  79. Sobol, I. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55, 271–280 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  80. Xiu, D. & Karniadakis, G. E. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24, 619–644 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  81. Tanner, L. H. & Blows, L. G. A study of the motion of oil films on surfaces in air flow, with application to the measurement of skin friction. J. Phys. E Sci. Instrum. 9, 194–202 (1976).

    Article  ADS  Google Scholar 

  82. Nagib, H. M., Christophorou, C., Rüedi, J.-D., Monkewitz, P. A. & Österlund, J. M. Can we ever rely on results from wall-bounded turbulent flows without direct measurements of wall shear stress? 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference (AIAA, 2004).

  83. Rezaeiravesh, S., Vinuesa, R. & Schlatter, P. On numerical uncertainties in scale-resolving simulations of canonical wall turbulence. Comput. Fluids 227, 105024 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  84. Fan, D. et al. A robotic intelligent towing tank for learning complex fluid-structure dynamics. Sci. Robot. 4, eaay5063 (2019).

    Article  Google Scholar 

  85. Manohar, K., Brunton, B. W., Kutz, J. N. & Brunton, S. L. Data-driven sparse sensor placement for reconstruction: demonstrating the benefits of exploiting known patterns. IEEE Contr. Syst. Mag. 38, 63–86 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  86. Brunton, S. L. & Noack, B. R. Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67, 050801-1–050801-48 (2015).

    Article  ADS  Google Scholar 

  87. Morton, J., Witherden, F. D., Jameson, A. & Kochenderfer, M. J. Deep dynamical modeling and control of unsteady fluid flows. In 32nd Conference on Neural Information Processing Systems (NeurIPS 2018) (Curran Associates, Inc., 2018).

  88. Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N. & Dellnitz, M. Deep model predictive flow control with limited sensor data and online learning. Theoret. Computat. Fluid Dyn. 34, 577–591 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  89. Suzuki, T. & Hasegawa, Y. Estimation of turbulent channel flow at Reθ = 100 based on the wall measurement using a simple sequential approach. J. Fluid Mech. 830, 760–796 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  90. Encinar, M. & Jiménez, J. Logarithmic-layer turbulence: a view from the wall. Phys. Rev. Fluids 4, 114603 (2019).

    Article  ADS  Google Scholar 

  91. Borée, J. Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Exp. Fluids 35, 188–192 (2003).

    Article  Google Scholar 

  92. Agostini, L. & Leschziner, M. Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28, 015107 (2016).

    Article  ADS  Google Scholar 

  93. Mathis, R., Hutchins, N. & Marusic, I. Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337 (2009).

    Article  ADS  MATH  Google Scholar 

  94. Güemes, A., Discetti, S. & Ianiro, A. Sensing the turbulent large-scale motions with their wall signature. Phys. Fluids 31, 125112 (2019).

    Article  ADS  Google Scholar 

  95. Kim, J. & Lee, C. Prediction of turbulent heat transfer using convolutional neural networks. J. Fluid Mech. 882, A18 (2020).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  96. Goodfellow, I. et al. Generative adversarial networks. Commun. ACM 63, 139–144 (2020).

    Article  Google Scholar 

  97. Abbassi, M. R., Baars, W. J., Hutchins, N. & Marusic, I. Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures. Int. J. Heat Fluid Flow 67, 30–41 (2017).

    Article  Google Scholar 

  98. Geetha Balasubramanian, A., Vinuesa, R. & Tammisola, O. Prediction of wall-bounded turbulence in a viscoelastic channel flow using convolutional neural networks. In Proc. European Drag Reduction and Flow Control Meeting (EDRFCM) (EDRFCM, 2022).

  99. Mahmoudabadbozchelou, M., Kamani, K. M., Rogers, S. A. & Jamali, S. Digital rheometer twins: learning the hidden rheology of complex fluids through rheology-informed graph neural networks. Proc. Natl Acad. Sci. USA 119, e2202234119 (2022).

    Article  Google Scholar 

  100. Brunton, S. L. & Kutz, J. N. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (Cambridge Univ. Press, 2022).

  101. Vinuesa, R. & Sirmacek, B. Interpretable deep-learning models to help achieve the sustainable development goals. Nat. Mach. Intell. 3, 926 (2021).

    Article  Google Scholar 

  102. Lundberg, S. M. & Lee, S.-I. A unified approach to interpreting model predictions. In 31st Conference on Neural Information Processing Systems (NIPS 2017) (Curran Associates, Inc., 2017).

  103. Lee, S., Yang, J., Forooghi, P., Stroh, A. & Bagheri, S. Predicting drag on rough surfaces by transfer learning of empirical correlations. J. Fluid Mech. 933, A18 (2022).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  104. Mahfoze, O. A., Moody, A., Wynn, A., Whalley, R. D. & Laizet, S. Reducing the skin-friction drag of a turbulent boundary-layer flow with low-amplitude wall-normal blowing within a Bayesian optimization framework. Phys. Rev. Fluids 4, 094601 (2019).

    Article  ADS  Google Scholar 

  105. Kornilov, V. I. & Boiko, A. V. Efficiency of air microblowing through microperforated wall for flat plate drag reduction. AIAA J. 50, 724–732 (2012).

    Article  ADS  Google Scholar 

  106. Li, R., Noack, B. R., Cordier, L., Borée, J. & Harambat, F. Drag reduction of a car model by linear genetic programming control. Exp. Fluids 58, 103 (2017).

    Article  Google Scholar 

  107. Minelli, G., Dong, T., Noack, B. & Krajnović, S. Upstream actuation for bluff-body wake control driven by a genetically inspired optimization. J. Fluid Mech. 893, A1 (2020).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  108. Choi, H., Moin, P. & Kim, J. Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110 (1994).

    Article  ADS  MATH  Google Scholar 

  109. Marusic, I. et al. An energy-efficient pathway to turbulent drag reduction. Nat. Commun. 12, 5805 (2021).

    Article  ADS  Google Scholar 

  110. Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction Vol. 1 (MIT Press, 1998).

  111. Recht, B. A tour of reinforcement learning: the view from continuous control. Annu. Rev. Control Robot. Auton. Syst. 2, 253–279 (2019).

    Article  Google Scholar 

  112. Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529 (2015).

    Article  ADS  Google Scholar 

  113. Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140–1144 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  114. Reddy, S., Dragan, A. D. & Levine, S. Shared autonomy via deep reinforcement learning. Preprint at https://arxiv.org/abs/1802.01744 (2018).

  115. Vinyals, O. et al. Grandmaster level in StarCraft II using multi-agent reinforcement learning. Nature 575, 350–354 (2019).

    Article  ADS  Google Scholar 

  116. Verma, S., Novati, G. & Koumoutsakos, P. Efficient collective swimming by harnessing vortices through deep reinforcement learning. Proc. Natl Acad. Sci. USA 115, 5849–5854 (2018).

    Article  ADS  Google Scholar 

  117. Novati, G., Mahadevan, L. & Koumoutsakos, P. Controlled gliding and perching through deep-reinforcement-learning. Phys. Rev. Fluids 4, 093902 (2019).

    Article  ADS  Google Scholar 

  118. Rabault, J., Kuchta, M., Jensen, A., Réglade, U. & Cerardi, N. Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J. Fluid Mech. 865, 281–302 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  119. Wang, Q. et al. DRLinFluids: an open-source Python platform of coupling deep reinforcement learning and OpenFOAM. Phys. Fluids 34, 081801 (2022).

    Article  Google Scholar 

  120. Fan, D., Yang, L., Wang, Z., Triantafyllou, M. S. & Karniadakis, G. E. Reinforcement learning for bluff body active flow control in experiments and simulations. Proc. Natl Acad. Sci. USA 117, 26091–26098 (2020).

    Article  ADS  Google Scholar 

  121. Novati, G., de Laroussilhe, H. L. & Koumoutsakos, P. Automating turbulence modelling by multi-agent reinforcement learning. Nat. Mach. Intell. 3, 87–96 (2021).

    Article  Google Scholar 

  122. Gunnarson, P., Mandralis, I., Novati, G., Koumoutsakos, P. & Dabiri, J. O. Learning efficient navigation in vortical flow fields. Nat. Commun. 12, 7143 (2021).

    Article  ADS  Google Scholar 

  123. Vinuesa, R., Lehmkuhl, O., Lozano-Durán, A. & Rabault, J. Flow control in wings and discovery of novel approaches via deep reinforcement learning. Fluids 7, 62 (2022).

    Article  ADS  Google Scholar 

  124. Bae, H. J. & Koumoutsakos, P. Scientific agent reinforcement learning for wall-models of turbulent flows. Nat. Commun. 13, 1443 (2022).

    Article  ADS  Google Scholar 

  125. Guastoni, L., Rabault, J., Schlatter, P., Azizpour, H. & Vinuesa, R. Deep reinforcement learning for turbulent drag reduction in channel flows. Eur. Phys. J. E 46, 27 (2023).

    Article  Google Scholar 

  126. Sonoda, T., Liu, Z., Itoh, T. & Hasegawa, Y. Reinforcement learning of control strategies for reducing skin friction drag in a fully developed channel flow. J. Fluid Mech. 960, A30 (2023).

    Article  ADS  MathSciNet  Google Scholar 

  127. Vignon, C., Rabault, J. & Vinuesa, R. Recent advances in applying deep reinforcement learning for flow control: perspectives and future directions. Phys. Fluids 35, 031301 (2023).

    Article  ADS  Google Scholar 

  128. Eastwood, C. & Williams, C. K. I. A framework for the quantitative evaluation of disentangled representations. In International Conference on Learning Representations (2018).

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Acknowledgements

The authors gratefully acknowledge valuable discussions with B. Noack early in the development of this Perspective article. R.V. acknowledges financial support from ERC grant no. 2021-CoG-101043998, DEEPCONTROL. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. S.L.B. acknowledges support from the National Science Foundation AI Institute in Dynamic Systems (grant no. 2112085). B.J.M. is grateful for the support of the U.S. ONR through a Vannevar Bush Faculty Fellowship, N00014-17-1-3022.

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Authors and Affiliations

  1. FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden

    Ricardo Vinuesa

  2. Swedish e-Science Research Centre (SeRC), Stockholm, Sweden

    Ricardo Vinuesa

  3. Department of Mechanical Engineering, University of Washington, Seattle, WA, USA

    Steven L. Brunton

  4. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Beverley J. McKeon

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  1. Ricardo Vinuesa
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  2. Steven L. Brunton
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  3. Beverley J. McKeon
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Correspondence to Ricardo Vinuesa.

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Vinuesa, R., Brunton, S.L. & McKeon, B.J. The transformative potential of machine learning for experiments in fluid mechanics. Nat Rev Phys 5, 536–545 (2023). https://doi.org/10.1038/s42254-023-00622-y

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