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Predictions of turbulent shear flows using deep neural networks

P. A. Srinivasan1,2,3, L. Guastoni1,3, H. Azizpour2,3, P. Schlatter1,3, and R. Vinuesa1,3,*

  • 1Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
  • 2School of Electrical Engineering and Computer Science, KTH, SE-100 44 Stockholm, Sweden
  • 3Swedish e-Science Research Centre (SeRC), SE-100 44 Stockholm, Sweden

  • *rvinuesa@mech.kth.se
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Phys. Rev. Fluids 4, 054603 – Published 10 May, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.054603

Abstract

In the present work, we assess the capabilities of neural networks to predict temporally evolving turbulent flows. In particular, we use the nine-equation shear flow model by Moehlis et al. [New J. Phys. 6, 56 (2004)] to generate training data for two types of neural networks: the multilayer perceptron (MLP) and the long short-term memory (LSTM) networks. We tested a number of neural network architectures by varying the number of layers, number of units per layer, dimension of the input, and weight initialization and activation functions in order to obtain the best configurations for flow prediction. Because of its ability to exploit the sequential nature of the data, the LSTM network outperformed the MLP. The LSTM led to excellent predictions of turbulence statistics (with relative errors of 0.45% and 2.49% in mean and fluctuating quantities, respectively) and of the dynamical behavior of the system (characterized by Poincaré maps and Lyapunov exponents). This is an exploratory study where we consider a low-order representation of near-wall turbulence. Based on the present results, the proposed machine-learning framework may underpin future applications aimed at developing accurate and efficient data-driven subgrid-scale models for large-eddy simulations of more complex wall-bounded turbulent flows, including channels and developing boundary layers.

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References (36)

  1. D. H. Hubel and T. N. Wiesel, Receptive fields, binocular interaction, and functional architecture in the cat's visual cortex, J. Physiol. 160, 106 (1962).
  2. K. Duraisamy, G. Iaccarino, and H. Xiao, Turbulence modeling in the age of data, Annu. Rev. Fluid Mech. 51, 357 (2019).
  3. J. Ling, A. Kurzawski, and J. Templeton, Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, J. Fluid Mech. 807, 155 (2016).
  4. J.-L. Wu, H. Xiao, and E. Paterson, Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework, Phys. Rev. Fluids 3, 074602 (2018).
  5. M. Milano and P. Koumoutsakos, Neural network modeling for near wall turbulent flow, J. Comput. Phys. 182, 1 (2002).
  6. C. J. Lapeyre, A. Misdariis, N. Cazard, D. Veynante, and T. Poinsot, Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates, Combust. Flame 203, 255 (2019).
  7. A. D. Beck, D. G. Flad, and C.-D. Munz, Deep neural networks for data-driven turbulence models, arXiv:1806.04482.
  8. C. Lee, J. Kim, D. Babcock, and R. Goodman, Application of neural networks to turbulence control for drag reduction, Phys. Fluids 9, 1740 (1997).
  9. N. Gautier, J.-L. Aider, T. Duriez, B. R. Noack, M. Segond, and M. Abel, Closed-loop separation control using machine learning, J. Fluid Mech. 770, 442 (2015).
  10. M. Shimizu and G. Kawahara, Construction of low-dimensional system reproducing low-Reynolds-number turbulence by machine learning, arXiv:1803.08206.
  11. K. Fukami, Y. Nabae, K. Kawai, and K. Fukagata, A synthetic turbulent inflow generator using machine learning, arXiv:1806.08903.
  12. J. Jiménez, Machine-aided turbulence theory, J. Fluid Mech. 854, R1 (2018).
  13. J. N. Kutz, Deep learning in fluid dynamics, J. Fluid Mech. 814, 1 (2017).
  14. J. Moehlis, H. Faisst, and B. Eckhardt, A low-dimensional model for turbulent shear flows, New J. Phys. 6, 56 (2004).
  15. L. Kim, Transient growth for a sinusoidal shear flow model, Master's thesis, University of California, Santa Barbara, CA, 2005.
  16. M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard et al., Tensorflow: A system for large-scale machine learning, in Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI '16) (USENIX Association, 2016), Vol. 16, pp. 265–283.
  17. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Learning internal representations by error propagation, Tech. Rep. No. ICS-8506, California University at San Diego La Jolla Institute for Cognitive Science, San Diego, CA, 1985 (unpublished).
  18. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Learning representations by back-propagating errors, Nature (London) 323, 533 (1986).
  19. D. P. Kingma and L. J. Ba, Adam: A method for stochastic optimization, in Proceedings of the International Conference for Learning Representations (Informatics Institute, Ithaca, NY, 2015).
  20. X. Glorot and Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS) 2010, Chia Laguna Resort, Sardinia, Italy (JMLR W&CP, 2010), Vol. 9, pp. 249–256.
  21. K. He, X. Zhang, S. Ren, and J. Sun, Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, in Proceedings of the IEEE International Conference on Computer Vision, 11-18 December 2015, Araucano Park, Las Condes, Chile (IEEE, Piscataway, NJ, 2015), pp. 1026–1034.
  22. Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015).
  23. V. Nair and G. E. Hinton, Rectified linear units improve restricted Boltzmann machines, in Proceedings of the 27th International Conference on Machine Learning (ICML-10), Haifa, Israel (Omni Press, 2010), pp. 807–814.
  24. A. L. Maas, A. Y. Hannun, and A. Y. Ng, Rectifier nonlinearities improve neural network acoustic models, in Proceedings of the 30th International Conference on Machine Learning, Atlanta, Georgia, USA, 2013 (JMLR W&CP, 2013), Vol. 28, p. 3.
  25. D.-A. Clevert, T. Unterthiner, and S. Hochreiter, Fast and accurate deep network learning by exponential linear units (ELUs), arXiv:1511.07289v5.
  26. P. A. A. Srinivasan, Deep learning models for turbulent shear flow, Master's thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2018.
  27. P. J. Werbos, Backpropagation through time: What it does and how to do it, Proc. IEEE 78, 1550 (1990).
  28. S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural Comput. 9, 1735 (1997).
  29. R. Vinuesa, C. Prus, P. Schlatter, and H. M. Nagib, Convergence of numerical simulations of turbulent wall-bounded flows and mean cross-flow structure of rectangular ducts, Meccanica 51, 3025 (2016).
  30. R. King, O. Hennigh, A. Mohan, and M. Chertkov, From deep to physics-informed learning of turbulence: Diagnostics, arXiv:1810.07785.
  31. J. M. Hamilton, J. Kim, and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech. 287, 317 (1995).
  32. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
  33. I. Hubara, M. Courbariaux, D. Soudry, R. El-Yaniv, and Y. Bengio, Quantized neural networks: Training neural networks with low precision weights and activations, J. Mach. Learn. Res. 18, 1 (2018).
  34. N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser, A synthetic-eddy-method for generating inflow conditions for large-eddy simulations, Int. J. Heat Fluid Flow 27, 585 (2006).
  35. Y. Mizuno and J. Jiménez, Wall turbulence without walls, J. Fluid Mech. 723, 429 (2013).
  36. P. A. Srinivasan, H. Azizpour, P. Schlatter, and R. Vinuesa, DeepTurbulence, https://github.com/KTH-Nek5000/DeepTurbulence.

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Phys. Rev. Fluids 4, 054603– Published 10 May, 2019
  • Received 23 November 2018
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