Skip to main content

A neural network approach for the blind deconvolution of turbulent flows

  • R. Maulik (a1) and O. San (a1)

We present a single-layer feed-forward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse-grained computations such as those encountered in large eddy simulations. We stress that the deconvolution procedure proposed in this investigation is blind, i.e. the deconvolved field is computed without any pre-existing information about the filtering procedure or kernel. This may be conceptually contrasted to the celebrated approximate deconvolution approaches where a filter shape is predefined for an iterative deconvolution process. We demonstrate that the proposed blind deconvolution network performs exceptionally well in the a priori testing of two-dimensional Kraichnan, three-dimensional Kolmogorov and compressible stratified turbulence test cases, and shows promise in forming the backbone of a physics-augmented data-driven closure for the Navier–Stokes equations.

Corresponding author
Email address for correspondence:
Hide All
Albert, A. 1972 Regression and the Moore–Penrose Pseudoinverse. Academic.
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1980 Improved subgrid-scale models for large-eddy simulation. AIAA Paper 80-1357.
Bos, W. J. & Bertoglio, J. 2006 Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18 (7), 071701.
Bright, I., Lin, G. & Kutz, J. N. 2013 Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Phys. Fluids 25 (12), 127102.
Brunton, S. L., Proctor, J. L. & Kutz, J. N. 2016 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 113 (15), 39323937.
Bull, J. R. & Jameson, A. 2015 Simulation of the Taylor–Green vortex using high-order flux reconstruction schemes. AIAA J. 53, 27502761.
Cichocki, A. & Amari, S. 2002 Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons.
Dabov, K., Foi, A., Katkovnik, V. & Egiazarian, K. 2007 Color image denoising via sparse 3D collaborative filtering with grouping constraint in luminance-chrominance space. In IEEE International Conference on Image Processing, pp. 313316.
Demuth, H. B., Beale, M. H., De Jess, O. & Hagan, M. T. 2014 Neural Network Design. Martin Hagan.
Duraisamy, K., Zhang, Z. J. & Singh, A. P. 2015 New approaches in turbulence and transition modeling using data-driven techniques. AIAA Paper 2015-1284.
Foresee, F. D. & Hagan, M. T. 1997 Gauss–Newton approximation to Bayesian learning. In IEEE International Conference on Neural Networks, pp. 19301935.
Frisch, U. 1996 Turbulence: the Legacy of A. N. Kolmogorov. Cambridge University Press.
Gamahara, M. & Hattori, Y. 2017 Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2 (5), 054604.
Gautier, N., Aider, J. L., Duriez, T., Noack, B. R., Segond, M. & Abel, M. 2015 Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442457.
Germano, M. 2015 The similarity subgrid stresses associated to the approximate Van Cittert deconvolutions. Phys. Fluids 27 (3), 035111.
Hornik, K., Stinchcombe, M. & White, H. 1989 Multilayer feedforward networks are universal approximators. Neural Netw. 2 (5), 359366.
Huang, G., Zhu, Q. & Siew, C. 2004 Extreme learning machine: a new learning scheme of feedforward neural networks. In IEEE International Joint Conference on Neural Networks, pp. 985990.
Huang, G., Zhu, Q. & Siew, C. 2006 Extreme learning machine: theory and applications. Neurocomput. 70 (1), 489501.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301305.
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 14171423.
Kutz, J. N. 2017 Deep learning in fluid dynamics. J. Fluid Mech. 814, 14.
Layton, W. & Lewandowski, R. 2003 A simple and stable scale-similarity model for large eddy simulation: energy balance and existence of weak solutions. Appl. Maths Lett. 16 (8), 12051209.
Layton, W. J. & Rebholz, L. G. 2012 Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis. Springer.
Lee, C., Kim, J., Babcock, D. & Goodman, R. 1997 Application of neural networks to turbulence control for drag reduction. Phys. Fluids 9 (6), 17401747.
Ling, J., Jones, R. & Templeton, J. 2016a Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318, 2235.
Ling, J., Kurzawski, A. & Templeton, J. 2016b Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155166.
Ling, J. & Templeton, J. 2015 Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier–Stokes uncertainty. Phys. Fluids 27 (8), 085103.
Mackay, D. J. C. 1992 Bayesian interpolation. Neural Comput. 4 (3), 415447.
Maulik, R. & San, O. 2017 Resolution and energy dissipation characteristics of implicit LES and explicit filtering models for compressible turbulence. Fluids 2 (2), 14.
Maulik, R. & San, O. 2018 Explicit and implicit LES closures for Burgers turbulence. J. Comput. Appl. Maths 327, 1240.
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182 (1), 126.
Parish, E. J. & Duraisamy, K. 2016 A paradigm for data-driven predictive modeling using field inversion and machine learning. J. Comput. Phys. 305, 758774.
Raissi, M. & Karniadakis, G. E.2016 Deep multi-fidelity Gaussian processes. arXiv:1604.07484.
Raissi, M. & Karniadakis, G. E.2017 Hidden physics models: Machine learning of nonlinear partial differential equations. arXiv:1708.00588.
San, O. & Staples, A. E. 2012 High-order methods for decaying two-dimensional homogeneous isotropic turbulence. Comput. Fluids 63, 105127.
Schmidt, M. & Lipson, H. 2009 Distilling free-form natural laws from experimental data. Science 324 (5923), 8185.
Serre, D. 2002 Matrices: Theory and Applications. Springer.
Stolz, S. & Adams, N. A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 16991701.
Stolz, S., Adams, N. A. & Kleiser, L. 2001 The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys. Fluids 13 (10), 29853001.
Sytine, I. V., Porter, D. H., Woodward, P. R., Hodson, S. W. & Winkler, K. 2000 Convergence tests for the piecewise parabolic method and Navier–Stokes solutions for homogeneous compressible turbulence. J. Comput. Phys. 158 (2), 225238.
Tracey, B., Duraisamy, K. & Alonso, J. 2013 Application of supervised learning to quantify uncertainties in turbulence and combustion modeling. AIAA Paper 2013-0259.
Wang, J., Wu, J. & Xiao, H.2016 Physics-informed machine learning for predictive turbulence modeling: Using data to improve RANS modeled Reynolds stresses. arXiv:1606.07987.
Wang, J., Wu, J. & Xiao, H. 2017 Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Phys. Rev. Fluids 2 (3), 034603.
Wang, L., Huang, Y., Luo, X., Wang, Z. & Luo, S. 2011 Image deblurring with filters learned by extreme learning machine. Neurocomput. 74 (16), 24642474.
Weatheritt, J. & Sandberg, R. 2016 A novel evolutionary algorithm applied to algebraic modifications of the RANS stress–strain relationship. J. Comput. Phys. 325, 2237.
Zhang, G., Patuwo, B. E. & Hu, M. Y. 1998 Forecasting with artificial neural networks: the state of the art. Intl J. Forecast. 14 (1), 3562.
Zhang, Z. J. & Duraisamy, K. 2015 Machine learning methods for data-driven turbulence modeling. AIAA Paper 2015-2460.
Zhou, Y., Grinstein, F. F., Wachtor, A. J. & Haines, B. M. 2014 Estimating the effective Reynolds number in implicit large-eddy simulation. Phys. Rev. E 89 (1), 013303.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 14
Total number of PDF views: 507 *
Loading metrics...

Abstract views

Total abstract views: 989 *
Loading metrics...

* Views captured on Cambridge Core between 13th October 2017 - 19th August 2018. This data will be updated every 24 hours.