Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T13:57:59.616Z Has data issue: false hasContentIssue false
  • English
  • Français

A neural network approach for the blind deconvolution of turbulent flows

Published online by Cambridge University Press:  13 October 2017

R. Maulik  and
O. San Open the ORCID record for O. San [Opens in a new window]
R. Maulik
Affiliation:
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
O. San*
Affiliation:
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 831 , 25 November 2017 , pp. 151 - 181
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, A. 1972 Regression and the Moore–Penrose Pseudoinverse. Academic.Google Scholar
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1980 Improved subgrid-scale models for large-eddy simulation. AIAA Paper 80-1357.Google Scholar
Bos, W. J. & Bertoglio, J. 2006 Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18 (7), 071701.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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), 3932–3937.CrossRefGoogle ScholarPubMed
Bull, J. R. & Jameson, A. 2015 Simulation of the Taylor–Green vortex using high-order flux reconstruction schemes. AIAA J. 53, 2750–2761.CrossRefGoogle Scholar
Cichocki, A. & Amari, S. 2002 Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons.CrossRefGoogle Scholar
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. 313–316.Google Scholar
Demuth, H. B., Beale, M. H., De Jess, O. & Hagan, M. T. 2014 Neural Network Design. Martin Hagan.Google Scholar
Duraisamy, K., Zhang, Z. J. & Singh, A. P. 2015 New approaches in turbulence and transition modeling using data-driven techniques. AIAA Paper 2015-1284.Google Scholar
Foresee, F. D. & Hagan, M. T. 1997 Gauss–Newton approximation to Bayesian learning. In IEEE International Conference on Neural Networks, pp. 1930–1935.Google Scholar
Frisch, U. 1996 Turbulence: the Legacy of A. N. Kolmogorov. Cambridge University Press.Google Scholar
Gamahara, M. & Hattori, Y. 2017 Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2 (5), 054604.CrossRefGoogle Scholar
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, 442–457.CrossRefGoogle Scholar
Germano, M. 2015 The similarity subgrid stresses associated to the approximate Van Cittert deconvolutions. Phys. Fluids 27 (3), 035111.CrossRefGoogle Scholar
Hornik, K., Stinchcombe, M. & White, H. 1989 Multilayer feedforward networks are universal approximators. Neural Netw. 2 (5), 359–366.CrossRefGoogle Scholar
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. 985–990.Google Scholar
Huang, G., Zhu, Q. & Siew, C. 2006 Extreme learning machine: theory and applications. Neurocomput. 70 (1), 489–501.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 1417–1423.CrossRefGoogle Scholar
Kutz, J. N. 2017 Deep learning in fluid dynamics. J. Fluid Mech. 814, 1–4.CrossRefGoogle Scholar
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), 1205–1209.CrossRefGoogle Scholar
Layton, W. J. & Rebholz, L. G. 2012 Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis. Springer.CrossRefGoogle Scholar
Lee, C., Kim, J., Babcock, D. & Goodman, R. 1997 Application of neural networks to turbulence control for drag reduction. Phys. Fluids 9 (6), 1740–1747.CrossRefGoogle Scholar
Ling, J., Jones, R. & Templeton, J. 2016a Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318, 22–35.CrossRefGoogle Scholar
Ling, J., Kurzawski, A. & Templeton, J. 2016b Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155–166.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Mackay, D. J. C. 1992 Bayesian interpolation. Neural Comput. 4 (3), 415–447.CrossRefGoogle Scholar
Maulik, R. & San, O. 2017 Resolution and energy dissipation characteristics of implicit LES and explicit filtering models for compressible turbulence. Fluids 2 (2), 14.CrossRefGoogle Scholar
Maulik, R. & San, O. 2018 Explicit and implicit LES closures for Burgers turbulence. J. Comput. Appl. Maths 327, 12–40.CrossRefGoogle Scholar
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182 (1), 1–26.CrossRefGoogle Scholar
Parish, E. J. & Duraisamy, K. 2016 A paradigm for data-driven predictive modeling using field inversion and machine learning. J. Comput. Phys. 305, 758–774.CrossRefGoogle Scholar
Raissi, M. & Karniadakis, G. E.2016 Deep multi-fidelity Gaussian processes. arXiv:1604.07484.Google Scholar
Raissi, M. & Karniadakis, G. E.2017 Hidden physics models: Machine learning of nonlinear partial differential equations. arXiv:1708.00588.CrossRefGoogle Scholar
San, O. & Staples, A. E. 2012 High-order methods for decaying two-dimensional homogeneous isotropic turbulence. Comput. Fluids 63, 105–127.CrossRefGoogle Scholar
Schmidt, M. & Lipson, H. 2009 Distilling free-form natural laws from experimental data. Science 324 (5923), 81–85.CrossRefGoogle ScholarPubMed
Serre, D. 2002 Matrices: Theory and Applications. Springer.Google Scholar
Stolz, S. & Adams, N. A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 1699–1701.CrossRefGoogle Scholar
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), 2985–3001.CrossRefGoogle Scholar
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), 225–238.CrossRefGoogle Scholar
Tracey, B., Duraisamy, K. & Alonso, J. 2013 Application of supervised learning to quantify uncertainties in turbulence and combustion modeling. AIAA Paper 2013-0259.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Wang, L., Huang, Y., Luo, X., Wang, Z. & Luo, S. 2011 Image deblurring with filters learned by extreme learning machine. Neurocomput. 74 (16), 2464–2474.CrossRefGoogle Scholar
Weatheritt, J. & Sandberg, R. 2016 A novel evolutionary algorithm applied to algebraic modifications of the RANS stress–strain relationship. J. Comput. Phys. 325, 22–37.CrossRefGoogle Scholar
Zhang, G., Patuwo, B. E. & Hu, M. Y. 1998 Forecasting with artificial neural networks: the state of the art. Intl J. Forecast. 14 (1), 35–62.CrossRefGoogle Scholar
Zhang, Z. J. & Duraisamy, K. 2015 Machine learning methods for data-driven turbulence modeling. AIAA Paper 2015-2460.Google Scholar
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.Google ScholarPubMed