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Super-resolution reconstruction of turbulent flows with machine learning

Published online by Cambridge University Press:  07 May 2019

Kai Fukami ,
Koji Fukagata Open the ORCID record for Koji Fukagata [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
Kai Fukami*
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
Koji Fukagata
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan
Kunihiko Taira
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine learning models are developed, namely, the convolutional neural network (CNN) and the hybrid downsampled skip-connection/multi-scale (DSC/MS) models. These machine learning models are applied to a two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbulence. The CNN and DSC/MS models are found to reconstruct turbulent flows from extremely coarse flow field images with remarkable accuracy. For the turbulent flow problem, the machine-leaning-based super-resolution analysis can greatly enhance the spatial resolution with as little as 50 training snapshot data, holding great potential to reveal subgrid-scale physics of complex turbulent flows. With the growing availability of flow field data from high-fidelity simulations and experiments, the present approach motivates the development of effective super-resolution models for a variety of fluid flows.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Homogeneous turbulence Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 106 - 120
Copyright
© 2019 Cambridge University Press 

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References

Colonius, T. & Taira, K. 2008 A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Meth. Appl. Mech. Engng 197, 2131–2146.Google Scholar
Dong, C., Loy, C. C., He, K. & Tang, X. 2016 Image super-resolution using deep convolutional networks. IEEE Trans. Pattern Anal. Mach. Intell. 38 (2), 295–307.Google Scholar
Du, X., Qu, X., He, Y. & Guo, D. 2018 Single image super-resolution based on multi-scale competitive convolutional neural network. Sensors 18 (789), 1–17.Google Scholar
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid. Mech. 51, 357–377.Google Scholar
Fukami, K., Kawai, K. & Fukagata, K. 2018 A synthetic turbulent inflow generator using machine learning. Phys. Rev. Fluids (submitted), arXiv:1806.08903.Google Scholar
He, K., Zhang, X., Ren, S. & Sun, J. 2016 Deep residual learning for image recognition. In Proceedings of Computer Vision and Pattern Recognition, pp. 770–778.Google Scholar
Hou, W., Darakananda, D. & Eldredge, J. D.2019 Machine learning based detection of flow disturbances using surface pressure measurements. AIAA Paper 2019–1148.Google Scholar
Keys, R. 1981 Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust. Speech Signal Process. 29 (6), 1153–1160.Google Scholar
Kingma, D. & Ba, J.2014 A method for stochastic optimization. arXiv:1412.6980.Google Scholar
Koizumi, H., Tsutsumi, S. & Shima, E.2010 Feedback control of Karman vortex shedding from a cylinder using deep reinforcement learning. AIAA Paper 2018–3691.Google Scholar
Kutz, J. N. 2016 Deep learning in fluid dynamics. J. Fluid Mech. 814, 1–4.Google Scholar
Le, Q., Ngiam, J., Chen, Z., Chia, D. & Koh, P. 2010 Tiled convolutional neural networks. Adv. Neural Inform. Proc. Syst. 23, 1279–1287.Google Scholar
Lecun, Y., Bottou, L., Bengio, Y. & Haffner, P. 1998 Gradient-based learning applied to document recognition. Proc. IEEE 86 (11), 2278–2324.Google Scholar
Ling, J., Kurzawski, A. & Templeton, J. 2016 Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155–166.Google Scholar
Leoni, P. C. D., Mazzino, A. & Biferale, L. 2018 Inferring flow parameters and turbulent configuration with physics-informed data assimilation and spectral nudging. Phys. Rev. Fluids 3, 104604.Google Scholar
Maulik, R. & San, O. 2017 A neural network approach for the blind deconvolution of turbulent flows. J. Fluid Mech. 831, 151–181.Google Scholar
Nair, V. & Hinton, G. E. 2010 Rectified linear units improve restricted Boltzmann machines. In Proc. 27th International Conference on Machine Learning.Google Scholar
Prechelt, L. 1998 Automatic early stopping using cross validation: quantifying the criteria. Neural Networks 11 (4), 761–767.Google Scholar
Romano, Y., Ishidoro, J. & Milanfar, P. 2017 RAISR: rapid and accurate image super resolution. IEEE Trans. Comput. Imaging 3 (1), 110–125.Google Scholar
Salehipour, H. & Peltier, W. R. 2019 Deep learning of mixing by two ‘atoms’ of stratified turbulence. J. Fluid Mech. 861 (R4), 1–14.Google Scholar
San, O. & Maulik, R. 2018 Extreme learning machine for reduced order modeling of turbulent geophysical flows. Phys. Rev. E 97, 042322.Google Scholar
Shanker, M., Hu, M. Y. & Hung, M. S. 1996 Effect of data standardization on neural network training. Omega 24 (4), 385–397.Google Scholar
Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys. 225 (2), 2118–2137.Google Scholar
Taira, K., Nair, A. G. & Brunton, S. L. 2016 Network structure of two-dimensional decaying isotropic turbulence. J. Fluid Mech. 795 (R2), 1–11.Google Scholar
Zhang, Y., Sung, W. & Mavris, D.2018 Application of convolutional neural network to predict airfoil lift coefficient. AIAA Paper 2018–1903.Google Scholar