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Deep learning of vortex-induced vibrations

Published online by Cambridge University Press:  19 December 2018

Maziar Raissi Open the ORCID record for Maziar Raissi [Opens in a new window] ,
Zhicheng Wang Open the ORCID record for Zhicheng Wang [Opens in a new window] ,
Michael S. Triantafyllou Open the ORCID record for Michael S. Triantafyllou [Opens in a new window]  and
George Em Karniadakis
Maziar Raissi*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Zhicheng Wang
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Michael S. Triantafyllou
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
George Em Karniadakis
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: [email protected]
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Abstract

Vortex-induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not straightforward to solve using standard computational fluid dynamics methods, especially since no information is provided for the pressure. An even greater challenge is to infer the lift and drag forces given some dye or smoke visualizations of the flow field. Here we employ deep neural networks that are extended to encode the incompressible Navier–Stokes equations coupled with the structure’s dynamic motion equation. In the first case, given scattered data in space–time on the velocity field and the structure’s motion, we use four coupled deep neural networks to infer very accurately the structural parameters, the entire time-dependent pressure field (with no prior training data), and reconstruct the velocity vector field and the structure’s dynamic motion. In the second case, given scattered data in space–time on a concentration field only, we use five coupled deep neural networks to infer very accurately the vector velocity field and all other quantities of interest as before. This new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 119 - 137
Copyright
© 2018 Cambridge University Press 

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References

Abadi, M. et al. 2016 Tensorflow: large-scale machine learning on heterogeneous distributed systems. arXiv:1603.04467.Google Scholar
Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. 2018 Automatic differentiation in machine learning: a survey. J. Machine Learning Res. 18 (153), 1–43.Google Scholar
Beidokhti, R. S. & Malek, A. 2009 Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques. J. Franklin Inst. 346, 898–913.Google Scholar
Bourguet, R., Karniadakis, G. E. & Triantafyllou, M. S. 2011 Vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 677, 342–382.Google Scholar
Chen, T. Q., Rubanova, Y., Bettencourt, J. & Duvenaud, D.2018 Neural ordinary differential equations. arXiv:1806.07366.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
Evangelinos, C. & Karniadakis, G. E. 1999 Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. J. Fluid Mech. 400, 91–124.Google Scholar
Hagge, T., Stinis, P., Yeung, E. & Tartakovsky, A. M.2017 Solving differential equations with unknown constitutive relations as recurrent neural networks. arXiv:1710.02242.Google Scholar
Hirn, M., Mallat, S. & Poilvert, N. 2017 Wavelet scattering regression of quantum chemical energies. Multiscale Model. Simul. 15, 827–863.Google Scholar
Hornik, K., Stinchcombe, M. & White, H. 1989 Multilayer feedforward networks are universal approximators. Neural Networks 2, 359–366.Google Scholar
Karniadakis, G. E. & Sherwin, S. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.Google Scholar
Kingma, D. P. & Ba, J.2014 Adam: a method for stochastic optimization. arXiv:1412.6980.Google Scholar
Kondor, R.2018 N-body networks: a covariant hierarchical neural network architecture for learning atomic potentials. arXiv:1803.01588.Google Scholar
Kondor, R. & Trivedi, S. 2018 On the generalization of equivariance and convolution in neural networks to the action of compact groups. In Proceedings of the Thirty-fifth International Conference on Machine Learning, Stockholm, Sweden, ICML.Google Scholar
Lagaris, I. E., Likas, A. & Fotiadis, D. I. 1998 Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Networks 9, 987–1000.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
Ling, J. & Templeton, J. 2015 Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty. Phys. Fluids 27, 085103.Google Scholar
Mallat, S. 2016 Understanding deep convolutional networks. Phil. Trans. R. Soc. Lond. A 374, 20150203.Google Scholar
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182, 1–26.Google Scholar
Newman, D. J. & Karniadakis, G. E. 1997 A direct numerical simulation study of flow past a freely vibrating cable. J. Fluid Mech. 344, 95–136.Google Scholar
Owhadi, H. 2015 Bayesian numerical homogenization. Multiscale Model. Simul. 13, 812–828.Google Scholar
Owhadi, H., Scovel, C. & Sullivan, T. 2015 Brittleness of Bayesian inference under finite information in a continuous world. Electron. J. Statist. 9, 1–79.Google Scholar
Paidoussis, M. P. 1998 Fluid–Structure Interactions: Slender Structures and Axial Flow, vol. 1. Academic Press.Google Scholar
Paidoussis, M. P. 2004 Fluid–Structure Interactions: Slender Structures and Axial Flow, vol. 2. Academic Press.Google Scholar
Pang, G., Yang, L. & Karniadakis, G. E.2018 Neural-net-induced Gaussian process regression for function approximation and PDE solution. arXiv:1806.11187.Google 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.Google Scholar
Perdikaris, P., Raissi, M., Damianou, A., Lawrence, N. D. & Karniadakis, G. E. 2017 Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. Proc. R. Soc. Lond. A 473, 20160751.Google Scholar
Perdikaris, P., Venturi, D. & Karniadakis, G. E. 2016 Multifidelity information fusion algorithms for high-dimensional systems and massive data sets. SIAM J. Sci. Comput. 38, B521–B538.Google Scholar
Psichogios, D. C. & Ungar, L. H. 1992 A hybrid neural network-first principles approach to process modeling. AIChE J. 38, 1499–1511.Google Scholar
Raghu, M., Poole, B., Kleinberg, J., Ganguli, S. & Sohl-Dickstein, J.2016 On the expressive power of deep neural networks. arXiv:1606.05336.Google Scholar
Raissi, M.2017 Parametric Gaussian process regression for big data. arXiv:1704.03144.Google Scholar
Raissi, M.2018a Deep hidden physics models: deep learning of nonlinear partial differential equations. arXiv:1801.06637.Google Scholar
Raissi, M.2018b Forward-backward stochastic neural networks: deep learning of high-dimensional partial differential equations. arXiv:1804.07010.Google Scholar
Raissi, M. & Karniadakis, G.2016 Deep multi-fidelity Gaussian processes. arXiv:1604.07484.Google Scholar
Raissi, M. & Karniadakis, G. E. 2018 Hidden physics models: machine learning of nonlinear partial differential equations. J. Comput. Phys. 357, 125–141.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E.2017a Physics informed deep learning (part II): data-driven discovery of nonlinear partial differential equations. arXiv:1711.10566.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E.2017b Physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations. arXiv:1711.10561.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E. 2017c Inferring solutions of differential equations using noisy multi-fidelity data. J. Comput. Phys. 335, 736–746.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E. 2017d Machine learning of linear differential equations using Gaussian processes. J. Comput. Phys. 348, 683–693.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E. 2018a Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. SIAM J. Sci. Comput. 40, A172–A198.Google Scholar
Raissi, M., Perdikaris, P. & Karniadakis, G. E.2018b Multistep neural networks for data-driven discovery of nonlinear dynamical systems. arXiv:1801.01236.Google Scholar
Raissi, M., Yazdani, A. & Karniadakis, G. E.2018 Hidden fluid mechanics: a Navier–Stokes informed deep learning framework for assimilating flow visualization data. arXiv:1808.04327.Google Scholar
Rasmussen, C. E. & Williams, C. K. 2006 Gaussian Processes for Machine Learning, vol. 1. MIT Press.Google Scholar
Rico-Martinez, R., Anderson, J. & Kevrekidis, I. 1994 Continuous-time nonlinear signal processing: a neural network based approach for gray box identification. In Neural Networks for Signal Processing IV. Proceedings of the 1994 IEEE Workshop, pp. 596–605. IEEE.Google Scholar
Shahriari, B., Swersky, K., Wang, Z., Adams, R. P. & De Freitas, N. 2016 Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104, 148–175.Google Scholar
Tripathy, R. & Bilionis, I.2018 Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification. arXiv:1802.00850.Google Scholar
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P. & Koumoutsakos, P.2018 Data-driven forecasting of high-dimensional chaotic systems with long-short term memory networks. arXiv:1802.07486.Google Scholar
Wang, J.-X., Wu, J., Ling, J., Iaccarino, G. & Xiao, H.2017 A comprehensive physics-informed machine learning framework for predictive turbulence modeling. arXiv:1701.07102.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibration. Annu. Rev. Fluid Mech. 36, 413–455.Google Scholar
Zhang, Z. J. & Duraisamy, K.2015 Machine learning methods for data-driven turbulence modeling. AIAA Paper 2015–2460.Google Scholar
Zhu, Y. & Zabaras, N.2018 Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification. arXiv:1801.06879.Google Scholar