[1] WANG Z, XIAO D, FANG F, et al. Model identification of reduced order fluid dynamics systems using deep learning[J]. International Journal for Numerical Methods in Fluids, 2018, 86(4):255-268.
[2] 寇家庆, 张伟伟, 高传强. 基于POD和DMD方法的跨声速抖振模态分析[J]. 航空学报, 2016, 37(9):2679-2689. KOU J Q, ZHANG W W, GAO C Q. Modal analysis of transonic buffet based on POD and DMD method[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(9):2679-2689(in Chinese).
[3] BERKOOZ G, HOLMES P, LUMLEY J L. The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual Review of Fluid Mechanics, 1993, 25(1):539-575.
[4] RAVINDRAN S S. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition[J]. International Journal for Numerical Methods in Fluids, 2000, 34(5):425-448.
[5] WU X, ZHANG W, PENG X,et al. Benchmark aerodynamic shape optimization with the POD-based CST airfoil parametric method[J]. Aerospace Science and Technology, 2019, 84:632-640.
[6] DUBIEF Y, DELCAYRE F. On coherent-vortex identification in turbulence[J]. Journal of Turbulence, 2000, 1:N11.
[7] XIONG S, YANG Y. Identifying the tangle of vortex tubes in homogeneous isotropic turbulence[J]. Journal of Fluid Mechanics, 2019, 874:952-978.
[8] HINTON G, DENG L, YU D, et al. Deep neural networks for acoustic modeling in speech recognition:the shared views of four research groups[J]. IEEE Signal Processing Magazine, 2012, 29(6):82-97.
[9] KRIZHEVSKY A, SUTSKEVER I, HINTON G E. ImageNet classification with deep convolutional neural networks[J]. Communications of the ACM, 2017, 60(6):84-90.
[10] SZEGEDY C, LIU W, JIA Y, et al. Going deeper with convolutions[C]//2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015:1-9.
[11] SIMONYAN K, ZISSERMAN A. Very deep convolutional networks for large-scale image recognition[C]//3rd International Conference on Learning Representations, ICLR 2015- Conference Track Proceedings, 2015.
[12] HE K, ZHANG X, REN S, et al. Deep residual learning for image recognition[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016:770-778.
[13] MANNING C, SURDEANU M, BAUER J, et al. The stanford CoreNLP natural language processing toolkit[C]//Proceedings of 52nd Annual Meeting of the Association for Computational Linguistics:System Demonstrations. Stroudsburg:Association for Computational Linguistics, 2014:55-60.
[14] CHEN C, SEFF A, KORNHAUSER A, et al. Deep driving:Learning affordance for direct perception in autonomous driving[C]//2015 IEEE International Conference on Computer Vision (ICCV), 2015:2722-2730.
[15] TRACEY B, DURAISAMY K, ALONSO J. Application of supervised learning to quantify uncertainties in turbulence and combustion modeling[C]//51 st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston:AIAA, 2013.
[16] LING J, KURZAWSKI A, TEMPLETON J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance[J]. Journal of Fluid Mechanics, 2016, 807:155-166.
[17] WANG J X, WU J L, XIAO H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data[J]. Physical Review Fluids, 2017, 2(3):034603.
[18] ZHANG Z, SONG X, YE S, et al. Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data[J]. Journal of Hydrodynamics, 2019, 31(1):58-65.
[19] 陈海昕, 邓凯文, 李润泽. 机器学习技术在气动优化中的应用[J]. 航空学报, 2019, 40(1):522480. CHEN H X, DENG K W, LI R Z. Utilization of machine learning technology in aerodynamic optimization[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522480(in Chinese).
[20] 韩忠华, 许晨舟, 乔建领, 等. 基于代理模型的高效全局气动优化设计综述方法研究进展[J]. 航空学报, 2020, 41(5):623344. HAN Z H, XU C Z, QIAO J L, et al. Recent progress of efficient global aerodynamic shape optimization using surrogate-based approach[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(5):623344(in Chinese).
[21] BRUNTON S L, NOACK B R, KOUMOUTSAKOS P. Machine learning for fluid mechanics[J]. Annual Review of Fluid Mechanics, 2020, 52(1):477-508.
[22] LI T, WU T, LIU Z. Nonlinear unsteady bridge aerodynamics:Reduced-order modeling based on deep LSTM networks[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2020, 198:104116.
[23] WIEWEL S, BECHER M, THUEREY N. Latent space physics:Towards learning the temporal evolution of fluid flow[J]. Computer Graphics Forum, 2019, 38(2):71-82.
[24] LECUN Y, BENGIO Y, HINTON G. Deep learning[Z].2015. DOI:10.1038/nature14539.
[25] KINGMA D P, BA J L. Adam:A method for stochastic gradient descent[C]//International Conference on Learning Representations, 2015.
[26] LIU Y, LU Y, WANG Y, et al. A CNN-based shock detection method in flow visualization[J]. Computers & Fluids, 2019, 184:1-9.
[27] LOVELY D, HAIMES R. Shock detection from computational fluid dynamics results[C]//Proceedings of the AIAA 14th Computational Fluid Dynamics Conference, 1999.
[28] ZHANG Y, AZMAN A N, XU K W, et al. Two-phase flow regime identification based on the liquid-phase velocity information and machine learning[J]. Experiments in Fluids, 2020, 61(10):212.
[29] 魏晓良,潮群,陶建峰, 等. 基于LSTM和CNN的高速柱塞泵故障诊断[J]. 航空学报, 2020, 41(3):423876. WEI X L, CHAO Q, TAO J F, et al. Cavitation fault diagnosis method for high-speed plunger pumps based on LSTM and CNN[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(3):423876(in Chinese).
[30] STROFER C M, WU J L, XIAO H, et al. Data-driven, physics-based feature extraction from fluid flow fields using convolutional neural networks[J]. Communications in Computational Physics, 2019, 25(3):625-650.
[31] GUPTA K, VOELKER L, BACH C. CFD-based aeroelastic analysis of the X-43 hypersonic flight vehicle[C]//39th Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 2001.
[32] SILVA W. Identification of linear and nonlinear aerodynamic impulse responses using digital filter techniques[J]. 1997.
[33] 陈刚, 李跃明. 非定常流场降阶模型及应用研究进展与展望[J]. 力学进展, 2011, 41(6):686-701. CHEN G, LI Y M. Advances and prospects of the reduced order model for unsteady flow and its application[J]. Advances in Mechanics, 2011, 41(6):686-701(in Chinese).
[34] GHOMAN S S, WANG Z, CHEN P C. Hybrid optimization framework with proper-orthogonal-decomposition-based order reduction and design-space evolution scheme[J]. Journal of Aircraft, 2013, 50(6):1776-1786.
[35] DUAN Y, CAI J, LI Y. Gappy proper orthogonal decomposition-based two-step optimization for airfoil design[J]. AIAA Journal, 2012, 50(4):968-971.
[36] CARLSON H A, VERBERG R, HARRIS C A. Aeroservoelastic modeling with proper orthogonal decomposition[J]. Physics of Fluids, 2017, 29(2):020711.
[37] LIU H F S, WOLF W R. Construction of reduced-order models for fluid flows using deep feedforward neural networks[J]. Journal of Fluid Mechanics, 2019, 872:963-994.
[38] WU P, SUN J, CHANG X. Data-driven reduced order model with temporal convolutional neural network[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 360:112766.
[39] MIYANAWALA T P, JAIMAN R K. A hybrid data-driven deep learning technique for fluid-structure interaction[C]//American Society of Mechanical Engineers, CFD and FSI, 2019.
[40] RENGANATHAN S A, MAULIK R, RAO V. Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil[J]. Physics of Fluids, 2020, 32(4):047110.
[41] WANG M, CHEUNG S W, LEUNG W T, et al. Reduced-order deep learning for flow dynamics. The interplay between deep learning and model reduction[J]. Journal of Computational Physics, 2020, 401:108939.
[42] PAWAR S, RAHMAN S M, VADDIREDDY H. A deep learning enabler for nonintrusive reduced order modeling of fluid flows[J]. Physics of Fluids, 2019, 31(8):085101.
[43] ALLA A, KUTZ J N. Nonlinear model order reduction via dynamic mode decomposition[J]. SIAM Journal on Scientific Computing, 2017, 39(5):B778-B796.
[44] HAN J, TAO J, WANG C. FlowNet:a deep learning framework for clustering and selection of streamlines and stream surfaces[J]. IEEE Transactions on Visualization and Computer Graphics, 2019, 26(4):1-1.
[45] OMATA N, SHIRAYAMA S. A novel method of low-dimensional representation for temporal behavior of flow fields using deep autoencoder[J]. AIP Advances, 2019, 9(1):015006.
[46] FONDA E, PANDEY A, SCHUMACHER J. Deep learning in turbulent convection networks[J]. Proceedings of the National Academy of Sciences, 2019, 116(18):8667-8672.
[47] LORE K G, STOECKLEIN D, DAVIES M. A deep learning framework for causal shape transformation[J]. Neural Networks, 2018, 98:305-317.
[48] KIM B, GÜNTHER T. Robust reference frame extraction from unsteady 2D vector fields with convolutional neural networks[J]. Computer Graphics Forum, 2019, 38(3):285-295.
[49] ZEILER M D, FERGUS R. Visualizing and understanding convolutional networks[M]//Computer Vision-ECCV 2014. Cham:Springer International Publishing, 2014:818-833.
[50] MURATA T, FUKAMI K, FUKAGATA K. Nonlinear mode decomposition with convolutional neural networks for fluid dynamics[J]. Journal of Fluid Mechanics, 2020, 882:A13.
[51] HADIKHANI P, BORHANI N, H. HASHEMI S M. Learning from droplet flows in microfluidic channels using deep neural networks[J]. Scientific Reports, 2019, 9(1):8114.
[52] TENNEY A S, GLAUSER M N, RUSCHER C J. Application of artificial neural networks to stochastic estimation and jet noise modeling[J]. AIAA Journal, 2020, 58(2):647-658.
[53] CHANG C W, DINH N T. Classification of machine learning frameworks for data-driven thermal fluid models[J]. International Journal of Thermal Sciences, 2019, 135:559-579.
[54] FUKAMI K, FUKAGATA K, TAIRA K. Assessment of supervised machine learning methods for fluid flows[J]. Theoretical and Computational Fluid Dynamics, 2020, 34(4):497-519.
[55] MIYANAWALA T P, JAIMAN R K. An efficient deep learning technique for the navier-stokes equations:application to unsteady wake flow dynamics[DB/OL]. arXiv e-prints:1710.09099,2017.
[56] BHATNAGAR S, AFSHAR Y, PAN S. Prediction of aerodynamic flow fields using convolutional neural networks[J]. Computational Mechanics, 2019, 64(2):525-545.
[57] YE S, ZHANG Z, SONG X. A flow feature detection method for modeling pressure distribution around a cylinder in non-uniform flows by using a convolutional neural network[J]. Scientific Reports, 2020, 10(1):4459.
[58] JIN X, CHENG P, CHEN W L. Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder[J]. Physics of Fluids, 2018, 30(4):047105.
[59] ZHU L, ZHANG W, KOU J. Machine learning methods for turbulence modeling in subsonic flows around airfoils[J]. Physics of Fluids, 2019, 31(1):015105.
[60] THUEREY N, WEISSENOW K, PRANTL L. Deep learning methods for reynolds-averaged navier-stokes simulations of airfoil flows[J]. AIAA Journal, 2020, 58(1):25-36.
[61] HUI X, BAI J, WANG H. Fast pressure distribution prediction of airfoils using deep learning[J]. Aerospace Science and Technology, 2020, 105:105949.
[62] GUO X, LI W, IORIO F. Convolutional neural networks for steady flow approximation[C]//Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York:ACM, 2016:481-490.
[63] SEKAR V, KHOO B C. Fast flow field prediction over airfoils using deep learning approach[J]. Physics of Fluids, 2019, 31(5):057103.
[64] UMETANI N. Exploring generative 3D shapes using autoencoder networks[C]//SIGGRAPH Asia 2017 Technical Briefs on-SA'17. New York:ACM Press, 2017:1-4.
[65] UMETANI N, BICKEL B. Learning three-dimensional flow for interactive aerodynamic design[J]. ACM Transactions on Graphics, 2018, 37(4):1-10.
[66] GAYMANN A, MONTOMOLI F. Deep neural network and monte carlo tree search applied to fluid-structure topology optimization[J]. Scientific Reports, 2019, 9(1):15916.
[67] SEKAR V, ZHANG M, SHU C. Inverse design of airfoil using a deep convolutional neural network[J]. AIAA Journal, 2019, 57(3):993-1003.
[68] CUNNINGHAM J, TUCKER C S. A Validation Neural Network (VNN) metamodel for predicting the performance of deep generative designs[C]//ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2018.
[69] HU L, ZHANG J, XIANG Y. Neural networks-based aerodynamic data modeling:A comprehensive review[J]. IEEE Access, 2020, 8:90805-90823.
[70] LIU B, TANG J, HUANG H. Deep learning methods for super-resolution reconstruction of turbulent flows[J]. Physics of Fluids, 2020, 32(2):025105.
[71] CAI S, LIANG J, GAO Q. Particle image velocimetry based on a deep learning motion estimator[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 69(6):3538-3554.
[72] CHU M, THUEREY N. Data-driven synthesis of smoke flows with CNN-based feature descriptors[J]. ACM Transactions on Graphics, 2017, 36(4):1-14.
[73] FUKAMI K, FUKAGATA K, TAIRA K. Super-resolution reconstruction of turbulent flows with machine learning[J]. Journal of Fluid Mechanics, 2019, 870:106-120.
[74] FERDIAN E, SUINESIAPUTRA A, DUBOWITZ D J. 4DFlowNet:super-resolution 4D flow MRI using deep learning and computational fluid dynamics[J]. Frontiers in Physics, 2020, 8.
[75] YANG C, YANG X, XIAO X. Data-driven projection method in fluid simulation[J]. Computer Animation and Virtual Worlds, 2016, 27(3-4):415-424.
[76] TOMPSON J, SCHLACHTER K, SPRECHMANN P. Accelerating Eulerian fluid simulation with convolutional networks[C]//PRECUP D, TEH Y W, ed. International Convention Centre. Sydney:PMLR, 2017:3424-3433.
[77] OZBAY A G, LAIZET S, TZIRAKIS P. Poisson CNN:Convolutional neural networks for the solution of the poisson equation with varying meshes and dirichlet boundary conditions[DB/OL]. arXiv e-prints:1910.08613, 2019.
[78] LONG Z, LU Y, MA X. PDE-Net:Learning PDEs from data[C]//35th International Conference on Machine Learning, 2018.
[79] LONG Z, LU Y, DONG B. PDE-Net 2.0:Learning PDEs from data with a numeric-symbolic hybrid deep network[J]. Journal of Computational Physics, 2019, 399:108925.
[80] GOODFELLOW I J, POUGET-ABADIE J, MIRZA M. Generative adversarial nets[C]//Advances in Neural Information Processing Systems 27(NIPS 2014), 2014.
[81] KARRAS T, AILA T, LAINE S. Progressive growing of gans for improved quality, stability, and variation[DB/OL]. arXiv eprints:1710.10196,2017.
[82] ISOLA P, ZHU J Y, ZHOU T. Image-to-image translation with conditional adversarial networks[Z]. 2016.
[83] WANG X, YU K, WU S. ESRGAN:Enhanced super-resolution generative adversarial networks[Z]. 2018.
[84] FARIMANI A B, GOMES J, PANDE V. Deep learning fluid mechanics[C]//70th Annual Meeting of the APS Division of Fluid Dynamics, 2017.
[85] LIU Y, WANG Y, DENG L. A novel in situ compression method for CFD data based on generative adversarial network[J]. Journal of Visualization, 2019, 22(1):95-108.
[86] WU H, LIU X, AN W. A deep learning approach for efficiently and accurately evaluating the flow field of supercritical airfoils[J]. Computers & Fluids, 2020, 198:104393.
[87] XIE Y, FRANZ E, CHU M. tempoGAN[J]. ACM Transactions on Graphics, 2018, 37(4):1-15.
[88] LEE J, LEE S, YOU D. Deep learning approach in multi-scale prediction of turbulent mixing-layer[Z]. 2018.
[89] LEE S, YOU D. Data-driven prediction of unsteady flow over a circular cylinder using deep learning[J]. Journal of Fluid Mechanics, 2019, 879:217-254.
[90] WU J, KASHINATH K, ALBERT A. Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems[J]. Journal of Computational Physics, 2020, 406:109209.
[91] LIN J, LENSINK K, HABER E. Fluid flow mass transport for generative networks[Z]. 2019.