智能赋能流体力学展望

doi:10.7527/S1000-6893.2020.24689

Abstract

Abstract: Artificial Intelligence (AI) is an advanced technology in the 21 st century. For researchers in related fields, rejuvenation of fluid mechanics in the age of intelligence is worth consideration. This paper proposes intelligence empowered fluid mechanics, explaining and summarizing its meaning, important topics, research progress, and research difficulties. The future development of intelligent fluid mechanics is also discussed. The research points out that the data generated in computational fluid dynamics or experiments are inherently big data, and how to use these data through machine learning methods, like the deep neural network, random forest, and reinforcement learning, to alleviate or even replace the dependence on human brain is a new research paradigm; at the theoretical and methodological level, main research topics cover machine learning of the governing equations and turbulence modeling, the intellectualization of dimensional and scaling analysis, as well as numerical simulation; there is also an urge to develop the intellectualization of flow feature extraction and data fusion from multiple sources through AI; in this branch, data mining of flow dynamics and intelligent fusion of multi-source aerodynamic data are mainly included; moreover, the development of multidisciplinary and multiphysics modeling for fluid mechanics is in urgent need in many engineering applications, involving modeling of multi-field coupling problems, multi-disciplinary intelligent optimization design and adaptive flow control.

Key words: turbulence modeling, data fusion, feature extraction, flow control, Artificial Intelligence (AI)

CLC Number:

V211.1⁺5

ZHANG Weiwei, KOU Jiaqing, LIU Yilang. Prospect of artificial intelligence empowered fluid mechanics[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(4): 524689-524689.

References

[1] 百度百科. 人工智能[EB/OL].[2020-09-22].https://baike.baidu.com/item/人工智能/9180?fr=aladdin. Baidu Baike. Artificial intelligence[EB/OL].[2020-09-22]. https://baike.baidu.com/item/人工智能/9180?fr=aladdin (in Chinese).
[2] BRUNTON S L, NOACK B R, KOUMOUTSAKOS P. Machine learning for fluid mechanics[J]. Annual Review of Fluid Mechanics, 2020, 52(1):477-508.
[3] DURAISAMY K, IACCARINO G, XIAO H. Turbulence modeling in the age of data[J]. Annual Review of Fluid Mechanics, 2019, 51(1):357-377.
[4] XIAO H, CINNELLA P. Quantification of model uncertainty in RANS simulations:A review[J]. Progress in Aerospace Sciences, 2019, 108:1-31.
[5] REN F, HU H, TANG H. Active flow control using machine learning:A brief review[J]. Journal of Hydrodynamics, 2020, 32(2):247-253.
[6] 张天姣, 钱炜祺, 周宇, 等. 人工智能与空气动力学结合的初步思考[J]. 航空工程进展, 2019, 10(1):1-11. ZHANG T J, QIAN W Q, ZHOU Y et al. Preliminary thoughts on the combination of artificial intelligence and aerodynamics[J]. Advances in Aeronautical Science and Engineering, 2019, 10(1):1-11(in Chinese).
[7] 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).
[8] DURIEZ T, BRUNTON S L, NOACK B R. Machine learning control-taming nonlinear dynamics and turbulence[M]. Berlin:Springer, 2017.
[9] 周志华. 机器学习[M]. 北京:清华大学出版社, 2016. ZHOU Z H. Machine learning[M]. Beijing:Tsinghua University Press, 2016(in Chinese).
[10] YARLANKI S, RAJENDRAN B, HAMANN H. Estimation of turbulence closure coefficients for data centers using machine learning algorithms[C]//Proceedings of the 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 2012.
[11] TRACEY B D, DURAISAMY K, ALONSO J J. A machine learning strategy to assist turbulence model development[C]//Proceedings of the 53rd AIAA Aerospace Sciences Meeting, 2015.
[12] ZHANG Z J, DURAISAMY K. Machine learning methods for data-driven turbulence modeling[C]//Proceedings of the 22nd AIAA Computational Fluid Dynamics Conference. Reston:AIAA, 2015.
[13] ARGYROPOULOS C D, MARKATOS N C. Recent advances on the numerical modelling of turbulent flows[J]. Applied Mathematical Modelling, 2015, 39(2):693-732.
[14] 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.
[15] BONGARD J, LIPSON H. Automated reverse engineering of nonlinear dynamical systems[J]. Proceedings of the National Academy of Sciences, 2007, 104(24):9943-9948.
[16] SCHMIDT M, LIPSON H. Distilling free-form natural laws from experimental data[J]. Science, 2009, 324(5923):81-85.
[17] KOZA J R. Genetic programming:on the programming of computers by means of natural selection[M]. Massachusetts:MIT Press, 1992.
[18] BRUNTON S L, PROCTOR J L, KUTZ J N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems[J]. Proceedings of the National Academy of Sciences, 2016, 113(5):3932-3937.
[19] CHANG H B, ZHANG D X. Machine learning subsurface flow equations from data[J]. Computational Geosciences, 2019, 23(5):895-910.
[20] SCHMELZER M, DWIGHT R P, CINNELLA P. Discovery of algebraic reynolds-stress models using sparse symbolic regression[J]. Flow Turbulence and Combustion, 2020, 104(2-3):579-603.
[21] LI S, KAISER E, LAIMA S, et al. Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems[J]. Physical Review E, 2019, 100(2-1):022220.
[22] RUDY S H, BRUNTON S L, PROCTOR J L, et al. Data-driven discovery of partial differential equations[J]. Science Advance, 2017, 3(4):e1602614.
[23] SCHAEFFER H. Learning partial differential equations via data discovery and sparse optimization[J]. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2017, 473(2197):20160446.
[24] LONG Z, LU Y, MA X, et al. PDE-Net:Learning PDEs from data[J]. Proceedings of Machine Learning Research, 2018, 80:3208-3216.
[25] LONG Z C, LU Y P, 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.
[26] CHANG H, ZHANG D. Identification of physical processes via combined data-driven and data-assimilation methods[J]. Journal of Computational Physics, 2019, 393:337-350.
[27] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Machine learning of linear differential equations using Gaussian processes[J]. Journal of Computational Physics, 2017, 348:683-693.
[28] RAISSI M, KARNIADAKIS G E. Hidden physics models:Machine learning of nonlinear partial differential equations[J]. Journal of Computational Physics, 2018, 357:125-141.
[29] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics informed deep learning (part i):Data-driven solutions of nonlinear partial differential equations[DB/OL]. Arxiv preprint:1711.10561,2017.
[30] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics informed deep learning (part Ⅱ):Data-driven discovery of nonlinear partial differential equations[DB/OL]. Arxiv preprint:1711.10561, 2017.
[31] ZHANG J, MA W J. Data-driven discovery of governing equations for fluid dynamics based on molecular simulation[J]. Journal of Fluid Mechanics, 2020, 892:A5.
[32] DURAISAMY K, ZHANG Z J, SINGH A P. New approaches in turbulence and transition modeling using data-driven techniques[C]//Proceedings of the 53rd AIAA Aerospace Sciences Meeting, 2015.
[33] SINGH A P, DURAISAMY K, ZHANG Z J. Augmentation of turbulence models using field inversion and machine learning[C]//Proceedings of the 55th AIAA Aerospace Sciences Meeting, 2017.
[34] 张亦知, 程诚, 范钇彤, 等. 基于物理知识约束的数据驱动式湍流模型修正及槽道湍流计算验证[J]. 航空学报, 2020, 41(3):123282. ZHANG Y Z, CHENG C, FAN Y T, et al. Data-driven correction of turbulence model with physics knowledge constrains in channel flow[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(3):123282(in Chinese).
[35] 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 E, 2017(2):034603.
[36] KUTZ J N. Deep learning in fluid dynamics[J]. Journal of Fluid Mechanics, 2017, 814:1-4.
[37] ZHU L, ZHANG W, KOU J, et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils[J]. Physics of Fluids, 2019, 31(1):015105.
[38] GAMAHARA M, HATTORI Y. Searching for turbulence models by artificial neural network[J]. Physical Review Fluids, 2017, 2(5):054604.
[39] MAULIK R, SAN O, RASHEED A, et al. Subgrid modelling for two-dimensional turbulence using neural networks[J]. Journal of Fluid Mechanics, 2019, 858:122-144.
[40] WANG Z, LUO K, LI D, et al. Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation[J]. Physics of Fluids, 2018, 30:125101.
[41] XIE C, WANG J, LI H, et al. Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence[J]. Physics of Fluids, 2019, 99(51):053113.
[42] ZHOU Z, HE G, WANG S, et al. Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network[J]. Computers & Fluids, 2019, 195:104319.
[43] EDELING W N, CINNELLA P, DWIGHT R P, et al. Bayesian estimates of parameter variability in the k-ε turbulence model[J]. Journal of Computational Physics, 2014, 258:73-94.
[44] CHEUNG S H, OLIVER T A, PRUDENCIO E E, et al. Bayesian uncertainty analysis with applications to turbulence modeling[J]. Reliability Engineering & System Safety, 2011, 96(9):1137-1149.
[45] OLIVER T A, MOSER R D. Bayesian uncertainty quantification applied to RANS turbulence models[J]. Journal of Physics:Conference Series, 2011, 318:042032.
[46] MARGHERI L, MELDI M, SALVETTI M V, et al. Epistemic uncertainties in RANS model free coefficients[J]. Computers & Fluids, 2014, 102:315-335.
[47] XIAO H, WANG J X, GHANEM R G. A random matrix approach for quantifying model-form uncertainties in turbulence modeling[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 313:941-965.
[48] DOW E, WANG Q. Quantification of structural uncertainties in the k-w turbulence model[C]//Proceedings of the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2012.
[49] PLATTEEUW P D A, LOEVEN G J A, BIJL H. Uncertainty quantification applied to the k-epsilon model of turbulence using the probabilistic collocation method[C]//Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2012.
[50] LING J, TEMPLETON J. Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty[J]. Physics of Fluids, 2015, 27(8):085103.
[51] LING J, KURZAWSKI A. Data-driven adaptive physics modeling for turbulence simulations[C]//Proceedings of the 23rd AIAA Computational Fluid Dynamics Conference, 2017.
[52] LING J. Using machine learning to understand and mitigate model form uncertainty in turbulence models[C]//Proceedings of the 14th International Conference on Machine Learning and Applications (ICMLA), 2015.
[53] SINGH A P, MEDIDA S, DURAISAMY K. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils[J]. AIAA Journal, 2017, 55(7):2215-2227.
[54] BECK A, FLAD D, MUNZ C D. Deep neural networks for data-driven LES closure models[J]. Journal of Computational Physics, 2019, 398:108910.
[55] WU J L, PATERSON E. Physics-informed machine learning approach for augmenting turbulence models:A comprehensive framework[J]. Physical Review Fluids, 2018, 3(7):074602.
[56] WEATHERITT J, SANDBERG R. A novel evolutionary algorithm applied to algebraic modifications of the RANS stress-strain relationship[J]. Journal of Computational Physics, 2016, 325:22-37.
[57] LING J, JONES R, TEMPLETON J. Machine learning strategies for systems with invariance properties[J]. Journal of Computational Physics, 2016, 318:22-35.
[58] KARPATNE A, WATKINS W, READ J, et al. Physics-guided neural networks (pgnn):An application in lake temperature modeling[DB/OL]. arXiv preprint:1710.11431,2017.
[59] ZHANG C, BENGIO S, HARDT M, et al. Understanding deep learning requires rethinking generalization[DB/OL]. arXiv preprint:1611.03530, 2017.
[60] NAGARAJAN V, KOLTER J Z. Uniform convergence may be unable to explain generalization in deep learning[C]//Proceedings of the Advances in Neural Information Processing Systems 32(NIPS 2019), 2019.
[61] WU J, XIAO H, SUN R, et al. Reynolds-averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned[J]. Journal of Fluid Mechanics, 2019, 869:553-586.
[62] 张伟伟, 朱林阳, 刘溢浪, 等. 机器学习在湍流模型构建中的应用进展[J]. 空气动力学学报, 2019, 37(3):444-451. ZHANG W W, ZHU L Y, LIU Y L, et al. Progresses in the application of machine learning in turbulence modeling[J]. Acta Aerodynamica Sinica, 2019, 37(3):444-451(in Chinese).
[63] BARENBLATT G I. Scaling, self-similarity, and intermediate asymptotics[M]. Cambridge:Cambridge University Press, 1996.
[64] LANGHAAR H L. Dimensional analysis and theory of models[M]. 1951.
[65] 谈庆明. 量纲分析[M]. 合肥:中国科技大学出版社, 2007. Tan Q M. Dimensional analysis[M]. Hefei:University of Science and Technology of China Press, 2007(in Chinese).
[66] 徐婕, 詹士昌, 田晓岑. 量纲分析的基本理论及其应用[J]. 大学物理, 2004, 23(5):54-58. XU J, ZHAN S C, TIAN X C. The basis theory of dimensional analysis and its application[J]. College Physics, 2004, 23(5):54-58(in Chinese).
[67] 佘振苏, 苏卫东. 湍流中的层次结构和标度律[J]. 力学进展, 1999, 29(3):289-303. SHE Z S, SU W D. Hierarchical structures and scalings in turbulence[J]. Advances in Mechanics, 1999, 29(3):289-303(in Chinese).
[68] KOLMOGOROV A N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers[J]. Proceedings of the Royal Society of London Series A:Mathematical and Physical Sciences, 1997, 434(1890):9-13.
[69] KOLMOGOROV A N. Dissipation of energy in the locally isotropic turbulence[J]. Doklady Akademii Nauk SSSR, 1941, 32:16-18.
[70] KOLMOGOROV A N. On degeneration of isotropic turbulence in an incompressible viscous liquid[J]. Doklady Akademii Nauk SSSR, 1991, 31:538-540.
[71] WANG Y, WILLIS S, TSOUTSOURAS V, et al. Deriving equations from sensor data using dimensional function synthesis[J]. ACM Transactions on Embedded Computing Systems, 2019, 18(5s):1-22.
[72] JOFRE L, DEL ROSARIO Z R, IACCARINO G. Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow[J]. International Journal of Multiphase Flow, 2020, 125:103198.
[73] MURARI A, VEGA J, MAZON D, et al. Machine learning for the identification of scaling laws and dynamical systems directly from data in fusion[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 2010, 623(2):850-854.
[74] LUO C, HU Z, ZHANG S L, et al. Adaptive space transformation:An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles[J]. Engineering Applications of Artificial Intelligence, 2015, 46:93-103.
[75] LUO C, ZHANG S L. Parse-matrix evolution for symbolic regression[J]. Engineering Applications of Artificial Intelligence, 2012, 25(6):1182-1193.
[76] SEKAR V, KHOO B C. Fast flow field prediction over airfoils using deep learning approach[J]. Physics of Fluids, 2019, 31(5):057103.
[77] FUKAMI K, FUKAGATA K, TAIRA K. Super-resolution reconstruction of turbulent flows with machine learning[J]. Journal of Fluid Mechanics, 2019, 870:106-120.
[78] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks:A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 2019, 378:686-707.
[79] RAISSI M, WANG Z, TRIANTAFYLLOU M S, et al. Deep learning of vortex-induced vibrations[J]. Journal of Fluid Mechanics, 2019, 861:119-137.
[80] RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics:Learning velocity and pressure fields from flow visualizations[J]. Science, 2020, 367(6481):1026-1030.
[81] JAGTAP A D, KHARAZMI E, KARNIADAKIS G E. Conservative physics-informed neural networks on discrete domains for conservation laws:Applications to forward and inverse problems[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 365:113028.
[82] MAO Z, JAGTAP A D, KARNIADAKIS G E. Physics-informed neural networks for high-speed flows[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 360:112789.
[83] ZHU Y, ZABARAS N, KOUTSOURELAKIS P-S, et al. Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data[J]. Journal of Computational Physics, 2019, 394:56-81.
[84] GENEVA N, ZABARAS N. Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks[J]. Journal of Computational Physics, 2020, 403:109056.
[85] KARUMURI S, TRIPATHY R, BILIONIS I, et al. Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks[J]. Journal of Computational Physics, 2020, 404:109120.
[86] SUN L, GAO H, PAN S, et al. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361:112732.
[87] WEI S, JIN X, LI H. General solutions for nonlinear differential equations:a rule-based self-learning approach using deep reinforcement learning[J]. Computational Mechanics, 2019, 64(5):1361-1374.
[88] FOURES D P G, DOVETTA N, SIPP D, et al. A data-assimilation method for Reynolds-averaged Navier Stokes-driven mean flow reconstruction[J]. Journal of Fluid Mechanics, 2014, 759:404-431.
[89] SYMON S, DOVETTA N, MCKEON B J, et al. Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil[J]. Experiments in Fluids, 2017, 58(5):61.
[90] SYMON S, SIPP D, SCHMID P J, et al. Mean and Unsteady Flow Reconstruction Using Data-Assimilation and Resolvent Analysis[J]. AIAA Journal, 2019, 58(2):575-588.
[91] KATO H, YOSHIZAWA A, UENO G, et al. A data assimilation methodology for reconstructing turbulent flows around aircraft[J]. Journal of Computational Physics, 2015, 283:559-581.
[92] KATO H, OBAYASHI S. Approach for uncertainty of turbulence modeling based on data assimilation technique[J]. Computers & Fluids, 2013, 85:2-7.
[93] LI Z, ZHANG H, BAILEY S C C, et al. A data-driven adaptive Reynolds-averaged Navier-Stokes k-ω model for turbulent flow[J]. Journal of Computational Physics, 2017, 345:111-131.
[94] DENG Z, HE C, WEN X, et al. Recovering turbulent flow field from local quantity measurement:turbulence modeling using ensemble-Kalman-filter-based data assimilation[J]. Journal of Visualization, 2018, 21(6):1043-1063.
[95] MONS V, CHASSAING J C, GOMEZ T, et al. Reconstruction of unsteady viscous flows using data assimilation schemes[J]. Journal of Computational Physics, 2016, 316:255-280.
[96] LABAHN J W, WU H, HARRIS S R, et al. Ensemble Kalman filter for assimilating experimental data into large-eddy simulations of turbulent flows[J]. Flow, Turbulence and Combustion, 2020, 104(4):861-893.
[97] LI Y, ZHANG J, DONG G, et al. Small-scale reconstruction in three-dimensional Kolmogorov flows using four-dimensional variational data assimilation[J]. Journal of Fluid Mechanics, 2020, 885:A9.
[98] YU J, HESTHAVEN J S. Flowfield reconstruction method using artificial neural network[J]. AIAA Journal, 2019, 57(2):482-498.
[99] CAI S, LIANG J, GAO Q, et al. Particle image velocimetry based on a deep learning motion estimator[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 69(6):3538-3554.
[100] XU P, BABANEZHAD M, YARMAND H, et al. Flow visualization and analysis of thermal distribution for the nanofluid by the integration of fuzzy c-means clustering ANFIS structure and CFD methods[J]. Journal of Visualization, 2020, 23(1):97-110.
[101] SANCHEZ-GONZALEZ A, GODWIN J, PFAFF T, et al. Learning to simulate complex physics with graph networks[DB/OL]. arXiv preprint:2002.09405, 2020.
[102] LIU Y, LU Y, WANG Y, et al. A CNN-based shock detection method in flow visualization[J]. Computers & Fluids, 2019, 184:1-9.
[103] DENG L, WANG Y, LIU Y, et al. A CNN-based vortex identification method[J]. Journal of Visualization, 2018, 22(1):65-78.
[104] RAY D, HESTHAVEN J S. An artificial neural network as a troubled-cell indicator[J]. Journal of Computational Physics, 2018, 367:166-191.
[105] RAY D, HESTHAVEN J S. Detecting troubled-cells on two-dimensional unstructured grids using a neural network[J]. Journal of Computational Physics, 2019, 397:108845.
[106] DISCACCIATI N, HESTHAVEN J S, RAY D. Controlling oscillations in high-order discontinuous Galerkin schemes using artificial viscosity tuned by neural networks[J]. Journal of Computational Physics, 2020, 409:109304.
[107] STEVENS B, COLONIUS T. Enhancement of shock-capturing methods via machine learning[J]. Theoretical and Computational Fluid Dynamics, 2020, 34(4):483-496.
[108] BARBAGALLO A, SIPP D, SCHMID P J. Closed-loop control of an open cavity flow using reduced-order models[J]. Journal of Fluid Mechanics, 2009, 641:1-50.
[109] LINDHORST K, HAUPT M C, HORST P. Efficient surrogate modelling of nonlinear aerodynamics in aerostructural coupling schemes[J]. AIAA Journal, 2014, 52(9):1952-1966.
[110] LIU Y, WANG G, YE Z. Dynamic mode extrapolation to improve the efficiency of dual time stepping method[J]. Journal of Computational Physics, 2018, 352:190-212.
[111] LIU Y, ZHANG W, KOU J. Mode multigrid-a novel convergence acceleration method[J]. Aerospace Science and Technology, 2019, 92:605-619.
[112] CHEN W, ZHANG W, LIU Y, et al. Accelerating the convergence of steady adjoint equations by dynamic mode decomposition[J]. Structural and Multidisciplinary Optimization, 2020, 62(2):747-756.
[113] LUMLEY J L. The structure of inhomogeneous turbulence[C]//Proceedings of the International Colloquium on the Fine Scale Structure of the Atmosphere and Its Influence on Radio Wave Propagation, 1967.
[114] SCHMID P J, SESTERHENN J. Dynamic mode decomposition of numerical and experimental data[C]//Proceedings of the Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008.
[115] ROWLEY C W, MEZIC' I, BAGHERI S, et al. Spectral analysis of nonlinear flows[J]. Journal of Fluid Mechanics, 2009, 641:115-127.
[116] SCHMID P J. Dynamic mode decomposition of numerical and experimental data[J]. Journal of Fluid Mechanics, 2010, 656:5-28.
[117] AUBRY N, HOLMES P, LUMLEY J L, et al. The dynamics of coherent structures in the wall region of a turbulent boundary layer[J]. Journal of Fluid Mechanics, 1988, 192:115-173.
[118] NOACK B R, AFANASIEV K, MORZYN'SKI M, et al. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake[J]. Journal of Fluid Mechanics, 2003, 497:335-363.
[119] ROWLEY C W, COLONIUS T, MURRAY R M. Model reduction for compressible flows using POD and Galerkin projection[J]. Physica D:Nonlinear Phenomena, 2004, 189(1-2):115-129.
[120] ÖSTH J, NOACK B R, KRAJNOVIC' S, et al. On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body[J]. Journal of Fluid Mechanics, 2014, 747:518-544.
[121] WALTON S, HASSAN O, MORGAN K. Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions[J]. Applied Mathematical Modelling, 2013, 37(20-21):8930-8945.
[122] WINTER M, BREITSAMTER C. Efficient unsteady aerodynamic loads prediction based on nonlinear system identification and proper orthogonal decomposition[J]. Journal of Fluids and Structures, 2016, 67:1-21.
[123] LUI 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.
[124] CHEN K K, TU J H, ROWLEY C W. Variants of dynamic mode decomposition:boundary condition, Koopman, and Fourier analyses[J]. Journal of Nonlinear Science, 2012, 22(6):887-915.
[125] WYNN A, PEARSON D S, GANAPATHISUBRAMANI B, et al. Optimal mode decomposition for unsteady flows[J]. Journal of Fluid Mechanics, 2013, 733:473-503.
[126] JOVANOVIĆ M R, SCHMID P J, NICHOLS J W. Sparsity-promoting dynamic mode decomposition[J]. Physics of Fluids, 2014, 26(2):024103.
[127] SAYADI T, SCHMID P J, RICHECOEUR F, et al. Parametrized data-driven decomposition for bifurcation analysis, with application to thermo-acoustically unstable systems[J]. Physics of Fluids, 2015, 27(3):037102.
[128] KOU J, ZHANG W. A criterion to select dominant modes of dynamic mode decomposition[J]. European Journal of Mechanics-B/Fluids, 2017, 62:109-129.
[129] PROCTOR J L, BRUNTON S L, KUTZ J N. Dynamic mode decomposition with control[J]. SIAM Journal on Applied Dynamical Systems, 2016, 15(1):142-161.
[130] ANNONI J, SEILER P. A method to construct reduced-order parameter-varying models[J]. International Journal of Robust and Nonlinear Control, 2017, 27(4):582-597.
[131] KOU J, ZHANG W. Dynamic mode decomposition with exogenous input for data-driven modeling of unsteady flows[J]. Physics of Fluids, 2019, 31(5):057106.
[132] NOACK B R, STANKIEWICZ W, MORZYN'SKI M, et al. Recursive dynamic mode decomposition of transient and post-transient wake flows[J]. Journal of Fluid Mechanics, 2016, 809:843-872.
[133] SIEBER M, PASCHEREIT C O, OBERLEITHNER K. Spectral proper orthogonal decomposition[J]. Journal of Fluid Mechanics, 2016, 792:798-828.
[134] 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).
[135] 高传强, 张伟伟. 机翼跨声速抖振数值模拟及模态分析[J]. 航空学报, 2019, 40(7):122597. GAO C Q, ZHANG W W. Numerical simulation and modal analysis of transonic buffet flow over wings[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(7):122597(in Chinese).
[136] 张扬, 张来平, 邓小刚, 等. 飞行器大攻角复杂流动的POD和DMD对比分析[J]. 气体物理, 2018, 3(5):30-40. ZHANG Y, ZHANG L P, DENG X G, et al. Pod and dmd analysis of complex separation flows over a aircraft model at high angle of attack[J]. Physics of Gases, 2018, 3(5):30-40(in Chinese).
[137] 胡佳伟, 王掩刚, 刘汉儒, 等. 压气机叶栅非定常分离流动的模态分解方法对比研究[J]. 西北工业大学学报, 2020, 38(1):121-129. HU J W, WANG Y G, LIU H R, et al. Comparative study on modal decomposition methods of unsteady separated flow in compressor cascade[J]. Journal of Northwestern Polytechnical University, 2020, 38(1):121-129(in Chinese).
[138] YU M, HUANG W X, XU C X. Data-driven construction of a reduced-order model for supersonic boundary layer transition[J]. Journal of Fluid Mechanics, 2019, 874:1096-1114.
[139] 寇家庆, 张伟伟. 动力学模态分解及其在流体力学中的应用[J]. 空气动力学学报, 2018, 36(2):163-179. KOU J Q, ZHANG W W. Dynamic mode decomposition and its applications in fluid dynamics[J]. Acta Aerodynamica Sinica, 2018, 36(2):163-179(In Chinese).
[140] KOOPMAN B O. Hamiltonian systems and transformation in Hilbert space[J]. Proceedings of the National Academy of Sciences, 1931, 17(5):315-318.
[141] MEZIĆ I. Spectral properties of dynamical systems, model reduction and decompositions[J]. Nonlinear Dynamics, 2005, 41(1):309-325.
[142] WILLIAMS M O, KEVREKIDIS I G, ROWLEY C W. A data-driven approximation of the Koopman operator:extending dynamic mode decomposition[J]. Journal of Nonlinear Science, 2015, 25(6):1307-1346.
[143] WILLIAMS M O, ROWLEY C W, KEVREKIDIS I G. A kernel-based method for data-driven Koopman spectral analysis[J]. Journal of Computational Dynamics, 2017, 2(2):247-265.
[144] KAISER E, NOACK B R, CORDIER L, et al. Cluster-based reduced-order modelling of a mixing layer[J]. Journal of Fluid Mechanics, 2014, 754:365-414.
[145] MIFSUD M. Reduced-order modelling for high-speed aerial weapon aerodynamics[D]. Cranfield:Cranfield University, 2008.
[146] FRANZ T, ZIMMERMANN R, GÖRTZ S, et al. Interpolation-based reduced-order modelling for steady transonic flows via manifold learning[J]. International Journal of Computational Fluid Dynamics, 2014, 28(3-4):106-121.
[147] EHLERT A, NAYERI C N, MORZYNSKI M, et al. Locally linear embedding for transient cylinder wakes[DB/OL]. Arxiv preprint:1906.07822, 2019.
[148] MILANO M, KOUMOUTSAKOS P. Neural network modeling for near wall turbulent flow[J]. Journal of Computational Physics, 2002, 182(1):1-26.
[149] MURATA T, FUKAMI K, FUKAGATA K. Nonlinear mode decomposition with convolutional neural networks for fluid dynamics[J]. Journal of Fluid Mechanics, 2020, 882:A13.
[150] HUANG J, LIU H, CAI W. Online in situ prediction of 3-D flame evolution from its history 2-D projections via deep learning[J]. Journal of Fluid Mechanics, 2019, 875:R2.
[151] 惠心雨, 袁泽龙, 白俊强, 等. 基于深度学习的非定常周期性流动预测方法[J]. 空气动力学学报, 2019, 37(3):462-469. HUI X Y, YUAN Z L, BAI J Q, et al. A method of unsteady periodic flow field prediction based on the deep learning[J]. Acta Aerodynamica Sinica, 2019, 37(3):462-469(in Chinese).
[152] 叶舒然, 张珍, 宋旭东, 等. 自动编码器在流场降阶中的应用[J]. 空气动力学学报, 2019, 37(3):498-504. YE S R, ZHANG Z, SONG X D, et al. Applications of autoencoder in reduced-order modeling of flow field[J]. Acta Aerodynamica Sinica, 2019, 37(3):498-504(in Chinese).
[153] CAI S, ZHOU S, XU C, et al. Dense motion estimation of particle images via a convolutional neural network[J]. Experiments in Fluids, 2019, 60(4):73.
[154] 蔡声泽, 许超, 高琪, 等. 基于深度神经网络的粒子图像测速算法[J]. 空气动力学学报, 2019, 37(3):455-461. CAI S Z, XU C, GAO Q, et al. Particle image velocimetry based on a deep neural network[J]. Acta Aerodynamica Sinica, 2019, 37(3):455-461(in Chinese).
[155] AMSALLEM D, FARHAT C. Interpolation method for adapting reduced-order models and application to aeroelasticity[J]. AIAA Journal, 2008, 46(7):1803-1813.
[156] DEGROOTE J, VIERENDEELS J, WILLCOX K E. Interpolation among reduced-order matrices to obtain parameterized models for design, optimization and probabilistic analysis[J]. International Journal for Numerical Methods in Fluids, 2010, 63(2):207-230.
[157] AMSALLEM D, ZAHR M J, FARHAT C. Nonlinear model order reduction based on local reduced-order bases[J]. International Journal for Numerical Methods in Engineering, 2012, 92(10):891-916.
[158] QUARTERONI A, MANZONI A, NEGRI F. Reduced basis methods for partial differential equations:an introduction[M]. Springer, 2015.
[159] CHINESTA F, LADEVÈZE P, CUETO E. A short review on model order reduction based on proper generalized decomposition[J]. Archives of Computational Methods in Engineering, 2011, 18(4):395.
[160] BUI-THANH T, WILLCOX K, GHATTAS O, et al. Goal-oriented, model-constrained optimization for reduction of large-scale systems[J]. Journal of Computational Physics, 2007, 224(2):880-896.
[161] DESHMUKH R, MCNAMARA J J, LIANG Z, et al. Model order reduction using sparse coding exemplified for the lid-driven cavity[J]. Journal of Fluid Mechanics, 2016, 808(10):189-223.
[162] ROWLEY C W. Model reduction for fluids, using balanced proper orthogonal decomposition[J]. International Journal of Bifurcation and Chaos, 2005, 15(3):997-1013.
[163] WILLCOX K, PERAIRE J. Balanced model reduction via the proper orthogonal decomposition[J]. AIAA Journal, 2002, 40(11):2323-2330.
[164] ALVERGUE L, BABAEE H, GU G, et al. Feedback stabilization of a reduced-order model of a jet in crossflow[J]. AIAA Journal, 2015, 53(9):2472-2481.
[165] ZHANG H, ROWLEY C W, DEEM E A, et al. Online dynamic mode decomposition for time-varying systems[J]. SIAM Journal on Applied Dynamical Systems, 2019, 18(3):1586-1609.
[166] PEHERSTORFER B, WILLCOX K. Dynamic data-driven reduced-order models[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 291(1):21-41.
[167] VENTURI D, KARNIADAKIS G E. Gappy data and reconstruction procedures for flow past a cylinder[J]. Journal of Fluid Mechanics, 2004, 519:315-336.
[168] WILLCOX K. Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition[J]. Computers & Fluids, 2006, 35(2):208-226.
[169] ASTRID P, WEILAND S, WILLCOX K, et al. Missing point estimation in models described by proper orthogonal decomposition[J]. IEEE Transactions on Automatic Control, 2008, 53(10):2237-2251.
[170] BARRAULT M, MADAY Y, NGUYEN N C, et al. An ‘empirical interpolation’ method:application to efficient reduced-basis discretization of partial differential equations[J]. Comptes Rendus Mathematique, 2004, 339(9):667-672.
[171] CHATURANTABUT S, SORENSEN D. Nonlinear model reduction via discrete empirical interpolation[J]. SIAM Journal on Scientific Computing, 2010, 32(5):2737-2764.
[172] BRUNTON S L, TU J H, BRIGHT I, et al. Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems[J]. SIAM Journal on Applied Dynamical Systems, 2014, 13(4):1716-1732.
[173] MANOHAR K, BRUNTON B W, KUTZ J N, et al. Data-driven sparse sensor placement for reconstruction:Demonstrating the benefits of exploiting known patterns[J]. IEEE Control Systems Magazine, 2018, 38(3):63-86.
[174] 何开锋, 钱炜祺, 汪清, 等. 数据融合技术在空气动力学研究中的应用[J]. 空气动力学学报, 2014, 32(6):777-782. HE K, QIAN W Q, WANG Q, et al. Application of data fusion technique in aerodynamics studies[J]. Acta Aerodynamica Sinica, 2014, 32(6):777-782(in Chinese).
[175] NAVON I M. Data assimilation for numerical weather prediction:A review[M]//Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Berlin, Heidelberg:Springer, 2009:21-65.
[176] FERNÁNDEZ-GODINO M G, PARK C, KIM N H, et al. Review of multi-fidelity models[DB/OL]. arXiv preprint:1609.07196, 2016.
[177] 杜涛, 陈闽慷, 李凰立, 等. 变精度模型(VCM)的自适应预处理方法研究[J]. 空气动力学学报, 2018, 36(2):315-319. DU T, CHEN M K, LI H L, et al. Research on adaptive preconditioning method for variable complexity model[J]. Acta Aerodynamica Sinica, 2018, 36(2):315-319(in Chinese).
[178] MOHAMMADI-AMIN M, ENTEZARI M M, ALIKHANI A. An efficient surrogate-based framework for aerodynamic database development of manned reentry vehicles[J]. Advances in Space Research, 2018, 62(5):997-1014.

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