In this paper, we conducted a selective review on the recent progress in physics insight and modeling of flexible cylinder flow-induced vibrations (FIVs). FIVs of circular cylinders include vortex-induced vibrations (VIVs) and wake-induced vibrations (WIVs), and they have been the center of the fluid-structure interaction (FSI) research in the past several decades due to the rich physics and the engineering significance. First, we summarized the new understanding of the structural response, hydrodynamics, and the impact of key structural properties for both the isolated and multiple circular cylinders. The complex FSI phenomena observed in experiments and numerical simulations are explained carefully via the analysis of the vortical wake topology. Following up with several critical future questions to address, we discussed the advancement of the artificial intelligent and machine learning (AI/ML) techniques in improving both the understanding and modeling of flexible cylinder FIVs. Though in the early stages, several AL/ML techniques have shown success, including auto-identification of key VIV features, physics-informed neural network in solving inverse problems, Gaussian process regression for automatic and adaptive VIV experiments, and multi-fidelity modeling in improving the prediction accuracy and quantifying the prediction uncertainties. These preliminary yet promising results have demonstrated both the opportunities and challenges for understanding and modeling of flexible cylinder FIVs in today's big data era.
References
1.
T.
Sarpkaya
, “Vortex-induced oscillations: A selective review
,” J. Appl. Mech.
46
, 241
–258
(1979
).2.
P. W.
Bearman
, “Vortex shedding from oscillating bluff bodies
,” Annu. Rev. Fluid Mech.
16
, 195
–222
(1984
).3.
T.
Sarpkaya
, “A critical review of the intrinsic nature of vortex-induced vibrations
,” J. Fluids Struct.
19
, 389
–447
(2004
).4.
C. H. K.
Williamson
and R.
Govardhan
, “Vortex-induced vibrations
,” Annu. Rev. Fluid Mech.
36
, 413
–455
(2004
).5.
R. D.
Gabbai
and H.
Benaroya
, “An overview of modeling and experiments of vortex-induced vibration of circular cylinders
,” J. Sound Vib.
282
, 575
–616
(2005
).6.
C. H. K.
Williamson
and R.
Govardhan
, “A brief review of recent results in vortex-induced vibrations
,” J. Wind Eng. Ind. Aerodyn.
96
, 713
–735
(2008
).7.
R. A.
Kumar
, C.
Sohn
, and B. H. L.
Gowda
, “Passive control of vortex-induced vibrations: An overview
,” Recent Pat. Mech. Eng.
1
, 1
–11
(2008
).8.
X.
Huang
, H.
Zhang
, and X.
Wang
, “An overview on the study of vortex-induced vibration of marine riser
,” Int. J. Mar. Sci.
27
, 95
–101
(2009
); available at https://en.cnki.com.cn/Article_en/CJFDTotal-DHHY200904014.htm.9.
P. W.
Bearman
, “Circular cylinder wakes and vortex-induced vibrations
,” J. Fluids Struct.
27
, 648
–658
(2011
).10.
X.
Wu
, F.
Ge
, and Y.
Hong
, “A review of recent studies on vortex-induced vibrations of long slender cylinders
,” J. Fluids Struct.
28
, 292
–308
(2012
).11.
J.
Wang
, D.
Fan
, and K.
Lin
, “A review on flow-induced vibration of offshore circular cylinders
,” J. Hydrodyn.
32
, 415
–440
(2020
).12.
J. M.
Dahl
, “Vortex-induced vibration of a circular cylinder with combined in-line and cross-flow motion
,” Ph.D. thesis (Massachusetts Institute of Technology
, 2008
).13.
J. K.
Vandiver
, D.
Allen
, and L.
Li
, “The occurrence of lock-in under highly sheared conditions
,” J. Fluids Struct.
10
, 555
–561
(1996
).14.
W.
Chen
, Q.
Zhang
, H.
Li
, and H.
Hu
, “An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow
,” J. Fluids Struct.
54
, 297
–311
(2015
).15.
C.
Ji
, Y.
Hua
, D.
Xu
, G.
Xing
, and W.
Chen
, “Numerical simulation of vortex-induced vibration of a flexible cylinder exposed to shear flow at different shear rates
,” Chin. J. Theor. Appl. Mech.
50
, 21
(2018
).16.
J.
Wu
, H.
Lie
, C. M.
Larsen
, S.
Liapis
, and R.
Baarholm
, “Vortex-induced vibration of a flexible cylinder: Interaction of the in-line and cross-flow responses
,” J. Fluids Struct.
63
, 238
–258
(2016
).17.
E. D.
Gedikli
, D.
Chelidze
, and J. M.
Dahl
, “Observed mode shape effects on the vortex-induced vibration of bending dominated flexible cylinders simply supported at both ends
,” J. Fluids Struct.
81
, 399
–417
(2018
).18.
Z.
Chen
and S.
Rhee
, “Effect of traveling wave on the vortex-induced vibration of a long flexible pipe
,” Appl. Ocean Res.
84
, 122
–132
(2019
).19.
J. K.
Vandiver
, V.
Jaiswal
, and V.
Jhingran
, “Insights on vortex-induced, traveling waves on long risers
,” J. Fluids Struct.
25
, 641
–653
(2009
).20.
J. K.
Vandiver
, L.
Ma
, and Z.
Rao
, “Revealing the effects of damping on the flow-induced vibration of flexible cylinders
,” J. Sound Vib.
433
, 29
–54
(2018
).21.
D.
Fan
, Z.
Wang
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow
,” J. Fluid Mech.
881
, 815
–858
(2019
).22.
P.
Voie
, J.
Wu
, T. L.
Resvanis
, C. M.
Larsen
, J. K.
Vandiver
, M. S.
Triantafyllou
, and R.
Baarholm
, “Consolidation of empirics for calculation of VIV response
,” in Proceedings of the 24th International Conference on Offshore Mechanics and Arctic Engineering
(American Society of Mechanical Engineers
, 2017
), Vol. 57649
.23.
M. S.
Triantafyllou
, G. S.
Triantafyllou
, Y. S.
Tein
, and B. D.
Ambrose
, “Pragmatic riser VIV analysis
,” in Offshore Technology Conference
(1999
).24.
C. M.
Larsen
, K.
Vikestad
, R.
Yttervik
, E.
Passano
, and G. S.
Baarholm
, Vivana Theory Manual
(Marintek
, Trondheim
, Norway
, 2001
).25.
J. R.
Chaplin
, P. W.
Bearman
, Y.
Cheng
, E.
Fontaine
, J. M. R.
Graham
, K.
Herfjord
, F. J.
Huera-Huarte
, M.
Isherwood
, K.
Lambrakos
, C. M.
Larsen
et al., “Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser
,” J. Fluids Struct.
21
, 25
–40
(2005
).26.
M. I.
Jordan
and T. M.
Mitchell
, “Machine learning: Trends, perspectives, and prospects
,” Science
349
, 255
–260
(2015
).27.
D.
Silver
, J.
Schrittwieser
, K.
Simonyan
, I.
Antonoglou
, A.
Huang
, A.
Guez
, T.
Hubert
, L.
Baker
, M.
Lai
, A.
Bolton
et al., “Mastering the game of go without human knowledge
,” Nature
550
, 354
–359
(2017
).28.
J.
Jumper
, R.
Evans
, A.
Pritzel
, T.
Green
, M.
Figurnov
, O.
Ronneberger
, K.
Tunyasuvunakool
, R.
Bates
, A.
Žídek
, A.
Potapenko
et al., “Highly accurate protein structure prediction with alphafold
,” Nature
596
, 583
–589
(2021
).29.
G.
Chandrashekar
and F.
Sahin
, “A survey on feature selection methods
,” Comput. Electr. Eng.
40
, 16
–28
(2014
).30.
J.
Wang
, J.
Wu
, and H.
Xiao
, “Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data
,” Phys. Rev. Fluids
2
, 034603
(2017
).31.
M.
Raissi
, P.
Perdikaris
, and G. E.
Karniadakis
, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
,” J. Comput. Phys.
378
, 686
–707
(2019
).32.
M.
Raissi
, A.
Yazdani
, and G. E.
Karniadakis
, “Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
,” Science
367
, 1026
–1030
(2020
).33.
C.
Park
, R. T.
Haftka
, and N. H.
Kim
, “Remarks on multi-fidelity surrogates
,” Struct. Multidiscip. Optim.
55
, 1029
–1050
(2017
).34.
D.
Brika
and A.
Laneville
, “Vortex-induced vibrations of a long flexible circular cylinder
,” J. Fluid Mech.
250
, 481
–508
(1993
).35.
J. R.
Chaplin
, P. W.
Bearman
, F. J.
Huera-Huarte
, and R. J.
Pattenden
, “Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current
,” J. Fluids Struct.
21
, 3
–24
(2005
).36.
F. J.
Huera-Huarte
, “Multi-mode vortex-induced vibrations of a flexible circular cylinder
,” Ph.D. thesis (University of London
, 2006
).37.
F. J.
Huera-Huarte
and P. W.
Bearman
, “Wake structures and vortex-induced vibrations of a long flexible cylinder—Part 1: Dynamic response
,” J. Fluids Struct.
25
, 969
–990
(2009
).38.
F. J.
Huera-Huarte
and P. W.
Bearman
, “Wake structures and vortex-induced vibrations of a long flexible cylinder–Part 2: Drag coefficients and vortex modes
,” J. Fluids Struct.
25
, 991
–1006
(2009
).39.
C.
Grouthier
, S.
Michelin
, Y.
Modarres-Sadeghi
, and E.
de Langre
, “Self-similar vortex-induced vibrations of a hanging string
,” J. Fluid Mech.
724
, R2
(2013
).40.
G. R.
Franzini
, C. P.
Pesce
, R. T.
Gonçalves
, A. L. C.
Fujarra
, and P.
Mendes
, “Experimental investigations on vortex-induced vibrations with a long flexible cylinder. Part I: Modal-amplitude analysis with a vertical configuration
,” in 11th International Conference on Flow-Induced Vibration
(2016
).41.
B.
Seyed-Aghazadeh
and Y.
Modarres-Sadeghi
, “Reconstructing the vortex-induced-vibration response of flexible cylinders using limited localized measurement points
,” J. Fluids Struct.
65
, 433
–446
(2016
).42.
E. D.
Gedikli
and J. M.
Dahl
, “Mode excitation hysteresis of a flexible cylinder undergoing vortex-induced vibrations
,” J. Fluids Struct.
69
, 308
–322
(2017
).43.
M. A.
Tognarelli
, S. T.
Slocum
, W. R.
Frank
, and R. B.
Campbell
, “Viv response of a long flexible cylinder in uniform and linearly sheared currents
,” in Offshore Technology Conference
(OnePetro
, 2004
).44.
A. D.
Trim
, H.
Braaten
, H.
Lie
, and M. A.
Tognarelli
, “Experimental investigation of vortex-induced vibration of long marine risers
,” J. Fluids Struct.
21
, 335
–361
(2005
).45.
Y.
Modarres-Sadeghi
, H.
Mukundan
, J. M.
Dahl
, F. S.
Hover
, and M. S.
Triantafyllou
, “The effect of higher harmonic forces on fatigue life of marine risers
,” J. Sound Vib.
329
, 43
–55
(2010
).46.
Y.
Modarres-Sadeghi
, F.
Chasparis
, M. S.
Triantafyllou
, M.
Tognarelli
, and P.
Beynet
, “Chaotic response is a generic feature of vortex-induced vibrations of flexible risers
,” J. Sound Vib.
330
, 2565
–2579
(2011
).47.
Y.
Gao
, S.
Fu
, J.
Wang
, L.
Song
, and Y.
Chen
, “Experimental study of the effects of surface roughness on the vortex-induced vibration response of a flexible cylinder
,” Ocean Eng.
103
, 40
–54
(2015
).48.
Y.
Gao
, S.
Fu
, Y.
Xiong
, Y.
Zhao
, and L.
Liu
, “Experimental study on response performance of vortex-induced vibration on a flexible cylinder
,” Ships Offshore Struct.
12
, 116
–134
(2017
).49.
M. L.
Facchinetti
, E.
De Langre
, and F.
Biolley
, “Coupling of structure and wake oscillators in vortex-induced vibrations
,” J. Fluids Struct.
19
, 123
–140
(2004
).50.
R.
Violette
, E.
De Langre
, and J.
Szydlowski
, “Computation of vortex-induced vibrations of long structures using a wake oscillator model: Comparison with DNS and experiments
,” Comput. Struct.
85
, 1134
–1141
(2007
).51.
N.
Srinil
and H.
Zanganeh
, “Modelling of coupled cross-flow/in-line vortex-induced vibrations using double duffing and van der pol oscillators
,” Ocean Eng.
53
, 83
–97
(2012
).52.
N.
Srinil
, P. A.
Opinel
, and F.
Tagliaferri
, “Empirical sensitivity of two-dimensional nonlinear wake–cylinder oscillators in cross-flow/in-line vortex-induced vibrations
,” J. Fluids Struct.
83
, 310
–338
(2018
).53.
D. J.
Newman
and G. E.
Karniadakis
, “A direct numerical simulation study of flow past a freely vibrating cable
,” J. Fluid Mech.
344
, 95
–136
(1997
).54.
C.
Evangelinos
and G. E.
Karniadakis
, “Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations
,” J. Fluid Mech.
400
, 91
–124
(1999
).55.
Y.
Bao
, R.
Palacios
, M.
Graham
, and S.
Sherwin
, “Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders
,” J. Comput. Phys.
321
, 1079
–1097
(2016
).56.
Y.
Bao
, H.
Zhu
, P.
Huan
, R.
Wang
, D.
Zhou
, Z.
Han
, R.
Palacios
, M.
Graham
, and S.
Sherwin
, “Numerical prediction of vortex-induced vibration of flexible riser with thick strip method
,” J. Fluids Struct.
89
, 166
–173
(2019
).57.
K.
Lin
and J.
Wang
, “Numerical simulation of vortex-induced vibration of long flexible risers using a SDVM-FEM coupled method
,” Ocean Eng.
172
, 468
–486
(2019
).58.
H.
Zheng
and J.
Wang
, “A numerical study on the vortex-induced vibration of flexible cylinders covered with differently placed buoyancy modules
,” J. Fluids Struct.
100
, 103174
(2021
).59.
K.
Lin
, D.
Fan
, and J.
Wang
, “Dynamic response and hydrodynamic coefficients of a cylinder oscillating in crossflow with an upstream wake interference
,” Ocean Eng.
209
, 107520
(2020
).60.
K.
Raghavan
and M. M.
Bernitsas
, “Experimental investigation of reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports
,” Ocean Eng.
38
, 719
–731
(2011
).61.
Y.
Wang
, D.
Gao
, and J.
Fang
, “Coupled dynamic analysis of deepwater drilling riser under combined forcing and parametric excitation
,” J. Nat. Gas Sci. Eng.
27
, 1739
–1747
(2015
).62.
G.
Riches
, R.
Martinuzzi
, and C.
Morton
, “Proper orthogonal decomposition analysis of a circular cylinder undergoing vortex-induced vibrations
,” Phys. Fluids
30
, 105103
(2018
).63.
R.
Bourguet
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow
,” J. Fluid Mech.
717
, 361
–375
(2013
).64.
N.
Jauvtis
and C. H. K.
Williamson
, “The effect of two degrees of freedom on vortex-induced vibration at low mass and damping
,” J. Fluid Mech.
509
, 23
–62
(2004
).65.
H.
Zheng
, J. M.
Dahl
, Y.
Modarres-Sadeghi
, and M. S.
Triantafyllou
, “Coupled inline-cross flow vortex-induced vibration hydrodynamic coefficients database
,” in Proceedings of the 33th OMAE Conference
(American Society of Mechanical Engineers
, 2014
).66.
D.
Fan
and M. S.
Triantafyllou
, “Vortex-induced vibration of riser with low span to diameter ratio buoyancy modules
,” in The 27th International Ocean and Polar Engineering Conference
(International Society of Offshore and Polar Engineers
, 2017
).67.
H.
Braaten
and H.
Lie
, “NDP riser high mode VIV tests
,” Report No. 512394.00.01 (Norwegian Marine Technology Research Institute
, 2004
).68.
Z.
Wang
, D.
Fan
, and M. S.
Triantafyllou
, “Illuminating the complex role of the added mass during vortex induced vibration
,” Phys. Fluids
33
, 085120
(2021
).69.
J. K.
Vandiver
, “Drag coefficients of long flexible cylinders
,” in Offshore Technology Conference
(OnePetro
, 1983
).70.
J. K.
Vandiver
and J.
Jong
, “The relationship between in-line and cross-flow vortex-induced vibration of cylinders
,” J. Fluids Struct.
1
, 381
–399
(1987
).71.
R.
Bruschi
, G.
Buresti
, A.
Castoldi
, and E.
Migliavacca
, “Vortex shedding oscillations for submarine pipelines: Comparison between full-scale experiments and analytical models
,” in 14th Offshore Technology Conference
(Offshore Technology Conference
, 1982
), Vol. 4232
.72.
F.
Webster
, “Vertical profiles of horizontal ocean currents
,” Deep Sea Res. Oceanogr. Abstr.
16
, 85
–98
(1969
).73.
F.
Rowe
and J.
Young
, “An ocean current profiler using Doppler sonar
,” in OCEANS'79
(IEEE
, 1979
), pp. 292
–297
.74.
Y.
Kim
, J. K.
Vandiver
, and R.
Holler
, “Vortex-induced vibration and drag coefficients of long cables subjected to sheared flows
,” J. Energy Resour. Technol.
108
, 77
–83
(1986
).75.
J. K.
Vandiver
and A.
Marcollo
, “High mode number VIV experiments
,” in IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments: Proceedings of the IUTAM Symposium
(Springer
, 2003
), pp. 211
–231
.76.
J. K.
Vandiver
, H.
Marcollo
, S.
Swithenbank
, and V.
Jhingran
, “High mode number vortex-induced vibration field experiments
,” in Offshore Technology Conference
(OnePetro
, 2005
).77.
J. K.
Vandiver
, S. B.
Swithenbank
, V.
Jaiswal
, and V.
Jhingran
, “Fatigue damage from high mode number vortex-induced vibration
,” in Proceedings of the 25th OMAE Conference
(2006
).78.
H.
Marcollo
, H.
Chaurasia
, and J. K.
Vandiver
, “Phenomena observed in VIV bare riser field tests
,” in International Conference on Offshore Mechanics and Arctic Engineering
(ASME
, OMAE
, 2007
), Vol. 4269
, pp. 989
–995
.79.
P. K.
Stansby
, “The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows
,” J. Fluid Mech.
74
, 641
–665
(1976
).80.
D.
Allen
, E.
Dension
, and J.
Bos
, “Vortex-induced vibration of cylindrical structures in sheared flow
” (Shell and MIT
, 1992
).81.
H.
Lie
, K.
Mo
, and J. K.
Vandiver
, “VIV model test of a bare-and a staggered buoyancy riser in a rotating rig
,” in Offshore Technology Conference
(OnePetro
, 1998
).82.
D.
Lucor
, L.
Imas
, and G. E.
Karniadakis
, “Vortex dislocations and force distribution of long flexible cylinders subjected to sheared flows
,” J. Fluids Struct.
15
, 641
–650
(2001
).83.
N.
Srinil
, “Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities
,” J. Fluids Struct.
26
, 1098
–1122
(2010
).84.
N.
Srinil
, “Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents
,” Appl. Ocean Res.
33
, 41
–53
(2011
).85.
R.
Bourguet
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “Vortex-induced vibrations of a long flexible cylinder in shear flow
,” J. Fluid Mech.
677
, 342
–382
(2011
).86.
R.
Bourguet
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows
,” J. Fluids Struct.
41
, 33
–42
(2013
).87.
P. W.
Bearman
, M. J.
Downie
, J. M. R.
Graham
, and E. D.
Obasaju
, “Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers
,” J. Fluid Mech.
154
, 337
–356
(1985
).88.
C. H. K.
Williamson
, “Fluid forces on a small cylinder in the presence of a large cylinder in relative oscillatory flow
,” Appl. Ocean Res.
7
, 124
–127
(1985
).89.
T.
Sarpkaya
, “Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers
,” J. Fluid Mech.
165
, 61
–71
(1986
).90.
D.
Fan
, X.
Zhang
, M. S.
Triantafyllou
et al., “Drag coefficient enhancement of dual cylinders in oscillatory flow
,” in The 27th International Ocean and Polar Engineering Conference
(International Society of Offshore and Polar Engineers
, 2017
).91.
D.
Zhang
, Xa
Fan
, D.
Wan
et al., “Numerical study of oscillatory dual cylinders in tandem arrangement
,” in Proceedings of the Twenty-Seventh (2017) International Ocean and Polar Engineering Conference San Francisco, CA
(2017
).92.
S.
Fu
, J.
Wang
, R.
Baarholm
, J.
Wu
, and C. M.
Larsen
, “Features of vortex-induced vibration in oscillatory flow
,” J. Offshore Mech. Arct. Eng.
136
, 011801
(2014
).93.
J.
Wang
, S.
Xiang
, S.
Fu
, P.
Cao
, J.
Yang
, and J.
He
, “Experimental investigation on the dynamic responses of a free-hanging water intake riser under vessel motion
,” Mar. Struct.
50
, 1
–19
(2016
).94.
J.
Wang
, S.
Fu
, J.
Wang
, H.
Li
, and M. C.
Ong
, “Experimental investigation on vortex-induced vibration of a free-hanging riser under vessel motion and uniform current
,” J. Offshore Mech. Arct. Eng.
139
(4
), 041703
(2017
).95.
T. L.
Resvanis
, “Vortex-induced vibration of flexible cylinders in time-varying flows
,” Ph.D. thesis (Massachusetts Institute of Technology
, 2014
).96.
C. H. K.
Williamson
, “Vortex dynamics in the cylinder wake
,” Annu. Rev. Fluid Mech.
28
, 477
–539
(1996
).97.
M. J.
Thorsen
, S.
Sævik
, and C. M.
Larsen
, “Time domain simulation of vortex-induced vibrations in stationary and oscillating flows
,” J. Fluids Struct.
61
, 1
–19
(2016
).98.
J. V.
Ulveseter
, M. J.
Thorsen
, S.
Sævik
, and C. M.
Larsen
, “Time domain simulation of riser VIV in current and irregular waves
,” Mar. Struct.
60
, 241
–260
(2018
).99.
Z.
Lu
, S.
Fu
, M.
Zhang
, and H.
Ren
, “An efficient time-domain prediction model for vortex-induced vibration of flexible risers under unsteady flows
,” Mar. Struct.
64
, 492
–519
(2019
).100.
W.
Xu
, Y.
Ma
, C.
Ji
, and C.
Sun
, “Laboratory measurements of vortex-induced vibrations of a yawed flexible cylinder at different yaw angles
,” Ocean Eng.
154
, 27
–42
(2018
).101.
W.
Xu
, Y.
Luan
, Q.
Han
, C.
Ji
, and A.
Cheng
, “The effect of yaw angle on VIV suppression for an inclined flexible cylinder fitted with helical strakes
,” Appl. Ocean Res.
67
, 263
–276
(2017
).102.
L.
Ma
, “Using superposition of undamped modes to model non-orthogonally damped systems
,” Ph.D. thesis (Massachusetts Institute of Technology
, 2017
).103.
L.
Ma
, T. L.
Resvanis
, and J. K.
Vandiver
, “Using machine learning to identify important parameters for flow-induced vibration
,” in International Conference on Offshore Mechanics and Arctic Engineering
(American Society of Mechanical Engineers
, 2020
), Vol. 84355
.104.
L.
Ma
, “Understanding flow-induced vibration via a physics-constrained, data-driven approach
,” Ph.D. thesis (Massachusetts Institute of Technology
, 2021
).105.
Z.
Wang
, D.
Fan
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “A large-eddy simulation study on the similarity between free vibrations of a flexible cylinder and forced vibrations of a rigid cylinder
,” J. Fluids Struct.
101
, 103223
(2021
).106.
Y.
Chen
, S.
Fu
, Y.
Xu
, and D.
Fan
, “High order force components of a near-wall circular cylinder oscillating in transverse direction in a steady current
,” Ocean Eng.
74
, 37
–47
(2013
).107.
J. L.
Garrec
, D.
Fan
, B.
Wu
, and M. S.
Triantafyllou
, “Experimental investigation of cross flow-inline coupled vortex-induced vibration on riser with finite length buoyancy module
,” in OCEANS 2016 MTS/IEEE Monterey
(IEEE
, 2016
), pp. 1–7.108.
B.
Wu
, J. L.
Garrec
, D.
Fan
, and M. S.
Triantafyllou
, “Kill line model cross flow inline coupled vortex-induced vibration
,” in Proceedings of the 36th OMAE Conference
(American Society of Mechanical Engineers
, 2017
), Vol. 57649
.109.
F. J.
Huera-Huarte
, P. W.
Bearman
, and J. R.
Chaplin
, “On the force distribution along the axis of a flexible circular cylinder undergoing multi-mode vortex-induced vibrations
,” J. Fluids Struct.
22
, 897
–903
(2006
).110.
G.
Tang
, L.
Lu
, B.
Teng
, H.
Park
, J.
Song
, and J.
Zhang
, “Identification of hydrodynamic coefficients from experiment of vortex-induced vibration of slender riser model
,” Sci. China Technol. Sci.
54
, 1894
–1905
(2011
).111.
J.
Wu
, “Hydrodynamic force identification from stochastic vortex induced vibration experiments with slender beams
,” Ph.D. thesis (Norwegian University of Science and Technology
, 2011
).112.
L.
Song
, S.
Fu
, J.
Cao
, L.
Ma
, and J.
Wu
, “An investigation into the hydrodynamics of a flexible riser undergoing vortex-induced vibration
,” J. Fluids Struct.
63
, 325
–350
(2016
).113.
Q.
Han
, Y.
Ma
, W.
Xu
, D.
Fan
, and E.
Wang
, “Hydrodynamic characteristics of an inclined slender flexible cylinder subjected to vortex-induced vibration
,” Inter. J. Mech. Sci.
148
, 352
–365
(2018
).114.
Z.
Rao
, T. L.
Resvanis
, and J. K.
Vandiver
, “The identification of power-in region in vortex-induced vibration of flexible cylinders
,” in Proceedings of the 33th OMAE Conference
(American Society of Mechanical Engineers
, 2014
), Vol. 45400
115.
D.
Fan
, L.
Yang
, Z.
Wang
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “Reinforcement learning for bluff body active flow control in experiments and simulations
,” Proc. Natl. Acad. U. S. A.
117
, 26091
–26098
(2020
).116.
D.
Fan
, G.
Jodin
, T. R.
Consi
, L.
Bonfiglio
, Y.
Ma
, L. R.
Keyes
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “A robotic intelligent towing tank for learning complex fluid-structure dynamics
,” Sci. Rob.
4
, eaay5063
(2019
).117.
R.
Bourguet
, Y.
Modarres-Sadeghi
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “Wake-body resonance of long flexible structures is dominated by counterclockwise orbits
,” Phys. Rev. Lett.
107
, 134502
(2011
).118.
Z. A.
Bangash
and F. J.
Huera-Huarte
, “On the flow around the node to anti-node transition of a flexible cylinder undergoing vortex-induced vibrations
,” Phys. Fluids
27
, 065112
(2015
).119.
H.
Zhu
, D.
Zhou
, Y.
Bao
, R.
Wang
, J.
Lu
, D.
Fan
, and Z.
Han
, “Wake characteristics of stationary catenary risers with different incoming flow directions
,” Ocean Eng.
167
, 142
–155
(2018
).120.
Z.
Zhang
, C.
Ji
, M. M.
Alam
, and D.
Xu
, “Dns of vortex-induced vibrations of a yawed flexible cylinder near a plane boundary
,” Wind Struct.
30
, 465
–474
(2020
).121.
C.
Ji
, Z.
Peng
, M. M.
Alam
, W.
Chen
, D.
Xu
et al., “Vortex-induced vibration of a long flexible cylinder in uniform cross-flow
,” Wind Struct.
26
, 267
–277
(2018
).122.
Z.
Zhang
, C.
Ji
, and D.
Xu
, “Temporal and spatial evolution of vortex shedding for flow around a cylinder close to a wall
,” Ocean Eng.
228
, 108964
(2021
).123.
Z.
Zhang
, C.
Ji
, W.
Chen
, Y.
Hua
, and N.
Srinil
, “Influence of boundary layer thickness and gap ratios on three-dimensional flow characteristics around a circular cylinder in proximity to a bottom plane
,” Ocean Eng.
226
, 108858
(2021
).124.
C.
Ji
, Z.
Zhang
, D.
Xu
, and N.
Srinil
, “Direct numerical simulations of horizontally oblique flows past three-dimensional circular cylinder near a plane boundary
,” J. Offshore Mech. Arct. Eng.
142
(5
), 051903
(2020
).125.
S.
Zhao
, C.
Ji
, Z.
Sun
, H.
Yu
, and Z.
Zhang
, “Effect of the yaw angle and spanning length on flow characteristics around a near-wall cylindrical structure
,” Ocean Eng.
235
, 109340
(2021
).126.
R.
Bourguet
, G. E.
Karniadakis
, and M. S.
Triantafyllou
, “On the validity of the independence principle applied to the vortex-induced vibrations of a flexible cylinder inclined at 60
,” J. Fluids Struct.
53
, 58
–69
(2015
).127.
128.
R. N.
Govardhan
and C. H. K.
Williamson
, “Defining the ‘modified griffin plot’ in vortex-induced vibration: Revealing the effect of Reynolds number using controlled damping
,” J. Fluid Mech.
561
, 147
–180
(2006
).129.
H.
Marcollo
, T.
Resvanis
, C.
Dillon
, A.
Kilner
, and J.
Vandiver
, Shear7 v4.10 User Guide
(Massachusetts Institute of Technology
, Cambridge, MA
, 2018
).130.
J. K.
Vandiver
and L.
Ma
, “Does more tension reduce VIV?
” in International Conference on Offshore Mechanics and Arctic Engineering
(American Society of Mechanical Engineers
, 2017
), Vol. 57700
.131.
Y.
Kim
, “Vortex-induced responses and drag coefficients of long cables in ocean current
,” Ph.D. thesis (Massachusetts Institute of Technology
, 1985
).132.
J.
Wu
, D.
Yin
, H.
Lie
, S.
Riemer-Sørensen
, S.
Sævik
, and M. S.
Triantafyllou
, “Improved VIV response prediction using adaptive parameters and data clustering
,” J. Mar. Sci. Eng.
8
, 127
(2020
).133.
B.
Seyed-Aghazadeh
, M.
Edraki
, and Y.
Modarres-Sadeghi
, “Effects of boundary conditions on vortex-induced vibration of a fully submerged flexible cylinder
,” Exp. Fluids
60
, 38
(2019
).134.
C.
Grouthier
, S.
Michelin
, R.
Bourguet
, Y.
Modarres-Sadeghi
, and E.
De Langre
, “On the efficiency of energy harvesting using vortex-induced vibrations of cables
,” J. Fluids Struct.
49
, 427
–440
(2014
).135.
G. R. S.
Assi
, P. W.
Bearman
, and J. R.
Meneghini
, “On the wake-induced vibration of tandem circular cylinders: The vortex interaction excitation mechanism
,” J. Fluid Mech.
661
, 365
–401
(2010
).136.
J.
Wang
and D.
Fan
, “An active learning strategy to study the flow control of a stationary cylinder with two asymmetrically attached rotating cylinders
,” in The 30th ISOPE Conference
(OnePetro
, 2020
).137.
D.
Fan
, L.
Yang
, Z.
Wang
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “Deep reinforcement learning for bluff body active flow control in experiments and simulations
,” in APS Division of Fluid Dynamics Meeting Abstracts
(2020
).138.
M. M.
Zdravkovich
, “Review of interference-induced oscillations in flow past two parallel circular cylinders in various arrangements
,” J. Wind. Eng. Ind.
28
, 183
–199
(1988
).139.
F. J.
Huera-Huarte
and P. W.
Bearman
, “Vortex and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with near wake interference
,” J. Fluids Struct.
27
, 193
–211
(2011
).140.
F. J.
Huera-Huarte
and M.
Gharib
, “Vortex-and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with far wake interference
,” J. Fluids Struct.
27
, 824
–828
(2011
).141.
W.
Xu
, Y.
Ma
, A.
Cheng
, and H.
Yuan
, “Experimental investigation on multi-mode flow-induced vibrations of two long flexible cylinders in a tandem arrangement
,” Int. J. Mech. Sci.
135
, 261
–278
(2018
).142.
W.
Xu
, Y.
Li
, W.
Ma
, K.
Liang
, and Y.
Yu
, “Effects of spacing ratio on the fiv fatigue damage characteristics of a pair of tandem flexible cylinders
,” Appl. Ocean Res.
102
, 102299
(2020
).143.
A.
Bokaian
and F.
Geoola
, “Wake-induced galloping of two interfering circular cylinders
,” J. Fluid Mech.
146
, 383
–415
(1984
).144.
F. S.
Hover
and M. S.
Triantafyllou
, “Galloping response of a cylinder with upstream wake interference
,” J. Fluids Struct.
15
, 503
–512
(2001
).145.
G. R. S.
Assi
, P. W.
Bearman
, B. S.
Carmo
, J. R.
Meneghini
, S. J.
Sherwin
, and R. H. J.
Willden
, “The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair
,” J. Fluid Mech.
718
, 210
–245
(2013
).146.
H.
Jing
, F.
Huang
, X.
He
, and C.
Cai
, “Wake-induced vibrations of tandem flexible cable models in a wind tunnel
,” Ocean Eng.
233
, 109188
(2021
).147.
R.
King
and D. J.
Johns
, “Wake interaction experiments with two flexible circular cylinders in flowing water
,” J. Sound Vib.
45
, 259
–283
(1976
).148.
K.
Lin
, J.
Wang
, D.
Fan
, and M. S.
Triantafyllou
, “Flow-induced cross-flow vibrations of long flexible cylinder with an upstream wake interference
,” Phys. Fluids
33
, 065104
(2021
).149.
D. W.
Allen
and D. L.
Henning
, “Vortex-induced vibration current tank tests of two equal-diameter cylinders in tandem
,” J. Fluids Struct.
17
, 767
–781
(2003
).150.
F. J.
Huera-Huarte
, Z. A.
Bangash
, and L. M.
González
, “Multi-mode vortex and wake-induced vibrations of a flexible cylinder in tandem arrangement
,” J. Fluids Struct.
66
, 571
–588
(2016
).151.
H.
Liu
, F.
Wang
, G.
Jiang
, X.
Guo
, and H.
Li
, “Laboratory measurements of vortex-and wake-induced vibrations of a tandem arrangement of two flexible risers
,” China Ocean Eng.
30
, 47
–56
(2016
).152.
B.
Seyed-Aghazadeh
, N.
Anderson
, and S.
Dulac
, “Flow-induced vibration of high-mass ratio isolated and tandem flexible cylinders with fixed boundary conditions
,” J. Fluids Struct.
103
, 103276
(2021
).153.
P.
Jiang
, Z.
Li
, L.
Feng
, Y.
Wang
, L.
Liu
, and H.
Guo
, “Experimental investigation on the VIV of two side-by-side risers fitted with triple helical strakes under coupled interference effect
,” J. Fluids Struct.
101
, 103202
(2021
).154.
F. J.
Huera-Huarte
and M.
Gharib
, “Flow-induced vibrations of a side-by-side arrangement of two flexible circular cylinders
,” J. Fluids Struct.
27
, 354
–366
(2011
).155.
B.
Sanaati
and N.
Kato
, “A study on the proximity interference and synchronization between two side-by-side flexible cylinders
,” Ocean Eng.
85
, 65
–79
(2014
).156.
W.
Xu
, Y.
Li
, K.
Jia
, and Y.
Yu
, “Fiv induced fatigue damage of two side-by-side flexible cylinders in a uniform flow
,” Ocean Eng.
217
, 107898
(2020
).157.
D.
Brika
and A.
Laneville
, “The flow interaction between a stationary cylinder and a downstream flexible cylinder
,” J. Fluids Struct.
13
, 579
–606
(1999
).158.
W.
Xu
, A.
Cheng
, Y.
Ma
, and X.
Gao
, “Multi-mode flow-induced vibrations of two side-by-side slender flexible cylinders in a uniform flow
,” Mar. Struct.
57
, 219
–236
(2018
).159.
W.
Xu
, W.
Qin
, and Y.
Yu
, “Flow-induced vibration of two identical long flexible cylinders in a staggered arrangement
,” Int. J. Mech. Sci.
180
, 105637
(2020
).160.
W.
Xu
, Q.
Zhang
, J.
Lai
, Q.
Wang
, and Y.
Yu
, “Flow-induced vibration of two staggered flexible cylinders with unequal diameters
,” Ocean Eng.
211
, 107523
(2020
).161.
Q.
Han
, Y.
Ma
, W.
Xu
, and S.
Zhang
, “An experimental study on the hydrodynamic features of two side-by-side flexible cylinders undergoing flow-induced vibrations in a uniform flow
,” Mar. Struct.
61
, 326
–342
(2018
).162.
E.
Wang
, Q.
Xiao
, Q.
Zhu
, and A.
Incecik
, “The effect of spacing on the vortex-induced vibrations of two tandem flexible cylinders
,” Phys. Fluids
29
, 077103
(2017
).163.
H.
Chen
, C.
Chen
, and K.
Huang
, “CFD simulation of vortex-induced and wake-induced vibrations of dual vertical risers
,” in The 23rd ISOPE Conference
(OnePetro
, 2013
).164.
A.
Krizhevsky
, I.
Sutskever
, and G. E.
Hinton
, “Imagenet classification with deep convolutional neural networks
,” Adv. Neural Inf. Process. Syst.
25
, 1097
–1105
(2012
).165.
K. R.
Chowdhary
, “Natural language processing
,” Fundamentals Artificial Intelligence
(Spring Nature
, 2020
), pp. 603
–649
.166.
O.
Vinyals
, I.
Babuschkin
, W. M.
Czarnecki
, M.
Mathieu
, A.
Dudzik
, J.
Chung
, D. H.
Choi
, R.
Powell
, T.
Ewalds
, P.
Georgiev
et al., “Grandmaster level in Starcraft II using multi-agent reinforcement learning
,” Nature
575
, 350
–354
(2019
).167.
S. L.
Brunton
, B. R.
Noack
, and P.
Koumoutsakos
, “Machine learning for fluid mechanics
,” Annu. Rev. Fluid Mech.
52
, 477
–508
(2020
).168.
M. P.
Brenner
, J. D.
Eldredge
, and J. B.
Freund
, “Perspective on machine learning for advancing fluid mechanics
,” Phys. Rev. Fluids
4
, 100501
(2019
).169.
K.
Fukami
, K.
Fukagata
, and K.
Taira
, “Assessment of supervised machine learning methods for fluid flows
,” Theor. Comput. Fluid. Dyn.
34
, 497
–519
(2020
).170.
F.
Ren
, C.
Wang
, and H.
Tang
, “Active control of vortex-induced vibration of a circular cylinder using machine learning
,” Phys. Fluids
31
, 093601
(2019
).171.
F.
Ren
, C.
Wang
, and H.
Tang
, “Bluff body uses deep-reinforcement-learning trained active flow control to achieve hydrodynamic stealth
,” Phys. Fluids
33
, 093602
(2021
).172.
Y.-F.
Mei
, C.
Zheng
, N.
Aubry
, M.-G.
Li
, W.-T.
Wu
, and X.
Liu
, “Active control for enhancing vortex induced vibration of a circular cylinder based on deep reinforcement learning
,” Phys. Fluids
33
, 103604
(2021
).173.
S.
Li
, S.
Laima
, and H.
Li
, “Physics-guided deep learning framework for predictive modeling of bridge vortex-induced vibrations from field monitoring
,” Phys. Fluids
33
, 037113
(2021
).174.
S. H.
Rudy
, S. L.
Brunton
, J. L.
Proctor
, and J. N.
Kutz
, “Data-driven discovery of partial differential equations
,” Sci. Adv.
3
, e1602614
(2017
).175.
S.
Li
, E.
Kaiser
, S.
Laima
, H.
Li
, S. L.
Brunton
, and J. N.
Kutz
, “Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems
,” Phys. Rev. E
100
, 022220
(2019
).176.
L.
Ma
, T. L.
Resvanis
, and J. K.
Vandiver
, “A weighted sparse-input neural network technique applied to identify important features for vortex-induced vibration
,” in AAAI Spring Symposium: MLPS
(AAAI
, 2020
).177.
L.
Ma
, “Interpretable machine learning for insight extraction from rigid cylinder flow-induced vibration phenomena
,” Appl. Ocean Res.
119
, 102975
(2022
).178.
L.
Ma
, T. L.
Resvanis
, and J. K.
Vandiver
, “Enhancing machine learning models with prior physical knowledge to aid in VIV response prediction
,” in International Conference on Offshore Mechanics and Arctic Engineering
(American Society of Mechanical Engineers
, 2021
).179.
S.
Riemer-Sørensen
, J.
Wu
, H.
Lie
, S.
Sævik
, and S. W.
Kim
, “Data-driven prediction of vortex-induced vibration response of marine risers subjected to three-dimensional current
,” in Symposium of the Norwegian AI Society
(Springer
, 2019
), pp. 78
–89
.180.
M.
Apolinario
and R.
Coutinho
, “Understanding the biofouling of offshore and deep-sea structures
,” in Advances in Marine Antifouling Coatings and Technologies
(Elsevier
, 2009
), pp. 132
–147
.181.
H.
Mukundan
, Y.
Modarres-Sadeghi
, F. S.
Dahl
, J. M.
Hover
, and M. S.
Triantafyllou
, “Monitoring VIV fatigue damage on marine risers
,” J. Fluids Struct.
25
, 617
–628
(2009
).182.
A. C.
Phadke
, “Marine composite riser for structural health monitoring using piezoelectricity
,” U.S. patent 8,800,665 (2014
).183.
J. K.
Vandiver
, “Research challenges in the vortex-induced vibration prediction of marine risers
,” in Offshore Technology Conference
(OnePetro
, 1998
).184.
S. W.
Doebling
, C. R.
Farrar
, M. B.
Prime
, and D. W.
Shevitz
, “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review
,” U.S. Department of Energy Office of Scientific and Technical Information (1996
).185.
W.
Staszewski
, C.
Boller
, and G. R.
Tomlinson
, Health Monitoring of Aerospace Structures: Smart Sensor Technologies and Signal Processing
(John Wiley & Sons
, 2004
).186.
Y.
Xu
, S.
Fu
, Q.
Zhong
, D.
Fan
, Y.
Zhang
, and R.
Li
, “Online safety monitor design of the jacket platform based on structural members failure study
,” in International Conference on Offshore Mechanics and Arctic Engineering
(American Society of Mechanical Engineers
, 2013
), Vol. 55317
.187.
S.
Khatir
, K.
Dekemele
, M.
Loccufier
, T.
Khatir
, and M. A.
Wahab
, “Crack identification method in beam-like structures using changes in experimentally measured frequencies and particle swarm optimization
,” C. R. Méc.
346
, 110
–120
(2018
).188.
E.
Kharazmi
, D.
Fan
, Z.
Wang
, and M. S.
Triantafyllou
, “Inferring vortex induced vibrations of flexible cylinders using physics-informed neural networks
,” J. Fluids Struct.
107
, 103367
(2021
).189.
Z.
Mao
, A. D.
Jagtap
, and G. E.
Karniadakis
, “Physics-informed neural networks for high-speed flows
,” Comput. Methods Appl. Mech. Eng.
360
, 112789
(2020
).190.
L.
Yang
, D.
Zhang
, and G. E.
Karniadakis
, “Physics-informed generative adversarial networks for stochastic differential equations
,” arXiv:1811.02033 (2018
).191.
Y.
Yang
and P.
Perdikaris
, “Adversarial uncertainty quantification in physics-informed neural networks
,” J. Comput. Phys.
394
, 136
–152
(2019
).192.
R.
Gopalkrishnan
, “Vortex-induced forces on oscillating bluff cylinders
,” Ph.D. thesis (Massachusetts Institute of Technology
, 1993
).193.
Y.
Xu
, S.
Fu
, Y.
Chen
, Q.
Zhong
, and D.
Fan
, “Experimental investigation on vortex induced forces of oscillating cylinder at high Reynolds number
,” Ocean Syst. Eng.
3
, 167
–180
(2013
).194.
C. J.
Chang
, R. A.
Kumar
, and M. M.
Bernitsas
, “Viv and galloping of single circular cylinder with surface roughness at
,” Ocean Eng.
38
, 1713
–1732
(2011
).195.
S.
Rudy
, D.
Fan
, J. D. A.
Ferrandis
, T.
Sapsis
, and M. S.
Triantafyllou
, “Learning optimal parametric hydrodynamic database for vortex-induced crossflow vibration prediction of both freely-mounted rigid and flexible cylinders
,” in The 31st International Ocean and Polar Engineering Conference
(OnePetro
, 2021
).196.
X.
Meng
, Z.
Wang
, D.
Fan
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “A fast multi-fidelity method with uncertainty quantification for complex data correlations: Application to vortex-induced vibrations of marine risers
,” Comput. Methods Appl. Mech. Eng.
386
, 114212
(2021
).197.
E.
Kharazmi
, Z.
Wang
, D.
Fan
, S.
Rudy
, T.
Sapsis
, M. S.
Triantafyllou
, and G. E.
Karniadakis
, “From data to assessment models, demonstrated through a digital twin of marine risers
,” in Offshore Technology Conference
(OnePetro
, 2021
).198.
L.
Bonfiglio
, P.
Perdikaris
, S.
Brizzolara
, and G. E.
Karniadakis
, “Multi-fidelity optimization of super-cavitating hydrofoils
,” Comput. Methods Appl. Mech. Eng.
332
, 63
–85
(2018
).199.
A.
Patra
, R.
Batra
, A.
Chandrasekaran
, C.
Kim
, T. D.
Huan
, and R.
Ramprasad
, “A multi-fidelity information-fusion approach to machine learn and predict polymer bandgap
,” Comput. Mater. Sci.
172
, 109286
(2020
).200.
X.
Wang
, J.
Kou
, and W.
Zhang
, “Multi-fidelity surrogate reduced-order modeling of steady flow estimation
,” Int. J. Numer. Methods Fluids
92
, 1826
–1844
(2020
).201.
K.
Yoo
, O.
Bacarreza
, and M. F.
Aliabadi
, “A novel multi-fidelity modelling-based framework for reliability-based design optimisation of composite structures
,” Eng. Comput.
2020
, 1
–14
.202.
T.
Lee
, I.
Bilionis
, and A. B.
Tepole
, “Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression
,” Comput. Methods Appl. Mech. Eng.
359
, 112724
(2020
).203.
F. S.
Costabal
, P.
Perdikaris
, E.
Kuhl
, and D. E.
Hurtado
, “Multi-fidelity classification using Gaussian processes: Accelerating the prediction of large-scale computational models
,” Comput. Methods Appl. Mech. Eng.
357
, 112602
(2019
).204.
Q.
Zhou
, Y.
Wu
, Z.
Guo
, J.
Hu
, and P.
Jin
, “A generalized hierarchical co-Kriging model for multi-fidelity data fusion
,” Struct. Multidiscip. Optim.
62
, 1885
–1904
(2020
).205.
K.
Tian
, Z.
Li
, L.
Huang
, K.
Du
, L.
Jiang
, and B.
Wang
, “Enhanced variable-fidelity surrogate-based optimization framework by Gaussian process regression and fuzzy clustering
,” Comput. Methods Appl. Mech. Eng.
366
, 113045
(2020
).206.
S.
Li
, W.
Xing
, R.
Kirby
, and S.
Zhe
, “Multi-fidelity Bayesian optimization via deep neural networks
,” in Advances in Neural Information Processing Systems
(2020
), Vol. 33
.207.
X.
Meng
and G. E.
Karniadakis
, “A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
,” J. Comput. Phys.
401
, 109020
(2020
).208.
W.
Samek
, T.
Wiegand
, and K. R.
Müller
, “Explainable artificial intelligence: Understanding, visualizing and interpreting deep learning models
,” arXiv:1708.08296 (2017
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
