Variable-fidelity surrogate models leverage low-fidelity data with low cost to assist in constructing high-precision models, thereby improving modeling efficiency. However, traditional machine learning methods require high correlation between low-precision and high-precision data. To address this issue, a variable-fidelity deep neural network surrogate model based on transfer learning (VDNN-TL) is proposed. VDNN-TL selects and retains information encapsulated in different fidelity data through transfer neural network layers, reducing the model's demand for data correlation and enhancing modeling robustness. Two case studies are used to simulate scenarios with poor data correlation, and the predictive accuracy of VDNN-TL is compared with that of traditional surrogate models (e.g., Kriging and Co-Kriging). The obtained results demonstrate that, under the same modeling cost, VDNN-TL achieves higher predictive accuracy. Furthermore, in waverider shape multidisciplinary design optimization practice, the application of VDNN-TL improves optimization efficiency by 98.9%. After optimization, the lift-to-drag ratio of the waverider increases by 7.86%, and the volume ratio increases by 26.2%. Moreover, the performance evaluation error of the model for both the initial and optimized configurations is less than 2%, further validating the accuracy and effectiveness of VDNN-TL.

1.
Z. H.
Han
, “
Kriging surrogate model and its application to design optimization: A review of recent progress
,”
Acta Aeronaut. Astronaut. Sin.
37
(
11
),
3197
3225
(
2016
).
2.
D. J. J.
Toal
,
N. W.
Bressloff
,
A. J.
Keane
et al, “
The development of a hybridized particle swarm for kriging hyperparameter tuning
,”
Eng. Optim.
43
(
6
),
675
699
(
2011
).
3.
T. T.
Zhang
,
W.
Huang
,
Z. G.
Wang
et al, “
A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method
,”
J. Zhejiang Univ.-Sci. A (Appl. Phys. Eng.)
17
(
8
),
632
645
(
2016
).
4.
P. F.
Li
,
B. Q.
Zhang
, and
Y. C.
Chen
, “
Research on wing optimization design method based on response surface and genetic algorithm
,”
J. Northwest. Polytech. Univ.
30
(
3
),
395
401
(
2012
).
5.
X.
Hu
,
B.
Yang
,
Y.
Lei
et al, “
Automotive shape optimization using the radial basis function model based on a parametric surface grid
,”
Proc. Inst. Mech. Eng., Part D: J. Automob. Eng.
230
(
13
),
1808
1821
(
2016
).
6.
L.
Peng
,
L.
Liu
, and
T.
Long
, “
Optimization strategy based on dynamic radial basis function surrogate model
,”
J. Mech. Eng.
47
(
7
),
164
170
(
2011
).
7.
X.
Chen
and
R.
Agarwal
, “
Optimization of flatback airfoils for wind-turbine blades using a genetic algorithm
,”
J. Aircr.
49
(
2
),
622
629
(
2012
).
8.
L.
Zhu
and
Z. H.
Gao
, “
Research on wing optimization design method based on neural network
,”
Aeronaut. Comput. Tech.
37
(
3
),
33
36
(
2007
).
9.
Y.
Ju
,
C.
Zhang
, and
L.
Ma
, “
Artificial intelligence metamodel comparison and application to wind turbine airfoil uncertainty analysis
,”
Adv. Mech. Eng.
8
(
5
),
168781401664731
(
2016
).
10.
D.
Mi
,
Z. Y.
Yin
,
Z. M.
Qian
et al, “
Optimization design method for centrifugal impeller structure based on experimental design and support vector machine
,”
J. Aerosp. Power
27
(
10
),
2336
2341
(
2012
).
11.
X.
Wang
,
C. J.
Ning
,
W. Z.
Wang
et al, “
Intelligent fusion method for multi-source aerodynamic data oriented to flight experiments
,”
Acta Aerodyn. Sin.
41
(
2
),
12
20
(
2023
).
12.
F.
Lin
,
C. L.
Hai
, and
L. Q.
Mei
, “
Multi-source aerodynamic data fusion modeling with XGBoost
,”
Acta Aerodyn. Sin.
41
,
1
9
(
2023
).
13.
D. E.
Myers
, “
Matrix formulation of co-kriging
,”
Math. Geol.
14
(
3
),
249
257
(
1982
).
14.
B.
Zhang
, “
Research on aerodynamic shape optimization design of aircraft based on free-form deformation and surrogate optimization
,” Ph.D. dissertation (
National University of Defense Technology
,
2019
).
15.
K. R.
Quinlan
,
J.
Movva
,
B. T.
Burchett
et al, “
Evaluation of multi-fidelity approaches with active learning for automated database generation
,” AIAA Paper No. 2023-4023,
2023
, p.
4023
.
16.
G. C.
Tao
,
W.
Wang
,
Z. T.
Ye
et al, “
Multi-fidelity and multi-objective aerodynamic short nacelle shape optimisation under different flight conditions
,”
Aeronaut. J.
127
,
1
30
(
2023
).
17.
M.
Xiao
,
G.
Zhang
,
P.
Breitkopf
et al, “
Extended co-kriging interpolation method based on multi-fidelity data
,”
Appl. Math. Comput.
323
,
120
131
(
2018
).
18.
Z. H.
Han
and
S.
Görtz
, “
Hierarchical kriging model for variable-fidelity surrogate modeling
,”
AIAA J.
50
(
9
),
1885
1896
(
2012
).
19.
B. Z.
Han
,
W. X.
Huang
, and
C. X.
Xu
, “
Multi-fidelity Bayesian optimization for spatially distributed control of flow over a circular cylinder
,”
Phys. Fluids
35
(
11
),
115144
(
2023
).
20.
L.
Zhang
,
J. T.
Chen
,
F. F.
Xiong
et al, “
Meta-learning based multi-fidelity deep neural networks metamodel method
,”
J. Mech. Eng.
58
(
1
),
190
200
(
2022
).
21.
F.
Xiong
,
C.
Ren
,
B.
Mo
et al, “
A new adaptive multi-fidelity metamodel method using meta-learning and Bayesian deep learning
,”
Struct. Multidiscip. Optim.
66
(
3
),
58
(
2023
).
22.
M.
Li
,
Z.
Liu
,
L.
Huang
et al, “
A new multi-fidelity surrogate modelling method for engineering design based on neural network and transfer learning
,”
Eng. Comput.
39
(
6
),
2209
2230
(
2022
).
23.
P.
Liao
,
W.
Song
,
P.
Du
et al, “
Multi-fidelity convolutional neural network surrogate model for aerodynamic optimization based on transfer learning
,”
Phys. Fluids
33
(
12
),
127121
(
2021
).
24.
X.
Zhang
,
F.
Xie
,
T.
Ji
et al, “
Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization
,”
Comput. Methods Appl. Mech. Eng.
373
,
113485
(
2021
).
25.
F.
Wen
,
Z.
Li
,
C.
Wan
et al, “
Cost reduction for data acquisition based on data fusion: Reconstructing the surface temperature of a turbine blade
,”
Phys. Fluids
35
(
1
),
016110
(
2023
).
26.
Y.
Lyu
,
X.
Zhao
,
Z.
Gong
et al, “
Multi-fidelity prediction of fluid flow based on transfer learning using Fourier neural operator
,”
Phys. Fluids
35
(
7
),
077118
(
2023
).
27.
L.
Le Gratiet
and
J.
Garnier
, “
Recursive co-kriging model for design of computer experiments with multiple levels of fidelity
,”
Int. J. Uncert. Quantif.
4
(5),
365
386
(
2014
).
28.
T. P.
Lillicrap
,
A.
Santoro
,
L.
Marris
et al, “
Backpropagation and the brain
,”
Nat. Rev. Neurosci.
21
(
6
),
335
346
(
2020
).
29.
K.
Weiss
,
T. M.
Khoshgoftaar
, and
D. D.
Wang
, “
A survey of transfer learning
,”
J. Big Data
3
(
1
),
1
40
(
2016
).
30.
A.
Forrester
,
A.
Sobester
, and
A.
Keane
,
Engineering Design via Surrogate Modelling: A Practical Guide
(
John Wiley and Sons
,
2008
).
31.
L.
Huang
,
Z.
Gao
, and
D.
Zhang
, “
Research on multi-fidelity aerodynamic optimization methods
,”
Chin. J. Aeronaut.
26
(
2
),
279
286
(
2013
).
32.
S.
Kang
and
K.
Lee
, “
Rapid Estimation of the aerodynamic coefficients of a missile via co-kriging
,”
J. Korean Soc. Aeronaut. Space Sci.
48
(
1
),
13
21
(
2020
).
33.
R.
Wang
,
Y.
Yang
,
X.
Wang
et al, “
Co-kriging based multi-fidelity aerodynamic optimization for flying wing UAV with multi-shape wingtip design
,” in
2021 IEEE International Conference on Unmanned Systems (ICUS)
, Beijing, China, 2021, pp.
93
98
.
34.
A.
Nelson
,
J.
Alonso
, and
T.
Pulliam
, “
Multi-fidelity aerodynamic optimization using treed meta-models
,” AIAA Paper No. 2007-4057,
2007
, p.
4057
.
35.
O.
Pinti
,
R.
Niemiec
,
A. A.
Oberai
et al, “
A multi-fidelity approach to predicting rotor aerodynamic interactions
,” AIAA Paper No. 2020-2796,
2020
, p.
2796
.
36.
Z. H.
Han
,
C. Z.
Xu
,
L.
Zhang
et al, “
Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids
,”
Chin. J. Aeronaut.
33
(
1
),
31
47
(
2020
).
37.
Z. T.
Zhao
,
W.
Huang
,
H. S.
Jin
et al, “
Influence of Mach number discretization method on configuration and aerodynamic performance of tangent-cone variable Mach number waverider
,”
Acta Aeronaut. Astronaut. Sin.
41
(
12
),
173
189
(
2020
).
38.
T. T.
Zhang
, “
Research on multidisciplinary design optimization technology for intake-type wide-speed-range cruising aircraft
,” Ph.D. dissertation (
National University of Defense Technology
,
2020
).
39.
Y.
Shen
,
W.
Huang
,
T.
Zhang
et al, “
Parametric modeling and aerodynamic optimization of EXPERT configuration at hypersonic speeds
,”
Aerosp. Sci. Technol.
84
,
641
649
(
2019
).
40.
C.
Segal
,
The Scramjet Engine Processes and Characteristics
(
Cambridge University Press
,
Cambridge
,
2009
).
41.
A.
Sheidani
,
S.
Salavatidezfouli
,
G.
Stabile
,
M. B.
Gerdroodbary
, and
G.
Rozza
, “
Assessment of icing effects on the wake shed behind a vertical axis wind turbine
,”
Phys. Fluids
35
(
9
),
095135
(
2023
).
42.
J. X.
Leng
,
Y.
Shen
,
T. T.
Zhang
et al, “
Parameterized modeling and optimization of reusable launch vehicles based on reverse design approach
,”
Acta Astronaut.
178
,
36
50
(
2021
).
43.
S. X.
Li
,
Typical Shape Hypersonic Flow Characteristics
(
National Defence Industry Press
,
Beijing
,
2007
).
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