Condition-Enhanced Generative Adversarial Network for Aerodynamic Configuration Design of Commercial Aircraft
Authors: Youzheng Yu, Jiaqing Kou, Weiwei Zhang
Organizations: School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China · International Joint Institute of Artificial Intelligence on Fluid Mechanics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China · National Key Laboratory of Aircraft Configuration Design, Xi’an, 710072, People’s Republic of China
Generative machine learning provides an end-to-end framework for aerodynamic design optimization by generating diverse aerodynamic configurations conditioned on target performance. However, the generated designs may violate geometric constraints or deviate from the prescribed aerodynamic performance. Therefore, we propose a Condition-Enhanced Generative Adversarial Network (CEGAN) that embeds geometric and aerodynamic information into the generative process. A condition-informed loss function is developed by combining a geometry-guided feasibility penalty with an aerodynamic performance penalty evaluated by surrogate models trained on the same dataset. Additionally, an output filtering mechanism discards infeasible designs using these surrogate models, ensuring compliance with prescribed conditions. The method is demonstrated on aircraft configurations similar to the Cessna Citation X. Each configuration is represented by 28 shape parameters, whose aerodynamic performance is evaluated using OpenVSP. Interpolation and extrapolation tests are conducted for different network architectures and conditioning strategies. Compared with the baseline model, CEGAN reduces the average generation error by at least 36% for interpolated conditions and by at least 46% under extreme extrapolation conditions, while successfully producing diverse and physically feasible designs that extend beyond the training distribution. Therefore, the proposed CEGAN framework offers a robust and accurate tool for rapid aerodynamic configuration exploration during the conceptual design phase.
Figures & tables
α =
angle of attack
a =
tolerance threshold for geometric penalty
AR =
aspect ratio
c =
condition vector
CL =
lift coefficient
CD =
drag coefficient
CM =
pitching moment coefficient
Table 1
Figure 1: Model structure of CGAN.
Figure 2: Model structure of CWGAN-GP.
Figure 3: Aerodynamic performance-guided enhancement applied to CWGAN-GP.
LMSE,i=N1∑j=1N[fi(x(j))−CiVSP(x(j))]2.
Algorithm 1 Training of a Single-Output Surrogate Model based on MLP
Figure 4: Output filtering applied to generator.
Figure 5: Overall structure of CEGAN.
Figure 6: Accuracy and diversity evaluation of generative models via probability density distributions.
Figure 7: Three-view drawing and geometric parameters of the small general aviation aircraft, derived from the Cessna Citation X model in [ 58 ] .
Figure 8: Distribution of training samples in the geometric-aerodynamic condition space, composed of the aspect ratio and the lift-to-drag ratio.
Figure 9: Computational grid of the aircraft model for validation.
Figure 10: Comparison of numerical simulation results between CFD and OpenVSP.
Figure 11: An example of convergence process of the loss function (CWGAN-GP).
Figure 12: Error of generator across different iteration steps.
Figure 13: Input and Output of the Generator.
Figure 14: Scatter plots of predicted versus true aerodynamic coefficients. The dashed line indicates perfect prediction ( y=x ). Points closer to the line denote higher accuracy of the surrogate models.
Condition
S/ m2
L/m
Λ/∘
CM
CD
CL
Cond-A
48
10
20
-0.75
0.0125
0.21
Cond-B
50
11
10
-0.8
0.012
0.225
Cond-C
50
10
10
-0.8
0.0125
0.23
Cond-D
LHS
Table 4: Different configurations of the conditions for model validation.
Figure 15: Distribution of test conditions in the geometric-aerodynamic condition space.
Model
Loss
Output Filtering
Lbase
Lgeo
Laero
CWGAN-GP (Baseline)
✓
CE-geo
✓
✓
CE-aero
✓
✓
CEGAN-Unfiltered
✓
✓
✓
CEGAN
✓
✓
✓
✓
Table 5: Specific configurations of different models.
Configuration
a
λS
λL
λΛ
Geo-1
0
10
10
10
Geo-2
0
30
20
10
Geo-3
0.02
10
10
10
Geo-4
0.02
10
20
30
Table 6: Hyperparameter settings for different models.
Figure 16: MRE comparison of geometric conditions under different hyperparameter configurations, for the CE-geo model framework. Configurations Geo-1 to Geo-4 correspond to Table 6 .
Figure 17: PDFs of the absolute relative errors for the six design conditions under Cond-A. The first two rows compare CE-geo with CWGAN-GP: (a–c) geometric conditions ( S , L , Λ ) and (d–f) aerodynamic conditions ( CL , CD , CM ). The last two rows compare CE-aero with CWGAN-GP: (g–i) geometric conditions and (j–l) aerodynamic conditions.
Figure 18: Distribution of generated geometric parameters for different models under Cond-A.
Figure 19: Generation accuracy under extreme design conditions (Cond-C).
Figure 20: Generation results of CWGAN-GP vs. CEGAN in different condition spaces under extreme design conditions (Cond-C). (a)–(c) CWGAN-GP; (d)–(f) CEGAN.
Figure 21: Distribution of generated geometric parameters for different models under extreme design conditions (Cond-C).
Figure 22: Low-dimensional visualization of generated geometries by different models under different sets of design conditions.
Figure 23: Visualization of generated geometries based on CEGAN.
Figure 24: Error Distribution of CWGAN-GP and CEGAN (Cond-D).
Figure 25: Performance comparison of different models.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 26: Validation of the output filtering method. (a)-(b) Conditions: CL=0.21 , CD=0.0125 ; (c)-(d) Conditions: CL=0.225 , CD=0.012 .
Figure 27: Generation accuracy under interpolated aerodynamic and geometric conditions (Cond-B, on the boundary of the condition space among the training dataset).
Figure 28: Generation results of CEGAN vs. CWGAN-GP in different low-dimensional spaces under Cond-B. (a)–(c) CWGAN-GP; (d)–(f) CEGAN.
Figure 29: Errors of the surrogate models relative to VSPAERO for CEGAN configurations under Cond-A–D. The panels show (a) CL , (b) CD and (c) CM .
Condition
N
MRE, %
CL
CD
CM
Cond-A
500
0.121
0.254
0.175
Cond-B
500
0.206
0.357
0.193
Cond-C
500
0.366
0.781
0.841
Cond-D
2000
0.342
7.211
0.513
Appendix
Table 9: Errors of the surrogate models on generated CEGAN configurations.
Nominal R2
RCL2
RCD2
RCM2
R2
0.99
0.9983
0.9944
0.9996
0.9974
0.95
0.9500
0.9499
0.9500
0.9500
0.90
0.9000
0.8991
0.9000
0.8997
0.80
0.7999
0.7973
0.7999
0.7991
0.50
0.4995
0.4960
0.4999
0.4985
Appendix
Table 10: Measured coefficients of determination on the validation set for the surrogate checkpoints used in the CE-aero sensitivity study.
Figure 30: Relation between the errors of the surrogate models and those of the CE-aero generators for (a) CL , (b) CD and (c) CM .
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Zhijie Yang, Min Tang, Peng Du +1
State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, 310027, China
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Ying Yan, Liwei Hu, Xiaoming Zhang
School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, 050091, China
Engineering inverse design is often limited by the high computational cost of iterative solvers for optimization problems constrained by partial differential equations (PDEs) and by their sensitivity to initialization. Deep generative models can produce candidate designs without rerunning the simulator at inference time. Generative adversarial networks (GANs) sample in one forward pass, whereas diffusion models require iterative reverse-time integration. In this work, we add conditional flow matching (CFM) to EngiOpt and compare it with a conditional diffusion model and a conditional generative adversarial network (cGAN) on structural (beams2d) and thermal (heatconduction2d) benchmarks from EngiBench using the same downstream optimization protocol. We use cumulative optimality gap (COG) and final optimality gap (FOG) as the primary metrics for evaluating the generated designs as warm starts for gradient-based refinement. On the evaluated EngiOpt implementations and two EngiBench tasks, CFM achieves the lowest measured COG, FOG, maximum mean discrepancy (MMD), and volume-fraction deviation on both tasks. CFM has mean volume-fraction deviations of 0.4% and 1.0% on beams2d and heatconduction2d, respectively, compared with 3.8% and 11.2% for diffusion. At Euler s = 16, CFM achieves 53.2 samples/s on beams2d, about 66 times the measured throughput of the evaluated diffusion baseline using 1000 network evaluations under the same timing protocol, with COG 1.182 +/- 3.126, compared with 1.173 +/- 3.100 for Euler s = 32. Across the two tasks, CFM produces warm starts with lower measured COG than both baselines and uses fewer network evaluations than diffusion.