Condition-Enhanced Generative Adversarial Network for Aerodynamic Configuration Design of Commercial Aircraft

Youzheng Yu; Jiaqing Kou; Weiwei Zhang

cs.LGOct 25, 2026

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

Abstract

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

$\alpha$ =	angle of attack
$a$ =	tolerance threshold for geometric penalty
$AR$ =	aspect ratio
$\bm{c}$ =	condition vector
$C_{L}$ =	lift coefficient
$C_{D}$ =	drag coefficient
$C_{M}$ =	pitching moment coefficient

Table 1

Figure 3: Aerodynamic performance-guided enhancement applied to CWGAN-GP.

\mathcal{L}_{\mathrm{MSE},i}=\frac{1}{N}\sum_{j=1}^{N}\left[f_{i}(\bm{x}^{(j)})-C_{i}^{\mathrm{VSP}}(\bm{x}^{(j)})\right]^{2}.

Algorithm 1 Training of a Single-Output Surrogate Model based on MLP

Figure 4: Output filtering applied to generator.

Panel of Figure 6 — Figure 6: Accuracy and diversity evaluation of generative models via probability density distributions.

Panel of Figure 7 — 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.

Panel of Figure 9 — Figure 9: Computational grid of the aircraft model for validation.

Panel of Figure 10 — Figure 10: Comparison of numerical simulation results between CFD and OpenVSP.

Figure 11: An example of convergence process of the loss function (CWGAN-GP).

Panel of Figure 12 — Figure 12: Error of generator across different iteration steps.

Figure 13: Input and Output of the Generator.

Panel of Figure 14 — 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/ $m^{2}$	$L/m$	$\Lambda/^{\circ}$	$C_{M}$	$C_{D}$	$C_{L}$
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.

Panel of Figure 15 — Figure 15: Distribution of test conditions in the geometric-aerodynamic condition space.

Model	Loss			Output Filtering
Model	$\mathcal{L}_{\text{base}}$	$\mathcal{L}_{\text{geo}}$	$\mathcal{L}_{\text{aero}}$	Output Filtering
CWGAN-GP (Baseline)	$\checkmark$
CE-geo	$\checkmark$	$\checkmark$
CE-aero	$\checkmark$		$\checkmark$
CEGAN-Unfiltered	$\checkmark$	$\checkmark$	$\checkmark$
CEGAN	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

Table 5: Specific configurations of different models.

Configuration	$a$	$\lambda_{S}$	$\lambda_{L}$	$\lambda_{\Lambda}$
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 .

Panel of Figure 17 — 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 ( $S$ , $L$ , $\Lambda$ ) and (d–f) aerodynamic conditions ( $C_{L}$ , $C_{D}$ , $C_{M}$ ). The last two rows compare CE-aero with CWGAN-GP: (g–i) geometric conditions and (j–l) aerodynamic conditions.

Panel of Figure 18 — Figure 18: Distribution of generated geometric parameters for different models under Cond-A.

Panel of Figure 19 — Figure 19: Generation accuracy under extreme design conditions (Cond-C).

Panel of Figure 20 — 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.

Panel of Figure 21 — Figure 21: Distribution of generated geometric parameters for different models under extreme design conditions (Cond-C).

Panel of Figure 22 — 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.

Panel of Figure 24 — 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

Panel of Figure 26 — Figure 26: Validation of the output filtering method. (a)-(b) Conditions: $C_{L}=0.21$ , $C_{D}=0.0125$ ; (c)-(d) Conditions: $C_{L}=0.225$ , $C_{D}=0.012$ .

Panel of Figure 27 — Figure 27: Generation accuracy under interpolated aerodynamic and geometric conditions (Cond-B, on the boundary of the condition space among the training dataset).

Panel of Figure 28 — Figure 28: Generation results of CEGAN vs. CWGAN-GP in different low-dimensional spaces under Cond-B. (a)–(c) CWGAN-GP; (d)–(f) CEGAN.

Panel of Figure 29 — Figure 29: Errors of the surrogate models relative to VSPAERO for CEGAN configurations under Cond-A–D. The panels show (a) $C_{L}$ , (b) $C_{D}$ and (c) $C_{M}$ .

Condition	$N$	MRE, %
		$C_{L}$	$C_{D}$	$C_{M}$
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 $R^{2}$	$R^{2}_{C_{L}}$	$R^{2}_{C_{D}}$	$R^{2}_{C_{M}}$	$\overline{R^{2}}$
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.

Panel of Figure 30 — Figure 30: Relation between the errors of the surrogate models and those of the CE-aero generators for (a) $C_{L}$ , (b) $C_{D}$ and (c) $C_{M}$ .

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Airfoil shape design is a fundamental task in aerospace engineering, with a direct impact on flight stability and fuel consumption. Deep learning has recently emerged as a promising tool for this task, but existing deep generative approaches remain limited in both geometric validity and physical controllability. They offer little control over the generated shapes, yielding invalid geometries, and they typically do not condition effectively on aerodynamic performance. To address these issues, this paper proposes AirfoilGen, a valid-by-construction and performance-aware latent diffusion model for airfoil. It first introduces a novel airfoil representation scheme, the circle sweeping representation, to constrain the generative process so that output shapes respect essential airfoil characteristics. It then enables explicit control over aerodynamic performance (e.g., lift and drag coefficients) by operating in a learned latent space: a transformer model encodes airfoil shapes into vector embeddings, and a conditional diffusion model denoises Gaussian noise into these latent embeddings while incorporating target aerodynamic performance. In addition, this paper presents a new dataset of over 200,000 airfoils, which is substantially larger than the widely used UIUC airfoil dataset (1,650 airfoils) and more suitable for training modern deep generative models. Experiments demonstrate that AirfoilGen enables airfoil generation with far greater geometric validity and aerodynamic performance controllability than previously achievable, with an average performance-conditioning accuracy of 98.41%.

Abstract

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