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

Nomenclature

• α denotes angle of attack, while CL, CD, and CM denote lift, drag, and pitching-moment coefficients; c is the condition vector.The specified geometry and aerodynamic condition values are also denoted gk,cond and Ci,cond.Source: Nomenclature · p. 2
• D and G denote the discriminator and generator, while x denotes aerodynamic configuration parameters and z denotes random noise.θG and θD are their trainable parameters; CVSP_i(x) is the VSPAERO result for the same configuration.Source: Nomenclature · p. 2
• Lgeo and Laero denote the geometry-guided and aerodynamic performance-guided loss terms.λk and λCi are loss weighting coefficients; a is the geometric-penalty tolerance threshold.Source: Nomenclature · pp. 2–3

1. Introduction

• Conceptual design aims to rapidly generate and screen configurations, yet initial choices rely heavily on expert knowledge and may prolong iterations or raise development costs.This phase is described as determining fundamental performance characteristics and life-cycle cost despite comprising 20%–30% of the design cycle.Source: §1 · p. 3
• Iterative aerodynamic optimization converges to a single solution, making it impractical for conceptual design’s extensive exploration; gradient-free approaches also incur high cost in high-dimensional spaces.Gradient-based methods can be sensitive to initial guesses and converge to local optima.Source: §1 · pp. 3–4
• GANs, VAEs, and diffusion models offer generative alternatives, with GAN training instability, VAE sample-detail limitations, and diffusion training and inference costs noted.Generative models are presented as an end-to-end route for aircraft conceptual design exploration.Source: §1 · p. 4
• Prior aerodynamic generative methods include conditional and performance-guided designs, but accuracy under multiple coupled conditions remains an area for improvement.The introduction identifies simultaneous satisfaction of geometric and aerodynamic conditions as a further challenge.Source: §1 · p. 5
• CEGAN augments a CWGAN-GP loss with geometry-guided and surrogate-based aerodynamic enhancements, then filters physically inconsistent designs during inference.The framework is presented as improving accuracy under multiple conditions while preserving diversity and addressing extrapolation degradation.Source: §1 · pp. 5–6

2.1.1. CGAN

• CGAN conditions both generator and discriminator on design requirements, but can retain training instability and produce insufficiently diverse samples in sparse or complex condition spaces.CWGAN-GP instead uses Wasserstein distance and gradient penalty to mitigate training instability.Source: §2.1.1 · pp. 7–8, §2.1.2 · p. 8

2.1.2. CWGAN-GP

• CWGAN-GP combines conditional generation with Wasserstein distance and gradient penalty, which encourages the critic's gradient norm on interpolated samples to remain close to 1.The gradient penalty is described as alleviating adverse effects of the weight-clipping strategy used in the original WGAN.Source: §2.1.2 · pp. 8–9

2.2.1. Geometry-Guided Enhancement

• The geometry-guided loss penalizes relative geometric-condition errors only when they exceed a predefined tolerance.The method targets quantities such as wing area, span, and sweep angle, which also relate to manufacturing feasibility and operational constraints.Source: §2.2.1 · pp. 9–10

2.2.2. Aerodynamic Performance-Guided Enhancement

• The aerodynamic enhancement trains surrogate models to map geometry to lift, drag, and moment coefficients, then penalizes prediction differences from specified conditions.Separate single-output feedforward networks are trained for the aerodynamic coefficients using the generative model's dataset.Source: §2.2.2 · pp. 10–11

2.3. Output Filtering

• Output filtering uses trained surrogates for aerodynamic checks and directly evaluates geometric quantities, retaining only samples that satisfy all specified conditions within tolerance.Filtering continues until enough valid samples are obtained; appendix validation reports improved accuracy when filtering is combined with aerodynamic performance-guided enhancement.Source: §2.3 · pp. 11–12

2.4. Overall Model Structure

• CEGAN combines geometry-guided and aerodynamic performance-guided losses during training with output filtering during generation.The geometric term targets geometric constraints, while the aerodynamic term aligns samples with specified aerodynamic conditions.Source: §2.4 · p. 13
• The generator receives Gaussian noise and a condition vector containing geometric and aerodynamic targets, while its loss combines adversarial, geometric, and aerodynamic terms.The gradient penalty is used only for discriminator updates.Source: §2.4 · pp. 13–14
• The relative weights of geometric and aerodynamic penalties can be adjusted to reflect engineering priorities, and the framework may be extended to other conditions such as payload or range.The training dataset is used to train both the generative model and surrogate models; surrogates are also used during output filtering.Source: §2.4 · p. 17

2.5. Model Evaluation

• MRE measures relative error between generated geometric or aerodynamic values and their prescribed conditions.Geometric values are computed directly, while aerodynamic coefficients are evaluated using VSPAERO.Source: §2.5 · p. 17
• MNND averages each generated sample’s distance to its nearest neighbor in normalized geometric-parameter space.Larger MNND indicates more widely distributed designs; decreases when samples cluster, making it sensitive to mode collapse.Source: §2.5 · pp. 17–18
• Figure 6 compares probability-density distributions: aerodynamic parameters indicate accuracy, while key geometric parameters indicate diversity.Sharper, denser accuracy distributions indicate closer condition satisfaction; broader, flatter diversity distributions indicate more diverse feasible solutions.Source: §2.5 · pp. 18–19, Figure 6 · p. 18

3.1. Dataset Construction

• The dataset uses 28 design variables and 2,500 LHS samples; OpenVSP lift predictions agree with CFD within 10% mean relative error, while drag discrepancies are larger but trends agree.Samples were evaluated at Ma = 0.6, Re = 8 × 10^6, and α = 2°; the paper attributes drag deviations primarily to VLM accuracy limits but considers the method suitable for conceptual design.Source: §3.1 · pp. 21, 23, Figure 10 · p. 23

3.2. Optimal Network Architecture Selection

• The selected baseline uses a 256-128-64 generator with Tanh, a 128-64-32 discriminator with LeakyReLU, and 20,000 training steps.Increasing iteration steps improves conditional-generation accuracy overall but may reduce accuracy for some conditions.Source: §3.2 · p. 24, Figure 12 · p. 26

3.3. Test configurations

• The generator conditions on S, L, Λ, CL, CD, and CM; Cond-A tests interpolation, Cond-B a boundary case, Cond-C an extreme extrapolation, and Cond-D samples global conditions.Joint combinations can be extrapolative even when each prescribed value lies within its individual training range.Source: §3.3 · pp. 25, 27, 28

3.4.1. Condition-Informed Loss Function

• Geometry-guided loss improves geometric matching and aerodynamic-guided loss improves aerodynamic matching, but each can worsen the other conditions, motivating their combination in CEGAN.The enhancement strategies preserve geometric diversity; clearer aerodynamic improvements require surrogate models with mean validation R2 of about 0.95 or higher.Source: §3.4.1 · pp. 30–31

3.4.2. Output Filtering

• Under extreme Cond-C conditions, CEGAN improves accuracy over CWGAN-GP even without filtering, and output filtering further increases accuracy while discarding inaccurate exploratory samples.For strongly extrapolated conditions, CEGAN explores beyond the training distribution, whereas CWGAN-GP samples largely remain clustered near training data.Source: §3.4.2 · pp. 31, 36, Figure 19 · p. 34
• For Cond-D, CEGAN improves accuracy under strongly coupled conditions, especially high lift-to-drag and low aspect ratio, although single samples per condition limit statistical support.The lower-right extrapolation region also improves, but the paper describes it as having limited practical engineering value.Source: §3.4.2 · p. 36
• CEGAN reduces generation error by at least 36% for interpolation cases and at least 46% for strongly coupled extrapolation cases versus CWGAN-GP, with diversity loss remaining acceptable.The reported accuracy gains are accompanied by some diversity decay, while the model retains its ability to explore the design space.Source: §3.4.2 · pp. 36, 38
• Against a CWGAN-GP trained on 5,000 samples, complete CEGAN achieves comparable accuracy despite using 2,500 samples, while unfiltered CEGAN also beats the same-size baseline.The comparison reports consistent accuracy improvements across Cond-A, Cond-B, and Cond-C for geometric parameters and aerodynamic coefficients.Source: §3.4.2 · p. 38
• Output filtering improves generation accuracy for prescribed conditions.The passage also states that the method maximizes training-data utility and reduces reliance on large training datasets.Source: §3.4.2 · p. 39
• The method maximizes training-data utility, reducing reliance on large training datasets.The passage links this data efficiency to better generation accuracy.Source: §3.4.2 · p. 39

4. Conclusions

• A condition-informed loss combines geometry-guided and aerodynamic performance-guided enhancements, while output filtering discards physically inconsistent samples.Source: §4 · pp. 40–41
• Generation error falls by at least 36% for interpolation cases Cond-A and Cond-B and 46% for strongly extrapolated Cond-C versus CWGAN-GP; accuracy also improves across global condition space Cond-D.Source: §4 · p. 41
• CEGAN preserves reasonable geometric diversity and matches the accuracy of CWGAN-GP trained with twice as many samples.Source: §4 · p. 41
• The aerodynamic enhancement's benefit depends on surrogate accuracy; mean validation R2 near 0.95 and above yielded more consistent improvements in this tested setup.Source: §4 · p. 41
• The framework offers a practical, extensible pathway for generative modeling in aircraft conceptual design; future work targets adaptive enhancement and high-fidelity data.Source: §4 · pp. 41–42

Appendix A. Surrogate-Based Output Filtering: Methodology and Preliminary Validation

• Output filtering improved accuracy at a center condition (CL = 0.21, CD = 0.0125) and a training-distribution boundary condition (CL = 0.225, CD = 0.012).Source: Appendix A · p. 42

Appendix B. Ablation Study on Network Design

• Unless a row specifies otherwise, Table 8's activation function applies to both generator and discriminator; the table caption identifies architecture and activation-function ablations across training-sample counts.Source: Appendix B · p. 42, Table 8 · p. 44
• The selected generator architecture was 256-128-64, using Tanh for the generator and LeakyReLU for the discriminator, balancing generation accuracy with training-sample count.Source: Appendix B · p. 42
• Each model was evaluated over 500 LHS-sampled lift-and-drag condition vectors within the training range; lower MRE indicates higher generation accuracy and quality.Source: Appendix B · p. 42

Appendix C. Additional Validation Results for Condition B

• For boundary interpolation condition B, CEGAN without filtering improves accuracy over CWGAN-GP, and full CEGAN improves it further by filtering infeasible outputs.Source: Figure 27 · p. 45, Appendix C · p. 45
• Figure 28 presents CEGAN and CWGAN-GP generation results across different low-dimensional condition spaces under Condition B.Source: Figure 28 · p. 46

• The appendix first tests surrogate prediction accuracy on generated aircraft configurations.Source: Appendix D · p. 47
• It then examines how surrogate accuracy affects aerodynamic guidance during generator training.Source: Appendix D · p. 47
• Both tests use the same 28-parameter aircraft representation.Source: Appendix D · p. 47

• Each generated geometry is evaluated by its aerodynamic surrogate and VSPAERO, with surrogate error defined for CL, CD, and CM against the VSPAERO reference.Source: Appendix D.1 · p. 47
• 92.0% of generated samples under Cond-D have CD surrogate prediction errors below 10%.The test evaluates 2,000 Cond-D configurations; Cond-A, Cond-B, and Cond-C each contain 500.Source: Appendix D.1 · p. 47
• Figure 29 presents the surrogate-model error distributions for CL, CD, and CM under Cond-A–D, while Table 9 reports mean relative errors.Source: Figure 29 · p. 47, Appendix D.1 · p. 47, Table 9 · p. 48

• Five CE-aero generators were trained for 20,000 epochs with shared architecture, data, seed, and optimization settings, comparing surrogate models with nominal R2 values of 0.99, 0.95, 0.90, 0.80, and 0.50.Geometry-guided penalties and output filtering were disabled; all six design conditions remained generator inputs, and aerodynamic loss weights were 150, 1500, and 20 for CL, CD, and CM, respectively.Source: Appendix D.2 · p. 48, Table 10 · p. 48
• Each model was assessed on the same 500 Cond-D LHS condition vectors, with one configuration per vector and no selection by surrogate or VSPAERO error.VSPAERO evaluations used Ma = 0.6, Re = 8 × 10^6, angle of attack 2°, and 20 wake iterations, matching the main-text design case.Source: Appendix D.2 · p. 48
• Generation accuracy generally improves as surrogate accuracy increases, with surrogate models at R2 values about 0.95 or higher providing effective generator guidance.Some LHS condition combinations may be physically infeasible, which may explain samples with accurate surrogate predictions but poor generation accuracy.Source: Figure 30 · p. 49, Appendix D.2 · p. 49
• Figure 30 relates surrogate prediction accuracy to generation accuracy, showing mean errors across ten equal-count groups sorted by surrogate prediction error.The horizontal dashed line marks the historical mean error of CWGAN-GP on the same 500 vectors.Source: Figure 30 · p. 49, Appendix D.2 · p. 49