End-to-End Deep-Learning-Based Surrogate Modeling for Supersonic Airfoil Shape Optimization
Abstract
:1. Introduction
- a novel, end-to-end DL-based SM trained on openly accessible subsonic and transonic airfoil geometric data to predict aerodynamic coefficients from airfoil coordinates, for guiding the optimization routine in supersonic conditions;
- an InfoGAN trained to represent an aerodynamically valid design space that includes shapes suited for subsonic, transonic and supersonic conditions;
- a modular, real-time-capable optimization framework that integrates the SM with the generative design space representation, enabling rapid ASO for supersonic conditions.
2. Methodology
2.1. Overview
2.2. Airfoil Geometry Parameterization
2.3. Aerodynamic Coefficients Surrogate Modeling
2.4. Optimization Algorithm
3. Numerical Results and Discussion
3.1. Problem Formulation
3.2. DL Models Development
3.2.1. Data Collection
3.2.2. Dataset Splitting
3.2.3. InfoGAN Training
3.2.4. SM Training
3.3. GA Development
3.4. Aerodynamic Drag Minimization
4. Concluding Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Nodes in Off-Wall Direction | Number of Cells | Counts | Counts | Extrapolated Relative Error | CPU Time [s] |
---|---|---|---|---|---|
2048 | 499,468 | 55.07 | 973.7 | 0.01% | 2.4 × |
512 | 124,684 | 55.09 | 974.0 | 0.04% | 2.3 × |
128 | 30,988 | 55.14 | 975.9 | 0.23% | 8.7 × |
Richardson extrapolation | - | 973.2 | - | - |
Study | Model | Flight Condition | Training Samples | Modeling Variables | Application | Results RMSE (Counts) | NRMSE | |
---|---|---|---|---|---|---|---|---|
Nagawkar et al. [24] | PC-Cokriging | Transonic | 1074 | 8 | - | 6.00 | 2.5% | |
Subsonic | 81,000 | 16 | 0.26 %, 0.15% | - | - | |||
Li et al. [11] | GE-KPLS | Transonic | 32,400 | 10 | , | 0.83%, 0.40% | - | - |
Subsonic | 42,039 | 16 | 0.32%, 0.19% | - | - | |||
Bouhlel et al. [12] | MLP | Transonic | 4120 | 10 | , | 0.48%, 0.28% | - | - |
Subsonic | 45,696 | 29 | 2.26%, 2.34% | 2.77, 12.90 | 0.9%, 0.9% | |||
Du et al. [7] | MLP | Transonic | 39,505 | 29 | , | 4.65%, 2.87% | 8.76, 16.13 | 1.5%, 1.5% |
Zhang et al. [26] | CNN | Transonic | 1600 | 2403 | - | 70.71 | - | |
Proposed | CNN | Supersonic | 11,290 | 257 | , | 1.11%, 1.69% | 15.50, 2.42 | 0.4%, 0.5% |
Configuration | Test MSE | Number of Parameters |
---|---|---|
MLP | 1.20 × | 0.077 M |
CNN + Pooling | 6.70 × | 0.630 M |
Early fusion | 5.54 × | 1.450 M |
Without residual | 1.41 × | 0.474 M |
Proposed | 4.73 × | 0.507 M |
(Counts) | |||||||
---|---|---|---|---|---|---|---|
Optimal Airfoil | Theory | CFD | SM | Theory | CFD | SM | |
Biconvex | 4.82° | 0.194 | 0.200 | 0.193 | 465.5 | 483.6 | 487.9 |
CFD | 4.99° | 0.201 | 0.200 | 0.200 | 600.0 | 473.2 | 432.8 |
SM | 5.44° | 0.219 | 0.200 | 0.207 | 572.4 | 482.1 | 400.2 |
Optimal Aerofoil | Theory | SM | Theory | SM |
---|---|---|---|---|
Biconvex | −3.00% | −3.50% | −3.74% | 0.89% |
CFD | 0.50% | 0.00% | 26.80% | −8.54% |
SM | 9.50% | 3.50% | 18.73% | −16.99% |
Optimal Airfoil | (Counts) | Deviation | CPU Time [s] | CPU Time Deviation |
---|---|---|---|---|
CFD | 473.2 | - | 5.8 × | - |
SM | 482.1 | 1.88% | 1.9 × | −99.97% |
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Pereira, D.; Afonso, F.; Lau, F. End-to-End Deep-Learning-Based Surrogate Modeling for Supersonic Airfoil Shape Optimization. Aerospace 2025, 12, 389. https://doi.org/10.3390/aerospace12050389
Pereira D, Afonso F, Lau F. End-to-End Deep-Learning-Based Surrogate Modeling for Supersonic Airfoil Shape Optimization. Aerospace. 2025; 12(5):389. https://doi.org/10.3390/aerospace12050389
Chicago/Turabian StylePereira, Diogo, Frederico Afonso, and Fernando Lau. 2025. "End-to-End Deep-Learning-Based Surrogate Modeling for Supersonic Airfoil Shape Optimization" Aerospace 12, no. 5: 389. https://doi.org/10.3390/aerospace12050389
APA StylePereira, D., Afonso, F., & Lau, F. (2025). End-to-End Deep-Learning-Based Surrogate Modeling for Supersonic Airfoil Shape Optimization. Aerospace, 12(5), 389. https://doi.org/10.3390/aerospace12050389