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A Hybrid Framework for Airfoil Optimization: Combining PINNs and Genetic Algorithm (Student Abstract)
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Combines a PINN surrogate (trained on CFD data) with NSGA-II genetic algorithm to optimize an 11-parameter airfoil for maximum Cl/Cd, reporting PINN outperforming an ANN surrogate.
Problem
Airfoil shape optimization is computationally expensive because each design evaluation requires resource-intensive CFD simulations.
Approach
Uses a physics-informed neural network as a fast surrogate for airfoil aerodynamic coefficients and couples it with NSGA-II to search control-point geometries maximizing Cl/Cd, instead of running CFD in the loop.
Key results
- PINN surrogate achieved MSE 64.824, MAE 5.832, R² 0.483, MAPE 0.390 versus ANN's MSE 125.470, MAE 9.037, R² 0.001, MAPE 0.615.
- NSGA-II coupled with PINN reached an optimized Cl/Cd of about 44.49 versus about 16.89 with the ANN surrogate.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the ANN surrogate with PINNs | Airfoil flow-parameter prediction · Airfoil dataset | MSE: 125.470 -> 64.824 | Helped |
| replace the ANN surrogate with PINNs | Airfoil flow-parameter prediction · Airfoil dataset | MAE: 9.037 -> 5.832 | Helped |
| replace the ANN surrogate with PINNs | Airfoil flow-parameter prediction · Airfoil dataset | R²: 0.001 -> 0.483 | Helped |
| replace the ANN surrogate with PINNs | Airfoil flow-parameter prediction · Airfoil dataset | MAPE: 0.615 -> 0.390 | Helped |
| use PINNs instead of ANN as the surrogate in NSGA-II | Airfoil optimization · Airfoil optimization | Cl/Cd: around 16.89 -> around 44.49 | Helped |
Limitations
- No quantified computational speedup relative to CFD is reported.
- R² of 0.483 for the PINN indicates modest predictive fit.
- Small dataset and single flow condition (Re = 6e6) with limited description; baseline ANN architecture not specified.
Experimental setup
Datasets: CFD simulations of airfoils in ANSYS Fluent, sampled with Latin Hypercube Sampling, 0-15 degree angle of attack
Benchmarks: held-out CFD dataset (not named)
Metrics: MSE MAE R2 MAPE Cl/Cd achieved by optimization
Baselines: ANN surrogate
Builds on: PINNs NSGA-II
Closest papers by meaning
- Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · similarity 0.83)
- RoPINN: Region Optimized Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.83)
- Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective (NeurIPS 2025 · similarity 0.83)
- Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification (ICML 2024 · similarity 0.83)
- AFBench: A Large-scale Benchmark for Airfoil Design (NeurIPS 2024 · similarity 0.83)
- Aerodynamic Coefficients Prediction via Cross-Attention Fusion and Physical-Informed Training (AAAI 2025 · similarity 0.82)
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