Inverse Mapping for Airfoil Optimization Using Multifidelity Reduced-Order Neural Networks

Aerodynamic design optimization improves aircraft performance and reduces emissions, but conventional approaches iterate on high-fidelity simulations, creating a computational bottleneck. Surrogate-based design optimization can address this bottleneck, but training surrogate models is costly and surrogate-based design requires optimization iterations, which can be prohibitive for resource-limited applications. To eliminate the need for online optimization, we propose a new aerodynamic design architecture—inverse mapping. This architecture uses a surrogate to directly predict optimal airfoil shapes from design requirements, including constraints and flight conditions. The inverse mapping poses two challenges: high complexity and the cost of generating training samples through simulation-based optimizations. We address these challenges by exploiting a low-rank space via singular value decomposition to reduce the mapping complexity and by using multifidelity surrogate modeling to reduce the computational cost. We demonstrate the inverse-mapping architecture on airfoil design in transonic viscous flows with fixed constraints setup. A single-fidelity surrogate trained on the full set of design variables achieves 95% accuracy with 140 high-fidelity training samples, and training on the reduced-order variables lowers this to 120 samples. Combining the reduced-order representation with a multifidelity surrogate—using both high- and low-fidelity training data—further reduces the requirement to 80 high-fidelity and 100 low-fidelity samples, equivalent to 85 high-fidelity samples given the 20-to-1 cost ratio, a 29.2% reduction in computational cost. Robustness tests confirm consistently strong performance. In addition, a 95% accuracy in the airfoil shape variables yields 0.5% error in airfoil coordinates and 0.15% error in drag coefficients. The inverse-mapping architecture enables real-time design and generalizes to other engineering applications.