Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models
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Adjoint methods have become a powerful tool for aerodynamic shape optimization, enabling efficient computation of design sensitivities even for large, high-fidelity CFD models. In practice, however, turning these sensitivities into better designs remains difficult. Aerodynamic optimization problems are highly nonlinear, often have many local optima, and are sensitive to function and gradient scaling as well as optimizer settings. As a result, engineers frequently rely on manual tuning, heuristic bounds and constraints, and trial-and-error to guide the optimization process—often referred to as meta-optimization. This reliance undermines the robustness and efficiency that adjoint methods promise. In this talk, we present an adjoint-based optimization framework that addresses these practical challenges by incorporating prior knowledge from existing aerodynamic designs. We use a generative diffusion model trained on known airfoil shapes to learn a smooth space of aerodynamically realistic designs. Instead of searching directly in a large and unconstrained parameter space, the optimization is restricted to this learned design manifold, which naturally enforces shape realism and flow-physics consistency. A key contribution of our approach is that it remains fully compatible with adjoint methods. Sensitivities of aerodynamic objectives, such as drag and lift, are first computed using standard adjoint solvers and then backpropagated through the machine learning model using automatic differentiation. This allows gradient-based optimization to operate efficiently in the learned design space without modifying existing CFD or adjoint solvers. We demonstrate the method on transonic RANS airfoil optimization problems using standard nonlinear optimization algorithms. The results show improved robustness with respect to initial designs and optimizer choices, elimination of ad hoc parameter tuning and problem scaling, and consistently better aerodynamic performance compared to conventional approaches. Overall, this work illustrates how AI-based design priors can be effectively combined with adjoint methods to enable more reliable and practical high-fidelity aerodynamic shape optimization.
