Probabilistic Inverse Airfoil Design using the Large Airfoil Model

Conventional inverse design methods evaluate the aerodynamics of candidate airfoils using Computational Fluid Dynamics (CFD) simulations, which are computationally expensive and inherently deterministic. This paper offers an alternative approach by introducing a surrogate model-based probabilistic inverse formalism, in which both the target Cp and the resulting airfoil are represented as statistical distributions. Employing a design loop via stochastic variational inference, the process obtains the design distribution by minimizing the symmetrized Kullback-Leibler divergence loss. Inactive space analysis is then performed, characterizing the geometric perturbations that have minimal impact on the Cp distribution, i.e. the tolerance. The approach leverages the Large Airfoil Model (LAM), an experimentally-informed machine-learning surrogate capable of capturing key flow physics, including compressibility effects, transition, and the onset of separation. Its accuracy, computational efficiency, and automatic differentiation capability allow for rapid optimization. Across three test cases, the framework successfully reconstructed the desired geometries within the identified tolerance ranges. The largest thickness residuals (Δy/c) occurred for the RAE 2822 case with a normal shock, but remained below 1.97% of the maximum thickness. The framework achieved high computational speed, requiring under 255 seconds on a single A100 GPU.