Probabilistic Inverse Airfoil Design Using Experimentally-driven Machine Learning Models

Conventional inverse design methods evaluate the aerodynamics of candidate airfoils using Computational Fluid Dynamics (CFD) simulations, which are computationally expensive and inherently deterministic, limiting design space exploration and uncertainty quantification. This paper offers an alternative approach by introducing an experimentally-driven surrogate model-based probabilistic inverse formalism, in which both the target quantity of interest and the resulting design are represented as statistical distributions. Notably, the formulation of the target C p is generalized to enable inverse design across multiple operating conditions within a unified framework. Employing stochastic variational inference, the design loop obtains the design distribution by minimizing the symmetrized Kullback–Leibler divergence loss. Inactive subspace analysis is then performed, characterizing the geometric perturbations that have minimal impact on the C p distribution (i.e. the tolerance). The approach leverages the Large Airfoil Model (LAM), an uncertainty-aware machine learning surrogate trained entirely on an experimental dataset, whose accuracy, computational efficiency, and automatic differentiation capability enable rapid optimization. Across three test cases, the framework recovered the target geometries with thickness residuals below 0.5% of maximum thickness. The framework achieved substantial computational savings, requiring under 10.8 minutes for a single design point on a CPU and providing up to a 2.87 × speedup over an equivalent RANS-driven inverse design workflow using SU2, with further gains on a single A100 GPU, requiring only 255 s and 590.83 s for the single- and three-point design cases, respectively.