Learning from Imperfect Physical Verifiers for Generative Inverse Design of Airfoils

Inverse design increasingly relies on generative models conditioned on target performance, but in practice, supervision is provided by imperfect physics evaluators that may be noisy, biased, or failure-prone. We use inverse airfoil design in a two-stage learning framework as a controlled testbed to study how physics evaluator reliability affects physics-guided generative learning. A conditional WGAN learns the geometry manifold in Stage 1 represented using either raw coordinates or structured low-dimensional Kulfan representations, and is refined in Stage 2 using confidence-weighted aerodynamic feedback from a surrogate model (NeuralFoil). We analyze how geometry representation affects the availability of usable physics feedback and examine to what extent gains from surrogate-guided refinement are affected by evaluator-specific bias. Across random lift targets, NeuralFoil-guided refinement under target-only supervision more than doubles the fraction of XFoil-evaluated designs satisfying the prescribed target tolerance (*Good* design rate), and increases solver validity. We further analyze the effect of physics supervision strength. With stronger multi-objective physics supervision (e.g., lift, drag, shape factor), the *Good* design rate improves by up to 15$\times$ over the data-driven Stage 1 baseline, although this improvement is accompanied by reduced geometric diversity. These results suggest that verification in generative inverse design should be treated as a coupled problem involving geometry representation, evaluator reliability, and supervision strength rather than assuming physics feedback to be uniformly available and reliable.