Machine-Learning Surrogates for Airfoil Aerodynamics: Accuracy, Extrapolation, and the Role of Known Physics: A Case Study with a Panel-Method Testbed
Abstract
Abstract Aerodynamic coefficients of an airfoil can be computed with physics-based solvers, and machine-learning surrogates are trained to replace repeated solver runs. We ask how such surrogates behave, using a testbed in which the physics is known exactly: lift and drag coefficients of NACA 4-digit airfoils, generated by the author's own potential-flow panel method and a simple drag estimate. The panel method is checked against thin-airfoil theory, a lift computation from the surface pressure, and an exact conformal-map solution. A random forest and a linear-regression baseline are compared under repeated random splits, splits that hold out entire airfoil shapes, a learning curve, permutation feature importance, residual analysis, and 48 queries outside the training ranges. Inside the training range the forest reaches a mean held-out R 2 of 0.9994 (lift) and 0.9954 (drag), and the inputs it relies on match the physics: angle of attack and camber for lift, with thickness also mattering for drag. Outside the training range the forest's accuracy collapses (R 2 = 0.81 and 0.18), while linear regression extrapolates lift well (R 2 = 0.99). The spread of predictions across the forest's trees does not increase on out-of-range queries, so it gives no warning, whereas a simple input-range check flags every one. A two-stage model that builds in the known dependence of drag on lift extrapolates drag well (R 2 = 0.97), but only because that dependence generated the data. Because the…
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