A Stable Gray-Box Surrogate for Unsteady Aerodynamic Coefficients in Real-Time Simulation

Abstract Real-time flight simulation needs aerodynamic loads at every step; coefficient tables are quasi-steady and grow exponentially with their arguments. We study a compact gray-box sur-rogate: a bank of learnable second-order lags (digital filters whose response always decays), feeding a small neural network that supplies the nonlinear, stall-like map, plus a linear term for rate effects. It is benchmarked against twelve alternatives, including calibrated Hansen– Gaunaa–Madsen (HGM) and Goman–Khrabrov dynamic-stall models and GRU and LSTM networks, on measured two-dimensional airfoil data: 216 pitch-oscillation runs of three airfoils under cross-validation, and ramps of three further airfoils after training on oscillations only. On oscillations the surrogate is significantly more accurate than quasi-static tables and linear models; for unseen Reynolds numbers it is also more accurate than the calibrated semi-empirical models, but for unseen reduced frequencies it only matches them and is outperformed by rate-augmented memoryless maps. On ramps it outperforms those memoryless maps and predicts dynamic-stall peak loads better than the calibrated semi-empirical models, which nevertheless have the lower time-history error. Small gated recurrent networks are more accurate, by 7–53%, without a stability guarantee on their internal dynamics. The learned filters act as a stable basis of lags rather than as identified physical time constants.