Using the LSTM Network for Gray-Box Dynamic Identification of Aircraft at Post-Stall Maneuvers

Accurate aerodynamic modeling of aircraft during post-stall maneuvers remains challenging due to massive flow separation, vortex breakdown, and unsteady hysteresis. This paper presents a gray-box system identification framework that integrates a Long Short-Term Memory (LSTM) network into the physical equations of aircraft motion. Unlike black-box methods that sacrifice interpretability, the proposed architecture preserves the rigid-body Newton-Euler equations while replacing empirical aerodynamic coefficient models with an LSTM network. The LSTM directly predicts the aerodynamic coefficients, which are transformed into forces and moments via exact physical laws, ensuring hard constraint satisfaction. Validation using real flight test data from a large-scale (3/8) fighter aircraft at angles of attack up to 80° demonstrates that the method achieves regression coefficients exceeding 0.96 for all coefficients on unseen data, with near-zero mean errors. Quantitative comparisons show that the proposed method reduces prediction error by 50–70% compared to black-box LSTM and PINN baselines. The framework offers a practical balance of accuracy, interpretability, and extrapolation reliability for post-stall aerodynamic identification.