A data-driven strategy is developed to improve the internal models used for predictive control in nonlinear aeroelastic applications. A nonlinear modal formulation of the structure is retained, while an identified quadratic model for both the gravitational forces and the aerodynamics are obtained from a least-squares fit with LASSO regularisation from simulated flights. This is first seen to improve the accuracy of the resulting reduced-order model for open-loop predictions on both gust response and a payload drop problem. Its superior performance as internal model for nonlinear control and estimation is finally demonstrated numerically.