The aircraft wing structures are prone to fatigue during flight operations as they undergo complex loading conditions. The classical cycle-based formulation for fatigue crack growth has intrinsic difficulties in dealing with these complex loadings since they often cannot be described as cyclic. In this study, a time-based subcycle formulation for fatigue crack growth is adopted to address this difficulty. Meanwhile, real-time fatigue damage prognosis requires efficient prediction of aircraft dynamical responses. In order to reduce the computational costs, this study proposes a hybrid learning method to simulate the aircraft dynamics. The hybrid learning method integrates the underlying physics of the dynamical system into learning models such as neural networks to reduce the training and computational costs. For demonstration, the aircraft wing structure is modeled as a cantilever beam and the proposed method is adopted to conduct the fatigue damage prognosis.