The accurate prediction of flight trajectories is crucial for the real-time prognostics of air transportation system. However, the computation costs of predictions can be expensive or even prohibitive especially for a large number of aircrafts in the air traffic system. This study proposes the concept of physics-based learning, a hybrid approach based on data-driven learning and physical models, as a computationally efficient method for the simulation of aircraft dynamics. The physics-based learning integrates the underlying physics of dynamical systems into learning models such as neural networks to reduce the training and simulation costs. The application of physics-based learning for simulating aircraft dynamics is demonstrated using a recently introduced physics-aware network known as the deep residual recurrent neural network (DR-RNN) on a Boeing 747-100 aircraft. The aircraft dynamics are described using a six degrees-of-freedom aircraft model. The DR-RNN is first trained using the simulated responses of the aircraft and then the trained network is used to predict the response of aircraft under arbitrary control inputs and disturbances. The results show that the DR-RNN can accurately predict aircraft responses and has excellent extrapolation capabilities. Moreover, the DR-RNN exhibits superior computation efficiency compared with a classical numerical method, the fourth-order Runge-kutta method, highlighting its suitability in serving as surrogating models for aircraft dynamical systems.