Interaction between Earth’s magnetotail and its inner magnetosphere plays an important role in the transport of mass and energy in the ionosphere–magnetosphere coupled system. A number of first-principles models are devoted to understanding the associated dynamics. However, running these models, including both magnetohydrodynamic models and kinetic drift models, can be computationally expensive when self-consistency and high spatial resolution are required. In this study, we exploit an approach of building a parallel statistical model, based on the long short-term memory (LSTM) type of recurrent neural network, to forecast the results of a first-principles model, called the Rice Convection Model (RCM). The RCM is used to simulate the transient injection events, in which the flux-tube entropy parameter, dawn-to-dusk electric field component, and cumulative magnetic flux transport are calculated in the central plasma sheet. These key parameters are then used as initial inputs for training the LSTM. Using the trained LSTM multivariate parameters, we are able to forecast the plasma sheet parameters beyond the training time for several tens of minutes that are found to be consistent with the subsequent RCM simulation results. Our tests indicate that the recurrent neural network technique can be efficiently used for forecasting numerical simulations of magnetospheric models. The potential to apply this approach to other models is also discussed.