To reduce CO₂ emission, control region for automotive engine systems are near the boundary between normal and abnormal engine operations such as knocking and misfiring. In order to realize near boundary operation control, it has become essential to accurately identify the boundary between the operable region and the abnormal operation region with a numerical model.
  In this paper, we propose a dynamic model structure based on the Nonlinear Auto-Regressive with eXogenous inputs (NARX) model as a control model of the automotive engine systems. This model is learned using a deep learning or a Gaussian process regression. Furthermore, we clarify relationships between the number of learning data, prediction/estimation accuracy and learning time by using numerical simulations. This approach is useful for deciding how to select a model learning method with respect to the number of training data. As a result, when the number of learning data is small, the model based on the Gaussian process is effective, and in the case where the number of learning data is large, the model using deep learning is suitable.
  The effectiveness of the modeling strategy is demonstrated by an engine benchmark problem provided by the joint research committee of JSAE and SICE.