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The development and calibration of modern combustion engines is challenging in the area of continuously tightening emission limits and the necessity for meeting real driving emissions regulations. A focus is on the knowledge of the internal engine processes and the determination of pollutants formations in order to predict the engine emissions. A physical model-based development provides an insight into hardly measurable phenomena properties and is robust against changing input data. With increasing modeling depth the required computing capacities increase. As an alternative to physical modeling, data-driven machine learning methods can be used to enable high-performance modeling accuracy. However, these are dependent on the learned data. To combine the performance and robustness of both types of modeling a hybrid application of data-driven and physical models is developed in this paper as a grey box model for the exhaust emission prediction of a commercial vehicle diesel engine.