This paper considers nonlinear modeling based on a limited amount of experimental data and a simulator built from prior knowledge. The problem of how to best incorporate the data provided by the simulator, possibly biased, into the learning of the model is addressed. This problem, although particular, is very representative of numerous situations met in engine control, and more generally in engineering, where complex models, more or less accurate, exist and where the experimental data which can be used for calibration are difficult or expensive to obtain. The first proposed method constrains the function to fit to the values given by the simulator with a certain accuracy, allowing to take the bias of the simulator into account. The second method constrains the derivatives of the model to fit to the derivatives of a prior model previously estimated on the simulation data. The combination of these two forms of prior knowledge is also possible and considered. These approaches are impleme...