We present a hybrid ARX model that is useful for system identification of nonlinear models. Our motivation is to combine the advantages of linear and nonlinear models in the context of extrapolation outside of the training dataset. The proposed method uses a residual hybridization approach to ensure a large linear contribution. Based on this hybrid ARX model, the proposed learning method is evaluated using the available operating data of a specific aquatic center. The results obtained on this benchmark are compared to those of traditional linear and nonlinear identification, showing that the hybrid approach achieves both the accuracy of the pure nonlinear model and the consistency of the linear ARX model. Our approach provides a promising solution for nonlinear identification, particularly for dynamical systems partially explainable by a linear model. As in the strictly linear case, the proposed model can be learned from a small volume of data, but can be enriched to improve prediction accuracy. Its potential use for data-based predictive control is particularly useful.