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While machine learning techniques have been successfully applied in several fields, the black-box nature of the models presents challenges for interpreting and explaining the results. We develop a new framework called Adaptive Explainable Neural Networks (AxNN) for achieving the dual goals of good predictive performance and model interpretability. For predictive performance, we build a structured neural network made up of ensembles of generalized additive model networks and additive index models (through explainable neural networks) using a two-stage process. This can be done using either a boosting or a stacking ensemble. For interpretability, we show how to decompose the results of AxNN into main effects and higher-order interaction effects. The computations are inherited from Google's open source tool AdaNet and can be efficiently accelerated by training with distributed computing. The results are illustrated on simulated and real datasets.