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To plan safe maneuvers and act with foresight, autonomous vehicles must be capable of accurately predicting the uncertain future. In the context of autonomous driving, deep neural networks have been successfully applied to learning predictive models of human driving behavior from data. However, the predictions suffer from cascading errors, resulting in large inaccuracies over long time horizons. Furthermore, the learned models are black boxes, and thus it is often unclear how they arrive at their predictions. In contrast, rule-based models, which are informed by human experts, maintain long-term coherence in their predictions and are human-interpretable. However, such models often lack the sufficient expressiveness needed to capture complex real-world dynamics. In this work, we begin to close this gap by embedding the Intelligent Driver Model, a popular hand-crafted driver model, into deep neural networks. Our model's transparency can offer considerable advantages, e.g., in debugging the model and more easily interpreting its predictions. We evaluate our approach on a simulated merging scenario, showing that it yields a robust model that is end-to-end trainable and provides greater transparency at no cost to the model's predictive accuracy.