I think deep learning is better thought of as "science" than "engineering." Right now we're in the stage of the Greeks and Arabs where we know "if we do this then that happens." It will be awhile before we have a coherent model of it, and I don't think we will ever solve all of its mysteries.
We are getting closer with variational methods and kernel methods to achieving a more holistic framework for understanding machine learning (incl. traditional deep learning) training and inference. There is a deep unity in the fundamentals of machine learning, formed into a cohesive whole by applying the analytical techniques of statistical mechanics and Bayesian probability theory.
