NO! We have working training algorithms. We still don't have a complete understanding of why deep learning works in practice, and especially not why it works at the current level of scale. If you disagree, please cite me the papers because I'd love to read them.

To put in another way: Just because you can breed dogs, it doesn't necessary mean that you have a working theory of genes or even that you know they exist. Which was actually the human condition for most of history.