Hot rolling is a good example. For the last 30 years neural networks have been used to control the process. There’s a nice NeurIPS paper from 1991 [1].

And even with the non-deep networks from back in the day, people felt compelled to include prior knowledge and even used Bayesian priors to deal with a lack of data.

[1] http://papers.neurips.cc/paper/447-neural-control-for-rollin...