How to learn from multiple data sources with different input variables but the same underlying pattern? I will explain with an example:

Let's say you have 2 factories that produce pulp paper. Each have similar processes where the laws of physics give the same outcome. Now let's say this 2 factories have equipment and sensors from different manufacturers, so the output of those sensors is not comparable in any way (different number of variables, different metric system etc.). Although for both factories I can caculate the output easily and determine the learning target in a comparable way (eg. metric tonnes of paper).

Is there a way of using deep learning to learn from both datasets at the same time? I mean increase the predictive power upon a sample from factory 1 due to insights on factory 2?

What about having 3 DNN, 2 for reducing feature representation and standardizing output representation and the third one for learning the general pattern common to both and predicting the final output?
What you are referring to is multi-view learning. Multi-view learning basically tells us how multiple data sources or multiple feature subsets can be combined to create a more robust learning curve for the algorithm. 

In recent years, starting from 2013 a lot of research has been carried in this rapidly growing field. A good introduction to the topic can be found in the link below. It contains a more theoretical and mathematical approach to understanding the method.

http://research.ics.aalto.fi/airc/reports/R1011/msml.pdf