Yes, there is an active branch in deep learning (Bayesian deep learning) trying to model uncertainty measurements into neural networks.

Older ideas are http://mlg.eng.cam.ac.uk/yarin/blog_2248.html or http://papers.nips.cc/paper/7219-simple-and-scalable-predict...

Basically Bayesian neural networks were able to model confidence but are not applicable in current real-world scenarios. Thus, lots of methods rely on approximating bayesian methods.