The closest thing to real neurons are called spiking, neural networks. Here's a list of libraries for building them on GPU's:

https://github.com/open-neuromorphic/open-neuromorphic

For academic papers, the phrases they use include "biologically plausible," "Hebbian learning," and "backpropagation free." Searching for those with "neural networks" or "neurons" will turn up cutting-edge techniques.