The brain is a dynamic system and (some) neural networks are also dynamic systems, and a three layer neural network can learn to approximate any function. Thus, a neural network can approximate brain function arbitrarily well given time and space. Whether that simulation is conscious is another story.

The Computational Cognitive Neuroscience Lab has been studying this topic for decades and has an online textbook here:

http://grey.colorado.edu/CompCogNeuro

The "emergent" deep learning simulator is focused on using these kinds of models to model the brain:

http://grey.colorado.edu/emergent