A Text Sections Classifier
You might try to use the metadata of the individual sections for classification: 

Examples: 


Length -> Abstracts are usually short. 
Existence of Figures -> Do not usually appear in abstract of references
Relative Abundance of quotations. The references should have a significant higher share of reference keys than the others. 


You could then use the metadata as input for any supervised learning approach. For example a Neural Network or a (boosted) decision tree.