can neural network (ANN) perform well when there is overlapping between data?

My professor told me to search and find out if ANN can perform(be well trained, predict) when our input data overlap each other.

our research field is "multivariate calibration" and our data is 'UV-vis spectroscopy'. the figure attached can show what I'm talking about.

thanks

additional info: professor's paper here_ http://www.sciencedirect.com/science/article/pii/S1386142509006957