They're extensively used in particle physics as a method of performing multi-variate selections of data. It's a common case that we have a large data set which

They're extensively used in particle physics as a method of performing multi-variate selections of data. It's a common case that we have a large data set which contains the signal we're looking for. Each entry in the data set will have a large number of variables, some of which will provide some discriminating power between our signal and background. By training a neural network to use those variables to tell the difference between signal and background we can extract the maximum efficiency from our data. Of course we could use any other multi-variate method (boosted-decision trees are popular) but neural networks are becoming more and more common.