Factories could predict their demand for electricity. Then load shedding could be done to reduce the electric bill, and reduce impact on the power company. Fraud detection regarding credit cards, insurance or taxes could be automated using a neural network analysis of past incidents. Handwriting and typewriting can be recognized by imposing a grid over the writing, then each square of the grid becomes an input to the neural network. Machinery control could be automated by capturing the actions of experienced machine operators into a neural network.
Medical diagnosis is an ideal application for neural networks.
Medical research relies heavily on classical statistics to analyze research data. Perhaps a neural network should be included in the researcher's toolkit. Music composition has been tried using neural networks. The network is trained to recognize patterns in the pitch and tempo of certain music, then the network writes its own music. Each square of the grid becomes an input to the network.