Neural networks are perceived as a powerful regression tool. If a dataset contains of input/output relations, the neural network can adjust it's internal parameters to interpolate the missing data. In contrast to easier to realize regression techniques like the straight line in MS-Excel and the polynomial model in SPSS, neural network can also interpolate between multi-input data in a non-linear fashion. This is useful in domains of Artificial Intelligence in which the problem is multi-dimensional and can't be visualized in a standard 2d plot.
The ability of neural networks to adapt to a dataset for predicting missing values in between the data and extrapolate new data outside the dataset can be improved with the help of deep learning and LSTM-networks which have a stronger ability to learn datasets over a normal perceptron. The advantage of neural networks over classical statistical tools is so great, that sometimes neural networks are reduced to it's functionality in regression analysis.
Are applications available in which neural networks can be used outside of regression analysis for something different?
 Kaytez, Fazil, et al. "Forecasting electricity consumption: A comparison of regression analysis, neural networks and least squares support vector machines." International Journal of Electrical Power & Energy Systems 67 (2015): 431-438.