When there is no theoretical understanding of the target function, training from examples is one of few options. In many cases, however, there may be a physical model that can provide useful information even if it is not completely accurate. Possibilities include
a rough model exists that accounts for the main variables only and ignores small details;
an accurate model exists, but is too cumbersome to use in practice; or
an exact model exists, but it is difficult or expensive to measure all the variables needed by the model.
Models can be useful to generate artificial training data for cases where it is difficult to obtain real training data. In physical control systems, for example, it may not be practical to obtain data for unusual operating modes such as process faults. Use of a model to generate additional artificial data for unusual operating modes of a steel rolling mill is described by Röscheisen, Hofmann, and Tresp .