Artificial networks model systems with a set of inputs and outputs and expected behavior. To train a network for modeling such systems, hundreds, thousands, or millions of example inputs-output pairs may be required. This is called a labelled data set, and the network and its optimization algorithm are meant to find a set of network parameters that best match the I/O of the artificial network with the I/O of the system.
Are there any systems, for which sufficient labelled data sets exist, that have yet to be successfully modeled with artificial networks of any type (recurrent, deep, convolution, etc)?