The properties of latitudinal neural networks with potential power system applications

The properties of latitudinal neural network architecture are investigated. It is shown that the latitudinal neural networks structure possesses some nice properties which relate the approximation error to the number of neurons used in each sub-neural network and to the number of sub-neural networks. First, piecewise quadratic continuous functions can be approximated by a neural network with quadratic squashing sigmoidal functions in a constructive manner. Further, piecewise polynomial functions of degree m (greater than 2) can be approximated by a neural network with generalized sigmoidal functions, Then based on the introduction of total variation norm and finite smooth-decomposition, some convenient approximation properties of the latitudinal neural network structure can be derived. Finally, the potential application of the theoretical achievement in this paper to power systems, which is part of the ongoing project research, is discussed