Abstract
In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes generated on the fly. In this sense, PNN is a self-organizing network. The essence of the design procedure dwells on the Group Method of Data Handling (GMDH). Each node of the PNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. The experimental part of the study involves two representative time series such as Box–Jenkins gas furnace data and a pH neutralization process.