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In this study, we introduce and investigate a class of neural arhitectures 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 deveoped through learining. The number of layers of the PNN is not fixes in advance but is 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 netralization process.
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Projects co-financed by:
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.
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