Abstract

Artificial neural networks in general are used to identify patterns according to their entire relationship, responding to related patterns with a similar output of applying absolute values of variables. However, a lot of real data contain some unknown relations of variables. Learning of these dependencies could be a new way of modelling complex systems instead of usual time series prediction based on pattern similarity. Differential polynomial neural network, which constructs a differential equation of fractional terms using multi-parametric polynomial functions, is a new type of neural network developed by the author. Its functionality is based on principles, which are applied in human brain learning. The brain does not utilize absolute values of variables, but relative ones, which are created by time-delayed dynamic periodic activation functions of biological neurons. They take part in differential equation composition as partial derivative terms, describing a relative change of particular dependent variables.

Key words: Polynomial neural network, dependence of variables identification, differential equation approximation, rational integral function, modelling of complex system