Forecast Models of Partial Differential Equations Using Polynomial Networks

Abstract

Unknown data relations can describe lots of complex systems through partial differential equation solutions of a multi-parametric function approximation. Common neural network techniques of pattern classification or function approximation problems in general are based on whole-pattern similarity relationships of trained and tested data samples. They apply input variables of only absolute interval values, which may cause problems by far various training and testing data ranges. Differential polynomial neural network is a new type of neural network developed by the author, which constructs and substitutes an unknown general sum partial differential equation, defining a system model of dependent variables. It generates a total sum of fractional polynomial terms defining partial relative derivative dependent changes of some combinations of input variables. This type of regression is based only on trained generalized data relations. The character of relative data allows processing a wider range of test interval values than defined by the training set. The characteristics of differential equation solutions also in general facilitate a greater variety of model forms than allow standard soft computing methods.Keywordspolynomial neural networkpartial differential equation compositionsum relative derivative termmulti-parametric function approximation