Forecast Models of Partial Differential Equations

Authors: Ladislav Zjavka

Publish Date: 2014

Volume: , Issue: , Pages: 1-11

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Abstract

Unknown data relations can describe lots of complex systems through partial differential equation solutions of a multiparametric function approximation Common neural network techniques of pattern classification or function approximation problems in general are based on wholepattern 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

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