Constructing ordinary sum differential equations using polynomial networks

Abstract

Data relations can define general sum partial differential equations of a composite function additive derivative model. Time-series data observations can analogously describe an ordinary sum differential equation with time derivatives, which is possible to be solved using partial derivative term substitutions of time-dependent series. Differential polynomial neural network is a new type of neural network, which constructs and substitutes for an unknown general partial differential equation from data observations, developed by the author. It generates sum series of convergent partial polynomial derivative terms, which can describe an unknown complex function time-series. This type of non-linear regression decomposes a system model, described by the general differential equation, into many partial low order derivative specifications of selected relative sum terms. Common soft-computing techniques in general can apply input variables of only absolute interval values of a specific data range. The character of relative data allows processing a wider range of test interval values than defined by a training set. The characteristics of the composite sum differential equation solutions can facilitate a much greater variety of model forms than is allowed using standard soft computing methods. Recurrent neural network proved to form simple solid time-series models, most of which it is possible to describe using ordinary differential equations, so the comparisons were done.