An Engineering Solution to Taylor Series Expansion Coefficients Based on BP Neural Network

Abstract

One method of obtaining the Taylor Series Expansion Coefficients, which are suitable for engineering application, are presented: Artificial neural network(ANN) ， by virtue of its high nonlinear and learning abilities. The Taylor Series ( TS ) can be represented as a standard 3-layers feed-forward neural network after transforming in which the weights are correspond to the Taylor Coefficients. Therefore, the Taylor Coefficients can be determined by using Back Propagation(BP)algorithm. In the methods, we only need the sample space of the original function. So the method have the value of application in industries.

Polynomial Fitting Algorithm Based on Neural Network

“…The bias of each neuron in the hidden layer of the neural network is 0, and the weight between the neurons in the hidden layer and the neurons in the input layer is set to a constant: = 1( = 1,2, ⋯, ). For each neuron in the hidden layer of the neural network, its output is shown in formula (6).…”

“…Explicit polynomial fitting often uses Taylor series [5,6]. Taylor series are often used in the field of mathematics, especially in the research of approximate calculations.…”