Approximating polynomial functions by Feedforward Artificial Neural Networks: Capacity analysis and design

摘要

Polynomial functions are used in many applications. In this paper, we address the capacity of Feedforward Artificial Neural Networks (FANNs) in approximating polynomial functions. Instead of studying the capacity of a FANN with infinitely available hidden nodes, which was proved to be a universal approximator, we provide the capacity results of a FANN with finite hidden nodes in approximating polynomial functions. First, we show that there is a relationship between the capacity of a FANN in approximating polynomial functions and the number of hidden nodes used in the FANN. Then, we describe a procedure to realize a FANN in approximating polynomial functions. Two examples are given to show the procedure. Several experiments are reported which verifies that a FANN with a certain number of hidden nodes has the capability in learning given polynomial functions. An extension of the approach for solving multiple criteria decision making problems is discussed. The experiments also show that the proposed algorithm for training a FANN performs accurately.