A Method for Extrapolating Continuous Functions by Generating New Training Samples for Feedforward Artificial Neural Networks

Abstract

The goal of the present study is to find a method for improving the predictive capabilities of feedforward neural networks in cases where values distant from the input–output sample interval are predicted. This paper proposes an iterative prediction algorithm based on two assumptions. One is that predictions near the statistical sample have much lower error than those distant from the sample. The second is that a neural network can generate additional training samples and use them to train itself in order to get closer to a distant prediction point. This paper presents the results of multiple experiments with different univariate and multivariate functions and compares the predictions made by neural networks before and after their training with the proposed iterative algorithm. The results show that, having passed through the stages of the algorithm, artificial neural networks significantly improve their interpolation performance in long-term forecasting. The present study demonstrates that neural networks are capable of creating additional samples for their own training, thus increasing their approximating efficiency.

Keywords

• artificial neural networks
• extrapolation of continuous functions
• approximation of nonlinear processes