Determining functional relationships from trained neural networks

Research has shown that artificial neural networks (ANNs) can be trained to perform function mapping tasks. In this work, ANN mappings are approximated around an operating point by third-order polynomials (3OPs). A previously unknown function can be modeled by an ANN, and a 3OP can be derived from the ANN model. In addition, the sensitivity of an output to changes in the inputs can be easily determined from these polynomials in large neighborhoods around the operating points. Examples are shown that illustrate the use of the ANN-3OP mapping approach.