Capabilities of a structured neural network. Learning and comparison with classical techniques

摘要

The use of Artificial Neural Networks (ANN) to identify dynamic processes and non linear functions usually provides a black box with the same inputs and outputs as the identified system. Our purpose in this paper is to adapt the ANN architecture to the structure of the mathematical equations that describe the system. Using similar structures for the mathematical study of dynamic systems while we can apply mathematical well known techniques to ANN results. In this paper we present an architecture for ANN based on the state space description of dynamic systems. Such ANN uses lineal combinations of sines and cosines as activation functions. The knowledge of the number of Fourier coefficients used by the network allows finding, by analytical or numerical methods, the maximum learning capacity of the network, which is being compared with the real learning capacity of the system. While in the simplest cases this study can be carried out theoretically and we can state that the maximum can be achieved, in more complicated systems simulations had to be used to compare results.