AJUSTE E INTEGRACIÓN NUMÉRICA DE FUNCIONES MUY OSCILANTES USANDO REDES NEURONALES ARTIFICIALES SUPERVISADAS

Abstract

This paper presents a methodology to adjust and integrate numerically very oscillating functions, even with a discontinuity,
using a vectorial supervised artificial neural network (RNASV), which consists of three layers: one input, one output and one
hidden learning layer, in which the activation function is an array. It is proposed to adjust very oscillating functions as a
linear combination of cosine functions
We present the important properties of the Hessian matrix derived from the resulting matrix activation function in the case that
the nodes are equidistant , where is the spacing between nodes.
To adjust very oscillating functions, there are several training techniques of the RNASV, two constant factor learning and two
variable factor learning. Using known highly oscillating functions, shows the comparison between different training
techniques respect the number of training and time required to obtain a good fit.
Finally, we present the numerical approximation of definite integrals highly oscillating functions, obtained from the integral of
the linear combination that approximates cosine functions
This shows the comparison with exact results and Adaptive Simpson's method, for each of the different techniques of training
the neural network.