THE SOLUTION OF THE APPROXIMATION PROBLEM OF NONLINEAR DEPENDANCES USING ARTIFICIAL NEURAL NETWORKS - V. N. Ageyev (Научный вестник МГТУ ГА)
The paper discusses issues connected with the use of an artificial neural network (ANN) to approximate the experimental data. One of the problems in the development of the ANN is the choice of an appropriate activation function for neurons of the hidden layer and adjusting the parameters of the function in the learning process of the network. The article discusses a three-layer perceptron with one hidden layer, each neuron of which has the activation function in the form of a Gaussian curve. The choice of radial basis activation function allows the use of the direct method of determining the weight coefficients – method of least squares in the process of network training. Thus the quality of the approximation depends on the correct choice of the value parameter of the activation function, which in this case is the width of the Gaussian bell curve. In practice, this parameter is determined by conducting numerical experiments. This is a rather time-taking process. In this paper we propose to define the value of this parameter by the training set, representing the coordinates of the test curve points set with the desired properties. These properties are based on the a priori data of the approximated functions (linear, quadratic, logarithmic, exponential relationship). Because the test curve is given in explicit form, the parameter of activation function is determined from the condition of reaching the minimum of the integral from the squared difference between the values of the test functions and the output of the network. This approach guarantees obtaining the approximating curve with good properties, in particular, it is characterized by the absence of so-called "oscillations" – many inflection points in its graph.