Redes neurais artificiais: uma aplicação em petrofísica e estudo dos efeitos de estímulos persistentes

Abstract

Artificial Neural Networks are mathematical and computational devices which try to simulate some behaviors of biological neural networks. In the beginning of this work, we present a review about neural networks, showing an application of a Multi-Layered Perceptron for the estimative of petrophysical parameters. After that, we made an analytical and numerical study of the behavior of a neural network based on the Hopfield model on which we introduced in the system’s dynamics a parameter that acts as a field to simulate the effect of a persistent stimulus that privileges a stored pattern in the network. For the Hopfield’s model in the presence of this field, we present a review of the field’s effect in the model with dilution and asymmetry on the synaptic connections. After that, using a mean Field approximation, we have got a set of equations for the order parameters m and q in function of the parameters h (that simulates the persistent stimulus field),”alpha” (network’s storage capacity) and T (thermal noise), for the model on a fully connected network and symmetric connections. We analyze the recognition and storage capacity properties of the network, resulting on the phase diagram “alpha” x T for the model, showing the dependence of the recognition transition on the value of h. For the deterministic case (T = 0), we perform numerical simulations, where we develop and improve a computational algorithm using the multi-spin coding technique. Our simulation results show a good agreement with the analytical ones. All the results indicate na increase of the recognition capacity when increasing the h parameter, which controls the intensity of the stimulus field.