WELL RESERVOIR MODEL IDENTIFICATION USING TRANSLATION AND SCALE-INVARIANT HIGHER-ORDER NETWORKS

This paper describes the use of higher order neural networks to identi fy well reservoir response models from test data. Well reservoir respo nse models are characterised by a family of parametrically related cur ves. Neural networks can in principle offer an interesting approach to the identification problem as data are often uncertain and incomplete . However, it turns out that the well reservoir model, viewed as a cur ve in two dimensions, is invariant with respect to translation and cha nges of scale of the axes. This poses severe problems for a standard b ackpropagation network using the two-dimensional plot as an input reti na. This difficulty can be overcome by using a higher order network in which the output is forced to be invariant with respect to the requir ed transformations of the retina. In this way, the potentially huge nu mber of weights is significantly reduced using the in Variance conditi on as a constraint which acts so as to divide the weights into equival ence classes within which they ave equal. The resulting network can. t hen be trained using standard techniques. We contrast this network app roach with classical methods of model identification.