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A new approach to determine the neural network's domain of validity by elliptic expansion

In order to perform systems analysis or synthesis, it is important to deduce a model of the process. Artificial Neural Networks (ANN) have shown their suitability to identify nonlinear processes without modeling them theoretically. Consequently, only measured data is used to train the ANN. Since an ANN is an unsuitable extrapolator and only a finite data set is used for training, an ANN provides a parameterization that is both local and approximate [1]. Thus, to be able to assess the generalization capabilities, it is compulsory to estimate the neural network's domain of validity. The algorithms so far known for this purpose [2] either require a great deal of computational efforts for application or generate a gross overestimation. In this paper, a new approach is presented that creates an estimate of the ANN's domain of validity with a prescribed accuracy. To achieve this, hyperspheres that characterize a certain domain of validity around the points of the training set are introduced. They are united step by step to domains of validity with an elliptic hull. Finally, a sufficiently small number of elliptic domains of validity remain. Thus, both the computational efforts during application are greatly reduced and the learning data set is described by a domain of validity with a specified accuracy that is guaranteed [3].