Методи створення метамоделей: стан питання

Abstract

There has been performed the generalization of materials of modern research in the field of mathematical The classification was carried out on the basis of the method used to create metamodels. The complexity and feasibility of using various techniques in specific cases were evaluated. Particular attention was paid to the construction of metamodels for multidimensional response hypersurfaces complex in topology. The geometric, stochastic, and heuristic classes of used metamodels were critically considered. The concentrated attention was paid to polynomial and spline-metamodels as to representatives of the class of geometric metamodels. A brief description of the main ideas of their construction, the necessary mathematical apparatus of implementation, lists the disadvantages and advantages of correct practical use in numerical experiments. Similarly, stochastic surrogate models, to which it is advisable to attribute regression models based on Gaussian processes or kriging models and models based on radial basis functions, were considered. In addition, a class of heuristic metamodels, which includes models on artificial neural networks, models using the method of group accounting of arguments and support-vector machines, was considered. Regression models based on radial basis neural networks and multilayer perceptrons were analyzed. The results of theoretical studies on surrogate models using multiple neural networks, that is, associative machines, were generalized and systematized. The features of constructing such machines of a static structure with various methods for obtaining collective coordinated composite of solution networks, in particular, with ensemble averaging and boosting, were given. The effectiveness of increasing the accuracy of approximation capabilities of metamodels using hybrid techniques for the simultaneous use of neural network technologies and additive regression, decomposition of the search area, was noted. According to the results of studies, it was found that for response hypersurfaces of complex topology in order to increase the accuracy of approximation, it makes sense to use a hybrid approach, which consists of the simultaneous application of decomposition technologies of the search area and neural networks built on the techniques of associative machines with various methods for obtaining solutions.