Mathematical models of complex systems on the basis of artificial neural networks

Abstract

Neural networking technique with models based on ordinary/partial differential equations is applied to the known incorrect problems. Solutions to such problems by routine approaches are difficult. The problem approximate solution is found as the artificial neural network output with a prescribed architecture. Network weights are determined in the stepwise network training based on the error functional minimization process in general. The case of the system parameters given in some variation intervals and the parameter set as a part of input data is considered. The construction of robust parameter neural network models is examined using some problems in classical and non-classical statements. The direct problem solution and the inverse problem regularization for the offered neural network approach are constructed uniformly. The neurocomputing results for fixed and growing neural networks are given. The supercomputer use is discussed. The neural network approach advantages and some possible generalizations are mentioned.