A generalized-constraint neural network model: Associating partially known relationships for nonlinear regressions

In an attempt to enhance the neural network technique so that it can evolve from a ''black box'' tool into a semi-analytical one, we propose a novel modeling approach of imposing ''generalized constraints'' on a standard neural network. We redefine approximation problems by use of a new formalization with the aim of embedding prior knowledge explicitly into the model to the maximum extent. A generalized-constraint neural network (GCNN) model has therefore been developed, which basically consists of two submodels. One is constructed by the standard neural network technique to approximate the unknown part of the target function. The other is formed from partially known relationships to impose generalized constraints on the whole model. Three issues arising after combination of the two submodels are discussed: (a) the better approximation provided by the GCNN model compared with a standard neural network, (b) the identifiability of parameters in the partially known relationships, and (c) the discrepancy in the approximation due to removable singularities in the target function. Numerical studies of three benchmark problems show important findings that have not previously been reported in the literature. Significant benefits were observed from using the GCNN model in comparison with a standard neural network.