Embedding Theoretical Models in Neural Networks

A novel method for incorporating constraints and default models into neural networks is presented. The method involves a parallel arrangement of a default model and a radial basis function network. The training procedure accounts for equality and inequality constraints that must be satisfied for all future inputs to the network. In the case of linear equality constraints and no inequality constraints, training is reduced to a quadratic problem possessing an analytical solution. The extrapolation properties of the model-based network are controllable to a greater extent than previous network models.