The KBANN (Knowledge-Based Artificial Neural Networks) approach uses neural networks to refine knowledge that can be written in the form of simple propositional rules. This idea is extended by presenting the MANNIDENT (Multivariable Artificial Neural Network Identification) algorithm by which the mathematical equations of linear dynamic process models determine the topology and initial weights of a network, which is further trained using backpropagation. This method is applied to the task of modeling a nonisothermal chemical reactor in which a first-order exothermic reaction is occurring. This method produces statistically significant gains in accuracy over both a standard neural network approach and a linear model. Furthermore, using the approximate linear model to initialize the weights of the network produces statistically less variation in model fidelity. By structuring the neural network according to the approximate linear model, the model can be readily interpreted.