An industrial pharmaceutical company has provided industrial pilot scale fed-batch data from a biological process used to produce a foreign protein from fed-batch fermentation. This process had proven difficult to control due to the complex behavior of the bacteria after induction. Because of the difficulty of modeling the process fundamentally, neural networks are an attractive alternative. To capture dynamic systems a gray box model approach of parameter function neural networks was used. The parameter function neural network approach has been able to capture well this pilot scale fed-batch fermentation process. In order to obtain accurate training data, the data sets were fit and smoothed using smoothing cubic spline functions. Neural networks were found for the five critical parameter functions of growth rate, glucose consumption rate, oxygen consumption rate, acetate production rate, and protein production rate. Relatively simple networks were used in order to capture process behavior and not the significant noise in the industrial scale pilot data. Simulations using the neural network parameters predicted dynamic response data well. (c) 2006 Elsevier Ltd. All rights reserved.