Comparison of simple neural networks and nonlinear regression models for descriptive modeling of Lactobacillus helveticus growth in pH-controlled batch cultures.

A set of 20 Lactobacillus helveticus growth curves was obtained from pH-controlled batch cultures with different pH setpoints, whey permeate and yeast extract concentrations. To find the best descriptive model of the biomass concentration versus time (y = X(t)) growth curve, fitting results of a large number of models were compared with statistical and approximate methods. Models studied included simple neural networks, reparameterized Logistic, Gompertz, Richards, Schnute, Weibull, and Morgan-Mercier-Flodin models, Amrane-Prigent model, and four new models based on autonomous growth functions. Simple neural networks with only four weights were good descriptive models of the growth curves and fitting qualities were similar to those of the best existing four-parameter models, such as the Logistic model. However, meaningful parameters had to be calculated numerically and use of simple neural networks yielded no distinctive advantages over other models. A new five-parameter model, based on an autonomous growth function, yielded the best fitting results, even when the number of model parameters was accounted for in the comparisons. However, the maximum specific growth rate was not always well estimated. Therefore the five-parameter Richards model was chosen as the best descriptive model of the growth curve.