Recently, a generic bioprocess gray box modeling approach  used entropy measure to plan the feeding solution profile. Multiple industrial experiments showed that such modeling is useful in cultivations with limited substrate feeding. The feeding profile served as a scaled approximation of the cumulative biomass profile. The cumulative glucose volume served as uncertainty to find the gray box model parameters in the feedback control scenarios. The numeric convex approach passed an analysis of its sensitivity to different initial computational conditions. The validation showed that the numeric routines were independent of the selected initial conditions. Such simplicity makes it useful for practical industrial applications.
Maximization of entropy presented online estimation of biomass concentration in fed-batch cultures of four types of recombinant E.coli strains and Saccharomyces cerevisiae cells . Practical experience disclosed that entropy is a relevant measure for both limited substrate feeding and dosed substrate feeding biotechnological processes. Moreover, the approach showed neither numeric nor structural model dependence on the strain type.
Research progress revealed that entropy measure by the use of fundamental knowledge could make the general model (Luedeking-Piret) more common for technological use when estimating target protein, compared to a sophisticated artificial neural network (ANN) . In fact, it replaces the ANN approach without compromising estimation accuracy.
 Urniezius, R.; Galvanauskas, V.; Survyla, A.; Simutis, R.; Levisauskas, D. From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time. Entropy 2018, 20, 779.
 Urniezius, R.; Survyla, A.; Paulauskas, D.; Bumelis, V.A.; Galvanauskas, V. Generic estimator of biomass concentration for Escherichia coli and Saccharomyces cerevisiae fed-batch cultures based on cumulative oxygen consumption rate. Microb. Cell Fact. 2019, 18, 190.
 Urniezius, R.; Survyla, A. Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process. Entropy 2019, 21, 1221.
This project has received funding from European Regional Development Fund (project No 01.2.2-LMT-K-718-03-0039) under grant agreement with the Research Council of Lithuania (LMTLT).