A bootstrap-aggregated hybrid semi-parametric modeling framework for bioprocess development.

Hybrid semi-parametric modeling, combining mechanistic and machine-learning methods, has proven to be a powerful method for process development. This paper proposes bootstrap aggregation to increase the predictive power of hybrid semi-parametric models when the process data are obtained by statistical design of experiments. A fed-batch Escherichia coli optimization problem is addressed, in which three factors (biomass growth setpoint, temperature, and biomass concentration at induction) were designed statistically to identify optimal cell growth and recombinant protein expression conditions. Synthetic data sets were generated applying three distinct design methods, namely, Box-Behnken, central composite, and Doehlert design. Bootstrap-aggregated hybrid models were developed for the three designs and compared against the respective non-aggregated versions. It is shown that bootstrap aggregation significantly decreases the prediction mean squared error of new batch experiments for all three designs. The number of (best) models to aggregate is a key calibration parameter that needs to be fine-tuned in each problem. The Doehlert design was slightly better than the other designs in the identification of the process optimum. Finally, the availability of several predictions allowed computing error bounds for the different parts of the model, which provides an additional insight into the variation of predictions within the model components.