(576c) Multi-Objective Dynamic Reaction Process Design Based on Bayesian Optimization for Batch Reactors

In the field of fine chemicals and pharmaceutical manufacturing, leveraging dynamic conditions (i.e., time-varying condition control, such as temperature, feed rate, etc.) in batch and fed-batch reactors is crucial for exploring reaction spaces, extracting kinetic data, devising control trajectory and optimizing reaction results. The development of first-principle models for these nonlinear dynamic processes is challenging due to rather complex kinetics, and data-driven optimization methodologies, as a viable alternative, can be used to provide in-depth characterization of reaction processes based on experimental data and small amount of prior knowledge^1,2. Mathematical models and systematic experimental planning techniques, such as Dynamic Design of Experiments³, attempt to bridge knowledge gap in the complexity of reaction conditions, but often rely on offline optimization. These methods require extensive training data and resources, which restrict their effectiveness, especially in multi-objective experimental design.

To address this issue, this study introduces a novel Bayesian optimization-based methodology that significantly enhances the efficiency of multi-objective dynamic reaction processes in batch reactors. This data-driven approach in the optimization of dynamic processes involves the use of online Gaussian Process (GP) model, focusing on sequential decision-making rather than emulating an accurate response surface methodology model over the entire design space, leading to a decrease of experimental demands.

The proposed dynamic reaction multi-objective Bayesian optimization (DR-MOBO) framework, begins by extracting critical dynamic and static variables from experimental data. The dynamic variables, such as feeding profiles, are modeled by dynamic factors ω(τ), where τ denotes dimensionless time, scaled by the batch duration. These dynamic factors are represented through a finite linear combination of basis functions, such as shifted Legendre polynomials. This selection facilitates precise modeling of process dynamics across the reaction timeline. Afterwards, DR-MOBO constructs GPs and employs constrained genetic algorithms based on NSGA-II to approximate Pareto fronts. A bilateral trade-off acquisition function based on Pareto sets is developed to determine the next sampling points, which enhances the exploration of overall experimental design space and ensures improvements on the Pareto front by integrating uncertainty quantification with hypervolume criteria. Monte Carlo simulations and cross-validation are used to identify high-uncertainty regions, prioritizing them for subsequent sampling. The optimization process ends upon reaching the predefined maximum number of experiments.

The effectiveness of this methodology is validated through two case studies: (1) an in-silico penicillin fermentation in a semi-batch reactor and (2) the laboratory synthesis of Molnupiravir. Dynamic profile optimization aims at achieving desired product quality and batch duration. In the simulated case study on penicillin fermentation, the DR-MOBO algorithm demonstrated the efficiency by reducing the required number of experiments to 13, compared to 19 with the traditional Response Surface Methodology (RSM). This reduction was achieved while optimizing for the same batch duration and penicillin concentration, with a slight improvement attributed to a more comprehensive Pareto profile predicted by the algorithm. Additionally, in the experimental study of Molnupiravir synthesis, the algorithm iteratively enhanced the experimental process by recommending diverse factor values, avoiding local optima. These results have illustrated that the proposed method could systematically explore the experimental design space, thereby optimizing dynamic processes under constrained experimental conditions.

(1) Xing, Y.; Dong, Y.; Georgakis, C.; Zhuang, Y.; Zhang, L.; Du, J.; Meng, Q. Automatic Data‐driven Stoichiometry Identification and Kinetic Modeling Framework for Homogeneous Organic Reactions. AIChE J. 2022, 68 (7), e17713. https://doi.org/10.1002/aic.17713.

(2) Xing, Y.; Dong, Y.; Zhou, W.; Du, J.; Meng, Q. Optimization-Based Simultaneous Modelling of Stoichiometries and Kinetics in Complex Organic Reaction System. Chem. Eng. Sci. 2023, 276, 118758. https://doi.org/10.1016/j.ces.2023.118758.

(3) Georgakis, C. Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes. Ind. Eng. Chem. Res. 2013, 52 (35), 12369-12382. https://doi.org/10.1021/ie3035114.