Process-constrained batch Bayesian approaches for yield optimization in multi-reactor systems

TL;DR

This paper tackles yield optimization in multi-reactor systems under hierarchical process constraints. It introduces process-constrained batch Bayesian optimization with Thompson sampling (pc-BO-TS) and its hierarchical extension (hpc-BO-TS), designed to balance exploration and exploitation within constrained batch evaluations. Through extensive synthetic benchmarks (including GMM, Levy/Hartmann, and Rosenbrock-based tests) and a realistic ODHP case on the REALCAT Flowrence platform, the methods consistently outperform existing constrained BO approaches in convergence speed and robustness. The work advances digital catalysis by enabling efficient, data-driven optimization of complex, constraint-rich microreactor networks, with practical implications for accelerated catalyst development and process design.

Abstract

The optimization of yields in multi-reactor systems, which are advanced tools in heterogeneous catalysis research, presents a significant challenge due to hierarchical technical constraints. To this respect, this work introduces a novel approach called process-constrained batch Bayesian optimization via Thompson sampling (pc-BO-TS) and its generalized hierarchical extension (hpc-BO-TS). This method, tailored for the efficiency demands in multi-reactor systems, integrates experimental constraints and balances between exploration and exploitation in a sequential batch optimization strategy. It offers an improvement over other Bayesian optimization methods. The performance of pc-BO-TS and hpc-BO-TS is validated in synthetic cases as well as in a realistic scenario based on data obtained from high-throughput experiments done on a multi-reactor system available in the REALCAT platform. The proposed methods often outperform other sequential Bayesian optimizations and existing process-constrained batch Bayesian optimization methods. This work proposes a novel approach to optimize the yield of a reaction in a multi-reactor system, marking a significant step forward in digital catalysis and generally in optimization methods for chemical engineering.

Figures (9)

• Figure 1: A hierarchical process-constrained (hpc) framework within a Multi-Reactor System, showcasing levels $\ell_0$ to $\ell_{N-1}$ each with distinct batch sizes $B_i$ and process constraints. Parameters $x_k$ at each level are experimental conditions, with higher levels enforcing stricter constraints.
• Figure 2: Tree structure of the dataset $X_t$ used by the hierarchical process-constrained algorithm where ${\mathbf x}_{t,0}$ results from UCB-based optimization (in red), determined at line 27 in \ref{['algo:tree_hpc_bo']}.
• Figure 3: Randomly generated Gaussian mixture model based objective functions.
• Figure 4: Evaluation of optimization methods across different Gaussian mixture model cases. Presented are the median log normalized regrets on the right and the kernel density estimates of the final iteration regrets on the left for all methods. Both figures share the same y-axis.
• Figure 5: Process-constrained method performances on Levy and Hartmann 6D test functions with 3 constrained dimensions among 6: (left) evolution of the median of the log-normalized regret over iterations; (right) distribution of the last iteration optima estimated by each method. Both figures share the same y-axis.