Robust Bayesian optimization for flexibility analysis of expensive simulation-based models with rigorous uncertainty bounds

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The performance of emerging biochemical systems rests on their potential to adapt to uncertainties quickly and accurately. Flexibility analysis is a quantitative framework for determining if a system can maintain safe and feasible operation despite uncertainty. Most available methods assume access to equation-oriented models, which can be difficult to obtain in practice. In this paper, we propose a sequential black-box flexibility analysis method, BoFlex, that overcomes this challenge by constructing probabilistic surrogate models over the joint space of uncertain and recourse variables. BoFlex is based on a special alternating confidence bound procedure, which we show finitely converges to a correct solution under mild assumptions on the unknown functions. We also establish a rigorous upper bound on the convergence rate in terms of the maximum information gain of the surrogate model. The advantages of BoFlex are demonstrated on several case studies including a heat exchanger network and a bubble column reactor.