Computational models are increasingly used to investigate and predict the complex dynamics of biological and biochemical systems. Nevertheless, governing equations of a biochemical system may not be (fully) known, which would necessitate learning the system dynamics directly from, often limited and noisy, observed data. On the other hand, when expensive models are available, systematic and efficient quantification of the effects of model uncertainties on quantities of interest can be an arduous task. This paper leverages the notion of flow-map (de)compositions to present a framework that can address both of these challenges via learning data-driven models useful for capturing the dynamical behavior of biochemical systems. Data-driven flow-map models seek to directly learn the integration operators of the governing differential equations in a black-box manner, irrespective of structure of the underlying equations. As such, they can serve as a flexible approach for deriving fast-to-evaluate surrogates for expensive computational models of system dynamics, or, alternatively, for reconstructing the long-term system dynamics via experimental observations. We present a data-efficient approach to data-driven flow-map modeling based on polynomial chaos Kriging. The approach is demonstrated for discovery of the dynamics of various benchmark systems and a co-culture bioreactor subject to external forcing, as well as for uncertainty quantification of a microbial electrosynthesis reactor. Such data-driven models and analyses of dynamical systems can be paramount in the design and optimization of bioprocesses and integrated biomanufacturing systems.

The performance of advanced controllers depends on the selection of several tuning parameters that can affect the closed-loop control performance and constraint satisfaction in highly nonlinear and nonconvex ways. There has been a significant interest in auto-tuning of complex control structures using Bayesian optimization (BO). However, an open challenge is how to deal with uncertainties in the closed-loop system that cannot be attributed to a lumped, small-scale noise term. This paper develops an adversarially robust BO (ARBO) method that is suited to auto-tuning problems with significant time-invariant uncertainties in a plant simulator. ARBO uses a Gaussian process model that jointly describes the effect of the tuning parameters and uncertainties on the closed-loop performance. ARBO uses an alternating confidence-bound procedure to simultaneously select the next candidate tuning and uncertainty realizations, implying only one expensive closed-loop simulation is needed at each iteration. The advantages of ARBO are demonstrated on two case studies.