Robust Adaptive Design of Experiments—An Acquisition Function Based on Graph Theory and Topological Data Analysis

Bayesian optimization (BO) is an efficient method for searching the input space of expensive black-box functions – synthesis and characterization workflows -- relying on previous experiments to guide the selection of subsequent experiments. BO balances exploration of unknown regions and exploitation of regions likely to yield the maximum value of the quantity of interest (QoI). Common acquisition functions in BO, such as Upper Confidence Bound (UCB), Probability of Improvement (PI), and Expected Improvement (EI), utilize the mean and standard deviation at each point to determine the next experiment. However, these acquisition functions do not account for the QoI robustness, i.e. how sensitive is the quantity of interest (QoI) to perturbations of the input variables? This becomes an important consideration in automated workflows, where the ideal extremal value of the QoI may not be practically usable due to the inherent uncertainty and stochasticity in processing and synthesis conditions.<br/><br/>We introduce a novel acquisition function that searches and identifies robust maxima – i.e. that have a low sensitivity to perturbations in input parameters. We use concepts from topological data analysis, specifically persistence diagrams, and graph theory, specifically connected components, to define a robustness factor into standard acquisition functions. Both concepts are specifically chosen for their ease of use, algorithmic efficiency, and availability of optimized codes (in python) for democratized use.<br/>The new acquisition function is implemented for straightforward use into available BO toolboxes like BoTorch. We illustrate the new acquisition function using both computational as well as experimental workflows.