Efficient Closed-loop Maximization of Carbon Nanotube Growth Rate using Bayesian Optimization

A major technological challenge in materials research is the large and complex parameter space, which hinders experimental throughput and ultimately slows down development and implementation. In single-walled carbon nanotube (CNT) synthesis, for instance, the poor yield obtained from conventional catalysts is a result of limited understanding of input-to-output correlations. Autonomous closed-loop experimentation combined with advances in machine learning (ML) is uniquely suited for high-throughput research. Among the ML algorithms available, Bayesian optimization (BO) is especially apt for exploration and optimization within such high-dimensional and complex parameter space. BO is an adaptive sequential design algorithm for finding the global optimum of a black-box objective function with the fewest possible measurements. Here, we demonstrate a promising application of BO in CNT synthesis as an efficient and robust algorithm which can (1) improve the growth rate of CNT in the BO-planner experiments over the seed experiments up to a factor 8; (2) rapidly improve its predictive power (or learning); (3) Consistently achieve good performance regardless of the number or origin of seed experiments; (4) exploit a high-dimensional, complex parameter space, and (5) achieve the former 4 tasks in just over 100 hundred experiments (~8 experimental hours) – a factor of 5× faster than our previously reported results.