2, University at Buffalo, The State University of New York, Buffalo, New York, United States
3, Air Force Research Laboratory, Wpafb, Ohio, United States
Control over the properties (length, defect densities) and structure (diameter, semiconducting/metallic type) of carbon nanotubes (CNTs) is highly desirable for a number of applications. In this regard, we developed ARES (Autonomous Research System), which utilized a Random Forest algorithm to optimize carbon nanotube growth rate by evaluating in situ feedback from Raman spectroscopy during the growth process.1 Here we utilize Bayesian Optimization (BO) to control carbon nanotube diameters, which are critical for electronics applications. Previous implementations BO in materials development often use statistical models such as Gaussian Processes (GPs) to represent the experimental response function of interest. GPs make it difficult to specify fine-grained structure in the response function other through the specification kernel functions, which are often used to identify smoothness and periodicity of the function. In materials applications, however, other important structures of the response function must be considered. For example, the kinetics of materials synthesis can be parameterized through input variables such as temperature and gas flow rates, which affect certain kinetic processes over others. Hence, such a kinetic response is best modeled locally so that each local model captures only the relevant physics specific to input variables such as temperature. Here we demonstrate the use of local approximation belief models for to control CNT diameters. We show how to use such Bayesian beliefs inside the Knowledge Gradient (KG) decision policy to select information-rich experiments to run inside a closed-loop experimental system. Through this combination of local approximation belief models and the KG decision policy, we show how specific CNT properties such as diameter can be tuned and optimized over a small number of experiments.