  Materials design can be cast as an optimization problem with the goal of
achieving desired properties, by varying material composition, microstructure
morphology, and processing conditions. Existence of both qualitative and
quantitative material design variables leads to disjointed regions in property
space, making the search for optimal design challenging. Limited availability
of experimental data and the high cost of simulations magnify the challenge.
This situation calls for design methodologies that can extract useful
information from existing data and guide the search for optimal designs
efficiently. To this end, we present a data-centric, mixed-variable Bayesian
Optimization framework that integrates data from literature, experiments, and
simulations for knowledge discovery and computational materials design. Our
framework pivots around the Latent Variable Gaussian Process (LVGP), a novel
Gaussian Process technique which projects qualitative variables on a continuous
latent space for covariance formulation, as the surrogate model to quantify
"lack of data" uncertainty. Expected improvement, an acquisition criterion that
balances exploration and exploitation, helps navigate a complex, nonlinear
design space to locate the optimum design. The proposed framework is tested
through a case study which seeks to concurrently identify the optimal
composition and morphology for insulating polymer nanocomposites. We also
present an extension of mixed-variable Bayesian Optimization for multiple
objectives to identify the Pareto Frontier within tens of iterations. These
findings project Bayesian Optimization as a powerful tool for design of
engineered material systems.
