Minimum Energy Designs: From Nanostructure Synthesis to Sequential Optimization

Motivated by a problem in the synthesis of nanowires, a sequential space filling design, called Sequential Minimum Energy Design (SMED), is proposed for exploring and searching for the optimal conditions in complex black-box functions. The SMED is a novel approach to generate designs that can quickly carve out regions with no observable nanostructure morphology, do not involve parametric estimation, and allow for the exploration of complex response surfaces. It can be viewed as a sequential design procedure for stochastic functions and a global optimization procedure for deterministic functions. Guidelines for choosing the parameters of the design are proposed. Convergence of the algorithm is studied under certain regularity conditions. Performance of the algorithm has been studied using experimental data on nanowire synthesis as well as standard test functions.