Adaptive Exploration and Optimization of Materials Crystal Structures

Arvind Krishna (), Huan Tran (), Chaofan Huang (), Rampi Ramprasad () and V. Roshan Joseph ()
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Arvind Krishna: Department of Statistics and Data Science, Northwestern University, Evanston, Illinois 60208
Huan Tran: School of Material Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Chaofan Huang: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Rampi Ramprasad: School of Material Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
V. Roshan Joseph: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

INFORMS Joural on Data Science, 2024, vol. 3, issue 1, 68-83

Abstract: A central problem of materials science is to determine whether a hypothetical material is stable without being synthesized, which is mathematically equivalent to a global optimization problem on a highly nonlinear and multimodal potential energy surface (PES). This optimization problem poses multiple outstanding challenges, including the exceedingly high dimensionality of the PES, and that PES must be constructed from a reliable, sophisticated, parameters-free, and thus very expensive computational method, for which density functional theory (DFT) is an example. DFT is a quantum mechanics-based method that can predict, among other things, the total potential energy of a given configuration of atoms. DFT, although accurate, is computationally expensive. In this work, we propose a novel expansion-exploration-exploitation framework to find the global minimum of the PES. Starting from a few atomic configurations, this “known” space is expanded to construct a big candidate set. The expansion begins in a nonadaptive manner, where new configurations are added without their potential energy being considered. A novel feature of this step is that it tends to generate a space-filling design without the knowledge of the boundaries of the domain space. If needed, the nonadaptive expansion of the space of configurations is followed by adaptive expansion, where “promising regions” of the domain space (those with low-energy configurations) are further expanded. Once a candidate set of configurations is obtained, it is simultaneously explored and exploited using Bayesian optimization to find the global minimum. The methodology is demonstrated using a problem of finding the most stable crystal structure of aluminum.

Keywords: active learning; adaptive design; Bayesian optimization; computer experiments; crystal structure prediction; Gaussian process model; space-filling design (search for similar items in EconPapers)
Date: 2024
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