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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. History: Kwok Tsui served as the senior editor for this article. Funding: The authors acknowledge a U.S. National Science Foundation Grant DMREF-1921873 and XSEDE through Grant DMR170031. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://codeocean.com/capsule/3366149/tree and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0028 ). 

Abstract The sublimation enthalpy, , is a key thermodynamic parameter governing the phase transformation of a substance between its solid and gas phases. This transformation is at the core of many important materials' purification, deposition, and etching processes. While can be measured experimentally and estimated computationally, these approaches have their own different challenges. Here, we develop a machine learning (ML) approach to rapidly predict from data generated using density functional theory (DFT). We further demonstrate how combining ML and DFT methods with active learning can be efficient in exploring the materials space, expanding the coverage of the computed dataset, and systematically improving the ML predictive model of . With an error of kJ/mol in instantaneous predictions of , the ML model developed in this work will be useful for the community.