Adaptive Exploration and Optimization of Materials Crystal Structures
Adaptive Exploration and Optimization of Materials Crystal Structures
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DOI：
10.1287/ijds.2023.0028
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发表时间：
2022-12
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影响因子：
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通讯作者：
A. Krishna;H. Tran;Chao-Ta Huang;R. Ramprasad;V. R. Joseph
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作者：
A. Krishna;H. Tran;Chao-Ta Huang;R. Ramprasad;V. R. Joseph
材料科学的一个核心问题是确定一种假设的材料在没有合成的情况下是否稳定，这在数学上等价于一个高度非线性和多峰的势能面上的全局优化问题。这个优化问题提出了多个突出的挑战，包括PES的极高维度，并且PES必须用可靠的、复杂的、无参数的、因此非常昂贵的计算方法来构建，密度泛函理论(DFT)就是一个例子。DFT是一种基于量子力学的方法，它可以预测给定原子构型的总势能等。DFT虽然准确，但在计算上是昂贵的。在这项工作中，我们提出了一种新的扩展-勘探-开采框架来寻找PES的全局最小值。从几个原子构型开始，这个已知的空间被扩展，以构建一个大的候选集。扩展以非自适应方式开始，添加了新的配置，而不考虑其势能。这一步骤的一个新特点是，它倾向于在不知道域空间边界的情况下生成空间填充设计。如果需要，结构空间的非自适应扩展之后是自适应扩展，其中域空间的“有希望的区域”(那些具有低能量配置的区域)被进一步扩展。一旦获得候选配置集，就同时使用贝叶斯优化来探索和利用它来寻找全局最小值。通过寻找最稳定的铝的晶体结构的问题对该方法进行了验证。历史：郭翠曾担任本文的高级编辑。资助：作者承认美国国家科学基金会授予DMREF-1921873和XSEDE到GRANT DMR170031。数据伦理与再现性注意：代码包可在Code Ocean上获得，网址为https://codeocean.com/capsule/3366149/tree，也可在本文的电子手册中找到(可在https://doi.org/10.1287/ijds.2023.0028上获得)。
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 ).