Efficient Prediction of Grain Boundary Energies from Atomistic Simulations via Sequential Design,Advanced Theory and Simulations

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Efficient Prediction of Grain Boundary Energies from Atomistic Simulations via Sequential Design
Advanced Theory and Simulations ( IF 2.9 ) Pub Date : 2022-04-14 , DOI: 10.1002/adts.202100615
Martin Kroll ₁ , Timo Schmalofski ₂ , Holger Dette ₁ , Rebecca Janisch ₂

Affiliation

With the goal of improving data based materials design, it is shown that by a sequential design of experiment scheme the process of generating and learning from the data can be combined to discover the relevant sections of the parameter space. The application is the energy of grain boundaries as a function of their geometric degrees of freedom, calculated from a simple model, or via atomistic simulations. The challenge is to predict the deep cusps of the energy, which are located at irregular intervals of the geometric parameters. Existing sampling approaches either use large sets of datapoints or a priori knowledge of the cusps' positions. By contrast, the authors' technique can find unknown cusps automatically with a minimal amount of datapoints. Key point is a Kriging interpolator with Matérn kernel to estimate the energy function. Using the jackknife variance, the next point in the sequential design is a compromise between sampling the region of largest fluctuations and avoiding a clustering of datapoints. In this way, the cusps of the energy can be found within only a few iterations, and refined as desired. This approach will be advantageous for any application with strong, localized fluctuations in the values of the unknown function.

中文翻译：

通过顺序设计从原子模拟中有效预测晶界能

以改进基于数据的材料设计为目标，结果表明，通过实验方案的顺序设计，可以结合从数据中生成和学习的过程，以发现参数空间的相关部分。应用是晶界的能量作为其几何自由度的函数，通过简单模型或通过原子模拟计算得出。挑战在于预测能量的深尖点，这些尖点位于几何参数的不规则间隔处。现有的采样方法要么使用大量数据点，要么使用尖点位置的先验知识。相比之下，作者的技术可以用最少的数据点自动找到未知的尖点。关键点是一个带有 Matérn 核的 Kriging 插值器来估计能量函数。使用折刀方差，顺序设计中的下一个点是在对波动最大的区域进行采样和避免数据点聚类之间进行折衷。通过这种方式，只需几次迭代即可找到能量的尖点，并根据需要进行细化。这种方法对于任何在未知函数的值中具有强烈的局部波动的应用都是有利的。

更新日期：2022-04-14

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