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如今的化学、凝聚态物理和材料科学界，发现新材料全靠计算模拟，尤其是那些能精准预测在有限温度下热力学稳定晶体结构的模拟。电子结构计算非常强大，能帮我们预测很多材料的属性，比如形成能、带隙啥的，而且几乎不需要做太多假设。
Fig. 1 | Predicted uncertainties of on-hull configurations and the EI scores of the EI-hull-area method.
利物浦大学的温东升博士和普渡大学的Micheal Titus教授团队提出了一种新奇的办法——基于贝叶斯不确定性预测的采集函数。这函数厉害了，能结合多元合金能量凸包的几何特点，快速筛选团簇展开模型里的原子排列构型。也就是说，它能用少量的样本，就大大提升模型的预测能力，从而减少我们依赖第一性原理计算的程度。
Fig. 2 | Comparison of the acquisition policies when learning the target convex hull of the Co-Ni system.
他们把这个采集函数用在了几种不同的材料体系上，比如Co-Ni合金、Zr-O化合物、Ni-Al-Cr三元合金，还有金属间化合物(Ni1−x, Cox)3Al的层错缺陷系统中，发现新函数居然能减少30%以上的第一性原理计算任务，而且完全不影响模型的准确性。研究还揭示了几个关键点：（1）多元合金的能量凸包是个成分-能量的高维系统，得用不同采集函数组合才能搞定复杂的凸包几何；（2）采集函数需要设计出合理的目标方程，来平衡计算成本和收益，才能在贝叶斯优化中获得最大效益；（3）对于低对称性的系统，它们拥有更大的构型空间，这个新函数能最快速地探索构型空间里的低能量和高能量构型，有利于研究低温、高温和亚稳态结构。
Fig. 3 | Learning the ground-state line of the α-phase ZrOx system using the EI-hull-area, EIbelow-hull, and GA-CE-hull schemes.
总的来说，他们的计算方法在研究高温材料的稳态、亚稳态层错以及合金、金属间化合物的短程有序方面，有着重大意义。该文近期发表于npj Computational Materials 10:210 2024，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。
Bayesian optimization acquisition functions for accelerated search of cluster expansion convex hull of multi-component alloys
Dongsheng Wen, Victoria Tucker and Michael S. Titus
Atomistic simulations are crucial for predicting material properties and understanding phase stability, essential for materials selection and development. However, the high computational cost of density functional theory calculations challenges the design of materials with complex structures and composition. This study introduces new data acquisition strategies using Bayesian-Gaussian optimization that efficiently integrate the geometry of the convex hull to optimize the yield of batch experiments. We developed uncertainty-based acquisition functions to prioritize the computation tasks of configurations of multi-component alloys, enhancing our ability to identify the ground-state line. Our methods were validated across diverse materials systems including Co-Ni alloys, Zr-O compounds, Ni-Al-Cr ternary alloys, and a planar defect system in intermetallic (Ni1−x, Cox)3Al. Compared to traditional genetic algorithms, our strategies reduce training parameters and user interaction, cutting the number of experiments needed to accurately determine the ground-state line by over 30%. These approaches can be expanded to multi-component systems and integrated with cost functions to further optimize experimental designs.
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