具有组-子-组结构的材料的机器学习建模

Prakriti Kayastha, R. Ramakrishnan
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引用次数: 2

摘要

朗道的连续相变理论是材料科学的基石。由朗道型跃迁连接的晶体结构在数学上通过群-子群关系联系起来。在本研究中,我们引入了“组-子组学习”,并展示了在训练集中包括材料的小单元相,以减少建模大相的样本外误差。提出的方法是通用的,独立于ML的形式化、描述符或数据集;并可扩展到其他对称抽象,如自旋、价序或电荷顺序。由于可用的材料数据集是异构的,用于实现组-子组结构的示例太少,因此我们提出了均匀分布在七个frieze组中的8393 Q1D有机金属材料的“FriezeRMQ1D”数据集,并提供了概念验证。对于这些材料,我们报告使用Faber-Christensen-Huang-Lilienfeld描述符进行25%的训练,误差< 3%,并将其性能与编码材料成分和晶体学Wyckoff位置的指纹表示进行比较。
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Machine learning modeling of materials with a group-subgroup structure
A cornerstone of materials science is Landau’s theory of continuous phase transitions. Crystal structures connected by Landau-type transitions are mathematically related through groupsubgroup relationships. In this study, we introduce “group-subgroup learning” and show including small unit cell phases of materials in the training set to decrease out-of-sample errors for modeling larger phases. The proposed approach is generic and is independent of the ML formalism, descriptors, or datasets; and extendable to other symmetry abstractions such as spin-, valency-, or charge order. Since available materials datasets are heterogeneous with too few examples for realizing the group-subgroup structure, we present the “FriezeRMQ1D” dataset of 8393 Q1D organometallic materials uniformly distributed across seven frieze groups and provide a proof-of-the-concept. For these materials, we report < 3% error with 25% training with the Faber–Christensen–Huang–Lilienfeld descriptor and compare its performance with a fingerprint representation that encodes materials composition as well as crystallographic Wyckoff positions.
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