機(jī)器學(xué)習(xí)的在各領(lǐng)域的廣泛應(yīng)用也促生其在材料領(lǐng)域的應(yīng)用。它提供了一種革命性的工具，即能從高維數(shù)據(jù)中發(fā)現(xiàn)數(shù)據(jù)間的規(guī)律。有助于減少計(jì)算量從而加速對(duì)新材料的探索。對(duì)于復(fù)雜的數(shù)據(jù)集，如晶體化合物的數(shù)據(jù)集，一個(gè)至關(guān)重要的問題是如何從化學(xué)視角為晶體結(jié)構(gòu)構(gòu)建低維特征。糟糕的特征無法減低數(shù)據(jù)的復(fù)雜性或無法提取晶體的關(guān)鍵信息從而導(dǎo)致巨大的預(yù)測(cè)誤差。為了滿足覆蓋絕大多數(shù)晶體結(jié)構(gòu)和組成，特征需要滿足旋轉(zhuǎn)、平移和尺度不變性。因此完整、精確地?cái)?shù)字化描述晶體材料是一項(xiàng)具有挑戰(zhàn)性的任務(wù)。

來自北京大學(xué)深圳研究生院新材料學(xué)院的潘鋒教授和密歇根州立大學(xué)數(shù)學(xué)系的魏國衛(wèi)教授等提出，原子特殊的持續(xù)同調(diào)（ASPH）可作為機(jī)器學(xué)習(xí)預(yù)測(cè)材料形成能的特征，取得了較好的預(yù)測(cè)效果。不同于傳統(tǒng)拓?fù)涞母呒?jí)抽象，ASPH能將多尺度幾何信息嵌入拓?fù)洳蛔兞恐?，能有效地提取幾何空間中的獨(dú)立元件、環(huán)、空腔等獨(dú)特特征。

更具體來說，獨(dú)立元件由化學(xué)鍵彼此連接，而環(huán)和空腔則為多體相互作用。這一發(fā)現(xiàn)證明了代數(shù)拓?fù)淅碚撛谘芯烤w材料中可發(fā)揮重要作用。值得注意的是，相比于暨往方法，ASPH對(duì)晶體材料形成能的模擬計(jì)算有更準(zhǔn)確的預(yù)測(cè)能力，它的適用性可擴(kuò)展到所有空間群和絕大多數(shù)元素。這不僅提供了一種新型的晶體結(jié)構(gòu)描述方法，而且有助于利用計(jì)算機(jī)輔助設(shè)計(jì)和新材料發(fā)現(xiàn)。

該文近期發(fā)表于npj Computational Materials7:28(2021)，英文標(biāo)題與摘要如下，。

Topological representations of crystalline compounds for the machine-learning prediction of materials properties

Yi Jiang, Dong Chen, Xin Chen, Tangyi Li, Guo-Wei Wei & Feng Pan

Accurate theoretical predictions of desired properties of materials play an important role in materials research and development. Machine learning (ML) can accelerate the materials design by building a model from input data. For complex datasets, such as those of crystalline compounds, a vital issue is how to construct low-dimensional representations for input crystal structures with chemical insights.

In this work, we introduce an algebraic topology-based method, called atom-specific persistent homology (ASPH), as a unique representation of crystal structures. The ASPH can capture both pairwise and many-body interactions and reveal the topology-property relationship of a group of atoms at various scales.

Combined with composition-based attributes, ASPH-based ML model provides a highly accurate prediction of the formation energy calculated by density functional theory (DFT). After training with more than 30,000 different structure types and compositions, our model achieves a mean absolute error of 61 meV/atom in cross-validation, which outperforms previous work such as Voronoi tessellations and Coulomb matrix method using the same ML algorithm and datasets.

Our results indicate that the proposed topology-based method provides a powerful computational tool for predicting materials properties compared to previous works.

圖1：以BaTiO3為例，構(gòu)建晶體拓?fù)涮卣鞯倪^程

編輯：jq