Prediction of band gap of transition metal sulfide with Janus structure by deep learning atomic feature representation method

Sun Tao; Yuan Jian-Mei

doi:10.7498/aps.72.20221374

Abstract

With the development of artificial intelligence, machine learning (ML) is more and more widely used in material computing. To apply ML to the prediction of material properties, the first thing to do is to obtain effective material feature representation. In this paper, an atomic feature representation method is used to study a low-dimensional, densely distributed atomic eigenvector, which is applied to the band gap prediction in material design. According to the types and numbers of atoms in the chemical formula of material, the Transformer Encoder is used as a model structure, and a large number of material chemical formula data are trained to extract the features of the training elements. Through the clustering analysis of the atomic feature vectors of the main group elements, it is found that the element features can be used to distinguish the element categories. The Principal Component Analysis of the atomic eigenvector of the main group element shows that the projection of the atomic eigenvector on the first principal component reflects the outermost electron number corresponding to the element. It illustrates the effectiveness of atomic eigenvector extracted by using the transformer model. Subsequently, the atomic feature representation method is used to represent the material characteristics. Three ML methods named Random Forest (RF), Kernel Ridge Regression (KRR) and Support Vector Regression (SVR) are used to predict the band gap of the two-dimensional transition metal chalcogenide compound MXY (M represents transition metal, X and Y refer to the different chalcogenide elements) with Janus structure. The hyperparameters of ML model are determined by searching for parameters. To obtain stable results, the ML model is tested by 5-fold cross-validation. The results obtained from the three ML models show that the average absolute error of the prediction using atomic feature vectors based on deep learning is smaller than that obtained from the traditional Magpie method and the Atom2Vec method. For the atomic eigenvector method proposed in this paper, the prediction accuracy of the KRR model is better than that of the results obtained from the Magpie method and Atom2Vec method. It shows that the atomic feature vector proposed in this paper has a certain correlation between the features, and is a low-dimensional and densely distributed feature vector. Visual analysis and numerical experiments of material property prediction show that the atomic feature representation method based on deep learning extraction proposed in this paper can effectively characterize the material features and can be applied to the tasks of material band gap prediction.

Keywords:

Authors and contacts

Sun Tao^1,2,
Yuan Jian-Mei^1,2

1.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
2.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan 411105, China

Corresponding author: Yuan Jian-Mei, yuanjm@xtu.edu.cn

Funds: Project supported by the Natural Science Foundation of Hunan Province, China (Grant No. 2021JJ30650), the Innovation Project of Degree and Postgraduate of Hunan Province, China (Grant Nos. 2020JGYB097, 2020JGYB098), and the Research Innovation Project of Postgraduate Student in Hunan Province, China (Grant No. QL20210142).

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References

[1]	He K M, Zhang X Y, Ren S Q, Sun J 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Las Vegas, NV, USA, June 27–30, 2016 p770
[2]	Ren S Q, He K M, Girshick R, Sun J 2017 IEEE Trans. Pattern Anal. Mach. Intell. 39 1137 Google Scholar
[3]	Devlin J, Chang M W, Lee K, Toutanova K 2019 Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies Minneapolis, USA, June 3–5, 2019 p4171
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[5]	牛程程, 李少波, 胡建军, 但雅波, 曹卓, 李想 2020 材料导报 34 23100 Google Scholar Niu C C, Li S B, Hu J J, Dan Y B, Cao Z, Li X 2020 Mater. Rep. 34 23100 Google Scholar
[6]	Hu T T, Song H, Jiang T, Li S B 2020 Symmetry 12 1889 Google Scholar
[7]	Chen C, Ye W K, Zuo Y X, Zheng C, Ong S P 2019 Chem. Mater. 31 3564 Google Scholar
[8]	Li S B, Dan Y B, Li X, Hu T T, Dong R Z, Cao Z, Hu J J 2020 Symmetry 12 262 Google Scholar
[9]	Zhang L F, Han J Q, Wang H, Car R, E W N 2018 Phys. Rev. Lett. 120 143001 Google Scholar
[10]	de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, Gamst A 2016 Sci. Rep. 6 34256 Google Scholar
[11]	Zhou Q, Tang P Z, Liu S X, Pan J B, Yan Q M, Zhang S C 2018 Proc. Nat1. Acad. Sci. U. S. A. 115 6411 Google Scholar
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[15]	Hu M X, Yuan J M, Sun T, Huang M, Liang Q Y 2021 Comput. Mater. Sci. 200 110841 Google Scholar
[16]	Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser Ł, Polosukhin I 2017 31st Conference on Neural Information Processing Systems (NIPS 2017) Long Beach, CA, USA, December 4–9, 2017 p6000
[17]	Saal J E, Kirklin S, Aykol M, Meredig B, Wolverton C 2013 JOM 65 1501 Google Scholar
[18]	Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z M, Gimelshein N, Antiga L, Desmaison A, Köpf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J J, Chintala S 2019 Proceedings of the 33rd International Conference on Neural Information Processing Systems Vancouver, Canada, December 8–14, 2019 p8026
[19]	Wang G, Chernikov A, Glazov M M, Heinz T F, Marie X, Amand T, Urbaszek B 2018 Rev. Mod. Phys. 90 021001 Google Scholar
[20]	Riis-Jensen A C, Deilmann T, Olsen T, Thygesen K S 2019 ACS Nano 13 13354 Google Scholar
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Cited By

图 1 Transformer编码器结构

Figure 1. The Transformer encoder structure.

DownLoad: Full-Size Img PowerPoint

图 2 多头注意机构模块结构^[16]

Figure 2. Multi-attention mechanism module structure^[16].

DownLoad: Full-Size Img PowerPoint

图 3 模型训练示意图

Figure 3. Model training diagram.

DownLoad: Full-Size Img PowerPoint

图 4 主族元素层次聚类图

Figure 4. A hierarchical clustering diagram of the main family elements.

DownLoad: Full-Size Img PowerPoint

图 5 PCA1和PCA2散点图

Figure 5. PCA1 and PCA2 scatter maps.

DownLoad: Full-Size Img PowerPoint

图 6 PCA3和PCA4散点图

Figure 6. PCA3 and PCA4 scatter maps.

DownLoad: Full-Size Img PowerPoint

图 7 对MXY Janus 单分子层材料的带隙预测平均绝对误差

Figure 7. MAE of band gap prediction for MXY Janus monolayer materials.

DownLoad: Full-Size Img PowerPoint

表 1 随机森林模型参数

Table 1. The random forest model parameter.

机器学习方法	原子表征方法	随机森林中树的个数
随机森林	Magpie	50
	Atom2Vec	80
	Atom_DL	10

DownLoad: CSV

表 2 核岭回归模型参数

Table 2. Kernel ridge regression model parameter.

机器学习方法	原子表征方法	核函数	多项式核次数	正则化强度	伽马参数	零系数
核岭回归	Magpie	多项式核	1	1	0.010	1.0
	Atom2Vec	多项式核	2	1	0.001	0.5
	Atom_DL	多项式核	4	1	0.300	1.5

DownLoad: CSV

表 3 支持向量机回归模型参数

Table 3. Support vector regression model parameter.

机器学习方法	原子表征方法	核函数	多项式核次数	正则化参数	伽马参数	零系数
支持向量机	Magpie	多项式核	1	0.1	0.01	0.5
	Atom2Vec	多项式核	2	1.0	0.01	2.0
	Atom_DL	多项式核	3	1.0	0.15	2.5

DownLoad: CSV

表 4 测试集材料预测值和计算值对比

Table 4. Comparison of material predictive and experimental values in the test.

材料化合物	带隙计算值	随机森林			核岭回归			支持向量机
材料化合物	带隙计算值	Magpie	Atom2Vec	Atom_DL	Magpie	Atom2Vec	Atom _DL	Magpie	Atom2Vec	Atom _DL
ClSbTe	1.255	1.198	1.108	1.236	1.176	1.280	1.157	1.253	1.336	1.296
ISSb	1.219	0.885	0.988	1.061	0.849	1.111	1.114	1.068	0.765	1.219
ZrBrI	0.774	0.706	0.665	0.702	0.484	0.700	0.952	0.566	0.856	0.975
ClSbSe	1.172	1.321	1.283	1.343	1.446	1.461	1.282	1.294	1.443	1.397
ZrSSe	0.829	0.569	0.595	0.680	0.596	0.603	0.885	0.578	0.641	0.861
MoSSe	1.453	0.947	0.783	0.932	1.089	0.997	1.394	1.167	1.357	1.220
CrSeTe	0.572	0.258	0.247	0.205	0.382	0.240	0.338	0.349	0.409	0.395
TiClI	0.745	0.601	0.524	0.602	0.408	0.749	0.717	0.554	0.792	0.636
VClI	1.100	0.769	0.726	0.623	0.501	0.714	1.307	0.721	0.990	0.750
VBrCl	1.289	1.081	1.005	1.095	0.633	0.918	1.052	0.915	1.383	1.159
ZrBrCl	0.912	0.971	0.896	0.920	0.764	0.955	1.048	0.920	1.217	1.074
BiIS	0.401	0.698	0.692	0.700	0.541	0.723	0.509	0.659	0.869	0.838
WSTe	1.141	0.646	0.635	0.634	0.695	0.531	1.006	0.940	0.681	0.875
BiClSe	1.235	0.952	0.998	1.127	1.022	0.993	1.204	0.985	0.985	1.085
TiBrCl	0.830	1.106	0.860	0.776	0.536	0.918	0.863	0.751	1.125	0.887
ZrClI	0.877	0.633	0.638	0.633	0.610	0.794	0.982	0.700	0.994	0.772
AsClSe	1.717	1.494	1.549	1.512	1.559	1.433	1.490	1.475	1.579	1.498
AsBrS	1.417	1.447	1.417	1.468	1.342	1.184	1.211	1.465	1.429	1.444
ZrSTe	0.208	0.237	0.218	0.245	0.238	0.145	0.198	0.249	0.076	0.237
ISSb	0.794	0.741	0.817	0.919	0.851	1.113	0.971	1.070	0.944	1.297
BrSbTe	1.319	0.878	1.029	0.983	1.110	1.015	1.256	1.144	1.208	1.041
BiBrS	1.188	0.929	1.067	1.114	1.016	0.858	1.041	0.949	1.184	1.079
ZrSSe	0.613	0.581	0.706	0.766	0.595	0.603	0.538	0.577	0.448	0.651
BiITe	0.346	0.530	0.508	0.481	0.464	0.518	0.033	0.420	0.376	0.173
ClSbTe	1.255	1.198	1.108	1.236	1.176	1.280	1.157	1.253	1.336	1.296

DownLoad: CSV

[1]	He K M, Zhang X Y, Ren S Q, Sun J 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Las Vegas, NV, USA, June 27–30, 2016 p770
[2]	Ren S Q, He K M, Girshick R, Sun J 2017 IEEE Trans. Pattern Anal. Mach. Intell. 39 1137 Google Scholar
[3]	Devlin J, Chang M W, Lee K, Toutanova K 2019 Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies Minneapolis, USA, June 3–5, 2019 p4171
[4]	郭佳龙, 王宗国, 王彦棡, 赵旭山, 宿彦京, 刘志威 2021 数据与计算发展前沿 3 120 Google Scholar Guo J L, Wang Z G, Wang Y G, Zhao X S, Su Y J, Liu Z W 2021 Frontiers of Data and Computing 3 120 Google Scholar
[5]	牛程程, 李少波, 胡建军, 但雅波, 曹卓, 李想 2020 材料导报 34 23100 Google Scholar Niu C C, Li S B, Hu J J, Dan Y B, Cao Z, Li X 2020 Mater. Rep. 34 23100 Google Scholar
[6]	Hu T T, Song H, Jiang T, Li S B 2020 Symmetry 12 1889 Google Scholar
[7]	Chen C, Ye W K, Zuo Y X, Zheng C, Ong S P 2019 Chem. Mater. 31 3564 Google Scholar
[8]	Li S B, Dan Y B, Li X, Hu T T, Dong R Z, Cao Z, Hu J J 2020 Symmetry 12 262 Google Scholar
[9]	Zhang L F, Han J Q, Wang H, Car R, E W N 2018 Phys. Rev. Lett. 120 143001 Google Scholar
[10]	de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, Gamst A 2016 Sci. Rep. 6 34256 Google Scholar
[11]	Zhou Q, Tang P Z, Liu S X, Pan J B, Yan Q M, Zhang S C 2018 Proc. Nat1. Acad. Sci. U. S. A. 115 6411 Google Scholar
[12]	Calfa B A, Kitchin J R 2016 AIChE J. 62 2605 Google Scholar
[13]	Ward L, Agrawal A, Choudhary A, Wolverton C 2016 NPJ Comput. Mater. 2 16028 Google Scholar
[14]	Zhuo Y, Mansouri Tehrani A, Brgoch J 2018 J. Phys. Chem. Lett. 9 1668 Google Scholar
[15]	Hu M X, Yuan J M, Sun T, Huang M, Liang Q Y 2021 Comput. Mater. Sci. 200 110841 Google Scholar
[16]	Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser Ł, Polosukhin I 2017 31st Conference on Neural Information Processing Systems (NIPS 2017) Long Beach, CA, USA, December 4–9, 2017 p6000
[17]	Saal J E, Kirklin S, Aykol M, Meredig B, Wolverton C 2013 JOM 65 1501 Google Scholar
[18]	Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z M, Gimelshein N, Antiga L, Desmaison A, Köpf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J J, Chintala S 2019 Proceedings of the 33rd International Conference on Neural Information Processing Systems Vancouver, Canada, December 8–14, 2019 p8026
[19]	Wang G, Chernikov A, Glazov M M, Heinz T F, Marie X, Amand T, Urbaszek B 2018 Rev. Mod. Phys. 90 021001 Google Scholar
[20]	Riis-Jensen A C, Deilmann T, Olsen T, Thygesen K S 2019 ACS Nano 13 13354 Google Scholar
[21]	Gjerding M N, Taghizadeh A, Rasmussen A, Ali S, Bertoldo F, Deilmann T, Knøsgaard N R, Kruse M, Larsen A H, Manti S, Pedersen T G, Petralanda U, Skovhus T, Svendsen M K, Mortensen J J, Olsen T, Thygesen K S 2021 2D Mater. 8 044002 Google Scholar
[22]	Haastrup S, Strange M, Pandey M, Deilmann T, Schmidt P S, Hinsche N F, Gjerding M N, Torelli D, Larsen P M, Riis-Jensen A C, Gath J, Jacobsen K W, Jørgen Mortensen J, Olsen T, Thygesen K S 2018 2D Mater. 5 042002 Google Scholar
[23]	Schütt K T, Glawe H, Brockherde F, Sanna A, Müller K R, Gross E K U 2014 Phys. Rev. B 89 205118 Google Scholar
[24]	Wu Y R, Li H P, Gan X S 2013 Adv. Mater. Res. 848 122 Google Scholar
[25]	Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay É 2011 J. Mach. Learn. Res. 12 2825 Google Scholar

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