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基于深度学习原子特征表示方法的Janus过渡金属硫化物带隙预测

孙涛 袁健美

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基于深度学习原子特征表示方法的Janus过渡金属硫化物带隙预测

孙涛, 袁健美

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

Sun Tao, Yuan Jian-Mei
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  • 随着人工智能的发展, 机器学习在材料计算中的应用越来越广泛. 将机器学习应用到材料性质预测等任务中首要实现的是获得有效的材料特征表示. 本文采用一种原子特征表示方法, 研究一种低维、密集的分布式原子特征向量, 并用于材料带隙预测任务. 按照材料化学式中原子种类和原子个数, 使用Transformer编码器作为模型结构, 通过训练大量的材料化学式数据, 从而提取参与训练元素的特征. 利用该方法预测Janus结构过渡金属硫族化合物MXY (M代表过渡金属, X, Y是不同硫族元素)二维材料带隙. 基于深度学习得到的原子特征向量比传统的Magpie方法和Atom2Vec方法的预测平均绝对误差更小. 可视化分析和材料性质预测数值实验表明, 本文提出的基于深度学习提取的原子特征表示方法, 可以有效表征材料特征, 并且应用到材料带隙预测任务中.
    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.
      通信作者: 袁健美, yuanjm@xtu.edu.cn
    • 基金项目: 湖南省自然科学基金(批准号: 2021JJ30650)、湖南省学位与研究生教育改革研究项目(批准号: 2020JGYB097, 2020JGYB098)和湖南省研究生科研创新项目(批准号: QL20210142)资助的课题.
      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).
    [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 1137Google 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 120Google 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 120Google Scholar

    [5]

    牛程程, 李少波, 胡建军, 但雅波, 曹卓, 李想 2020 材料导报 34 23100Google Scholar

    Niu C C, Li S B, Hu J J, Dan Y B, Cao Z, Li X 2020 Mater. Rep. 34 23100Google Scholar

    [6]

    Hu T T, Song H, Jiang T, Li S B 2020 Symmetry 12 1889Google Scholar

    [7]

    Chen C, Ye W K, Zuo Y X, Zheng C, Ong S P 2019 Chem. Mater. 31 3564Google Scholar

    [8]

    Li S B, Dan Y B, Li X, Hu T T, Dong R Z, Cao Z, Hu J J 2020 Symmetry 12 262Google Scholar

    [9]

    Zhang L F, Han J Q, Wang H, Car R, E W N 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [10]

    de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, Gamst A 2016 Sci. Rep. 6 34256Google 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 6411Google Scholar

    [12]

    Calfa B A, Kitchin J R 2016 AIChE J. 62 2605Google Scholar

    [13]

    Ward L, Agrawal A, Choudhary A, Wolverton C 2016 NPJ Comput. Mater. 2 16028Google Scholar

    [14]

    Zhuo Y, Mansouri Tehrani A, Brgoch J 2018 J. Phys. Chem. Lett. 9 1668Google Scholar

    [15]

    Hu M X, Yuan J M, Sun T, Huang M, Liang Q Y 2021 Comput. Mater. Sci. 200 110841Google 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 1501Google 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 021001Google Scholar

    [20]

    Riis-Jensen A C, Deilmann T, Olsen T, Thygesen K S 2019 ACS Nano 13 13354Google 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 044002Google 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 042002Google Scholar

    [23]

    Schütt K T, Glawe H, Brockherde F, Sanna A, Müller K R, Gross E K U 2014 Phys. Rev. B 89 205118Google Scholar

    [24]

    Wu Y R, Li H P, Gan X S 2013 Adv. Mater. Res. 848 122Google 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 2825Google Scholar

  • 图 1  Transformer编码器结构

    Fig. 1.  The Transformer encoder structure.

    图 2  多头注意机构模块结构[16]

    Fig. 2.  Multi-attention mechanism module structure[16].

    图 3  模型训练示意图

    Fig. 3.  Model training diagram.

    图 4  主族元素层次聚类图

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

    图 5  PCA1和PCA2散点图

    Fig. 5.  PCA1 and PCA2 scatter maps.

    图 6  PCA3和PCA4散点图

    Fig. 6.  PCA3 and PCA4 scatter maps.

    图 7  对MXY Janus 单分子层材料的带隙预测平均绝对误差

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

    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Magpie50
    Atom2Vec80
    Atom_DL10
    下载: 导出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110.0101.0
    Atom2Vec多项式核210.0010.5
    Atom_DL多项式核410.3001.5
    下载: 导出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10.10.010.5
    Atom2Vec多项式核21.00.012.0
    Atom_DL多项式核31.00.152.5
    下载: 导出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
    MagpieAtom2VecAtom_DLMagpieAtom2VecAtom
    _DL
    MagpieAtom2VecAtom
    _DL
    ClSbTe1.2551.1981.1081.2361.1761.2801.1571.2531.3361.296
    ISSb1.2190.8850.9881.0610.8491.1111.1141.0680.7651.219
    ZrBrI0.7740.7060.6650.7020.4840.7000.9520.5660.8560.975
    ClSbSe1.1721.3211.2831.3431.4461.4611.2821.2941.4431.397
    ZrSSe0.8290.5690.5950.6800.5960.6030.8850.5780.6410.861
    MoSSe1.4530.9470.7830.9321.0890.9971.3941.1671.3571.220
    CrSeTe0.5720.2580.2470.2050.3820.2400.3380.3490.4090.395
    TiClI0.7450.6010.5240.6020.4080.7490.7170.5540.7920.636
    VClI1.1000.7690.7260.6230.5010.7141.3070.7210.9900.750
    VBrCl1.2891.0811.0051.0950.6330.9181.0520.9151.3831.159
    ZrBrCl0.9120.9710.8960.9200.7640.9551.0480.9201.2171.074
    BiIS0.4010.6980.6920.7000.5410.7230.5090.6590.8690.838
    WSTe1.1410.6460.6350.6340.6950.5311.0060.9400.6810.875
    BiClSe1.2350.9520.9981.1271.0220.9931.2040.9850.9851.085
    TiBrCl0.8301.1060.8600.7760.5360.9180.8630.7511.1250.887
    ZrClI0.8770.6330.6380.6330.6100.7940.9820.7000.9940.772
    AsClSe1.7171.4941.5491.5121.5591.4331.4901.4751.5791.498
    AsBrS1.4171.4471.4171.4681.3421.1841.2111.4651.4291.444
    ZrSTe0.2080.2370.2180.2450.2380.1450.1980.2490.0760.237
    ISSb0.7940.7410.8170.9190.8511.1130.9711.0700.9441.297
    BrSbTe1.3190.8781.0290.9831.1101.0151.2561.1441.2081.041
    BiBrS1.1880.9291.0671.1141.0160.8581.0410.9491.1841.079
    ZrSSe0.6130.5810.7060.7660.5950.6030.5380.5770.4480.651
    BiITe0.3460.5300.5080.4810.4640.5180.0330.4200.3760.173
    ClSbTe1.2551.1981.1081.2361.1761.2801.1571.2531.3361.296
    下载: 导出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 1137Google 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 120Google 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 120Google Scholar

    [5]

    牛程程, 李少波, 胡建军, 但雅波, 曹卓, 李想 2020 材料导报 34 23100Google Scholar

    Niu C C, Li S B, Hu J J, Dan Y B, Cao Z, Li X 2020 Mater. Rep. 34 23100Google Scholar

    [6]

    Hu T T, Song H, Jiang T, Li S B 2020 Symmetry 12 1889Google Scholar

    [7]

    Chen C, Ye W K, Zuo Y X, Zheng C, Ong S P 2019 Chem. Mater. 31 3564Google Scholar

    [8]

    Li S B, Dan Y B, Li X, Hu T T, Dong R Z, Cao Z, Hu J J 2020 Symmetry 12 262Google Scholar

    [9]

    Zhang L F, Han J Q, Wang H, Car R, E W N 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [10]

    de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, Gamst A 2016 Sci. Rep. 6 34256Google 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 6411Google Scholar

    [12]

    Calfa B A, Kitchin J R 2016 AIChE J. 62 2605Google Scholar

    [13]

    Ward L, Agrawal A, Choudhary A, Wolverton C 2016 NPJ Comput. Mater. 2 16028Google Scholar

    [14]

    Zhuo Y, Mansouri Tehrani A, Brgoch J 2018 J. Phys. Chem. Lett. 9 1668Google Scholar

    [15]

    Hu M X, Yuan J M, Sun T, Huang M, Liang Q Y 2021 Comput. Mater. Sci. 200 110841Google 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 1501Google 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 021001Google Scholar

    [20]

    Riis-Jensen A C, Deilmann T, Olsen T, Thygesen K S 2019 ACS Nano 13 13354Google 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 044002Google 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 042002Google Scholar

    [23]

    Schütt K T, Glawe H, Brockherde F, Sanna A, Müller K R, Gross E K U 2014 Phys. Rev. B 89 205118Google Scholar

    [24]

    Wu Y R, Li H P, Gan X S 2013 Adv. Mater. Res. 848 122Google 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 2825Google Scholar

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  • 被引次数: 0
出版历程
  • 收稿日期:  2022-07-11
  • 修回日期:  2022-10-09
  • 上网日期:  2022-11-01
  • 刊出日期:  2023-01-20

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