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基于机器学习的无机磁性材料磁性基态分类与磁矩预测

黎威 龙连春 刘静毅 杨洋

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基于机器学习的无机磁性材料磁性基态分类与磁矩预测

黎威, 龙连春, 刘静毅, 杨洋

Classification of magnetic ground states and prediction of magnetic moments of inorganic magnetic materials based on machine learning

Li Wei, Long Lian-Chun, Liu Jing-Yi, Yang Yang
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  • 磁性材料是信息时代重要的基础材料, 不同的磁性基态是磁性材料广泛应用的前提, 其中铁磁基态是高性能磁性材料的关键要求. 本文针对材料项目数据库中的无机磁性材料数据, 采用机器学习技术实现无机磁性材料铁磁、反铁磁、亚铁磁和顺磁基态的分类以及无机铁磁性材料磁矩的预测. 提取了材料的元素和结构属性特征, 通过两步式特征选择方法分别为磁性基态分类和磁矩预测筛选了20个材料特征, 发现材料特征中的电负性、原子磁矩和原子外围轨道未充满电子数对两种磁性性能具有重要贡献. 基于机器学习的随机森林算法, 构建了磁性基态分类模型和磁矩预测模型, 采用10折交叉验证的方法对模型进行定量评估, 结果表明所构建的模型具有足够的精度和泛化能力. 在测试检验中, 磁性基态分类模型的准确率为85.23%, 精确率为85.18%, 召回率为85.04%, F1分数为85.24%; 磁矩预测模型的拟合优度为91.58%, 平均绝对误差为0.098 μB/atom. 本研究为无机铁磁性材料的高通量分类筛选与磁矩预测提供了新的方法和选择, 可为新型无机磁性材料的设计研发提供参考.
    Magnetic materials are important basic materials in the information age. Different magnetic ground states are the prerequisite for the wide application of magnetic materials, among which the ferromagnetic ground state is a key requirement for future high-performance magnetic materials. In this paper, machine learning is used to study the classification of ferromagnetic, antiferromagnetic, ferrimagnetic and paramagnetic ground states of inorganic magnetic materials and the prediction of magnetic moments of inorganic ferromagnetic materials. We obtain 98888 inorganic magnetic materials data from the Materials Project database, containing material ids, chemical formulae, CIF files, magnetic ground states and magnetic moments, and extract 582 elemental and structural features for the inorganic magnetic materials by using Matminer. We design a two-step feature selection method. In the first step, RFECV is used to evaluate material features one by one to remove redundant features without degrading the model accuracy. In the second step, we rank the material features to further refine and select the most important material features for the model, and 20 material features are selected for the classification of magnetic ground states and the prediction of magnetic moments, respectively. Among the selected material features, it is found that the electronegativity, the atomic own magnetic moment and the number of unfilled electrons in the atomic peripheral orbitals all make important contributions to the classification of magnetic ground states and the prediction of magnetic moments. We build a magnetic ground state classification model and a magnetic moment prediction model by using the random forest, and quantitatively evaluate the machine learning models by using the 10-fold cross-validation approach, and the results show that the constructed machine learning models has sufficient accuracy and generalization capability. In the test set, the magnetic ground state classification model has an accuracy of 85.23%, a precision of 85.18%, a recall of 85.04%, and an F1 score of 85.24%; the magnetic moment prediction model has a goodness-of-fit of 91.58% and an average absolute error of 0.098 μB per atom. This study provides a new method and choice for high-throughput classification and screening of magnetic ground states of inorganic magnetic materials and predicting the magnetic moment of ferromagnetic materials.
      通信作者: 龙连春, longlc@bjut.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2018YFB0703500)资助的课题
      Corresponding author: Long Lian-Chun, longlc@bjut.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2018YFB0703500)
    [1]

    张志东 2015 物理学报 64 067503Google Scholar

    Zhang Z D 2015 Acta Phys. Sin. 64 067503Google Scholar

    [2]

    李绿洲, 蒋继乐, 卫荣汉, 李俊鹏, 田煜, 丁建宁 2016 物理学报 65 018103Google Scholar

    Li L Z, Jiang J L, Wei R H, Li J P, Tian Y, Ding J N 2016 Acta Phys. Sin. 65 018103Google Scholar

    [3]

    Sander D, Valenzuela S O, Makarov D, Marrows C H, Fullerton E E, Fischer P, McCord J, Vavassori P, Mangin S, Pirro P, Hillebrands B, Kent A D, Jungwirth T, Gutfleisch O, Kim C G, Berger A 2017 J. Phys. D: Appl. Phys. 50 363001Google Scholar

    [4]

    Vedmedenko E Y, Kawakami R K, Sheka D D, Gambardella P, Kirilyuk A, Hirohata A, Binek C, Chubykalo F O, Sanvito S, Kirby B J, Grollier J, Everschor S K, Kampfrath T, You C Y, Berger A 2020 J. Phys. D: Appl. Phys. 53 453001Google Scholar

    [5]

    Long T, Fortunato N M, Zhang Y X, Gutfleisch O, Zhang H B 2021 Mater. Res. Lett. 9 169Google Scholar

    [6]

    Yamada Y, Ueno K, Fukumura T, Yuan H T, Shimotani H, Iwasa Y, Gu L, Tsukimoto S, Ikuhara Y, Kawasaki M 2011 Science 332 1065Google Scholar

    [7]

    Yao Q S, Lu M, Du Y P, Wu F, Deng K M, Kan E J 2018 J. Mater. Chem. C 6 1709Google Scholar

    [8]

    何聪丽, 许洪军, 汤建, 王潇, 魏晋武, 申世鹏, 陈庆强, 邵启明, 于国强, 张广宇, 王守国 2021 物理学报 70 127501Google Scholar

    He C L, Xu H J, Tang J, Wang X, Wei J W, Shen S P, Chen Q Q, Shao Q M, Yu G Q, Zhang G Y, Wang S G 2021 Acta Phys. Sin. 70 127501Google Scholar

    [9]

    Gong C, Zhang X 2019 Science 363 eaav4450Google Scholar

    [10]

    王皓瑶, 刘海祎, 孙剑飞, 顾宁 2018 中国科学: 技术科学 48 921Google Scholar

    Wang H Y, Liu H Y, Sun J F, Gu N 2018 Sci. Sin. Technol. 48 921Google Scholar

    [11]

    Jha D, Choudhary K, Tavazza F, Liao W K, Choudhary A, Campbell C, Agrawal A 2020 Nat. Commun. 11 3643Google Scholar

    [12]

    Belsky A, Hellenbrandt M, Karen V L, Luksch P 2002 Acta Crystallogr., Sect. B: Struct. Sci. 58 364Google Scholar

    [13]

    Kirklin S, Saal J E, Meredig B, Thompson A, Doak J W, Aykol M, Ruhl S, Wolverton C 2015 NPJ Comput. Mater. 1 15010Google Scholar

    [14]

    Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A 2013 APL Mater. 1 011002Google Scholar

    [15]

    Schleder G R, Padilha A C M, Acosta C M, Costa M, Fazzio A 2019 J. Phys. Mater. 2 032001Google Scholar

    [16]

    Liu Y, Zhao T L, Ju W W, Shi S Q 2017 J. Materialomics 3 159Google Scholar

    [17]

    Isayev O, Oses C, Toher C, Gossett E, Curtarolo S, Tropsha A 2017 Nat. Commun. 8 15679Google Scholar

    [18]

    寇雯博, 董灏, 邹岷强, 韩均言, 贾西西 2021 物理学报 70 030701Google Scholar

    Kou W B, Dong H, Zou M Q, Han J Y, Jia X X 2021 Acta Phys. Sin. 70 030701Google Scholar

    [19]

    杨自欣, 高章然, 孙晓帆, 蔡宏灵, 张凤鸣, 吴小山 2019 物理学报 68 210502Google Scholar

    Yang Z X, Gao Z R, Sun X F, Cai H L, Zhang F M, Wu X S 2019 Acta Phys. Sin. 68 210502Google Scholar

    [20]

    Lu S H, Zhou Q H, Ouyang Y X, Guo Y L, Li Q, Wang J L 2018 Nat. Commun. 9 3405Google Scholar

    [21]

    Xu Y B, Yamazaki M, Villars P 2011 Jpn. J. Appl. Phys. 50 11RH02Google Scholar

    [22]

    Frey N C, Horton M K, Munro J M, Griffin S M, Persson K A, Shenoy V B 2020 Sci. Adv. 6 eabd1076Google Scholar

    [23]

    Yamamoto T https://storage.googleapis.com/rimcs_cgnn/cgnn_matsci_May_27_2019.pdf [2021-8-10]

    [24]

    Materials Project API https://materialsproject.org/open [2021-8-10]

    [25]

    Ward L, Dunn A, Faghaninia A, Zimmermann N E R, Bajaj S, Wang Q, Montoya J, Chen J M, Bystrom K, Dylla M, Chard K, Asta M, Persson K A, Snyder G J, Foster I, Jain A 2018 Comput. Mater. Sci. 152 60Google Scholar

    [26]

    Breiman L 2001 Mach. Learn. 45 5Google Scholar

    [27]

    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 E 2011 J. Mach. Learn. Res. 12 2825

  • 图 1  材料数据集的描述性统计 (a) 磁性基态分布直方图; (b) 晶胞磁矩频数分布图

    Fig. 1.  Descriptive statistics of material data set: (a) Distribution histogram of the magnetic ground state; (b) frequency distribution of the unit cell magnetic moment.

    图 2  机器学习模型的构建流程

    Fig. 2.  Construction process of the machine learning model.

    图 3  磁性基态分类模型的训练结果 (a) 10折交叉验证; (b) 材料特征排序

    Fig. 3.  Training results of the magnetic ground state classification model: (a) 10-fold cross-validation; (b) ranking of material features

    图 4  磁矩预测模型的训练结果 (a) 10折交叉验证; (b) 材料特征排序

    Fig. 4.  Training results of the magnetic moment prediction model: (a) 10-fold cross-validation; (b) ranking of material features

    图 5  磁性基态分类模型的检验结果 (a) 混淆矩阵; (b) 10折交叉验证

    Fig. 5.  Test results of the magnetic ground state classification model: (a) Confusion matrix; (b) 10-fold cross-validation.

    图 6  磁矩预测模型的检验结果 (a) 预测值与真实值的拟合情况; (b) 10折交叉验证

    Fig. 6.  Test results of the magnetic moment prediction model: (a) Fitting degree between predicted value and real value; (b) 10-fold cross validation.

    表 1  基于两步式特征选择法获得的材料特征

    Table 1.  Material features obtained by the two-step feature selection method.

    特征类型特征
    元素Mode Electronegativity*Mean NdUnfilled*Max MeltingT
    Min ElectronegativityAvg_dev NdUnfilled*Mode Number
    Range NUnfilledMax NdUnfilledMax Number
    Avg_dev NUnfilledMean GSmagmom*Min NValence
    Max NUnfilledRange GSmagmomRange NfValence
    Mode NfUnfilledAvg_dev GSmagmom*Avg_dev NfValence
    Mean NfUnfilledMax GSmagmomAvg_dev NdValence
    Range NfUnfilled*Max AtomicWeightMode MendeleevNumber
    Avg_dev NfUnfilledMode AtomicWeightAvg_dev MendeleevNumber
    Max NfUnfilledMean GSvolume_paMin MendeleevNumber
    Range NdUnfilledRange MeltingT
    结构VpaSine coulomb matrix 0
    * 该特征同时用于磁性基态分类和磁矩预测.
    下载: 导出CSV

    表 2  本研究中机器学习模型的超参数

    Table 2.  Hyperparameters of the machine learning model in this study.

    模型超参数
    RFCn = 400, features = 'log2', samples_split = 2, samples_leaf = 1
    RFRn = 300, features = 'auto', samples_split = 2, samples_leaf = 1
    下载: 导出CSV

    表 3  本研究磁性基态分类模型与其他研究者工作的定量评估对比

    Table 3.  Quantitative evaluation of the magnetic ground state classification model in this study and in comparison with other works.

    评价指标(平均值)本研究模型文献[5]文献[22]
    Accuracy/%85.2381.10
    Precision/%85.1884.29
    Recall/%85.0485.51
    F1 score/%85.2485.0885.00
    下载: 导出CSV

    表 4  本研究磁矩预测模型与其他研究者工作的定量评估对比

    Table 4.  Quantitative evaluation of the magnetic moment prediction model in this study and in comparison with other works.

    评价指标(平均值)本研究模型文献[23]
    R2/%91.58
    MAE/(μB·atom-1)0.0980.119
    下载: 导出CSV

    表 A1  基于两步式特征选择法获得的材料特征及其物理含义

    Table A1.  Material features and their physical meanings obtained by the two-step feature selection method.

    特征物理含义
    1Mode Electronegativity*材料组成元素电负性的众数
    2Min Electronegativity材料组成元素电负性的最小值
    3Range NUnfilled材料组成元素外围未充满电子数的范围
    4Avg_dev NUnfilled材料组成元素外围未充满电子数的平均偏差
    5Max NUnfilled材料组成元素外围未充满电子数的最大值
    6Mode NfUnfilled材料组成元素f轨道未充满电子数的众数
    7Mean NfUnfilled材料组成元素f轨道未充满电子数的平均值
    8Range NfUnfilled*材料组成元素f轨道未充满电子数的范围
    9Avg_dev NfUnfilled材料组成元素f轨道未充满电子数的平均偏差
    10Max NfUnfilled材料组成元素f轨道未充满电子数的最大值
    11Range NdUnfilled材料组成元素d轨道未充满电子数的范围
    12Mean NdUnfilled*材料组成元素d轨道未充满电子数的平均值
    13Avg_dev NdUnfilled*材料组成元素d轨道未充满电子数的平均偏差
    14Max NdUnfilled材料组成元素d轨道未充满电子数的最大值
    15Mean GSmagmom*材料组成元素磁矩的平均值
    16Range GSmagmom材料组成元素磁矩的范围
    17Avg_dev GSmagmom*材料组成元素磁矩的平均偏差
    18Max GSmagmom材料组成元素磁矩的最大值
    19Max AtomicWeight材料组成元素重量的最大值
    20Mode AtomicWeight材料组成元素重量的众数
    21Mean GSvolume_pa材料组成元素体积的平均值
    22Range MeltingT材料组成元素熔点的范围
    23Max MeltingT材料组成元素熔点的最大值
    24Mode Number材料组成元素原子序数的众数
    25Max Number材料组成元素原子序数的最大值
    26Min NValence材料组成元素价电子的最小值
    27Range NfValence材料组成元素f轨道价电子的范围
    28Avg_dev NfValence材料组成元素f轨道价电子的平均偏差
    29Avg_dev NdValence材料组成元素d轨道价电子的平均偏差
    30Mode MendeleevNumber材料组成元素门捷列夫数的众数
    31Avg_dev MendeleevNumber材料组成元素门捷列夫数的平均偏差
    32Min MendeleevNumber材料组成元素门捷列夫数的最小值
    33Vpa材料的晶胞体积
    34Sine coulomb matrix 0正弦库仑矩阵的第0个特征值
    * 该特征同时用于磁性基态分类和磁矩预测.
    下载: 导出CSV
  • [1]

    张志东 2015 物理学报 64 067503Google Scholar

    Zhang Z D 2015 Acta Phys. Sin. 64 067503Google Scholar

    [2]

    李绿洲, 蒋继乐, 卫荣汉, 李俊鹏, 田煜, 丁建宁 2016 物理学报 65 018103Google Scholar

    Li L Z, Jiang J L, Wei R H, Li J P, Tian Y, Ding J N 2016 Acta Phys. Sin. 65 018103Google Scholar

    [3]

    Sander D, Valenzuela S O, Makarov D, Marrows C H, Fullerton E E, Fischer P, McCord J, Vavassori P, Mangin S, Pirro P, Hillebrands B, Kent A D, Jungwirth T, Gutfleisch O, Kim C G, Berger A 2017 J. Phys. D: Appl. Phys. 50 363001Google Scholar

    [4]

    Vedmedenko E Y, Kawakami R K, Sheka D D, Gambardella P, Kirilyuk A, Hirohata A, Binek C, Chubykalo F O, Sanvito S, Kirby B J, Grollier J, Everschor S K, Kampfrath T, You C Y, Berger A 2020 J. Phys. D: Appl. Phys. 53 453001Google Scholar

    [5]

    Long T, Fortunato N M, Zhang Y X, Gutfleisch O, Zhang H B 2021 Mater. Res. Lett. 9 169Google Scholar

    [6]

    Yamada Y, Ueno K, Fukumura T, Yuan H T, Shimotani H, Iwasa Y, Gu L, Tsukimoto S, Ikuhara Y, Kawasaki M 2011 Science 332 1065Google Scholar

    [7]

    Yao Q S, Lu M, Du Y P, Wu F, Deng K M, Kan E J 2018 J. Mater. Chem. C 6 1709Google Scholar

    [8]

    何聪丽, 许洪军, 汤建, 王潇, 魏晋武, 申世鹏, 陈庆强, 邵启明, 于国强, 张广宇, 王守国 2021 物理学报 70 127501Google Scholar

    He C L, Xu H J, Tang J, Wang X, Wei J W, Shen S P, Chen Q Q, Shao Q M, Yu G Q, Zhang G Y, Wang S G 2021 Acta Phys. Sin. 70 127501Google Scholar

    [9]

    Gong C, Zhang X 2019 Science 363 eaav4450Google Scholar

    [10]

    王皓瑶, 刘海祎, 孙剑飞, 顾宁 2018 中国科学: 技术科学 48 921Google Scholar

    Wang H Y, Liu H Y, Sun J F, Gu N 2018 Sci. Sin. Technol. 48 921Google Scholar

    [11]

    Jha D, Choudhary K, Tavazza F, Liao W K, Choudhary A, Campbell C, Agrawal A 2020 Nat. Commun. 11 3643Google Scholar

    [12]

    Belsky A, Hellenbrandt M, Karen V L, Luksch P 2002 Acta Crystallogr., Sect. B: Struct. Sci. 58 364Google Scholar

    [13]

    Kirklin S, Saal J E, Meredig B, Thompson A, Doak J W, Aykol M, Ruhl S, Wolverton C 2015 NPJ Comput. Mater. 1 15010Google Scholar

    [14]

    Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A 2013 APL Mater. 1 011002Google Scholar

    [15]

    Schleder G R, Padilha A C M, Acosta C M, Costa M, Fazzio A 2019 J. Phys. Mater. 2 032001Google Scholar

    [16]

    Liu Y, Zhao T L, Ju W W, Shi S Q 2017 J. Materialomics 3 159Google Scholar

    [17]

    Isayev O, Oses C, Toher C, Gossett E, Curtarolo S, Tropsha A 2017 Nat. Commun. 8 15679Google Scholar

    [18]

    寇雯博, 董灏, 邹岷强, 韩均言, 贾西西 2021 物理学报 70 030701Google Scholar

    Kou W B, Dong H, Zou M Q, Han J Y, Jia X X 2021 Acta Phys. Sin. 70 030701Google Scholar

    [19]

    杨自欣, 高章然, 孙晓帆, 蔡宏灵, 张凤鸣, 吴小山 2019 物理学报 68 210502Google Scholar

    Yang Z X, Gao Z R, Sun X F, Cai H L, Zhang F M, Wu X S 2019 Acta Phys. Sin. 68 210502Google Scholar

    [20]

    Lu S H, Zhou Q H, Ouyang Y X, Guo Y L, Li Q, Wang J L 2018 Nat. Commun. 9 3405Google Scholar

    [21]

    Xu Y B, Yamazaki M, Villars P 2011 Jpn. J. Appl. Phys. 50 11RH02Google Scholar

    [22]

    Frey N C, Horton M K, Munro J M, Griffin S M, Persson K A, Shenoy V B 2020 Sci. Adv. 6 eabd1076Google Scholar

    [23]

    Yamamoto T https://storage.googleapis.com/rimcs_cgnn/cgnn_matsci_May_27_2019.pdf [2021-8-10]

    [24]

    Materials Project API https://materialsproject.org/open [2021-8-10]

    [25]

    Ward L, Dunn A, Faghaninia A, Zimmermann N E R, Bajaj S, Wang Q, Montoya J, Chen J M, Bystrom K, Dylla M, Chard K, Asta M, Persson K A, Snyder G J, Foster I, Jain A 2018 Comput. Mater. Sci. 152 60Google Scholar

    [26]

    Breiman L 2001 Mach. Learn. 45 5Google Scholar

    [27]

    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 E 2011 J. Mach. Learn. Res. 12 2825

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出版历程
  • 收稿日期:  2021-09-01
  • 修回日期:  2021-11-22
  • 上网日期:  2022-01-26
  • 刊出日期:  2022-03-20

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