基于机器学习训练金属离子吸附能预测模型的研究

doi:10.15541/jim20200748

无机材料学报 ›› 2021, Vol. 36 ›› Issue (11): 1178-1184.DOI: 10.15541/jim20200748

基于机器学习训练金属离子吸附能预测模型的研究

张瑞鸿¹(), 魏鑫², 卢占会¹, 艾玥洁³()

1.华北电力大学数理学院, 北京 102206
2.华北电力大学控制与计算机工程学院, 北京 102206
3.华北电力大学环境科学与工程学院资源与环境系统优化教育部重点实验室, 北京 102206

收稿日期:2020-12-31 修回日期:2021-04-15 出版日期:2021-11-20 网络出版日期:2021-06-01
通讯作者: 艾玥洁, 副教授. E-mail: aiyuejie@ncepu.edu.cn
作者简介:张瑞鸿(1996-), 女, 硕士研究生. E-mail: zhangruihong@ncepu.edu.cn
基金资助:
国家自然科学基金(22076044);国家重点研发计划(2017YFA0207002);中央高校基础研究经费(2017YQ001)

Training Model for Predicting Adsorption Energy of Metal Ions Based on Machine Learning

ZHANG Ruihong¹(), WEI Xin², LU Zhanhui¹, AI Yuejie³()

1. College of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
2. College of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
3. MOE Key Laboratory of Resources and Environmental System Optimization, College of Environmental Science and Engineering, North China Electric Power University, Beijing 102206, China

Received:2020-12-31 Revised:2021-04-15 Published:2021-11-20 Online:2021-06-01
Contact: AI Yuejie, associate professor. E-mail: aiyuejie@ncepu.edu.cn
About author:ZHANG Ruihong(1996-), femal, Master candidate. E-mail: zhangruihong@ncepu.edu.cn
Supported by:
National Natural Science Foundation of China(22076044);National Key Research and Development Program of China(2017YFA0207002);Fundamental Research Funds for the Central Universities(2017YQ001)

摘要/Abstract

摘要：

本研究通过密度泛函理论对氧化石墨烯和金属离子的吸附行为进行理论模拟。基于机器学习方法训练预测模型的过程中, 缺失值采用推荐系统中广泛使用的奇异值分解方法处理, 并用梯度提升机解释了影响吸附能的重要因素。结果发现吸附体系中存在九种特征可为吸附能提供90%的累积重要性, 分别为离子半径、零点振动能量、密立根电荷、沸点、偶极矩、原子量、摩尔定容热容、自旋多重度和键长。定量评估了六种回归方法的预测精度, 包括支持向量回归、岭回归、随机森林、极端随机森林、极端梯度提升和轻梯度提升机。结果表明, 机器学习方法可提供足够的吸附能预测准确性, 其中极端随机森林方法表现出最优的预测性能, 均方误差仅为0.075。该模型用于香兰素吸附金属离子的测试, 验证了基于机器学习训练金属离子吸附能预测模型的可行性, 但仍需进一步提高其泛化能力。本研究基于机器学习预测吸附能, 简化预测过程、节省计算时间, 可为吸附去除金属离子的理论和实验研究提供参考。

关键词: 机器学习, 密度泛函理论, 吸附能, 金属离子, 极端随机森林

Abstract:

The adsorption behavior of graphene oxide and metal ions was simulated theoretically by density functional theory. In the process of training the prediction model based on the machine learning method, the missing values were processed by matrix completion method, which was widely used in the recommendation systems, and gradient boosting machine (GBM) was trained to explain the importance of factors that affect the adsorption energy. The result showed that nine properties of the adsorption, namely ionic radius, zero-point vibration energy, Mulliken charge, boiling point, dipole moment, atomic weight, molar heat capacity at constant volume (CV), spin multiplicity and bond length, were found to provide 90% importance of the cumulative adsorption energy. Then six regression methods, including support vector regression, ridge regression, random forest, extremely randomized trees, extreme gradient boosting, and light gradient boosting machine, were used to quantitatively evaluate the prediction accuracy. The results showed that machine learning could provide sufficient accuracy to predict adsorption energy. Among them, extremely randomized trees displayed the best prediction performance, with a mean square error only 0.075. Furthermore, the trained model was tested in a system of vanillin adsorbing metal ions, verifying the feasibility of training the prediction model of adsorption energy based on machine learning. But it is still necessary to be further improved. In general, this research takes the advantage of machine learning on the basis of saving experimental time to provide an instructive reference for theoretical research on metal ion removal.

Key words: machine learning, density functional theory, adsorption energy, metal ions, extremely randomized trees

中图分类号:

TQ174

张瑞鸿, 魏鑫, 卢占会, 艾玥洁. 基于机器学习训练金属离子吸附能预测模型的研究[J]. 无机材料学报, 2021, 36(11): 1178-1184.

ZHANG Ruihong, WEI Xin, LU Zhanhui, AI Yuejie. Training Model for Predicting Adsorption Energy of Metal Ions Based on Machine Learning[J]. Journal of Inorganic Materials, 2021, 36(11): 1178-1184.

图/表 7

表1 基于DFT计算得到的21个特征描述符

Table 1 21 feature descriptors calculated based on DFT

No.	Feature descriptor	No.	Feature descriptor	No.	Feature descriptor
1	Charge	8	Ionic radius	15	CV (Cal/mol-K)
2	Spin	9	Melting point	16	S(Cal/mol-K)
3	Atomic radius	10	Boiling point	17	Zero-point vibrational energy/(kCal·mol^-1)
4	Atomic number	11	First ionization energy	18	Molecular mass
5	Atomic weight	12	Electronegativity	19	Mulliken charges
6	Density/(g·cm^-3)	13	M-O (bond length)	20	APT charges
7	Atomic volume	14	E(Thermal)/(kCal·mol^-1)	21	Dipole moment/D

图1 (a)相关系数>0.6的特征间相关性热力图和(b)GO吸附Cr3+的吸附结构示例

Fig. 1 (a) Thermal map of correlation between features with correlation coefficient>0.6, and (b) example of adsorption structure of GO adsorbing Cr3+ Note: 1 Cal=4.104 J

图2 特征重要性排名

Fig. 2 Feature importance ranking Note: 1 Cal=4.104 J; 1 D≈0.020819434 nm

表2 六种机器学习方法的最优超参数

Table 2 Optimal hyperparameters of six machine learning methods

Category	Method	Optimal hyperparameters
Kernel	Support vector regression (SVR)	C = 2, kernel=“ rbf ”
Kernel	Ridge regression	Alpha = 30
Random forest	Random forest (RF)	n_estimators = 31, max_depth = 6, max_features = 2
Random forest	Extremely randomized trees (ERT)	n_estimators = 31, max_depth = 7, random_state = 1
Boosting	Extreme gradient boosting (XGBoost)	n_estimators = 31, max_depth = 2, min_child_weight = 13, learning_rate =.32
Boosting	Light gradient boosting machine (LightGBM)	n_estimators =17, objective = ‘regression’, num_leaves = 31, learning_ rate = 0.32

图3 6种机器学习方法的模型拟合效果及评分

Fig. 3 Fitting effect diagram and score of six machine learning methods. (a) Support vector regression (SVR); (b) Ridge regression (Ridge); (c) Random forest (RF); (d) Extremely randomized trees (ERT); (e) Extreme gradient boosting (XGBoost); (f) Light gradient boosting machine (LightGBM)

图4 (a)四种集成方法的MSE; (b~e)四种集成方法真实值和预测值的相关图

Fig. 4 (a) Mean square error (MSE) of the four ensemble methods, and (b-e) correlation graphs of the true and predicted values of the four ensemble methods (b) Random forest (RF); (c) Extremely randomized trees (ERT); (d) Extreme gradient boosting (XGBoost); (e) Light gradient boosting machine (LightGBM)

图5 (a)香兰素单体吸附金属离子的结构示例图; (b)ERT用于VMA-Mn+吸附能的拟合效果图; (c)ERT用于VMA-Mn+吸附能的相关图

Fig. 5 (a) Example of the structure of vanillin monomer adsorbing metal ions; (b) Fitting effect graph of Extremely Randomized Trees (ERT) for VMA-Mn+ adsorption energy; (c) Correlation diagram of ERT for VMA-Mn+ adsorption energy

参考文献 34

[1]	PENG W J, LI H Q, LIU Y Y, et al. A review on heavy metalions adsorption from water by graphene oxide and its composites. Journal of Molecular Liquids, 2017, 230:496-504. DOI URL
[2]	AHMAD S Z N, SALLEH W N W, ISMAIL A F, et al. Adsorptive removal of heavy metal ions using graphene-based nanomaterials: toxicity, roles of functional groups and mechanisms. Chemosphere, 2020, 248:126008. DOI URL
[3]	LIU Y, ZHAO C F, ZHANG A R, et al. Theoretical study on the removal of uranyl by nitrogen, phosphorus and sulfur doped graphene materials. Scientia Sinica Chimica, 2019, 49(1):91-102. DOI URL
[4]	PENG X J, WANG Y F. Efficient stochastic simulation algorithm for chemically reacting systems based on support vector regression. Chinese Journal of Chemical Physics, 2009, 22(5):502-510. DOI URL
[5]	CAI C, LI L, DENG X, et al. Machine learning and high- throughput computational screening of metal-organic framework for separation of methane/ethane/propane. Acta Chimica Sinica, 2020, 78(5):427. DOI URL
[6]	ORUPATTUR N V, MUSHRIF S H, PRASAD V. Catalytic materials and chemistry development using a synergistic combination of machine learning and ab initio methods. Computational Materials Science, 2020, 174:109497-16. DOI URL
[7]	LI X, XI L L, YANG J. First principles high-throughput research on thermoelectric materials: a review. Journal of Inorganic Materials, 2019, 34(3):236-246. DOI URL
[8]	MENG Y, WANG X, YANG J, et al. Research on machine learning based model for predicting the impact status of laminated glass. Journal of Inorganic Materials, 2021, 36(1):61-68. DOI URL
[9]	FENG C, SHARMAN E, YE S, et al. A neural network protocol for predicting molecular bond energy. Sci. China Chem., 2019, 62(12):1698-1703. DOI URL
[10]	LU S, ZHOU Q, OUYANG Y, et al. Accelerated discovery of stable lead-free hybrid organic-inorganic perovskites via machine learning. Nature Communications, 2018, 9(1):3405. DOI URL
[11]	TEHRANI A M, OLIYNYK A O, PARRY M, et al. Machine learning directed search for ultraincompressible, superhard materials. Journal of the American Chemical Society, 2018, 140(31):9844-9853. DOI URL
[12]	KANG Y, LI L, LI B. Recent progress on discovery and properties prediction of energy materials: simple machine learning meets complex quantum chemistry. Journal of Energy Chemistry, 2020, 54:72-88. DOI URL
[13]	BROCKHERDE F, VOGT L, LI L, et al. By-passing the Kohn-Sham equations with machine learning. Nature Communications, 2017, 8(1):872. DOI URL
[14]	XIAO Y, MIARA L J, WANG Y, et al. Computational screening of cathode coatings for solid-state batteries. Joule, 2019, 3(5):1252-1275. DOI URL
[15]	PANAPITIYA G, AVENDANO-FRANCO G, REN P, et al. Machine learning prediction of CO adsorption in thiolated, Ag alloyed Au nanoclusters. Journal of the American Chemical Society, 2018, 140(50):17508-17514. DOI URL
[16]	PARDAKHTI M, MOHARRERI E, WANIK D, et al. Machine learning using combined structural and chemical descriptors for prediction of methane adsorption performance of metal organic frameworks (MOFs). ACS Combinatorial Science, 2017, 19(10):640-645. DOI URL
[17]	SI Y, SAMULSKIE T. Synthesis of water soluble graphene. Nano Letters, 2008, 8(6):1679-1682. DOI URL
[18]	CHEN D, FENG H, LI J. Graphene oxide: preparation, functionalization, and electrochemical applications. Chemical Reviews, 2012, 112(11):6027-6053. DOI URL
[19]	SHENG Z H, SHAO L, CHEN J J, et al. Catalyst free synthesis of nitrogen-doped graphene via thermal annealing graphite oxide with melamine and its excellent electrocatalysis. ACS Nano, 2011, 5(6):4350-4358. DOI URL
[20]	MAURIZIO C, VICENZO B, MICHAEL A R. A direct procedure for the evaluation of solvent effects in MC-SCF calculations. Journal of Chemical Physics, 1999, 111(12):5295-5302.
[21]	BRAND M. Incremental Singular Value Decomposition of Uncertain Data with Missing Values. Computer Vision-ECCV 2002, Berlin, Heidelberg, 2002: 707-720.
[22]	NEELAKANTAN A, VILNIS L, LEQ V, et al. Adding gradiant noise improves learning for very deep networks. arXiv: Machine Learning, 2015, 1511:06807.
[23]	迪安J A, 魏俊发. 兰氏化学手册, 2版. 北京: 科学出版社, 2003: 1-1579.
[24]	FRIEDMAN J H, JAO S. Greedy function approximation: a gradient boosting machine. Annals of Statistics, 2001, 29(5):1189-1232. DOI URL
[25]	LIASHCHYNSKYI P, LIASHCHYNSKYI P. Grid search, random search, genetic algorithm: a big comparison for NAS. arXiv: Learning, 2019, 1912:06059.
[26]	MARTENS H A, DARDENNE P J, CSYSTEMS I L. Validation and verification of regression in small data sets. ChemomERTics & Intelligent Laboratory Systems, 1998, 44(1/2):99-121.
[27]	FRIEDMAN J H. Stochastic gradient boosting. Computational Statistics & Data Analysis, 2002, 38(4):367-378. DOI URL
[28]	SMOLA A J, SCHOLKOPF B. A tutorial on support vector regression. Statistics and Computing, 2004, 14(3):199-222. DOI URL
[29]	RUPP M. Machine learning for quantum mechanics in a nutshell. International Journal of Quantum Chemistry, 2015, 115(16):1058-1073. DOI URL
[30]	SVETNIK V. Random forest: a classification and regression tool for compound classification and QSAR modeling. Journal of Chemical Information and Modeling, 2003, 43(6):1947-1958.
[31]	GEURTS P, ERNST D, WEHENKEL L. Extremely randomized trees. Machine Learning, 2006, 63(1):3-42.
[32]	DRUCKER H. Improving regressors using boosting techniques. Morgan Kaufmann Publishers Inc, 1997: 107-115.
[33]	FRANLLIN J. The elements of statistical learning: data mining, inference, and prediction. The Mathematical Intelligencer, 2005, 27(2):83-85.
[34]	SANTOS R I H, REIS D T, PEREIRA D H. A DFT based analysis of adsorption of Cd²⁺, Cr³⁺, Cu²⁺, Hg²⁺, Pb²⁺, and Zn²⁺, on vanillin monomer: a study of the removal of metalions from effluents. Journal of Molecular Modeling, 2019, 25(9):267.

基于机器学习训练金属离子吸附能预测模型的研究

Training Model for Predicting Adsorption Energy of Metal Ions Based on Machine Learning

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