机器学习方法预测含硼材料能隙

doi:10.6023/A23100473

摘要/Abstract

近年来, 含硼材料在新能源、催化等领域日益受到重视, 然而, 对于高附加值的含硼材料发展还存在很高的技术壁垒. 因此, 亟需深入研究含硼材料微观性质间的关联关系, 推动高端含硼材料的研发. 本工作面向材料研究从传统的试错法向数据驱动的研究范式转变的需求, 通过特征选择、网格搜索优化以及特征重要性分析, 探索了多种重要的机器学习算法在含硼材料能隙预测中的应用. 结果表明, 采用随机森林算法的能隙预测模型决定系数(R²)可达0.84, 并发现含硼材料的总磁化强度(total magnetization)特征与能隙存在显著的负相关关系, 即材料的总磁化强度越小, 其能隙越大. 本工作表明机器学习方法可用于定向设计具有特定能隙的含硼材料. 同时, 结果也表明, 作为一种集成学习模型, 随机森林具有较好的学习能力与稳定的预测性能, 可以应用到其它类型材料体系的能隙以及其它材料属性的预测, 加速材料性能的设计与优化过程, 对新型功能材料的快速筛选与高性能预测具有重要的科学意义.

关键词: 含硼材料, 能隙, 总磁化强度, 机器学习

New materials are an important driving force for social development. In recent years, attention on boron-containing materials is growing in the fields of new energy and catalysis, and calls for compelling need for in-depth study of their structure-property relationship to contribute to the research and development of boron-containing materials. In this work, on the aware of the shift of materials research from traditional trial-and-error paradigm to data-driven research paradigm, we explored the application of ten important machine learning algorithms in the prediction of band gaps of boron-containing materials through feature selection (Pearson correlation analysis), grid search-based optimization (Model optimal parameters), and feature importance analysis (interpretability analysis of the model). The results show that the band gap prediction model using the Random Forest algorithm outperforms the other models with a 84% prediction accuracy, and the total magnetization of boron-containing materials is identified to significantly correlate negatively with the band gap, i.e. the smaller the total magnetization of the material, the larger its band gap. The advantage of the Random Forest algorithm over other models is that it is better able to capture correlations between features. For example, the linear model is unable to detect the importance of the total magnetization of boron-containing materials from the material features, thus leading to a lower model prediction performance. This work shows that machine learning methods can be used to guide the design of boron-containing materials with specific band gap. Meanwhile, the results also show that, as an integrated learning model, Random Forest has good learning ability and stable prediction performance, and can be applied to the prediction of band gap and other material properties of other types of material systems, accelerating the design and optimization process of material properties, and is of great scientific significance for the rapid screening and high-performance prediction of new functional materials.

Key words: boron-containing materials, band gap, total magnetization, machine learning

引用此文

李珺卿, 宋千禧, 刘子义, 王东琪. 机器学习方法预测含硼材料能隙[J]. 化学学报, 2024, 82(4): 387-395.

Junqing Li, Qianxi Song, Ziyi Liu, Dongqi Wang. Machine Learning for Predicting Band Gap in Boron-containing Materials[J]. Acta Chimica Sinica, 2024, 82(4): 387-395.

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图/表 11

图1. 数据集分析: (a)含硼材料数据集中非B元素统计, (b)含硼材料晶系统计

Figure 1. Analysis of the dataset: (a) statistics of non-B elements in the dataset of boron-containing materials, (b) statistics of crystal systems of boron-containing materials

图2. 2~8元含硼材料的能隙的高斯核密度估计图(二元、三元(a), 四元(b), 五元、六元(c), 七元、八元(d))

Figure 2. Gaussian kernel density estimates for the band gap of boron-containing materials from 2 to 8 elements (binary, ternary (a); quaternary (b); quinary, senary (c); septenary, octary (d))

Features	Descriptions
total magnetization	total magnetizing strength of the material
dens	density of the material
energy	energy of the material
energy per atom	atomic energy per unit of energy
formation energy per atom	unit atomic formation energy
e above hull	phase stability energy (difference in energy between new phase and equilibrium phase)
minimum Number	minimum atomic number
minimum Mendeleev Number	minimum value of Mendeleev number of elements in compounds
maximum Melting T	compound melting temperature maximum
maximum Nd Valence	maximum number of d-valence orbitals filled
mean Np Unfilled	mean number of unfilled p-valence orbitals
maximum Nd Unfilled	maximum number of unfilled d-valence orbitals
maximum Nf Unfilled	maximum number of unfilled f-valence orbits
maximum Space Group Number	maximum space group of the ground state structure at 0 K
minimum oxidation state	minimum oxidation state

表1. 筛选后的特征及其描述

Table 1. Selected features and their descriptions

图3. 含硼材料的15种特征的皮尔森相关系数热图

Figure 3. Heatmap of Pearson correlation coefficients for 15 features of boron-containing materials

Models	145 features			15 features
Models	MAE	MSE	R²	MAE	MSE	R²
Lasso	1.24	2.38	0.31	1.38	2.65	0.20
Bayesian Ridge	0.87	1.48	0.57	1.10	1.96	0.41
Elastic Net	1.17	2.18	0.37	1.34	2.57	0.22
Support Vector Regression	1.38	2.92	0.15	1.50	3.25	0.02
Decision Tree Regression	0.67	1.22	0.65	0.65	1.02	0.69
Gradient Boosting Regression	0.58	0.66	0.81	0.61	0.70	0.79
AdaBoost Regression	0.91	1.21	0.65	0.89	1.22	0.63
Random Forest Regression	0.51	0.58	0.83	0.51	0.57	0.84
Extra Tree Regression	0.67	1.20	0.65	0.63	1.07	0.68

表2. 使用145种材料特征和15种材料特征作为训练样本的九种回归模型的测试集结果

Table 2. Test set results for nine regression models using 145 material features and 15 material features as training samples

图4. 四种集成学习模型的带隙预测性能: (a~d) 145种特征, (e~h) 15种特征

Figure 4. The band gap prediction performance of the four ensemble learning models: (a~d) 145 features, (e~h) 15 features

图5. 随机森林模型(145个特征)的SHAP特征重要性分析: SHAP特征的总体特征图(a), SHAP特征的重要性值(b)

Figure 5. SHAP feature importance analysis of the Random Forest model (145 features) for predicting band gap, with the overall feature map of SHAP features (a) and the importance values of SHAP features (b)

Models	Number of elemental species
Models	2	3	4	5	6	7	8
Linear Regression	0.42	0.44	0.46	0.26	0.33	–0.01	–2.15
Lasso	–0.07	0.16	0.23	–0.06	0.05	–1.14	–1.2
Bayesian Ridge	0.42	0.45	0.46	0.25	0.33	0	–2.09
Elastic Net	–0.11	0.2	0.28	–0.1	0.1	–1.52	–0.83
Support Vector Regression	–0.14	0.02	0.01	–0.18	–0.25	–0.72	–1.43
Decision Tree Regression	0.55	0.76	0.78	0.47	0.5	0.6	–4.75
Gradient Boosting Regression	0.64	0.81	0.81	0.73	0.57	0.07	–2.48
AdaBoost Regression	0.45	0.62	0.66	0.53	0.43	–0.65	–2.65
Random Forest Regression	0.72	0.84	0.86	0.73	0.68	0.37	–1.9
Extra Tree Regression	0.25	0.77	0.63	0.42	–0.29	0.84	–0.46

表3. 十种模型中对于多元含硼材料的能隙预测的R2值(使用15种材料特征作为训练样本的十种回归模型的测试集结果)

Table 3. R2 values for ten models (test set results of ten regression models using 15 material features as training samples)

Parameters
bootstrap: False, max_depth: 30, max_features: log2, min_samples_leaf: 1, min_samples_split: 2, n_estimators: 300

表4. 随机森林回归模型的训练参数

Table 4. Training parameters of Random Forest Regression Model

图6. 随机森林模型(15个特征)的SHAP特征重要性分析: SHAP 特征的总体特征图(a), SHAP特征的重要性值(b)

Figure 6. SHAP feature importance analysis of the Random Forest model (15 features) for predicting band gap, with the overall feature map of SHAP features (a) and the importance values of SHAP features (b)

图7. 总磁化强度和能隙的高斯核密度估计图

Figure 7. Contour map of the distribution of total magnetization as a function of band gap

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