機器學習在非晶合金開發中的應用

胡靜怡; 徐翔; 季小妹; 徐明賢; 姜岱峰; 王巹

doi:10.13374/j.issn2095-9389.2022.11.11.002

機器學習在非晶合金開發中的應用

doi: 10.13374/j.issn2095-9389.2022.11.11.002

胡靜怡^{1, 2,},
徐翔^{3, 4, ,},
季小妹¹,
徐明賢¹,
姜岱峰¹,
王巹¹

1.
齊魯工業大學（山東省科學院），山東省科學院高新技術產業（中試）基地（山東省科學院留學人員創業園），濟南 250000
2.
山東中小企業生產力促進中心，濟南 250000
3.
山東財經大學山東省區塊鏈金融重點實驗室，濟南 250000
4.
山東財經大學計算機科學與技術學院，濟南 250000

基金項目: 山東省重點研發計劃（軟科學項目）資助項目（2022RZB04031）

詳細信息

通訊作者:
E-mail: xuxiang8420@outlook.com

中圖分類號: TG139+.8
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- 文章訪問數: 292
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出版歷程
- 收稿日期: 2022-11-11
- 網絡出版日期: 2023-04-06
- 刊出日期: 2023-09-25

Machine learning in designing amorphous alloys

HU Jingyi^{1, 2
,},
XU Xiang^{3, 4
, ,},
JI Xiaomei¹,
XU Mingxian¹,
JIANG Daifeng¹,
WANG Jin¹

1.
Science and Technology Service Platform (Overseas Chinese Pioneer Park), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250000, China
2.
Shandong SME Productivity Promotion Center, Jinan 250000, China
3.
Shandong Key Laboratory of Blockchain Finance, Shandong University of Finance and Economics, Jinan 250000, China
4.
School of Computer Science and Technology, Shandong University of Finance and Economics, Jinan 250000, China

More Information

Corresponding author: E-mail: xuxiang8420@outlook.com

摘要

摘要: 在材料科學過去幾十年的發展過程中，經驗試錯法和基于密度泛函理論的方法等傳統的非晶合金開發方法，幫助研發人員探索出多種非晶合金體系。但是，這些方法由于開發周期長、效率低等缺點，目前已難以滿足研發人員的需求。而機器學習方法因其實驗成本低、性能強大以及開發周期短等優點，被越來越廣泛地應用到非晶合金材料的設計、分析和性能預測中。本文首先按照機器學習建模的主要流程闡述了各步驟的基本操作和發展情況。其次，著重介紹了數據預處理、模型構建以及模型驗證方面的研究工作，在數據預處理章節，簡述了數據收集、特征工程以及目前較為流行的數據預采樣方法；在模型構建章節，論述了四類在非晶合金開發中常用的機器學習算法，包括人工神經網絡、支持向量機、隨機森林以及極端梯度提升方法；在模型驗證章節，主要介紹了K折交叉驗證和留一法交叉驗證方法。最后，本文從多個角度對比分析了現有的機器學習應用，為后續的相關研究提供了可能的研究方向和思路。
- 非晶合金 /
- 機器學習 /
- 材料設計 /
- 性能預測 /
- 數據預處理 /
- 模型構建 /
- 模型驗證
Abstract: Metallic glasses have received a lot of interest because of their excellent mechanical, physical, and chemical qualities. For example, they have a stronger resistivity than crystalline metals composed of the same elements and a lower viscosity coefficient. However, the difficulty in creating alloy compositions has been a concern for researchers. Traditional amorphous alloy systems design approaches, such as empirical trial-and-error methods and methods based on density functional theory (DFT), have assisted researchers in exploring numerous amorphous alloy systems during the growth of materials science over the last few decades. However, with the continuous development of materials science, these methods have been difficult to meet the needs of researchers due to their long development cycles and low efficiency. Additionally, the complex and long-range disordered structure of metallic glasses makes it difficult to understand their structure and nature in a comprehensive and clear way by conventional methods. Amorphous alloy composition design and property analysis are now often conducted using machine learning techniques because of their low experimental cost, short development cycle, strong data processing capability, and high predictive performance, among other advantages. They present new approaches and chances to address significant key bottlenecks in the field of metallic glass. In this study, the main processes of machine learning model building were introduced. Subsequently, the related studies on data pre-processing, model construction, and model validation were presented. For data pre-processing, data selection, feature engineering, and advanced data balancing methods were primarily described. In the feature engineering part, the model performance with various input features was examined, and it was shown that either employing physical properties or directly using the alloy compositions as the model input might result in high performance. Four machine learning algorithms were used to generate the machine learning model: artificial neural networks (ANN), support vector machines (SVM), random forest (RF), and extreme gradient boosting (XGBoost). A comparison indicates that SVM models work best with small data sets, whereas the performance of all other models tends to get better as the amount of training data increases. Generally, the XGBoost method outperforms several other methods and is, therefore, often used in machine learning competitions. Model validation approaches: K-fold cross-validation and leave-one-out cross-validation methods were presented. A good metallic glass performance prediction method needs to perform well in both validation methods. Finally, this study provides several possible future research directions on feature engineering, dataset construction, validation, and machine learning models.
- metallic glasses /
- machine learning /
- alloy design /
- property prediction /
- data pre-processing /
- model selection /
- model validation

HTML全文

圖 1 機器學習模型搭建流程

Figure 1. Process of Machine learning model building

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圖 2 原始數據集（左）與平衡數據集（右）的數據分布（經過數據預處理后，平衡數據集在不同合金系統之間顯示出更均勻的數據分布）^[34]

Figure 2. Data distribution of the original dataset (left) and the balanced dataset (right) (after data processing, the balanced dataset showed a more uniform data distribution among the different alloy systems)^[34]

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圖 3 人工神經網絡架構（以非晶合金為例）

Figure 3. Artificial neural network framework (taking amorphous alloys as an example)

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圖 4 SVM算法原理圖

Figure 4. Schematic diagram of the SVM algorithm

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圖 5 隨機森林模型

Figure 5. Random forest model

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表 1 機器學習模型輸入特征和性能

Table 1. Input features and performance of machine learning model

Input features	Machine learning models	Features used	Performance
Physical properties	ANN (MLP)^[11]	Pauling’s electronegativity difference (Δχ), atomic size difference (δ), theoretical density (ρ), ΔT_x, parameter γ_m, fragility (m), enthalpy of mixing (H_mix), mismatch entropy (S_σ), configurational entropy (ΔS_c), bulk modulus (K), and valence electron concentration (VEC).	Accuracy (ACC) for ternary alloy prediction：77.8%~78.9%, ACC for multicomponent alloys ( n > 3) prediction：83%.
	ANN (MLP)^[34]	Atomic properties (e.g., atomic radii, atomic radius mismatch), atomic packing properties, and thermodynamic properties (e.g., heat of mixing and configurational entropy of mixing), covering a comprehensive list used for general-purpose as well as for the MG systems (e.g., δ, H_mix), etc., 131 features in total.	The model trained on the balanced dataset exhibits a 42% improvement in the alloy systems with sparse data and maintains the performance in the alloy systems with high-throughput data.
	ANN (MLP)^[52]	T_g, T_x, T_l.	R²: 0.776.
	ANN (MLP)^[53]	The combined variable of lateral displacement and lateral force.	MSE of validation dataset: 9.3158 × 10^?2～3.0303 × 10^?1, MSE of testing dataset: 9.9836 × 10^?2～2.9091 × 10^?1.
	ANN (CNN)^[52]	T_g, T_x, T_l.	R²: 0.716.
	SVM^[40]	2 atomic weights (aw1, aw2), the mixing enthalpy (ΔH), 2 atomic radii (r1, r2), 2 liquidus temperatures for each element (T_liq1, T_liq2), the fictive liquidus temperature (T_fic), the difference in liquidus temperature (ΔT_liq), and 2 contents of each element (c1, c2), etc., 11 features in total.	Using the customized evaluation criterion E, the optimum result is 3.96 ( E = P_Target² / P_all ).
	RF^[44]	145 features, which fall into four distinct categories: (1) Stoichiometric attributes, (2) Elemental property statistics, (3) Electronic structure attributes, (4) Ionic compound attributes.	ACC (for band gap prediction)：90%, ACC (for GFA prediction)：80.2%.
	RF^[45]	Inputting all features in paper [44] and adding three additional features: Cluster Packing Efficiency Attributes, Nearest Special Clusters and Mean Packing Efficiency.	ACC (for GFA prediction)：89%, MAE (for D_max prediction)：0.21 mm, MAE (for ΔT_x prediction)：8.8 K.
	XGBoost^[48]	Theoretical melting point (T_m), theoretical molar volume (V), mean atom radius ($ \stackrel{-}{r} $), δ, ΔS_c, ρ, electronegativity (χ), VEC, and valence electron concentration without FeCoNi (VEC')； 9 features in total.	R²: 0.942.
Alloy compositions	ANN (CNN)^[54]	Alloy compositions.	R²: 0.8137.

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表 2 機器學習在非晶合金開發中的應用算法分析

Table 2. Advantages and limitations of several common machine learning algorithms

Methodology	Advantages	Limitations analysis
ANN (1) Liu et al.^[11] used 11 alloy parameters or criteria as ANN inputs to predict GFA. The dataset they used contains 3227 data samples, achieving an accuracy of 77.8%~78.9% for ternary alloy prediction and 83% for multicomponent alloy (n > 3) prediction. (2) Yao et al.^[34] used 131 features as ANN inputs to predict GFA with a dataset containing 5725 data samples and proposed a data resampling method to balance the data sample size of different alloy systems. After data resampling, the model achieved a 42% performance improvement on data-barren alloy systems and maintained almost the same performance on data-sufficient alloy systems. (3) Lu et al.^[52] used T_g, T_x, and T_l as ANN input features to predict D_max for amorphous alloys. They used a dataset containing 663 data samples and achieved an R² of 0.776. In addition, they also used CNN for D_max prediction, but their R² of 0.717 is lower than that of the ANN. (4) Yu et al.^[53] used lateral force and lateral displacement as inputs to explore the deformation mechanism of plastic deformation of specific amorphous alloys using MLP regressions on the reconstructed lateral force. The MSEs for the validation and test datasets are 9.3158 × 10^?2 ~ 3.0303 × 10^?1 and 9.9836 × 10^?2 ~ 2.9091 × 10^?1, respectively. (5) Zhang et al.^[54] put all the elements that can make up the alloys into a 10 × 10 matrix, and used the alloy composition as the CNN model input to predict D_max , achieving an R² of 0.8137.	(1) A high degree of accuracy of the ANNs. (2) Better fault tolerance to data noise. (3) Can fit complex non-linear relationships more easily.	(1) A large number of hyperparameters to be tuned. (2) Longer training time (especially for the deep neural network) compared to other models. (3) The training process is difficult to observe, and the output is not interpretable, affecting the model credibility.
SVM (1) Sun et al.^[40] used 11 features to predict the GFA of binary alloys with a training dataset of 31 alloys and a validation dataset containing 339 amorphous data samples and 1131 unlabeled data representing the likelihood of their use of the full range of binary compositions. The best prediction model in their test (E = 3.96) is when SVM parameters C = 2^?6，γ = 2². (2) Wu et al.^[59] used SVM to structurally identify "liquid-like" atoms, which are prone to rearrangement, and "solid-like" atoms, which are not, and successfully identified the "liquid-like" atoms.	(1) Performs better on small datasets. (2) Good generalization capabilities.	(1) Not suitable for large datasets. (2) Lacks data sensitivity. (3) Performs poorly when there are some noises in the dataset.
RF (1) Ward et al.^[44] used 145 features as the input of the RF model. They predicted the band gap width of the alloy in a dataset containing 228,676 data samples and the amorphous state in a dataset containing 5,369 data samples, achieving 90% and 80.2% accuracy, respectively. (2) Ward et al.^[45] used 148 features as the input of the RF model, where 145 features are the same as Ward et al.^[44]. They predicted the GFA, D_max, and ΔT_x in three data sets, with an accuracy of 89% for GFA, an MAE of 0.21 mm for D_max, and an MAE of 8.8 K for ΔT_x.	(1) Easy to process high-dimensional feature data because the feature subset is randomly selected. (2) Fast training speed. (3) The interaction between input parameters can be detected in training. Also, the errors can be balanced for unbalanced data.	(1) When regression is performed, it is impossible to make predictions beyond the scope of the training set data. (2) Some specific noises will cause overfitting. (3) Hard to converge on small datasets or insufficient input parameters.
XGBoost (1) Li et al.^[48] used 9 input features to predict the saturated magnetization (B_s) of Fe-based MGs with a dataset containing 360 data samples. They tested the RF, ANN, and XGBoost methods, where XGBoost demonstrates the strongest correlation, with an R² of 0.942.	(1) Higher performance and accuracy compared to other algorithms. (2) Very flexible, as it can build weak learners using various models. (3) Adds the complexity of the tree model to the regular term to further avoid overfitting.	(1) Sensitive to outlier samples, which may receive higher weights in the iterations. (2) High space complexity. XGBoost needs to store the feature values and the indexes of the gradient statistics of the samples corresponding to the features.

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