Machine Learning-Based High Entropy Alloys-Algorithms and Workflow: A Review

doi:10.1007/s40195-025-01894-2

Abstract

Abstract:

High-entropy alloys (HEAs) have attracted considerable attention because of their excellent properties and broad compositional design space. However, traditional trial-and-error methods for screening HEAs are costly and inefficient, thereby limiting the development of new materials. Although density functional theory (DFT), molecular dynamics (MD), and thermodynamic modeling have improved the design efficiency, their indirect connection to properties has led to limitations in calculation and prediction. With the awarding of the Nobel Prize in Physics and Chemistry to artificial intelligence (AI) related researchers, there has been a renewed enthusiasm for the application of machine learning (ML) in the field of alloy materials. In this study, common and advanced ML models and strategies in HEA design were introduced, and the mechanism by which ML can play a role in composition optimization and performance prediction was investigated through case studies. The general workflow of ML application in material design was also introduced from the programmer’s point of view, including data preprocessing, feature engineering, model training, evaluation, optimization, and interpretability. Furthermore, data scarcity, multi-model coupling, and other challenges and opportunities at the current stage were analyzed, and an outlook on future research directions was provided.

Key words: Machine learning, High-entropy alloys, Artificial intelligence, Alloy design

Hao Cheng, Cheng-Lei Wang, Xiao-Du Li, Li Pan, Chao-Jie Liang, Wei-Jie Liu. Machine Learning-Based High Entropy Alloys-Algorithms and Workflow: A Review[J]. Acta Metallurgica Sinica (English Letters), 2025, 38(9): 1453-1480.

Figures/Tables 22

Fig. 1 Hardness prediction, a training set, b test set, c tenfold cross-validation of the training set, and d observed hardness function for LOOCV (N denotes the number of samples) of the training set. Reprinted with permission from the reference [60]

Fig. 2 a Evaluation indices obtained for each model and b predicted microhardness versus actual microhardness obtained for the XGBoost and RF models. Reprinted with permission from the reference [61]

Fig. 3 a Comparison of the microhardness of initial data with screened microhardness after different iterations. b Comparison of the microhardness of initial data collected in the Al-Co-Cr-Cu-Fe-Ni alloy system with screened microhardness after different iterations. c Relationship between the predicted and experimental hardness. d Although deviations are observed in compositions Nos. 2 and 11, this discrepancy occurs only during the initial half of the AL loop. e In the latter half of the AL loop, the experimental microhardness gradually aligns closely with the predicted values. Reprinted with permission from the reference [61]

Fig. 4 a Comparison of R2 and b RMSE between the NN model and the present model (with T&C). c Comparison of R2 and d RMSE among ML models other than the NN model and the present model. e Comparison of the experimental and predicted values of YS. f Comparison of the experimental and predicted values of UTS. Reprinted with permission from the reference [63]

Fig. 5 Hyperparameter optimization of the RF algorithm. Reprinted with permission from the reference [65]

Fig. 6 Comparison of the confusion matrices of the five algorithms. Reprinted with permission from the reference [65]

Table 1 Applicability, advantages, and disadvantages of SVM, XGBoost, NN, and RF

Model	Applicable mandates	Advantages	Limitations
SVM [66]	(1) Phase stability classification	(1) Excellent performance in high dimensional space	(1) Parameter selection is complex
	(2) Binary classification of corrosion resistance	(2) Small samples are valid	(2) Long training hours
	(2) Binary classification of corrosion resistance	(3) Non-linear processing	(3) Noise sensitivity
XGBoost [67]	(1) Strength/hardness prediction (regression)	(1) Automatic handling of missing data	(1) Parameter tuning is complex
	(2) Component-performance relationship modeling	(2) Feature importance analysis	(2) Long training hours
	(2) Component-performance relationship modeling	(3) Efficient handling of high-dimensional nonlinear data	(3) Possible overfitting
NN [68]	(1) Component-performance relationship modeling	(1) Automatic learning of complex nonlinear relationships	(1) A lot of data is required
	(2) Multi-scale feature fusion	(2) Processing of raw data	(2) Poor model Interpretability
	(2) Multi-scale feature fusion	(3) Suitable for end-to-end learning	(3) High consumption of computing resources
RF [69]	(1) Multi-objective classification (phase stability/corrosion behavior)	(1) Handling high-dimensional data	(1) High memory consumption
	(2) Feature importance ranking (key alloying element screening)	(2) Parallel computing is efficient	(2) Possible overfitting of high base features
		(3) Robustness is good	(3) Biased selection of dominant features

Fig. 7 a Predicted frequency distribution of L12 generated from the dataset for the structural probability of 1 nm voxels. b zx-SDMs generated from the data corresponding to regions 1, 2, and 3 in a. Reprinted with permission from the reference [77]

Fig. 8 a-c Comparison between the GNN model configurational energies (per atom) and those obtained from DFT (per atom). b, d Entropy (black curve) and heat capacity (red curve) at different temperatures using the mean-square error as an objective loss function. Reprinted with permission from the reference [84]

Fig. 9 Comparative analysis of data generated by GAN with original data. Reprinted with permission from the reference [91]

Table 2 Applicability, advantages, and disadvantages of CNN, GNN, and GAN

Model	Applicable mandates	Advantages	Limitations
CNN [95]	(1) Microstructure image analysis	(1) Automatic extraction of local spatial features	(1) A large amount of labeled image data is required
	(2) Atomic arrangement pattern recognition	(2) High potential for transfer learning	(2) Sensitive to image resolution
	(2) Atomic arrangement pattern recognition		(3) It is difficult to explain the feature learning process
GNN [96]	(1) Modeling atomic-scale composition-structure-property relationships	(1) Natural expression of interatomic topological relations	(1) High computational complexity
	(2) Crystal structure prediction	(2) Physical a priori can be fused	(2) A reasonable neighborhood truncation radius needs to be defined
	(2) Crystal structure prediction	(3) Support for non-Euclidean data modeling	(3) Lack of standardized graph structure definitions
GAN [97]	(1) Novel HEA composition generation	(1) Generate virtual alloys that conform to the laws of physics	(1) Training is erratic
	(2) Microstructure Synthesis	(2) Target performance can be optimized in conjunction with reinforcement learning	(2) Complex hyperparameter tuning is required
	(3) Data enhancement		(3) Low interpretability of generated results

Fig. 10 Active learning framework for designing and discovering target compositions of high-entropy Invar alloys with low coefficient of thermal expansion, combining ML modeling, DFT, thermodynamic simulations, and experimental feedback, after repeated iterations until the target alloy is discovered. Reprinted with permission from the reference [101]

Fig. 11 Transferable meta-learning algorithm frame consists of meta-learning based on adaptive migration Walrus optimizer, balanced-relative density peak clustering, and transfer strategy. Reprinted with permission from the reference [106]

Table 3 Main data sources and related information

Data categories	Subcategories	Applicability	Advantages	Limitations
Experimental data [109, 110]	(1) Experimental records	(1) Model validation	(1) High reliability and direct reflection of alloy behavior	(1) High acquisition cost and lack of data
	(1) Experimental records	(2) Critical performance prediction		(2) Experimental error
	(2) Published literature	(1) Multi-system comparisons	(1) High potential for cross-team data reuse	(1) Unharmonized data format
	(2) Published literature	(2) Data enhancement	(2) Covering multiple systems	(2) Publication bias
Computational simulation [111]	(1) Molecular dynamics	(1) Atomic scale dynamics studies (e.g., dislocation motion)	(1) Reveal micro-mechanisms	(1) Force field accuracy limitations
	(1) Molecular dynamics		(2) High throughput generation	(2) Limited time scales (nanoseconds)
	(2) Density functional theory	(1) Thermodynamic stability predictions	(1) Highly accurate quantum mechanical foundation	(1) Very high computational cost
	(2) Density functional theory	(2) Electronic performance calculations	(1) Highly accurate quantum mechanical foundation	(1) Very high computational cost
Data generation [112]	(1) GAN synthesis data	(1) Inverse design	(1) Fill experimental gaps	(1) Physical consistency needs to be verified
	(1) GAN synthesis data	(2) Data enhancement	(2) Support active learning	(2) May introduce implicit bias
	(2) Multi-physics field coupling simulation	(1) Extreme environment performance prediction (e.g., high-temperature oxidation)	(1) Reveal complex interactions	(1) Model simplification assumptions affect realism
	(2) Multi-physics field coupling simulation		(2) Support multi-objective optimization	(1) Model simplification assumptions affect realism
Public database	(1) Material project	(1) Preliminary material screening	(1) Structured data	(1) Low HEA coverage (< 5%) and lack of process parameters
	(1) Material project	(2) Characterization engineering	(2) API interface support	(1) Low HEA coverage (< 5%) and lack of process parameters
	(2) Database of in-situ experiments	(1) Phase transition mechanism studies	(1) Capture dynamic behavior	(1) Expensive equipment
	(2) Database of in-situ experiments	(2) Real-time process monitoring	(2) High spatial and temporal resolution	(2) Complex data processing

Table 3 Main data sources and related information

Data categories	Subcategories	Applicability	Advantages	Limitations
Experimental data [109, 110]	(1) Experimental records	(1) Model validation	(1) High reliability and direct reflection of alloy behavior	(1) High acquisition cost and lack of data
	(1) Experimental records	(2) Critical performance prediction		(2) Experimental error
	(2) Published literature	(1) Multi-system comparisons	(1) High potential for cross-team data reuse	(1) Unharmonized data format
	(2) Published literature	(2) Data enhancement	(2) Covering multiple systems	(2) Publication bias
Computational simulation [111]	(1) Molecular dynamics	(1) Atomic scale dynamics studies (e.g., dislocation motion)	(1) Reveal micro-mechanisms	(1) Force field accuracy limitations
	(1) Molecular dynamics		(2) High throughput generation	(2) Limited time scales (nanoseconds)
	(2) Density functional theory	(1) Thermodynamic stability predictions	(1) Highly accurate quantum mechanical foundation	(1) Very high computational cost
	(2) Density functional theory	(2) Electronic performance calculations	(1) Highly accurate quantum mechanical foundation	(1) Very high computational cost
Data generation [112]	(1) GAN synthesis data	(1) Inverse design	(1) Fill experimental gaps	(1) Physical consistency needs to be verified
	(1) GAN synthesis data	(2) Data enhancement	(2) Support active learning	(2) May introduce implicit bias
	(2) Multi-physics field coupling simulation	(1) Extreme environment performance prediction (e.g., high-temperature oxidation)	(1) Reveal complex interactions	(1) Model simplification assumptions affect realism
	(2) Multi-physics field coupling simulation		(2) Support multi-objective optimization	(1) Model simplification assumptions affect realism
Public database	(1) Material project	(1) Preliminary material screening	(1) Structured data	(1) Low HEA coverage (< 5%) and lack of process parameters
	(1) Material project	(2) Characterization engineering	(2) API interface support	(1) Low HEA coverage (< 5%) and lack of process parameters
	(2) Database of in-situ experiments	(1) Phase transition mechanism studies	(1) Capture dynamic behavior	(1) Expensive equipment
	(2) Database of in-situ experiments	(2) Real-time process monitoring	(2) High spatial and temporal resolution	(2) Complex data processing

Fig. 12 Common measures of data preprocessing. Reprinted with permission from the reference [121]

Fig. 13 a-c ROC curves of the three classes of SEFs on the SVM model with AUC values inserted in the figure. d Performance evaluation of the three classes of SEF algorithms on the confusion matrix. Reprinted with permission from the reference [125]

Fig. 14 a Comparison of actual SFE and ML-predicted SFE, with the black dashed line indicating the ideal case where the prediction is equal to the actual SFE. b Comparison of actual SFE and ML predicted SFE on test data. Reprinted with permission from the reference [125]

Fig. 15 a MLR model test set predictive control. b BPNN model test set predictive control. c RF model test set prediction control. d Prediction confidence of the three ML models. Reprinted with permission from the reference [128]

Fig. 16 Visual metrics for the five classifiers: a ROC curve for DT; b ROC curve for RF; c ROC curve for XGBoost; d ROC curve of Voting; and e ROC curve of Stacking. Reprinted with permission from the reference [113]

Fig. 17 Comparison of schematic diagrams of different hyperparameter optimization methods: a grid search, b random search, c PSO, and d BO. Reprinted with permission from the reference [129]

Fig. 18 a SBS, SFS, and RF selecting different numbers of features and their respective RMSE performance. b RMSE values of iterative curves for GA selecting feature sets. c SHAP analysis for eight feature sets selected by GA. Reprinted with permission from the reference [49]

Fig. 19 Interpretability of SHAP-driven constructed ML models. a SHAP aggregation of large-scale predictions made by GPR_Y. b SHAP aggregation of large-scale predictions made by GPR_ρ. c SHAP force diagrams of individual predictions made by GPR_Y and GPR_ρ, corresponding to the optimal elemental compositions suggested by GPR-driven MOGAs (cf. point 2 in the cited Fig. 8). d Prediction of the Al14. 95Ni24.78Cr20.05Fe21.82Co18.4 HEA configurations. e Interaction of Al and Co concentrations on the GPR_Y prediction mechanism. f Interaction of Al and Co concentrations on the GPR_ρ prediction mechanism. Reprinted with permission from the reference [133]

References 133

[1]	B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Mater. Sci. Eng. A 375, 213 (2004)
[2]	J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Adv. Eng. Mater. 6, 299 (2004)
[3]	D.B. Miracle, O.N. Senkov, Acta Mater. 122, 448 (2017)
[4]	P. Sathiyamoorthi, H.S. Kim, Prog. Mater. Sci. 123, 100709 (2022)
[5]	Z. Li, S. Zhao, R.O. Ritchie, M.A. Meyers, Prog. Mater. Sci. 102, 296 (2019)
[6]	W. Zhang, P.K. Liaw, Y. Zhang, Sci. China Mater. 61, 2 (2018)
[7]	N. Hashimoto, YAl. Zain, A. Yamamoto, T. Koyano, H.Y. Kim, S. Miyazaki, Mater. Lett. 287, 129286 (2021)
[8]	Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Prog. Mater. Sci. 61, 1 (2014)
[9]	L.J. Santodonato, Y. Zhang, M. Feygenson, M.P. Chad, C.G. Michael, J.K.W. Richard, C.N. Joerg, T. Zhi, K.L. Peter, Nat. Commun. 6, 5964 (2015) DOI PMID
[10]	W.L. Hsu, C.W. Tsai, A.C. Yeh, J.W. Yeh, Nat. Rev. Chem. 8, 471 (2024)
[11]	E.P. George, W.A. Curtin, C.C. Tasan, Acta Mater. 188, 435 (2020) DOI
[12]	W. Jiang, Y. Zhu, Y. Zhao, Front. Mater. 8, 792359 (2022)
[13]	Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Nature 534, 227 (2016)
[14]	W. Huo, H. Zhou, F. Fang, X. Hu, Z. Xie, J.Q. Jiang, Mater. Sci. Eng. A 689, 366 (2017)
[15]	Y.J. Zhou, S.Y. Peng, Y.L. Guo, X.X. Wu, C.M. Liu, Z.M. Li, Acta Metall. Sin. -Engl. Lett. 37, 1186 (2024)
[16]	Y.Z. Shi, B. Yang, P.K. Liaw, Metals 7, 43 (2017)
[17]	N. Birbilis, S. Choudhary, J.R. Scully, M.L. Taheri, NPJ Mater. Degrad. 5, 14 (2021)
[18]	W.Y. Huo, H.F. Shi, X. Ren, J.Y. Zhang, Adv. Mater. Sci. Eng. 16, 647351 (2015)
[19]	M.Z. Xu, L.P. Xie, S.S. Yang, C.G. Sui, Q.C. Wang, Q.H. Long, M.H. Chen, F.H. Wang, Acta Metall Sin.-Engl. Lett. 38, 164 (2025)
[20]	K.C. Atli, I.A. Karaman, Front. Met. Alloys 2, 1135826 (2023)
[21]	W. Xiong, A.X.Y. Guo, S. Zhan, C.T. Liu, S.C. Cao, J. Mater. Sci. Technol. 142, 196 (2023)
[22]	X.C. Xie, N. Li, W. Liu, S. Huang, Y.H. Xiao, Q.Y. Yu, H.P. Xiong, E.H. Wang, X.M. Hou, Chin. J. Mech. Eng. 35, 142 (2022)
[23]	X. Li, C.L. Wang, L.C. Zhang, S.F. Zhou, J. Huang, M.Y. Gao, C. Liu, M. Huang, Y.T. Zhu, H. Chen, J.Y. Zhang, Z.J. Tan, Acta Metall. Sin. -Engl. Lett. 37, 1858 (2024)
[24]	M.C. Gao, J.W. Yeh, P.K. Liaw, Y. Zhang, High-Entropy Alloys: Fundamentals and Applications, 1st edn. (Springer, Cham, 2016), p.80
[25]	W.Y. Wang, S.L. Shang, Y. Wang, F.B. Han, A.D. Kristopher, Y.D. Wu, NPJ Comput. Mater. 3, 23 (2017)
[26]	M.C. Troparevsky, J.R. Morris, P.R.C. Kent, A.R. Lupini, G.M. Stocks, Phys. Rev. X 5, 011041 (2015)
[27]	P. Sarker, T. Harrington, C. Toher, C. Oses, M. Samiee, J.P. Maria, D.W. Brenner, K.S. Vecchio, S. Curtarolo, Nat. Commun. 9, 4980 (2018)
[28]	R. Feng, P.K. Liaw, M.C. Gao, M. Widow, NPJ Comput. Mater. 3, 50 (2017)
[29]	W. Huang, P. Martin, H.L. Zhuang, Acta Mater. 169, 225 (2019)
[30]	S. Guo, C. Ng, J. Lu, C.T. Liu, J. Appl. Phys. 109, 1 (2011)
[31]	C. Nyshadham, M. Rupp, B. Bekker, A.V. Shapeev, T. Mueller, C.W. Rosenbrock, G. Csanyi, D.W. Wingate, G.L.W. Hart, NPJ Comput. Mater. 5, 51 (2019)
[32]	C.W. Rosenbrock, K. Gubaev, A.V. Shapeev, L.B. Partay, N. Bernstein, G. Csanyi, G.L.W. Hart, NPJ Comput. Mater. 7, 24 (2021)
[33]	Y.X. Zuo, C. Chen, X.G. Li, Z. Deng, Y.M. Chen, J. Behler, G. Csányi, A.V. Shapeev, A.P. Thompson, M.A. Wood, S.P. Ong, J. Phys. Chem. A 124, 731 (2020)
[34]	W. Jia, H. Wang, M. Chen, D.H. Lu, L. Lin, R. Car, Sto. Ana. IEEE. 12, 1 (2020)
[35]	Y. Li, D. Lau, Giant 6, 100277 (2024)
[36]	J.P. Yang, H.F. Zhang, H.C. Ji, N. Jia, Acta Metall. Sin. -Engl. Lett. 6, 1 (2024)
[37]	Z.H. Zhu, W.H. Ning, X.Y. Niu, Y.H. Zhao, Acta Metall. Sin. -Engl. Lett. 37, 453 (2024)
[38]	E.G. Flekkø, P.V. Coveney, Phys. Rev. Lett. 83, 1775 (1999)
[39]	X.L. Liu, J.C. Zhang, Z.R. Pei, Prog. Mater. Sci. 131, 101018 (2023)
[40]	G.L.W. Hart, T. Mueller, C. Toher, S. Curtarolo, Nat. Rev. Mater. 6, 730 (2021)
[41]	J.F. Durodola, Prog. Mater. Sci. 123, 100797 (2022)
[42]	X.L. Liu, J.X. Zhang, J.Q. Yin, S. Bi, M. Eisenbach, Y. Wang, Comput. Mater. Sci. 187, 110135 (2021)
[43]	J. Yin, Z.R. Pei, M.C. Gao, Nat. Comput. Sci. 8, 686 (2021)
[44]	J.M. Rickman, H.M. Chan, M.P. Harmer, J.A. Smeltzer, C.J. Marvel, A. Roy, G. Balasubramanian, Nat. Commun. 10, 2618 (2019) DOI PMID
[45]	Z.R. Pei, J.Q. Yin, J.A. Hawk, D.E. Alman, M.C. Gao, NPJ Comput. Mater. 6, 50 (2020)
[46]	R. Singh, A. Sharma, P. Singh, G. Balasubramanian, D. Johnson, Nat. Comput. Sci. 1, 54 (2021)
[47]	X.Y. Huang, L. Zheng, H.B. Xu, H.W. Fu, Mater. Des. 239, 112797 (2024)
[48]	R. Gruetzemacher, J. Whittlestone, Futures 135, 102884 (2022)
[49]	W. Ren, Y.F. Zhang, W.L. Wang, S.J. Ding, N. Li, Mater. Des. 235, 112454 (2023)
[50]	Y. Liu, T.L. Zhao, W.W. Ju, S.Q. Shi, J. Materiomics 3, 159 (2017)
[51]	Y.B. Sun, C. Hou, N.D. Tran, Y.H. Lu, Z.M. Li, Y. Chen, J. Ni, NPJ Comput. Mater. 11, 54 (2025)
[52]	L.F. Zhu, F. Körmann, Q. Chen, M. Selleby, J. Neugebauer, B. Grabowski, NPJ Comput. Mater. 10, 274 (2024)
[53]	M.W. Fagerland, D.W. Hosmer, Stata J. 12, 447 (2012)
[54]	X.N. Li, S.Y. Yi, A.B. Cundy, W.P. Chen, J. Clean. Prod. 371, 133612 (2022)
[55]	Ö.F. Ertuğrul, M.E. Tağluk, Appl. Soft Comput. 55, 480 (2017)
[56]	Y. Karimi, S.O. Prasher, R.M. Patel, S.H. Kim, Comput. Electron. Agric. 51, 99 (2006)
[57]	O. Ennaji, L. Vergütz, A.E. Allali, Artif. Intell. Agric. 9, 1 (2023)
[58]	B.I. Oluleye, D.W.M. Chan, P.A. Afari, Sustain. Prod. Consum. 35, 509 (2023)
[59]	J. Zupan, Acta Chim. Slov. 41, 327 (1994)
[60]	C. Yang, C. Ren, Y.F. Jia, G. Wang, M.J. Li, W.C. Lu, Acta Mater. 222, 117431 (2022)
[61]	S.L. Zhao, B. Jiang, K.K. Song, X.M. Liu, W.Y. Wang, D.K. Si, J.L. Zhang, X.Y. Chen, C.S. Zhou, P.P. Liu, D. Chen, Z.Q. Zhang, P. Ramasamy, J.L. Tang, W.Q. Lv, K.G. Prashanth, D. Şopu, J. Eckert, Mater. Des. 238, 112634 (2024)
[62]	A. Roy, T. Babuska, B. Krick, G. Balasubramanian, Scr. Mater. 185, 152 (2020)
[63]	J. Wang, H. Kwon, H.S. Kim, B. Lee, NPJ Comput. Mater. 9, 60 (2023)
[64]	Y.V. Krishna, U.K. Jaiswal, M.R. Rahul, Scr. Mater. 197, 113804 (2021)
[65]	S. Swateelagna, M. Singh, M.R. Rahul, Intermetallics 167, 108198 (2024)
[66]	J. Cervantes, F.G. Lamont, L.R. Mazahua, A. Lopez, Neurocomputing 408, 189 (2020)
[67]	T.Q. Chen, H. Tong, M. Benesty, R. Packag, Vers. 1, 1 (2015)
[68]	K. Gurney, An Introduction to Neural Networks, 1st edn. (CRC Press, Boca Raton, 1997), p.6
[69]	M. Belgiu, L. Drăguţ, ISPRS J. Photogramm. Remote Sens. 114, 24 (2016)
[70]	S. Dong, P. Wang, K. Abbas, Comput. Sci. Rev. 40, 100379 (2021)
[71]	A. Mayr, G. Klambauer, T. Unterthiner, S. Hochreiter, Front. Environ. Sci. 3, 80 (2016)
[72]	L.A. Akanbi, A.O. Oyedele, L.O. Oyedele, R.O. Salami, J. Clean. Prod. 274, 122843 (2020)
[73]	A. Mathew, P. Amudha, S. Sivakumari, Adv. Mach. Learn. Technol. Appl. Proc. AMLTA 202, 599 (2020)
[74]	W.L. Fang, L.Y. Ding, B.T. Zhong, P.E.D. Love, H.B. Luo, Adv. Eng. Inform. 37, 139 (2018)
[75]	F.N. Yuan, Z.X. Zhang, Z.J. Fang, Pattern Recogn. 136, 109228 (2023)
[76]	F. Shamshad, S. Khan, S.W. Zamir, M.H. Khan, M. Hayat, F.S. Khan, H. Fu, Med. Image Anal. 88, 102802 (2023)
[77]	Y. Li, X.Y. Zhou, T. Colnaghi, Y. Wei, A. Marek, H.X. Li, S. Bauer, M. Rampp, L.T. Stephenson, NPJ Comput. Mater. 7, 8 (2021)
[78]	Z.Q. Zhou, Y.J. Zhou, Q.F. He, Z.Y. Ding, F.C. Li, Y. Yang, NPJ Comput. Mater. 5, 128 (2019)
[79]	T. Nakamura, K. Fukami, K. Hasegawa, Y. Nabae, Phys. Flu. 33, 53 (2021)
[80]	X.G. Wang, Commun. CCF 11, 15 (2015)
[81]	J. Zhou, G.Q. Cui, S.D. Hu, Z.Y. Zhang, C. Yang, Z.Y. Liu, L.F. Wang, C.C. Li, M.S. Sun, AI Open. 1, 57 (2020)
[82]	Z.H. Wu, S.R. Pan, F.W. Chen, G.D. Long, C.Q. Zhang, IEEE Trans. Neural Netw. Learn. Syst. 32, 4 (2020)
[83]	F. Scarselli, M. Gori, A.C. Tsoi, M. Hagenbuchner, G. Monfardini, IEEE Trans. Neural Netw. 20, 61 (2008)
[84]	Z.Y. Fang, Q.M. Yan, NPJ Comput. Mater. 10, 91 (2024)
[85]	M.D. Witman, N.C. Bartelt, S. Ling, P.W. Guan, L. Way, M.D. Allendorf, V. Stavila, J. Phys. Chem. Lett. 15, 1500 (2024)
[86]	M.L. Pasini, G.S. Jung, S. Irle, Comput. Mater. Sci. 224, 112141 (2023)
[87]	T. Long, Z.L. Long, B. Pang, Mech. Mater. 191, 104945 (2024)
[88]	I.J. Goodfellow, J.P. Abadie, M. Mirza, B. Xu, D.W. Farley, S. Ozair, A. Courville, Y. Bengio, Adv. Neural. Inf. Process. Syst. 16, 27 (2014)
[89]	A. Creswell, T. White, V. Dumoulin, K. Arulkumaran, B. Sengupta, A. Bharath, IEEE Signal Process. Mag. 35, 53 (2018)
[90]	I.J. Goodfellow, J.P. Abadie, M. Mirza, B. Xu, D.W. Farley, S. Ozair, A. Courville, Y. Bengio, Commun. ACM 63, 139 (2020)
[91]	A. Roy, A. Hussain, P. Sharma, G. Balasubramanian, M.F.N. Taufique, R. Devanathan, P. Singh, D.D. Johnson, Acta Mater. 257, 119177 (2023)
[92]	Z.Y. Yang, S. Li, S. Li, J. Yang, D.R. Liu, Comput. Mater. Sci. 220, 112064 (2023)
[93]	Z. Li, N. Birbilis, Integr. Mater. Manuf. Innov. 13, 435 (2024)
[94]	C. Chen, H.R. Zhou, W.M. Long, G. Wang, J.L. Ren, Sci. China Technol. Sci. 66, 3615 (2023)
[95]	Z.W. Li, F. Liu, W.J. Yang, S.H. Peng, J. Zhou, IEEE Trans. Neural Netw. Learn. Syst. 33, 6999 (2021)
[96]	B. Müller, J. Reinhardt, M.T. Strickland, Neural Networks: An Introduction, 2nd edn. (Springer, Berlin Heidelberg, 1995), p.100
[97]	J. Gui, Z.N. Sun, Y.G. Wen, D.C. Tao, J.P. Ye, IEEE Trans. Knowl. Data Eng. 35, 3313 (2021)
[98]	Y.L. Liu, C.H. Yao, C. Niu, W.L. Li, J.C. Yin, T. Shen, Mater. Today Commun. 26, 102032 (2021)
[99]	S. Ament, M. Amsler, D.R. Sutherland, M.C. Chang, D. Guevarra, A.B. Connolly, J.M. Gregoire, M.O. Thompson, R.B.V. Dover, Sci. Adv. 7, 4930 (2021)
[100]	U. Aggarwal, A. Popescu, C. Hudelot, Active Learning for Imbalanced Datasets[C]// Proc. IEEE/CVF Winter Conf. Appl. Comput. Vis. 2020: 1428
[101]	Z. Rao, P.Y. Tung, R. Xie, Y. Wei, H. Zhang, A. Ferrari, T.P.C. Klaver, F. Körmann, P.T. Sukumar, A.K.D. Silva, Y. Chen, Z. Li, D. Ponge, J. Neugebauer, O. Gutfleisch, S. Bauer, D. Raabe, Science 378, 78 (2022)
[102]	L. Torrey, J. Shavlik, Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods, and Techniques, 1st ed. (IGI Global, Hershey, PA, 2010), p. 242
[103]	M.L. Hutchinson, E. Antono, B.M. Gibbons, S. Paradiso, J. Ling, B. Meredig, Prepr. arXiv 1711, 05099 (2017)
[104]	W.Y. Li, W.F. Li, Z.J. Qin, L.M. Tan, L. Huang, F. Liu, C. Xiao, Materials 15, 4251 (2022)
[105]	Y. Zhang, K. Yang, G.S. Hao, D. Gong, Acta Autom. Sin. 47, 652 (2021)
[106]	S. Hou, M.M. Zhou, M.J. Bai, W.W. Liu, H. Geng, B.K. Yin, H.T. Li, Appl. Sci. 14, 2076 (2024)
[107]	G.A. Sulley, J. Raush, M.M. Montemore, J. Hamm, Scr. Mater. 249, 116180 (2024)
[108]	Z.C. Song, Y.W. Feng, C. Lu, Mater. Sci. Eng. A 924, 147792 (2025)
[109]	Y. Meng, J.G. Feng, S. Han, Z.H. Xu, W.B. Mao, T. Zhang, J.S. Kim, I. Roh, Y.P. Zhao, D.H. Kim, Y. Yang, J.W. Lee, L. Yang, C.W. Qiu, S.H. Bae, Nat. Rev. Mater. 8, 498 (2023)
[110]	M. Chen, X.F. Zhang, X. Xiao, G.W. Li, JOM 73, 3411 (2021) DOI
[111]	C.F. Du, Y.P. Gao, M. Zha, C. Wang, H.L. Jia, H.Y. Wang, Acta Mater. 250, 118855 (2023)
[112]	Y. Mao, Q. He, X. Zhao, Sci. Adv. 6, 4169 (2020)
[113]	J. Gao, Y.F. Wang, J.X. Hou, J.H. You, K.Q. Qiu, S.D. Zhang, J.P. Wang, Metals 13, 283 (2023)
[114]	C. Nyby, X.L. Guo, J.E. Saal, S.C. Chien, A.Y. Angela, H. Ke, T. Li, P. Lu, C. Oberdorfer, S. Sahu, S. Li, C.D. Taylor, W. Windl, J.R. Scully, G.S. Frankel, Sci. Data 8, 58 (2021)
[115]	J. Lu, X.N. Huang, Y.N. Yue, J. Appl. Phys. 135, 135104 (2024)
[116]	C. Wen, H.C. Shen, Y.W. Tian, G.Q. Lou, N.C. Wang, Y.J. Su, Scr. Mater. 252, 116240 (2024)
[117]	M.I. Jordan, T.M. Mitchell, Mater. Lett. 358, 135871 (2024)
[118]	B. Mahesh, Int. J. Sci. Res. 9, 381 (2020)
[119]	N.I. Ei, M.J. Murphy, What Is Machine Learning? in Machine Learning in Radiation Oncology: Theory and Applications, 1st edn. (Springer, Berlin, 2015), p.3
[120]	A.D. Clayton, A.M. Schweidtmann, G. Clemens, J.A. Manson, C.J. Taylor, C.G. Niño, T.W. Chamberlain, N. Kapur, A.J. Blacker, A.A. Lapkin, R.A. Bourne, Chem. Eng. J. 384, 123340 (2020)
[121]	N. Radhika, M.S. Niketh, U.V. Akhil, A.A. Adediran, T.C. Jen, Results Eng. 23, 102780 (2024)
[122]	D. Dey, S. Das, A. Pal, S. Dey, C.K. Raul, P. Mandal, A. Chatterjee, S. Chatterjee, M. Ghosh, J. Alloys Metall. Syst. 9, 100144 (2025)
[123]	J.H. Fang, M. Xie, X.Q. He, J.M. Zhang, J.Q. Hu, Y.T. Chen, Y.C. Yang, Q.L. Jin, Mater. Today Commun. 33, 104900 (2022)
[124]	Y. Li, J.J. Gong, S.L. Liang, W. Wu, Y.X. Wang, Z. Chen, J. Mater. Res. Technol. 34, 1732 (2025)
[125]	X.Y. Zhang, R.F. Dong, Q.W. Guo, H. Hou, Y.H. Zhao, J. Mater. Res. Technol. 26, 4813 (2023)
[126]	E. Alpaydin, Introduction to Machine Learning, 4th edn. (MIT Press, Cambridge, MA, 2020), p. 1
[127]	S.L. Sun, Z.H. Cao, H. Zhu, J. Zhao, IEEE Trans. Cybern. 50, 3668 (2019)
[128]	J.G. Yu, F.P. Yu, Q. Fu, G. Zhao, C.Y. Gong, M.C. Wang, Q.X. Zhang, Nanomaterials 13, 968 (2023)
[129]	J.H. Qian, Y. Li, J.L. Hou, S.J. Wu, Y. Zou, J. Mater. Res. 39, 2115 (2024)
[130]	S.Y. Lee, S. Byeon, H.S. Kim, H. Jin, S. Lee, Mater. Des. 197, 109260 (2021)
[131]	D. Dey, A. Pal, P. Biyani, P. Mandal, S. Das, S. Dey, M. Ghosh, J. Mater. Sci. 60, 4820 (2025)
[132]	S.M. Lundberg, S.I. Lee, Adv. Neural. Inf. Process. Syst. 66, 30 (2017)
[133]	K.K. Gupta, S. Barman, S. Dey, T. Mukhopadhyay, Mach. Learn. Sci. Technol. 5, 025082 (2024)