REFERENCES
1. Rahman, A.; Hossain, M. S.; Siddique, A. Review: machine learning approaches for diverse alloy systems. J. Mater. Sci. 2025, 60, 12189-221.
2. Hu, M.; Tan, Q.; Knibbe, R.; et al. Recent applications of machine learning in alloy design: a review. Mater. Sci. Eng. R. Rep. 2023, 155, 100746.
3. Kumar, A.; Mukhopadhyay, N. K.; Yadav, T. P. Recent progresses on high entropy alloy development using machine learning: a review. Comput. Mater. Today. 2025, 8, 100038.
4. Cheng, M.; Fu, C. L.; Okabe, R.; et al. Artificial intelligence-driven approaches for materials design and discovery. Nat. Mater. 2026, 25, 174-90.
5. Hart, G. L. W.; Mueller, T.; Toher, C.; Curtarolo, S. Machine learning for alloys. Nat. Rev. Mater. 2021, 6, 730-55.
6. Merchant, A.; Batzner, S.; Schoenholz, S. S.; Aykol, M.; Cheon, G.; Cubuk, E. D. Scaling deep learning for materials discovery. Nature 2023, 624, 80-5.
7. Feng, L.; Li, J.; Lu, Q.; et al. Accelerated development of high-strength and high-conductivity Cu-Cr-Ti alloys based on data-driven design and experimental validation. Mater. Design. 2025, 253, 113948.
8. Yin, J.; Lei, Q.; Li, X.; et al. A novel neural network-based alloy design strategy: gated recurrent unit machine learning modeling integrated with orthogonal experiment design and data augmentation. Acta. Mater. 2023, 243, 118420.
9. Zhang, H.; Fu, H.; Zhu, S.; Yong, W.; Xie, J. Machine learning assisted composition effective design for precipitation strengthened copper alloys. Acta. Mater. 2021, 215, 117118.
10. Zhang, H.; Fu, H.; He, X.; et al. Dramatically enhanced combination of ultimate tensile strength and electric conductivity of alloys via machine learning screening. Acta. Mater. 2020, 200, 803-10.
11. Li, L.; Liu, G.; Yu, H.; et al. A machine learning strategy to achieve strength-conductivity-ductility synergy of high‐performance Cu-Ni-Co-Si alloys via rolling and aging process. J. Mater. Sci. Technol. 2026, 267, 184-97.
12. Sohail, Y.; Zhang, C.; Xue, D.; et al. Machine-learning design of ductile FeNiCoAlTa alloys with high strength. Nature 2025, 643, 119-24.
13. Vazquez, G.; Chakravarty, S.; Gurrola, R.; Arróyave, R. A deep neural network regressor for phase constitution estimation in the high entropy alloy system Al-Co-Cr-Fe-Mn-Nb-Ni. npj. Comput. Mater. 2023, 9, 1021.
14. Li, H.; Wang, J.; Xu, Q.; et al. High-strength medium-entropy alloy designed by precipitation-strengthening mechanism via machine learning. Mater. Sci. Eng. A. 2023, 882, 145443.
15. Vela, B.; Khatamsaz, D.; Acemi, C.; Karaman, I.; Arróyave, R. Data-augmented modeling for yield strength of refractory high entropy alloys: a Bayesian approach. Acta. Mater. 2023, 261, 119351.
16. Wang, J.; Kwon, H.; Kim, H. S.; Lee, B. A neural network model for high entropy alloy design. npj. Comput. Mater. 2023, 9, 1010.
17. Yin, J.; Rao, Z.; Wu, D.; et al. Interpretable predicting creep rupture life of superalloys: enhanced by domain-specific knowledge. Adv. Sci. 2024, 11, e2307982.
18. Lian, L.; Bao, Z.; Xiong, Q.; et al. Intelligent design of crack-resistant nickel-based superalloys for additive manufacturing by machine learning and multilayer filtering strategy. Mater. Today. Commun. 2025, 46, 112387.
19. Zhuang, X.; Antonov, S.; Li, W.; Lu, S.; Li, L.; Feng, Q. Alloying effects and effective alloy design of high-Cr CoNi-based superalloys via a high-throughput experiments and machine learning framework. Acta. Mater. 2023, 243, 118525.
20. Ma, Q.; Li, X.; Xin, R.; et al. Thermodynamic calculation and machine learning aided composition design of new nickel-based superalloys. J. Mater. Res. Technol. 2023, 26, 4168-78.
21. Yang, F.; Zhao, W.; Ru, Y.; et al. Deep learning accelerates the development of Ni-based single crystal superalloys: a physical-constrained neural network for creep rupture life prediction. Mater. Design. 2023, 232, 112174.
22. Xin, Y.; Zhong, Z.; Xie, A.; Luo, F.; Qiu, G.; Wang, Z. Building an effective deep learning model for mechanical properties prediction of steel. Mater. Lett. 2026, 402, 139262.
23. Kannan, R.; Nandwana, P. Accelerated alloy discovery using synthetic data generation and data mining. Scr. Mater. 2023, 228, 115335.
24. Wei, X.; van der Zwaag, S.; Jia, Z.; Wang, C.; Xu, W. On the use of transfer modeling to design new steels with excellent rotating bending fatigue resistance even in the case of very small calibration datasets. Acta. Mater. 2022, 235, 118103.
25. Ren, D.; Wang, C.; Wei, X.; Lai, Q.; Xu, W. Building a quantitative composition-microstructure-property relationship of dual-phase steels via multimodal data mining. Acta. Mater. 2023, 252, 118954.
26. Wu, J.; Torresi, L.; Hu, M.; et al. Inverse design workflow discovers hole-transport materials tailored for perovskite solar cells. Science 2024, 386, 1256-64.
27. Xu, P.; Chang, D.; Lu, T.; Li, L.; Li, M.; Lu, W. Search for ABO3 type ferroelectric perovskites with targeted multi-properties by machine learning strategies. J. Chem. Inf. Model. 2022, 62, 5038-49.
28. He, J.; Li, J.; Liu, C.; et al. Machine learning identified materials descriptors for ferroelectricity. Acta. Mater. 2021, 209, 116815.
29. Min, K.; Cho, E. Accelerated discovery of potential ferroelectric perovskite via active learning. J. Mater. Chem. C. 2020, 8, 7866-72.
30. Balachandran, P. V.; Kowalski, B.; Sehirlioglu, A.; Lookman, T. Experimental search for high-temperature ferroelectric perovskites guided by two-step machine learning. Nat. Commun. 2018, 9, 1668.
31. Liu, Q.; Polak, M. P.; Kim, S. Y.; et al. Beyond designer’s knowledge: generating materials design hypotheses via a large language model. Acta. Mater. 2025, 297, 121307.
32. Tian, S.; Jiang, X.; Wang, W.; et al. Steel design based on a large language model. Acta. Mater. 2025, 285, 120663.
33. Wang, P.; Jiang, Y.; Liao, W.; et al. Generalizable descriptors for automatic titanium alloys design by learning from texts via large language model. Acta. Mater. 2025, 296, 121275.
34. Polak, M. P.; Morgan, D. Extracting accurate materials data from research papers with conversational language models and prompt engineering. Nat. Commun. 2024, 15, 1569.
35. Senior, A. W.; Evans, R.; Jumper, J.; et al. Improved protein structure prediction using potentials from deep learning. Nature 2020, 577, 706-10.
36. Tep, P.; Bernacki, M. High-fidelity grain growth modeling: leveraging deep learning for fast computations. Acta. Mater. 2025, 301, 121486.
37. Yang, H.; Wang, W.; Li, C.; et al. Deep learning-based X-ray computed tomography image reconstruction and prediction of compression behavior of 3D printed lattice structures. Addit. Manuf. 2022, 54, 102774.
38. Lundberg, S.; Lee, S. I. A unified approach to interpreting model predictions. arXiv 2017, arXiv:1705.07874. https://doi.org/10.48550/arXiv.1705.07874. (accessed 2026-05-21).
39. Ribeiro, M. T.; Singh, S.; Guestrin, C. “Why should I trust you?”: Explaining the predictions of any classifier. arXiv 2016, arXiv:1602.04938. https://doi.org/10.48550/arXiv.1602.04938. (accessed 2026-05-21).
40. Alibagheri, E.; Ranjbar, A.; Khazaei, M.; Kühne, T. D.; Vaez Allaei, S. M. Remarkable optoelectronic characteristics of synthesizable square‐octagon haeckelite structures: machine learning materials discovery. Adv. Funct. Mater. 2024, 34, 2402390.
41. Xu, H.; Sun, X.; Peng, R. L.; et al. Machine learning enabled the prediction of γ′-depleted depth during interdiffusion of bond-coated IN792 superalloy. Surf. Coat. Technol. 2025, 513, 132448.
42. Chen, W.; Hilhorst, A.; Bokas, G.; Gorsse, S.; Jacques, P. J.; Hautier, G. A map of single-phase high-entropy alloys. Nat. Commun. 2023, 14, 2856.
43. Pearson, K. LIII. On lines and planes of closest fit to systems of points in space. Lond. Edinb. Dublin. Philos. Mag. J. Sci. 1901, 2, 559-72.
44. Srinivasan, S.; Broderick, S. R.; Zhang, R.; et al. Mapping chemical selection pathways for designing multicomponent alloys: an informatics framework for materials design. Sci. Rep. 2015, 5, 17960.
45. Tenenbaum, J. B.; de Silva, V.; Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 2000, 290, 2319-23.
46. McInnes, L.; Healy, J.; Melville, J. UMAP: uniform manifold approximation and projection for dimension reduction. arXiv 2018, arXiv:1802.03426. https://doi.org/10.48550/arXiv.1802.03426. (accessed 2026-05-21).
47. Zhao, S.; Li, J.; Wang, J.; Lookman, T.; Yuan, R. Closed-loop inverse design of high entropy alloys using symbolic regression-oriented optimization. Mater. Today. 2025, 88, 263-71.
48. Xue, D.; Xue, D.; Yuan, R.; et al. An informatics approach to transformation temperatures of NiTi-based shape memory alloys. Acta. Mater. 2017, 125, 532-41.
49. Pokorny, V. J.; Sponheim, S. R.; Rawls, E. Impact of reduced-dimensionality independent components analysis on event-related potential measurements. Psychophysiology 2023, 60, e14223.
50. Miracle, D.; Senkov, O. A critical review of high entropy alloys and related concepts. Acta. Mater. 2017, 122, 448-511.
51. Zhang, Y.; Wen, C.; Wang, C.; et al. Phase prediction in high entropy alloys with a rational selection of materials descriptors and machine learning models. Acta. Mater. 2020, 185, 528-39.
52. Machaka, R.; Motsi, G. T.; Raganya, L. M.; Radingoana, P. M.; Chikosha, S. Machine learning-based prediction of phases in high-entropy alloys: a data article. Data. Brief. 2021, 38, 107346.
53. Xue, D.; Balachandran, P. V.; Hogden, J.; Theiler, J.; Xue, D.; Lookman, T. Accelerated search for materials with targeted properties by adaptive design. Nat. Commun. 2016, 7, 11241.
54. Schölkopf, B.; Smola, A.; Müller, K. Nonlinear component analysis as a kernel eigenvalue problem. Neural. Comput. 1998, 10, 1299-319.
55. Roweis, S. T.; Saul, L. K. Nonlinear dimensionality reduction by locally linear embedding. Science 2000, 290, 2323-6.
56. Hefner, R. Warren S. Torgerson, Theory and methods of scaling. New York: John Wiley and Sons, Inc., 1958. Pp. 460. Syst. Res. 1959, 4, 245-7.
57. Tao, Q.; Xu, P.; Li, M.; Lu, W. Machine learning for perovskite materials design and discovery. npj. Comput. Mater. 2021, 7, 495.
58. Zhang, Y.; Zhou, Y.; Lin, J.; Chen, G.; Liaw, P. Solid‐solution phase formation rules for multi‐component alloys. Adv. Eng. Mater. 2008, 10, 534-8.
59. Zhang, Y.; Zuo, T. T.; Tang, Z.; et al. Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 2014, 61, 1-93.
60. Zarinejad, M.; Liu, Y. Dependence of transformation temperatures of NiTi‐based shape‐memory alloys on the number and concentration of valence electrons. Adv. Funct. Mater. 2008, 18, 2789-94.
61. Liu, Y.; Fu, X.; Yu, Q.; Zhang, M.; Liu, J. Significant reduction of phase-transition hysteresis for magnetocaloric (La1-xCex)2Fe11Si2Hy alloys by microstructural manipulation. Acta. Mater. 2021, 207, 116687.
62. Zhou, Y.; Cheng, J.; Hong, M.; et al. Orchestrating phase transition in GeTe thermoelectrics: an investigation into the role of electronegativity. Nano. Energy. 2024, 127, 109723.
63. Zurcher, R.; Muller, M.; Sachslehner, F.; Groger, V.; Zehetbauer, M. Dislocation resistivity in Cu: dependence of the deviations from Matthiessen’s rule on temperature, dislocation density and impurity content. J. Phys. Condens. Matter. 1995, 7, 3515-28.
64. Žnidarič, M. Modified Matthiessen’s rule: more scattering leads to less resistance. Phys. Rev. B. 2022, 105, 045140.





