Machine learning (ML) is a powerful tool for the accelerated design and development of various materials. However, the constructed ML models are often difficult to use by researchers other than the creator, that is, model sharing is a challenge. Here, we propose a method to avoid this issue by transforming the knowledge learned from ML models into material rules to obtain a generic design strategy. Specifically, we take the prediction of phase formation in multi-principal-element superalloys (MPESAs) as an example. First, we construct two classification models using ML algorithms to predict the presence or absence of the L12 phase and other phases, respectively. Then, the Shapley additive explanation method is used to extract knowledge from the models and transform them into understandable material insights. Based on this method, we obtain a generic design strategy for rapidly determining the phase formation of MPESAs, specifically the combination of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1578_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{{VEC}}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi mathvariant="italic">VEC</mi> </mrow> <mo>̅</mo> </mover> </math></EquationSource> </InlineEquation> > 8, −16.0 < ∆Hmix < −9.7 J∙mol−1 ∙ K−1, and 1671 < <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1578_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$\bar{{T}_{m}}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> <mo>̅</mo> </mover> </math></EquationSource> </InlineEquation> < 1822 K. This strategy enables the rapid and highly accurate (>98%) design of alloys with an “FCC + L12” dual-phase microstructure. We used this strategy to randomly select 12 candidates composed of different elements from the large design space for experimental preparation. The experimental results show that all these alloys exhibit the ideal “FCC + L12” dual-phase microstructure, verifying the accuracy of the design strategy. Notably, one of the alloys has a good combination of high solvus temperature (1218 °C) and very low density (7.77 g‧cm−3), superior to most MPESAs.

Transforming machine learning model knowledge into material insights for multi-principal-element superalloy phase design

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2025年4月14日

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Qiuling Tao,
Xintong Yang,
Longke Bao,
Yuexin Zhou,
Tao Yang,
Yilu Zhao,
Rongpei Shi,
Zhifu Yao,
Xingjun Liu

摘要

Machine learning (ML) is a powerful tool for the accelerated design and development of various materials. However, the constructed ML models are often difficult to use by researchers other than the creator, that is, model sharing is a challenge. Here, we propose a method to avoid this issue by transforming the knowledge learned from ML models into material rules to obtain a generic design strategy. Specifically, we take the prediction of phase formation in multi-principal-element superalloys (MPESAs) as an example. First, we construct two classification models using ML algorithms to predict the presence or absence of the L1₂ phase and other phases, respectively. Then, the Shapley additive explanation method is used to extract knowledge from the models and transform them into understandable material insights. Based on this method, we obtain a generic design strategy for rapidly determining the phase formation of MPESAs, specifically the combination of $\overline{{VEC}}$ $\overset{̅}{VEC}$ > 8, −16.0 < ∆H_mix < −9.7 J∙mol⁻¹ ∙ K⁻¹, and 1671 < $\bar{{T}_{m}}$ $\overset{̅}{T_{m}}$ < 1822 K. This strategy enables the rapid and highly accurate (>98%) design of alloys with an “FCC + L1₂” dual-phase microstructure. We used this strategy to randomly select 12 candidates composed of different elements from the large design space for experimental preparation. The experimental results show that all these alloys exhibit the ideal “FCC + L1₂” dual-phase microstructure, verifying the accuracy of the design strategy. Notably, one of the alloys has a good combination of high solvus temperature (1218 °C) and very low density (7.77 g‧cm⁻³), superior to most MPESAs.