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<p>Machine learning offers a transformative approach for accelerating the design of high-performance alloys. This study develops a dual-feature-selection strategy (PCC–MIC) integrated with support vector machine (SVM) modeling to predict hardness in NbTaW-based high-entropy alloys (HEAs), addressing multicomponent optimization challenges under limited experimental data constraints. A curated dataset of 62 NbTaW-based HEA samples was established, with 36 features (15 elemental + 21 physical descriptors) calculated for hardness correlation. Pearson’s correlation coefficient (PCC) and maximum information coefficient (MIC) analyses were employed to rank feature significance, identifying key contributors: Elements with substantial atomic radii (W, Mo, Zr, Nb) promote lattice distortion and solid solution strengthening, while carbon forms hardness-enhancing carbides with refractory metals. Physical descriptors—particularly A, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta_{r}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, γ, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\delta_{G}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mi>G</mi> </msub> </math></EquationSource> </InlineEquation>, and μ collectively govern the strengthening contribution through dislocation blocking mechanisms. The optimal SVM model incorporated 25 top-ranked features (12 elemental via MIC, 13 physicals via PCC). After rigorous k-fold cross-validation (k = 11) and hyperparameter optimization, the model achieved a coefficient of determination (<i>R</i><sup>2</sup>) of 0.9237 with MAE = 38.68 HV. This demonstrates significant potential for accelerating the design of next-generation NbTaW HEA thermal protection systems and high-temperature structural components.</p>

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Hardness Prediction of NbTaW-Based High-Entropy Alloys with Machine Learning

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Dunying Deng,
  • Junjie Han,
  • Hanqing Wen,
  • Yonggang Tong

摘要

Machine learning offers a transformative approach for accelerating the design of high-performance alloys. This study develops a dual-feature-selection strategy (PCC–MIC) integrated with support vector machine (SVM) modeling to predict hardness in NbTaW-based high-entropy alloys (HEAs), addressing multicomponent optimization challenges under limited experimental data constraints. A curated dataset of 62 NbTaW-based HEA samples was established, with 36 features (15 elemental + 21 physical descriptors) calculated for hardness correlation. Pearson’s correlation coefficient (PCC) and maximum information coefficient (MIC) analyses were employed to rank feature significance, identifying key contributors: Elements with substantial atomic radii (W, Mo, Zr, Nb) promote lattice distortion and solid solution strengthening, while carbon forms hardness-enhancing carbides with refractory metals. Physical descriptors—particularly A, \(\delta_{r}\) δ r , γ, \(\delta_{G}\) δ G , and μ collectively govern the strengthening contribution through dislocation blocking mechanisms. The optimal SVM model incorporated 25 top-ranked features (12 elemental via MIC, 13 physicals via PCC). After rigorous k-fold cross-validation (k = 11) and hyperparameter optimization, the model achieved a coefficient of determination (R2) of 0.9237 with MAE = 38.68 HV. This demonstrates significant potential for accelerating the design of next-generation NbTaW HEA thermal protection systems and high-temperature structural components.