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<p>This study presents a novel approach for analyzing and establishing high-dimensional phase diagrams in complex alloy systems. Through the introduction of ‘composition space volume’, a multi-dimensional metric and alloy composition variations can be quantitatively defined. Utilizing random sampling method, the study quantifies phase diagram space complexity through phase region density, and model training costs through data density. This leads to a strategic segmentation of the entire composition space and tailors to the complexity of each segment, thereby reducing computational efforts in model training. A key contribution of this study is the integration of segmented models using a Mixture of Experts (MoE) approach, ensuring accurate prediction of phase equilibria across diverse composition spaces. We demonstrate this technique by constructing a high-dimensional phase diagram for the Fe-Co-Ni-Ti system. The experts for the simple, moderate, and complex phase diagram spaces achieve classification accuracies of 97.2, 96.7, and 96.2%, respectively, and the MoE achieves 97.2% across the entire phase diagram space.</p>

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Uncovering High-Dimensional Phase Diagram Through the Mixture of Experts Approach and Machine Learning

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Zhengdi Liu,
  • Qi Huang,
  • Yong Du,
  • Xin Wang,
  • Yuling Liu,
  • Wenwen Sun

摘要

This study presents a novel approach for analyzing and establishing high-dimensional phase diagrams in complex alloy systems. Through the introduction of ‘composition space volume’, a multi-dimensional metric and alloy composition variations can be quantitatively defined. Utilizing random sampling method, the study quantifies phase diagram space complexity through phase region density, and model training costs through data density. This leads to a strategic segmentation of the entire composition space and tailors to the complexity of each segment, thereby reducing computational efforts in model training. A key contribution of this study is the integration of segmented models using a Mixture of Experts (MoE) approach, ensuring accurate prediction of phase equilibria across diverse composition spaces. We demonstrate this technique by constructing a high-dimensional phase diagram for the Fe-Co-Ni-Ti system. The experts for the simple, moderate, and complex phase diagram spaces achieve classification accuracies of 97.2, 96.7, and 96.2%, respectively, and the MoE achieves 97.2% across the entire phase diagram space.