Topological Data Analysis in Materials Science: Principles, Machine Learning Integration, and Application Landscapes

Area of Science:

• Materials Science
• Data Science
• Computational Materials Science

Background:

• Data-driven approaches are revolutionizing materials science, emphasizing digital data representation.
• Complex material systems contain intricate data patterns requiring advanced analytical methods.
• Discovering structure-property relationships is crucial for materials innovation.

Purpose of the Study:

• To introduce Topological Data Analysis (TDA) as a robust method for materials data analysis.
• To review TDA methodologies, including persistent homology and topological learning.
• To highlight TDA's applications and advantages in materials informatics and discovery.

Main Methods:

• Mathematical foundations of Topological Data Analysis (TDA).
• Focus on persistent homology, persistent GLMY homology, and Euler characteristic curves.
• Integration of TDA with machine learning for topological learning models.

Main Results:

• TDA offers unique robustness, interpretability, and universality for uncovering patterns in material data.
• Demonstrated applications of TDA in diverse material systems, molecular science, and biochemistry.
• Identified advantages of TDA in materials informatics for structure-property relationship discovery.

Conclusions:

• TDA provides a powerful framework for data-driven materials discovery and design.
• Topological learning enhances predictive modeling capabilities in materials science.
• Addressing current challenges will further unlock TDA's potential in advancing materials informatics.