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This study integrates machine learning with density functional theory to automatically identify clusters in data. This approach enhances data analysis across diverse scientific fields, from physics to biology.

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Area of Science:

  • Computational Physics
  • Materials Science
  • Bioinformatics

Background:

  • Density Functional Theory (DFT) is a fundamental tool in quantum chemistry and condensed matter physics.
  • Constructing the most probable density function in DFT often requires complex manual analysis.
  • Machine learning (ML) offers powerful pattern recognition capabilities applicable to scientific data.

Purpose of the Study:

  • To develop a novel method combining ML and DFT for automatic determination of density functions.
  • To establish a framework for unsupervised identification of cluster numbers and boundaries within complex systems.
  • To validate the proposed method across interdisciplinary applications.

Main Methods:

  • Integration of machine learning algorithms with Density Functional Theory principles.
  • Utilizing the properties of universal functionals and Hohenberg-Kohn theorems for density function construction.
  • Application of unsupervised learning techniques for cluster analysis.

Main Results:

  • Successful determination of cluster numbers and boundaries in uncharged atomic clusters.
  • High-accuracy clustering of the Fisher's iris dataset, demonstrating feasibility and flexibility.
  • Practical application in brain tumor detection from MRI data and neural network image segmentation.

Conclusions:

  • The proposed method effectively bridges physical theory (DFT) with machine learning techniques.
  • The approach offers a robust and automated solution for data clustering and analysis.
  • This work has the potential to significantly benefit clinical diagnoses and interdisciplinary research.