机器学习 K-Means 集群在交互分离密度拟合算法:在平面波中推进精确和高效的立方缩放密度功能扰乱理论计算.
Jielan Li1, Liu Yang1, Lingyun Wan1
1Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China.
The journal of physical chemistry. A
|March 5, 2024
概括
一个新的机器学习K-means算法加速了密度函数扰动理论 (DFPT) 的计算. 这种方法提高了融合,并降低了格子动力学模拟的计算成本.
科学领域:
- 计算材料科学 计算材料科学
- 凝聚物质物理学 凝聚物质物理学
- 量子化学是一种量子化学.
背景情况:
- 密度函数扰动理论 (DFPT) 对于格子动力学至关重要.
- 适应压缩极化 (ACP) 方法优化了DFPT,减少了复杂性.
- 目前的方法,如用于互插可分密度拟合 (ISDF) 的列旋转 (QRCP) 的QR因数分解,在计算上昂贵 (O(N^3)),并且可能存在收问题.
研究的目的:
- 开发一种更有效,更准确的方法来选择ISDF中的插值点,用于基于非洲和非洲的DFPT.
- 为了降低计算成本,并提高DFPT计算的收性.
主要方法:
- 实施了一种机器学习的K-means集群算法,用于ISDF点选择.
- 将K-means-ISDF算法集成到KSSOLV MATLAB工具箱中,用于平面波DFPT.
- 将K-means方法与传统的QRCP算法进行比较.
主要成果:
- K-means算法实现了二进制缩放 (O(N^2),显著超过了QRCP的立方缩放 (O(N^3).
- 在ISDF中,K-means的准确性与QRCP的准确性相当.
- 基于K-means的方法导致了基于ACP的DFPT计算的更好的趋同.
- 对插值点选择的计算成本减少了近两个数量级.
结论:
- K-means 集群算法为 DFPT 中的 ISDF 提供了一个计算效率高,准确的替代方案.
- 这种方法提高了基于ACP的DFPT的性能,特别是在复杂的系统中.
- K-means方法在加速材料模拟方面取得了重大进展.
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