原子结构特征映射的局部反转性和灵敏性
Sergey N Pozdnyakov1, Liwei Zhang2, Christoph Ortner2
1Laboratory of Computational Science and Modelling, Institute of Materials, Federal Institute of Technology (EPFL) CH-1015 Lausanne, Lausanne, 1015, Switzerland.
Open research Europe
|August 30, 2023
概括
对于原子模拟的机器学习需要了解原子坐标如何映射到描述符. 这项研究揭示了这些映射中的理想的对称感应奇点和有问题的虚假奇点,提供了识别它们的工具.
科学领域:
- 计算化学是一种计算化学.
- 材料科学 是一种材料科学.
- 机器学习是机器学习.
背景情况:
- 机器学习越来越多地用于原子级模拟.
- 了解从原子坐标到描述符的数学映射至关重要.
- 对称描述符对于在模型中强制执行物理约束至关重要.
研究的目的:
- 分析原子坐标和描述符之间的映射的灵敏度.
- 为了量化这种灵敏度,使用雅可比的奇数值分解 (SVD).
- 在描述符表示中识别奇点的来源.
主要方法:
- 雅可比矩阵的单数值分解 (SVD).
- 对原子位移的映射灵敏度的分析.
- 在不同的原子配置和描述器选择中进行调查.
主要成果:
- 对称性和平滑性在映射Jacobian中创造了可取的零奇数值.
- 虚假的奇点来自描述符的不完整性,其中不同的结构映射到相同的特征向量.
- 基础集合的积极切断可以引入额外的虚假奇点.
结论:
- 构建对称的原子表示涉及微妙的数学挑战.
- 奇点可以是物理上可取的 (强迫对称) 和有问题的 (由于不完整性或切断).
- 提供概念和数值工具,用于识别和分析原子表示中的奇点.
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