使用白金汉派的维度一致的学习
Joseph Bakarji1, Jared Callaham2, Steven L Brunton3
1Department of Mechanical Engineering, University of Washington, Seattle, WA, USA. jbakarji@uw.edu.
Nature computational science
|January 4, 2024
概括
本研究引入了基于数据的方法,使用白金汉Pi定理来发现无维群. 这些技术自动将复杂的物理系统数据分解成更低的维度,以便更好地分析.
科学领域:
- 物理 物理学 物理
- 应用数学 应用数学 应用数学
- 数据科学数据科学数据科学
背景情况:
- 维度分析对于理解物理系统至关重要,特别是当控制方程未知时.
- 巴金汉普数定理提供了一种方法来找到无维群,但不保证唯一性或最佳数据崩.
- 现有的方法往往需要先前了解系统动力学或控制方程.
研究的目的:
- 开发自动化,数据驱动的技术,以发现最佳的无维群.
- 为了利用测量数据固有的对称性来识别这些群体.
- 有效地减少复杂的物理系统数据的维度.
主要方法:
- 提出了三种新的数据驱动技术,这些技术受到白金汉Pi定理的约束.
- 方法1:通过非参数的拟合进行受约束优化.
- 方法2:用于参数空间投影的深度学习方法 (BuckiNet).
- 方法3:稀疏识别非线性动力学,以发现无维方程.
主要成果:
- 在三个基准问题中成功确定了关键的无维群:旋转圆圈上的珠子,层状边界层和雷利-贝纳德对流.
- 证明了开发方法的准确性,稳定性和计算效率.
- 展示了这些技术能够有效地将数据压缩到低维空间中的能力.
结论:
- 拟议的数据驱动方法为维度分析提供了强大的,自动化的方法.
- 这些技术增强了从测量数据中发现物理对称性和洞察力的发现.
- 这些方法为分析缺乏明确治理方程的系统提供了强大的替代方案.
相关概念视频
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The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
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01:15Determination of Pi Terms
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