使用神经网络的数据驱动的自我相似性的发现
Ryota Watanabe1, Takanori Ishii1, Yuji Hirono2
1Kyoto University, Department of Physics, Kyoto 606-8502, Japan.
Physical review. E
|March 19, 2025
概括
这项研究引入了一种新的神经网络方法,直接从数据中识别复杂物理系统中的自我相似性. 这种独立于模型的方法通过提取特征的权力法指数来揭示治理规律.
科学领域:
- 物理 物理学 物理
- 复杂的系统复杂的系统.
- 数据科学数据科学数据科学
背景情况:
- 识别自我相似性对于理解复杂的物理现象至关重要.
- 传统方法通常依赖于模型特定的假设,引入潜在的偏差.
- 需要一种独立于模型的方法,直接从观察到的数据中发现自我相似性.
研究的目的:
- 开发和验证一种基于神经网络的方法,在不假定物理模型的情况下发现自我相似性.
- 从数据中提取特征尺度转换对称性的权力定律指数.
- 为分析复杂系统提供强大的,与模型无关的工具.
主要方法:
- 神经网络架构的设计是为了结构性地结合权力规律的单项形式.
- 神经网络是使用观察数据 (合成和实验) 进行训练的.
- 成功的训练允许提取权力法指数.
主要成果:
- 神经网络成功地直接从数据中识别自我相似性.
- 提取了特征尺度转换对称性的权力定律指数.
- 该方法在合成和实验数据集上都表现出有效性.
结论:
- 建议的神经网络方法提供了一个强大的,独立于模型的工具,用于发现自我相似性.
- 这种方法有助于在复杂的物理系统中探索治理规律.
- 该技术在分析各种科学数据方面具有广泛的应用.
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