神经网络的复杂性,混乱和动荡
Tim Whittaker1, Romuald A Janik2, Yaron Oz3,4
1Département des sciences de la Terre et de l'atmosphère, Université du Québec à Montréal, Montréal, QC, H3C 3P8, Canada. whittaker.tim@courrier.uqam.ca.
The European physical journal. E, Soft matter
|July 20, 2023
概括
深度神经网络通过分析流体流动图像来量化混乱和动荡的复杂性. 这些网络识别出不同的特征,比如旋流相关性光谱,以区分动荡与混乱的政权.
科学领域:
- 物理 物理学 物理
- 流体动力学 流体动力学
- 计算科学 计算科学
背景情况:
- 混乱和动荡是复杂的物理现象,缺乏精确的定量复杂度指标.
- 深度神经网络 (DNN) 为分析复杂系统提供了一个新的视角.
- 了解DNN的计算复杂性对于区分物理模式至关重要.
研究的目的:
- 利用深度神经网络开发一种方法来量化混乱和动荡的相对复杂性.
- 分析DNN学习的内部特征表示,用于流体流量分类.
- 识别DNN用于区分混沌流体动力学和流体动力学的特定特征.
主要方法:
- 训练DNN在动荡和混乱状态下对流体配置图像进行分类,并与噪音和现实世界的图像一起进行分类.
- 通过DNN内部特征表示的内在维度量化计算复杂性.
- 计算网络使用的独立特征的有效数量.
- 构建对抗性示例来探讨网络决策.
主要成果:
- DNN可以有效地区分动荡和混乱的流体流动模式.
- 内在的维度和特征的有效数量提供了计算复杂性的数值估计.
- 敌对的例子显示,的两点相关性光谱是分类的关键特征.
- 复杂度指标描述神经网络在中间和最后阶段的处理.
结论:
- 深度神经网络可以作为一种工具,用于定量评估流和混乱等物理现象的复杂性.
- 该研究确定了特定的流体动力学特征 (旋转率相关性光谱),对于区分这些模式至关重要.
- 这种方法提供了对流体复杂性的性质和神经网络内部运作的洞察.
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