论文标题
混乱和湍流的神经网络复杂性
Neural Network Complexity of Chaos and Turbulence
论文作者
论文摘要
混乱和湍流是复杂的物理现象，但仍然缺乏量化它们的复杂性度量的精确定义。在这项工作中，我们从深层神经网络的角度考虑了混乱和湍流的相对复杂性。我们分析了一组分类问题，其中网络必须将湍流状态中流体剖面的图像与其他类别的图像区分，例如混乱制度中的流体剖面，各种噪声和现实世界图像的结构。我们分析了不可压缩的以及弱压缩的流体流。我们量化了网络通过内部特征表示的固有维度执行的计算的复杂性，并计算网络使用的有效数量的独立特征数量，以区分类别。除了提供计算复杂性的数值估计外，该度量还表征了中间和最终阶段的神经网络处理。我们构建对抗性示例，并使用它们来识别混乱和湍流涡度的两个点相关光谱作为网络用于分类的功能。
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.
