论文标题
使用深卷积Koopman网络从视频数据中提取离散光谱模式
Extraction of Discrete Spectra Modes from Video Data Using a Deep Convolutional Koopman Network
论文作者
论文摘要
Koopman理论中的最新深度学习扩展使非线性动力学系统的紧凑，可解释的表示能够适合线性分析。 Deep Koopman Networks试图学习Koopman本征函数，以捕获坐标转换为全球线性化系统动力学。这些特征函数可以与控制系统动力学行为的基础系统模式相关联。尽管许多相关的技术已经证明了它们在规范系统及其相关状态变量上的功效，但在这项工作中，系统动力学是光学观察到的（即视频格式）。我们证明了深卷积Koopman网络（CKN）在自动识别具有离散光谱的动态系统的独立模式中的能力。实际上，由于可观察到的可观察变量很容易获得数据，因此这具有系统数据收集的灵活性。博学的模型能够成功，稳健地识别管理系统的基础模式，即使有冗余的嵌入空间。使用简单的掩蔽过程鼓励模态分解。本工作中分析的所有系统都使用相同的网络体系结构。
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions which capture the coordinate transformation to globally linearize system dynamics. These eigenfunctions can be linked to underlying system modes which govern the dynamical behavior of the system. While many related techniques have demonstrated their efficacy on canonical systems and their associated state variables, in this work the system dynamics are observed optically (i.e. in video format). We demonstrate the ability of a deep convolutional Koopman network (CKN) in automatically identifying independent modes for dynamical systems with discrete spectra. Practically, this affords flexibility in system data collection as the data are easily obtainable observable variables. The learned models are able to successfully and robustly identify the underlying modes governing the system, even with a redundantly large embedding space. Modal disaggregation is encouraged using a simple masking procedure. All of the systems analyzed in this work use an identical network architecture.
