动力系统的信息理论公式：因果关系、建模与控制
Information-theoretic formulation of dynamical systems: causality, modeling, and control
摘要：
混沌，高维动力系统的因果关系，建模和控制的问题制定的信息论的语言。感兴趣的中心量是香农熵，它测量系统状态中的信息量。在这个框架内，因果关系被量化的动力系统中感兴趣的变量之间的信息流。降阶建模是一个与信息守恒相关的问题，其中模型的目标是从原始系统中保留最大量的相关信息。类似地，控制理论通过将串联传感器-致动器设想为减少待控制状态的未知信息的设备而被铸造在信息理论术语中。新的提法是用来解决三个问题的因果关系，建模和控制的湍流，这是一个主要的例子，混沌，高维动力系统。这些应用包括湍流叶栅中能量传递的因果关系、大涡模拟的亚网格尺度模型以及壁面湍流减阻的流动控制。
英文摘要：
The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality is quantified by the information flux among the variables of interest in the dynamical system. Reduced-order modeling is posed as a problem related to the conservation of information in which models aim at preserving the maximum amount of relevant information from the original system. Similarly, control theory is cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. The new formulation is used to address three problems about the causality, modeling, and control of turbulence, which stands as a primary example of a chaotic, high-dimensional dynamical system. The applications include the causality of the energy transfer in the turbulent cascade, subgrid-scale modeling for large-eddy simulation, and flow control for drag reduction in wall-bounded turbulence.
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