CAREER: Causation in Dynamical Systems: Bridging the Gap Between Data Analytics and System Identification

职业：动态系统中的因果关系：弥合数据分析和系统识别之间的差距

• 批准号: 1552218
• 负责人: Jonathan Rogers
• 金额: $ 50万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-03-01 至 2022-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1552218&HistoricalAwards=false
• 关键词: CAREER; Causation; Dynamical; Systems; Bridging

This Faculty Early Career Development (CAREER) project explores an innovative approach to system identification. System identification is the process of building a model for a physical system from observed experimental data. System ID processes are used in a wide variety of scientific and engineering applications from weather prediction to aircraft design. While numerous system ID algorithms have been developed to date, many current methods yield poorly performing models when applied to complicated physical systems involving numerous interacting components. However, recent advancements in data analytics have yielded new algorithms that can identify patterns, and specifically causal relationships, in data. This award supports fundamental research exploring how these new data analysis tools can inform the system ID process and enable a new class of system ID algorithms specifically applicable to large-scale, complex systems. The resulting algorithms may be useful in difficult modeling and prediction problems including atmospheric/climate prediction, modeling of biological systems, or financial market analysis. The approaches developed here may lead to better predictive models for many of these complex systems. The program has strong ties to engineering education since undergraduates will have the opportunity to participate in specific experimental aspects of the research.Despite extensive research in system identification over the past several decades, system ID tools for nonlinear or high-order systems are rather underdeveloped and oftentimes suffer from convergence or computational issues. The research to be performed here leverages very recent advances in the mathematics and data analytics communities to derive a fundamentally novel approach to system identification based on information theory. At the core of this research is the concept of causation entropy, an entropic measure of information transfer within a dynamical system that can be computed directly from measured output data. The project seeks to derive rigorous, causation entropy-based approaches for nonlinear parameter estimation and model order reduction, as well as establish a fundamental realization theory for linear Gaussian systems using causation entropy. Furthermore, the problem of identifying input-output dynamics will be addressed from an information theory perspective. A series of case studies will be generated which highlight performance and utility of the system identification methods in a wide range of real-world examples.

这个教师早期职业发展（Career）项目探索了一种创新的系统识别方法。系统识别是根据观察到的实验数据为物理系统建立模型的过程。系统ID过程广泛应用于各种科学和工程应用，从天气预报到飞机设计。虽然迄今为止已经开发了许多系统ID算法，但当应用于涉及许多相互作用组件的复杂物理系统时，许多当前方法产生的模型性能不佳。然而，数据分析的最新进展产生了新的算法，可以识别数据中的模式，特别是因果关系。该奖项支持基础研究，探索这些新的数据分析工具如何为系统ID过程提供信息，并使一类新的系统ID算法特别适用于大型复杂系统。由此产生的算法可能对困难的建模和预测问题有用，包括大气/气候预测，生物系统建模或金融市场分析。这里开发的方法可能会为许多这些复杂系统带来更好的预测模型。该项目与工程教育有着紧密的联系，因为本科生将有机会参与研究的具体实验方面。尽管在过去的几十年里对系统识别进行了广泛的研究，但用于非线性或高阶系统的系统识别工具相当不发达，并且经常受到收敛或计算问题的困扰。在这里进行的研究利用了数学和数据分析社区的最新进展，得出了一种基于信息论的系统识别的基本新颖方法。这项研究的核心是因果熵的概念，这是动态系统中信息传递的熵度量，可以直接从测量的输出数据中计算出来。该项目旨在推导出严格的、基于因果熵的非线性参数估计和模型降阶方法，并利用因果熵建立线性高斯系统的基本实现理论。此外，识别输入-输出动态的问题将从信息论的角度来解决。将生成一系列案例研究，突出系统识别方法在广泛的现实世界示例中的性能和效用。