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

这个学院早期职业发展(CALEAR)项目探索了一种创新的系统识别方法。系统辨识是根据观测到的实验数据为物理系统建立模型的过程。系统ID流程广泛应用于从天气预报到飞机设计的各种科学和工程应用中。虽然到目前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的组件的复杂物理系统时，许多当前方法产生性能较差的模型。然而，最近数据分析的进步产生了新的算法，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流程提供信息，并支持专门适用于大规模、复杂系统的新型系统ID算法。由此产生的算法可能在困难的建模和预测问题中有用，包括大气/气候预测、生物系统的建模或金融市场分析。这里开发的方法可能会为许多这样的复杂系统带来更好的预测模型。该项目与工程教育有很强的联系，因为本科生将有机会参与研究的特定实验方面。尽管过去几十年来在系统辨识方面进行了广泛的研究，但用于非线性或高阶系统的系统ID工具相当不发达，经常遇到收敛或计算问题。这里要进行的研究利用了数学和数据分析领域的最新进展，得出了一种基于信息论的全新的系统识别方法。这项研究的核心是因果关系熵的概念，这是一种动态系统内信息传递的熵度量，可以直接从测量的输出数据中计算出来。该项目旨在为非线性参数估计和模型降阶推导出严格的、基于因果熵的方法，并建立使用因果熵的线性高斯系统的基本实现理论。此外，还将从信息论的角度讨论确定投入产出动态的问题。将产生一系列案例研究，突出系统识别方法在各种真实世界实例中的性能和实用性。

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.