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.
