Elizabeth Qian
Caltech
Seminar Information
We consider the Bayesian inverse problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Balanced truncation is a system-theoretic method for model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which simultaneously maximize energies defined by reachability and observability Gramians. We show that in our inference setting, the prior covariance and Fisher information matrices can be naturally interpreted as reachability and observability Gramians, respectively. We use these connections to propose a balancing approach to model reduction for the inference setting. The resulting reduced model then inherits stability properties and error bounds from system theory, and yields an optimal posterior covariance approximation.
Dr. Elizabeth Qian is a von Kármán Postdoctoral Instructor in the Department of Computing + Mathematical Sciences at Caltech. Her research lies at the intersection of computational science and engineering application, developing scalable, reliable, and robust computational tools to support engineering decision-making and design. In particular, her work focuses on computationally efficient reduced modeling for engineering systems via scientific machine learning and model reduction, and multi-fidelity algorithms for optimization and uncertainty quantification that rigorously combine high- and low-fidelity models for computational acceleration while guaranteeing accuracy. Elizabeth holds SB, SM, and PhD degrees from MIT and has been a recipient of the NSF Graduate Fellowship, the Fannie and John Hertz Foundation Fellowship, and a Fulbright student grant.