Data Assimilation: Dynamical Interpolation, State Estimation, and Model Identification

Data assimilation is a technique that combines models with data to improve state estimation, prediction, and uncertainty quantification. It is distinguished from other forms of machine learning methods in that it utilizes a dynamical model of the system being analyzed. In this talk, I will start by introducing the general mathematical framework of data assimilation and its computational challenges. Then, I will present several aspects of scientific problems where data assimilation can play an important role. First, I will show that data assimilation can be utilized to dynamically interpolate missing observations of turbulent flows using statistically reduced-order models with a specific application to the Arctic Sea ice. Second, I will show that data assimilation facilitates data-driven model identification via a causality-based learning approach. I will also briefly discuss how machine learning can advance data assimilation.