An Ensemble of Novel Techniques for Non-Linear, Non-Gaussian Data Assimilation

Abstract

Data assimilation (DA) presents a theoretically rigorous framework for combining measurement data from real-world processes with simulations that attempt to mimic the said process. DA is a challenging task due to (i) computationally expensive, but uncertain model simulations, (ii) spatiotemporal sparsity and uncertain of measurements, (iii) the uncertainties not being Gaussian in general, and (iv) the inferred variables obeying constraints or features. In my work, DA is posed as a discrete-time Bayesian state estimation problem. Many state-of-the-art operational data assimilation methodologies make linear, Gaussian assumptions that fail to accurately describe the uncertainties in many problems of interest. Next, these methods are also agnostic to system constraints and features. Broadly, my research is about developing theoretically rigorous and computationally efficient methods for non-linear, non-Gaussian, multi-modal, high-dimensional data assimilation problems and if necessary, preserving system constraints and features.