Upcoming Event: PhD Dissertation Defense

Data-Consistent Assimilation: Theory, Algorithms, and Implementation for Predictability-Aware Variational Methods and Ensemble Spectral Filters

Rylan Spence, CSEM Ph.D Candidate

Abstract

Inverse problems and data assimilation seek to combine mathematical models with incomplete, noisy observations to estimate unknown parameters, recover evolving states, and quantify uncertainty. Standard approaches such as Bayesian inference and ensemble Kalman methods are powerful, but they are built around update rules that do not always align with the goal of reproducing observed output behavior while maintaining reliable uncertainty estimates. This dissertation develops a data-consistent approach to assimilation in which predictability and output-space structure guide both inference and computation.  The dissertation introduces a unified framework for data-consistent assimilation built on measure-theoretic ideas from Data-Consistent Inversion and the Maximal Updated Density estimator. At its foundation are pushforwards, disintegration, and density-based consistency, which provide a precise way to connect uncertainty in parameter or state space with uncertainty in observable quantities. Building on that foundation, the dissertation develops two complementary algorithmic directions. The first yields predictability-aware variational methods, including data-consistent 4D-Var and weighted-mean-error formulations, together with well-posedness results. The second yields deterministic ensemble spectral filters that reinterpret data-consistent updates in low-dimensional residual subspaces, clarifying both their relationship to and distinction from ensemble Kalman filtering. Together, these contributions present data-consistent assimilation as a coherent framework linking theory, algorithms, and implementation for practical inference in dynamical systems.

Biography

Rylan Spence is a PhD candidate in the Computational Science, Engineering, and Mathematics program at the University of Texas at Austin, advised by Dr. Clint Dawson. He received his MS in Computational Science, Engineering, and Mathematics from UT Austin and holds both an MA and BA in Mathematics from Dartmouth College. His research lies at the intersection of computational science, inverse problems, and data assimilation, with a focus on uncertainty quantification for dynamical systems.