AeroAstro-CSE PhD Thesis Defense | Kelvin Leung

Kelvin Leung, AeroAstro-CSE PhD Thesis Defense Announcement

Thesis Title: Structured Bayesian Inference for Spatio-Temporal Systems with Applications in Remote Sensing

Date: Thursday, August 7, 2025
Time: 10 AM ET
Location: 45-432 / Zoom

Thesis Committee:

• Prof. Youssef Marzouk, Department of Aeronautics and Astronautics, MIT
• Prof. Pierre Lermusiaux, Department of Mechanical Engineering, MIT
• Dr. Amy Braverman, Senior Research Scientist at NASA Jet Propulsion Laboratory

Readers:

• Dr. Jouni Susiluoto, Research Scientist at the NASA Jet Propulsion Laboratory
• Dr. Michael Brennan, Senior Research Scientist at Solea Energy

Abstract:

Satellite-based remote sensing observing systems are a key source of information for understanding Earth system dynamics. Bayesian inference provides a principled framework for retrieving physical parameters from satellite observations while quantifying uncertainty. However, the high dimensionality and spatio-temporal complexity of remote sensing problems pose major computational challenges for traditional inference methods. This thesis develops scalable algorithms for Bayesian inference for remote sensing systems by leveraging low-rank structure and sparse conditional dependence structure. The resulting methods enable accurate and efficient posterior estimation at scales relevant for modern satellite missions.

The first theme of this thesis is identifying low-rank structure in problems where the scientific goal is to estimate a small number of quantities of interest (QoIs) that are a function of the parameters of the inverse problem. Using a gradient-based dimension reduction framework, we construct informative subspaces of the observation space that are tailored to specific QoIs. This framework is integrated with transport maps to enable simulation-based inference directly on the QoIs without the need to recover the full posterior of the high-dimensional parameters. We demonstrate this approach on imaging spectroscopy data from NASA’s upcoming Surface Biology and Geology (SBG) mission and show that it achieves inference accuracy comparable to MCMC while requiring orders of magnitude less computational time. In addition, we examine the role of preconditioning in dimension reduction and demonstrate that the optimal choice depends on the nonlinearity of the forward model.

We also explore how conditional independence structure can be used to improve the scalability of inference algorithms relevant to remote sensing systems. We first consider a single-pixel setting and exploit within-state conditional independence to build sparse transport maps for hyperspectral retrievals. These sparse maps reduce computation over standard non-Gaussian inference methods while preserving accuracy. Extending beyond individual pixels, we develop an information filter that leverages spatio-temporal conditional independencies in satellite observing systems. By incorporating sparse inverse covariance structure into the filtering equations, we achieve significant improvements in both scalability and inference accuracy on data relevant to NASA’s OCO-2, EMIT, and SBG missions.

Building on this structure, this thesis also develops non-Gaussian extensions for spatio-temporal inference using transport maps. Drawing inspiration from belief propagation algorithms for Gaussian graphical models, we construct decomposed transport maps tailored to spatio-temporal graphs. These methods enable scalable inference while capturing non-Gaussian features of the posterior. We demonstrate their application to spatio-temporal systems, providing a viable framework for high-fidelity uncertainty quantification.