Ky Potter

Title: Scalable Statistical Methods for Complex and Heterogeneous Physical Systems
Date: July 8th, 2026
Time: 10am
Location: LIB 7200 & Zoom
Supervised by: David Stenning and Derek Bingham

Abstract:

This thesis presents scalable statistical methods for analyzing complex physical systems for which scientific interpretation depends on quantities, relationships, or distributions that are not available directly from observation or simulation output alone. Motivating applications exemplify common modeling challenges in the physical sciences: that observations are noisy or indirect, uncertainty varies across the input space, simulations may be expensive or stochastic, and quantities of scientific interest are often latent. These challenges are ad dressed through the construction of flexible models that remain computationally practical while capturing and quantifying scientifically meaningful uncertainty. Chapter 2 introduces Heteroskedastic Normalized Vecchia Gaussian Processes, a scalable approach for Gaussian process regression with input-dependent observation noise. The method is motivated by an application involving spacecraft plasma measurements for which locally adaptive uncertainty estimates are crucial for downstream analyses, but it more generally enables heteroskedastic uncertainty estimation with large, unreplicated datasets. Chapter 3 presents an emulator for stochastic exoplanet formation simulations. Unlike traditional emulators that target a deterministic response or conditional mean, the proposed method approximates the full conditional distribution of observed planetary system architectures, enabling fast simulation while preserving input-dependent variability, dependence among simulator outputs, mixed discrete-continuous structure, and rare-event behavior. Chapter 4 presents a physics-informed empirical Bayesian reconstruction framework for spatially varying ion-temperature and neutron-emission profiles from simulated neutron imaging data motivated by inertial confinement fusion diagnostics. The method formulates reconstruction as a weakly identified inverse problem with a mechanistic forward model, a Poisson detector-count likelihood, positive Gaussian-process latent-profile priors, and physics-informed constraints. The detector counts are modeled as conditionally indepen dent given the latent profiles and calibrated nuisance quantities, while the latent profile values themselves are coupled through Gaussian-process priors on the log profiles. A Stage 1 emission estimate is used to construct a learned emission prior for Stage-2 reconstruction, so that emission uncertainty is propagated in a controlled way while the ion-temperature profile remains the primary target of inference. The resulting posterior summaries are conditional on the learned emission prior, calibrated nuisance settings, forward-model fidelity, and physics-informed regularization. Together, these contributions demonstrate how scalable approximation, modular modeling, and Bayesian uncertainty quantification can be combined to analyze heterogeneous physical systems. Across the three applications, the thesis emphasizes that variability, weak identifiability, and uncertainty are not merely nuisances, but important features of the scientific problems themselves.