Research

I develop computational methods for structured inverse problems, with a particular interest in recovering hidden physical and geometric quantities from sparse, noisy, and indirect observations. My research asks how physical constraints, problem-specific structure, and prior information can be incorporated into inverse formulations to improve identifiability, regularization, and uncertainty quantification.

A central theme of my work is the inference of hidden geometry from surface observations. These problems are often strongly underdetermined: the available measurements constrain the unknown only indirectly, while physically meaningful structure can provide essential information for distinguishing plausible solutions. I am particularly interested in how this structure should enter the mathematical formulation itself, rather than being imposed only through generic smoothness assumptions.

Landslide thickness and basal-geometry estimation currently provide my main Earth-system testbed. In this setting, surface deformation and topographic observations are used to infer an inaccessible subsurface geometry. I develop and validate regularization strategies that incorporate kinematic, geological, and spatial structure into the inverse problem, with the goal of obtaining physically interpretable and robust reconstructions from limited real-world data.

More broadly, my work investigates the interaction between model structure, data information content, and uncertainty within both deterministic and Bayesian formulations. I am extending this perspective toward uncertainty quantification for inverse problems governed by complex physical systems, including uncertainty in observations, models, parameters, and inferred quantities.

While my current applications focus on landslides and slope instabilities, the underlying mathematical questions extend to a broader class of data-limited inverse problems in Earth science and engineering, particularly those involving hidden spatial or geometric structures inferred from indirect measurements.