My research applies mathematical and statistical modeling to explore key questions in metabolic dynamics, focusing on the interface of deterministic and stochastic behavior. Specifically, I investigate the dynamics of whole-body metabolism, including glucose-insulin dynamics and C-peptide dynamics, and use these models to solve clinically relevant inverse problems. By leveraging a Bayesian framework, we can obtain uncertainty information along with model-derived estimates.
A central aspect of my research program is the quantitative assessment of metabolic health, including the development of a Bayesian model for the precise functional estimation of an individual's insulin secretion rate (ISR), with uncertainty, from noisy, discretely sampled C-peptide data. A current project applies this model to oral glucose tolerance test (OGTT) data from youth study participants with cystic fibrosis in order to quantify post-prandial beta-cell function. Previous and ongoing projects include the assessment of beta-cell function and insulin senstivity for people with and without type 2 diabetes who undergo bariatric surgery, people with cystic fibrosis who receive treatment with a combination of elexacaftor, tezacaftor, and ivacaftor, and people with metabolic dysfunction-associated steatotic liver disease.
More generally, I am interested in creating and implementing data-analytic tools supported by theory from dynamical systems, functional analysis, and probability. For instance, the field of operator learning has grown rapidly in recent years. I'm interested in developing methods that can learn operators relevant to dynamical systems directly from data. This involves formulating and solving inverse problems that allow functional input and output, utilizing tools such as matrix- or operator-valued reproducing kernels within prescribed reproducing kernel Hilbert or Banach spaces, learning optimal kernels (or equivalently, hypothesis spaces) from data, and employing neural operator or other deep learning techniques.