In the analysis of physical and biological systems we collect noisy, sparse data that often only provide
a limited description of the underlying physical process. The goal of my research is to address how to
best use these data to identify key dynamics and forecast the evolution of the system. Mathematical
models can be used for this purpose, but the parametric equations within the model are often subject
to error caused by a lack of knowledge or oversimplification of the true governing dynamics. At the
other end of the spectrum exist model-free methods that attempt to learn the dynamics from the data.
The usefulness of these nonparametric methods though can be limited by the high-dimensionality of
systems and the requisite data needed to accurately reconstruct the system dynamics. Rather than
treat these approaches separately, I believe that modern methods of data analysis should instead use
these methods together, leveraging the complementary strengths of each to allow for a more robust
analysis of systems. Broadly speaking, my research is centered around the fields of data science and computational
mathematics and integrates techniques from data assimilation, inverse problems (state/parameter
estimation) and dynamical systems.