My research is motivated by the rapid expansion of model complexity and data availability in the applied sciences. Traditional parametric modeling is subject to model error and I believe that modern complex systems call for model-free and semi-parametric approaches. In order to avoid the curse-of-dimensionality, these approaches must effectively incorporate available prior knowledge and existing models. My goal is to develop these techniques with careful consideration of the goals and constraints of real world case studies.
Geometry of data: diffusion maps/local kernels, nonlinear dimensionality reduction and decomposition
Statistics: kernel density/operator estimation, semi-parametric modeling of dynamical systems
Dynamical systems: data assimilation, prediction/control, and uncertainty quantification
Harmonic analysis: Sampling theory on manifolds, connections to kernel based statistical estimates
