Research Interests

My research is motivated by the need for theoretical foundations for numerical algorithms performing probabilistic inference and prediction. In the areas of stochastic filtering and Bayesian inverse problems, which deal with the search for solutions to state estimation and parameter estimation problems, the ensemble Kalman methodology has been successful in application to highly non-linear and high-dimensional settings. Yet, firm theoretical foundations are only starting to emerge and can inform on how to address the algorithmic design challenges arising from problems in the computational sciences and engineering. 

I am also interested in the blending of machine learning (ML) and data assimilation (DA) and how ML can aid in the design of algorithms to perform accurate transport of probability distributions and provide new avenues for model error correction.

Similar questions arise in scientific computing, where theoretical guarantees are required for deployment of algorithms to physical systems and engineering problems. With this goal in view, I also work on the application of Gaussian process methods to the numerical solution of rough partial differential equations (PDE), arising for example in the study of stochastic PDEs.