My research program is focused on computational methods and numerical analysis for control, uncertainty quantification and optimization of complex dynamical systems. I worked on methods such as subspace based system identification, compressed sensing, and in particular model reduction, to utilize the structure and available data to achieve those tasks. More generally, I am interested in applying mathematical ideas to solve challenging problems arising in engineering, the life and geosciences.
Constructing surrogate models of large-scale systems has been a key enabler for optimization thereof. It has been observed frequently, that by using physics based models, and by exploiting structure and system theoretic properties, great benefits arise - both computationally, as well as in storage. Those achievements were complemented by black-box model optimization and model reduction methods, that are used when one is not in the luxurious setting of having access to governing equations. Both methods are equally important, and the specific problem environment often dictates their utility. I have worked on both data-driven (e.g., system identification, dynamic mode decomposition based sensing), as well as physics based model reduction (POD in Galerkin framework, solution of large-scale matrix equations related to control/filtering).
In my new position, I am working on uncertainty quantification for complex systems, with a focus on decision making. I also continue to work on leveraging the power of data-and physics based models for optimization and filtering.