I am interested in computational methods and numerical analysis for control, uncertainty quantification and optimization of complex and large-scale dynamical systems. Specifically, my research revolves around certified reduced-order surrogate modeling. As such, my research is interdisciplinary, both with respect to computational-science domains and applications. I have worked on multifidelity and data-driven modeling, optimization and control, uncertainty quantification, reliability-based design, and design under uncertainty. Ongoing and past research has been on large-scale computational models in engineering and science with a strong focus on (reactive/thermal) flows.
Data-driven ROMs and system identification
Reduced-order modeling is a mathematically sound framework to build computationally efficient surrogate models for large-scale systems. As a special case, data-driven reduced-order modeling becomes increasingly relevant due to 1) the vast availability of data, 2) hard-to-access legacy computer codes that make intrusive methods challenging, and 3) the monumental challenge of modeling complex, coupled, multiphysics, multiscale systems. My research in data-driven ROMs focuses on using data together with physics-based models. I have worked on both data-driven (e.g., Eigensystem Realization Algorithm, Dynamic Mode Decomposition, Operator Inference), as well as physics-based model reduction (Galerkin proper orthogonal decomposition; balanced truncation; large-scale matrix equations related to control/filtering).
ROMs for robust and adaptive control
Dynamical systems often depend on parameters that may change over time, which alters the solution behavior. Models used for control of such systems need to account for such uncertain and time-varying parameters. Additionally, models for time-critical control applications need to be computationally efficient, making ROMs an appealing model choice. My research interests are to use ROMs to make feedback controllers feasible (or faster) and robust to uncertainties in parameters.
Multifidelity uncertainty quantification (UQ)
Computing statistical information (mean, variance, failure probabilities, risk measures) from quantities of interest often requires a large number of model evaluations. Multifidelity UQ leverages information from surrogate models of varying fidelity and computational cost to efficiently solve the UQ task at hand. Such methods are attractive as they move most of the computational work to lower fidelity models and decrease the number of expensive high-fidelity model evaluations. My research includes ROMs in UQ/robust optimization/reliability-based design to reduce the computational cost while providing statistical guarantees for the overall method.