“Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals.” —Stanislaw Ulam
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Theory:
I am broadly interested in the theory of learning & control for linear and nonlinear dynamics, i.e., the mathematical analysis of data-driven and learning-based methods for modeling, optimization, model-reduction, and control of dynamical systems. Mainly, I am working on
learning linear and nonlinear dynamical systems,
theory of reproducing kernel Hilbert spaces and Gaussian processes,
Koopman operator theory, especially for complex systems,
data-driven and model-free controller tuning,
learning-based and data-driven predictive control,
distributed/cooperative control for large-scale systems,
infinite-dimensional and thermodynamic systems,
side-information in learning theory, e.g., system identification with prior knowledge, physics-informed neural networks, ...
mathematical biology and neuroscience.
Application:
Designing suitable learning & control techniques for practical implementation in real-world applications demands specific context considerations. More precisely, we need to take into account the physics and structure of underlying reality. I am particularly interested in conducting this line of research in the following energy and industrial domains:
district heating networks,
buildings & energy hubs,
seasonal storage facilities,
electric vehicles,
greenhouses,
aquifers,
robotics,
power systems,
biomedical and biological systems,
and similar ones.
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