“Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals.” —Stanislaw Ulam

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.