## Summary

My current research interests are the analysis of control and random dynamical systems in Reproducing Kernel Hilbert Spaces in view of developing data-based methods for the analysis and prediction of random dynamical systems and control strategies for nonlinear systems on the basis of observed data (rather than a pre-described model). I am particularly interested in developing a qualitative theory for dynamical systems in reproducing kernel Hilbert spaces with applications to systems with critical transitions.

In general, my research interests lie at the intersection(s) of:

* Control Theory

* Deterministic Dynamical Systems

* Learning Theory/Machine Learning

* Random Dynamical Systems

with a particular emphasis on the following problems:

- Kernel Methods for Dynamical Systems (and, in general, the intersection of the fields of Machine Learning and Dynamical Systems, click here and here for more details about this research direction).
- Control Theory from a Dynamical Systems Theory point of view (Dynamical Theory of Control)

## Publications

### Journals

Yang L, Sun X, Hamzi B, et al. , 2023, Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems

Lee J, De Brouwer E, Hamzi B, et al. , 2023, Learning dynamical systems from data: A simple cross-validation perspective, Part III: Irregularly-sampled time series, *Physica D-nonlinear Phenomena*, Vol:443, ISSN:0167-2789

Dingle K, Kamal R, Hamzi B, 2023, A note on a priori forecasting and simplicity bias in time series, *Physica A: Statistical Mechanics and Its Applications*, Vol:609, ISSN:0378-4371, Pages:128339-128339

Haasdonk B, Hamzi B, Santin G, et al. , 2021, Kernel methods for center manifold approximation and a weak data-based version of the Center Manifold Theorem, *Physica D-nonlinear Phenomena*, Vol:427, ISSN:0167-2789

Hamzi B, Owhadi H, 2021, Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows, *Physica D-nonlinear Phenomena*, Vol:421, ISSN:0167-2789