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)
et al., 2023, Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems
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
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