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., 2024, Learning dynamical systems from data: A simple cross-validation perspective, Part V: Sparse Kernel Flows for 132 chaotic dynamical systems, Physica D: Nonlinear Phenomena, Vol:460, ISSN:0167-2789
Hamzi B, Owhadi H, Kevrekidis Y, 2023, Learning dynamical systems from data: A simple cross-validation perspective, part IV: Case with partial observations, Physica D: Nonlinear Phenomena, Vol:454, ISSN:0167-2789
Gazor M, Hamzi B, Shoghi A, 2023, The infinite level normal forms for non-resonant double Hopf singularities, Systems & Control Letters, Vol:176, ISSN:0167-6911
Hamzi B, Owhadi H, Paillet L, 2023, A note on microlocal kernel design for some slow-fast stochastic differential equations with critical transitions and application to EEG signals, Physica A-statistical Mechanics and Its Applications, Vol:616, ISSN:0378-4371
Darcy M, Hamzi B, Livieri G, et al., 2023, One-shot learning of stochastic differential equations with data adapted kernels, Physica D: Nonlinear Phenomena, Vol:444, ISSN:0167-2789