Supervisor: Dr Oscar Bandtlow
Project description:
Oscar Bandtlow is interested in functional analysis and its applications to dynamical systems and statistical mechanics. A particular concern is to develop methods from operator theory to study the probabilistic behaviour of chaotic dynamical systems. Various projects are possible in this area, including the following one.
Dynamic Mode Decomposition for Chaotic Dynamical Systems
Over the last two decades, Dynamic Mode Decomposition (DMD) has emerged as a transformative tool, enabling researchers to analyse and predict complex systems from diverse fields such as fluid dynamics, neuroscience, epidemiology, power grid stability, and robotics. DMD uses spectral methods to reveal dynamically relevant patterns in observational data, offering powerful forecasting and control capabilities—without requiring explicit knowledge of the system's underlying physics.
This PhD project is concerned with the theoretical foundations of DMD. While DMD and its many variants have had considerable empirical success, the theoretical underpinnings have only recently been studied in greater detail. The main focus of this project, which sits at the interface of operator theory and dynamical systems is to study this method for low-dimensional chaotic dynamical systems from a rigorous perspective with a particular focus on convergence results and error estimates.
Further information:
How to apply
Entry requirements
Fees and funding