Dr. Rule's group studies computational neuroscience in the broad sense. Active research topics include:

1. Representational drift and learning dynamics in hippocampus
2. Mathematical models of spatiotemporal dynamics in the brain
3. Biological cybernetics applied to adaptive, closed-loop sensorimotor control

The group applies mathematics and engineering principles to neurophysiology and neural computation, with two broad approaches:

• Experimental–theory collaborations to adapt emerging AI and ML tools to answer specific questions using large datasets, or model experimentally observed phenomena.
• Mathematical and computational studies to advance our understand of machine and biological learning, and the mathematics underlying machine learning and simulation methods applied to neuroscience. 

The group has capacity to supervise up to 2 further Ph.D. students. Dedicated Ph.D. studentships are not currently available, but expressions of interest are welcome from externally funded doctoral students, and students currently accepted to the University of Bristol's Practice-Oriented Artificial Intelligence CDT and other funded doctoral training routes. Example topics might relate to, for example

• Mathematical and theoretical modelling of representational drift in ongoing learning — for a technically minded student interested in the AI/ML counterpart to ongoing neurophysiology collaborations;
• Control engineering principles applied to the pathophysiology of dystonias — for a creative and mathematically inclined student interested in the woolly particulars of our current understanding of neurophysiology.

The above are suggestive; new or collaborative topics are welcome. For a broader idea of topics that might be a good fit for the group, please see Dr. Rule 's Google scholar profile.

Proposals for new and opportune computational–experimental collaborations are always welcome.