The projects below give a flavour of the kinds of research I supervise. They are intended as starting points for discussion rather than fixed plans — most are deliberately broad so there is plenty of room for you to shape your own direction. If you have a related idea that is not listed here, I am very happy to hear from you.
For funding and application information, see the Work with me page. To apply, email david.barton@bristol.ac.uk with your CV and a short description of your research interests. Applications from all backgrounds are encouraged, especially under-represented groups.
Scientific machine learning and physics-based modelling
Scientific machine learning (SciML) seeks to combine traditional physics-based models with machine learnt models. The key question is how to exploit expert knowledge whilst also allowing model features to emerge from data. Projects in this area could involve novel SciML architectures, uncertainty quantification, or application to new engineering domains.
Control-based continuation for physical experiments
Control-based continuation (CBC) is a means for extracting nonlinear dynamical information from physical experiments, combining dynamical systems theory with control and stochastic dynamics. We have applied CBC to nonlinear oscillators and aeroelastic flutter in wind tunnel experiments. Projects here could involve extending CBC to multi-degree-of-freedom systems, developing machine-learning-enhanced variants, or applying it to new experimental platforms.
Online learning for tactile robotics
Without our sense of touch, humans struggle with many manipulation tasks. The TacTip tactile sensor gives robots this capability at low cost. Projects in this area explore generative online learning, allowing robots to learn sensor models in real time with very little prior data and extending these approaches to higher-dimensional tasks and a broader suite of robot actions.
Surrogate modelling for power electronics
Designing electrical power conversion devices involves navigating trade-offs across timescales from nanosecond switching to bulk behaviour over seconds. This project develops surrogate models using machine learning (e.g., reservoir computing) to accelerate design iteration for systems such as modular multi-level converters used in offshore wind turbines.
Stochastic nonlinear dynamics
More theoretically focused: developing robust, general-purpose tools for stochastic nonlinear systems, particularly those that undergo bifurcations. Currently, effective approaches tend to be highly problem-specific; the aim is to build general methods using the Julia differential equations ecosystem.
Numerical methods for dynamical systems
I am interested in general methods for investigating nonlinear systems, such as numerical continuation. Projects could involve composing different problem types within the Julia ecosystem (e.g., hybrid dynamical systems or manifold continuation).
See also the current research team and previous team members to get a sense of the range of projects already underway.