Posts

For anyone who is interested in data-driven approaches to engineering problems (or more general science), I’ve been appointed the co-director of a new PhD programme in Data-Driven Engineering and Sciences in the School of Engineering Mathematics and Technology at the University of Bristol. If you are interested in a fully-funded PhD in one of the research areas covered by the school, see our programme website for the application procedure. The deadline for applications is 26 February 2025. ...

An overview of ‘A Comparison of Mesh-Free Differentiable Programming and Data-Driven Strategies for Optimal Control under PDE Constraints’, Roussel D. Nzoyem Ngueguin, David A.W. Barton, Tom Deakin, SC23, Denver, USA Available on arXiv or via the ACM A BibTeX reference is also available. Editorial note: I’ve often intended to create blog posts of papers that I’ve been involved with but I’ve never managed to make time to do it. However, in the world of ChatGPT we can automatically (and largely accurately) generate them. ...

This is a potential research project for new research students. It is intended to be a starting point for discussion/further investigation rather than a complete research plan. If you are interested in working with me, see opportunities for new researchers. Keywords: aeroelastics, scientific machine learning, control-based continuation, nonlinear dynamics There is a drive towards high-efficiency and high-performance aircraft. This requires lighter and more fuel-efficient structural designs, which are often more flexible than traditional rigid designs. This flexibility can result in disastrous nonlinear behaviour; for example, the destruction of the NASA Helios prototype. This project seeks to develop new approaches to nonlinear behaviour in aircraft and so enable a new generation of low-carbon aircraft. ...

This is a potential research project for new research students. It is intended to be a starting point for discussion/further investigation rather than a complete research plan. If you are interested in working with me, see opportunities for new researchers. Keywords: online learning, machine learning, tactile robotics, generative models Machine learning (ML) equips robots with the ability to learn from and adapt to new environments, enhancing autonomy and efficiency in complex tasks. However, many ML approaches rely on extensive data for training. This heavy reliance on large volumes of data can hamstring a robot’s ability to function in dynamic real-world conditions—imagine a robotic assistant in a home struggling to recognize new types of objects because it was trained on a limited set of household items. Such data dependency limits the robots’ effectiveness in diverse real-world applications. We seek to overcome this problem in the context of tactile robotics by exploiting generative online learning, enabling robots to learn ‘in the moment’ and adapt swiftly to the unpredictability of real-world tasks. ...

This is a potential research project for new research students. It is intended to be a starting point for discussion/further investigation rather than a complete research plan. If you are interested in working with me, see opportunities for new researchers. Keywords: surrogate modelling, machine learning, reservoir computing, power electronics Designing new devices, particularly in electrical power conversion for renewable energy, is often challenging because of constraints on mass, volume, and cost. Designers must innovate within these boundaries, making trade-offs to meet specifications without compromising performance. This PhD project will employ surrogate modelling and machine learning to improve the efficiency of design processes. ...

I’ve got a postdoctoral position open at the University of Bristol, UK: https://www.bristol.ac.uk/jobs/find/details/?jobId=264809. It’s a one year position that must finish at some point before end June 2023 (end of grant, now extended beyond the date given in the advert). In short I’m looking for someone with experience in (nonlinear) differential equations, ideally engineering background and some interest in uncertainty quantification. (And who programs in Julia, obviously 😀) The group is small but supportive and work at the interface between (engineering-focused) physical experiments and mathematical methods. We’re part of a wider applied mathematics/engineering dynamics research group that covers a wide range of interests. ...

My PhD was on the topic of delay differential equations (DDEs) and, at the time, I wrote lots of utilities to do things like calculate the stability of linearised equations. All that code has been lost to the mists of time but I still have call for it every now and again (e.g., for real-time dynamic substructuring where I need to model the delays in the control loop). Here is some code in Julia that calculates the stability of a DDE in the form ...

SciML and physics-based machine learning Scientific machine learning is a rapidly growing area that seeks to combine traditional physics-based models with machine learnt models. In traditional physics-based modelling, you rely on expert knowledge to build the complete model (perhaps with some limited parameter fitting to experimental data); the machine learning approach replaces that expert knowledge with large quantities of data (that’s an over simplification but broadly correct). A key question is how to find the sweet spot in the middle whereby you make use of your expert knowledge but also include model features that emerge from the data. ...

Every now and again I’m asked how to compute the periodic orbits of ODEs using a boundary value solver. Each time, I go looking for old code that does this and, each time, I can’t find it and end up rewriting the collocation code from scratch. This time I thought I’d put my code here so that I have a better chance of finding it again in the future! The basic idea is to use a Fourier differentiation matrix to approximate the derivatives along the orbit and use a nonlinear solver to ensure that those derivatives match the vector field. If you want to know more about these types of spectral methods, take a look at the excellent (and short!) introduction by Trefethen in “Spectral Methods in MATLAB”, SIAM 2000. If you want more detail then the magnum opus by Boyd “Chebyshev and Fourier Spectral Methods”, Dover 2001 (freely available on his personal website) is also very good. ...

Broadcasting in Julia is a way of writing vectorised code (think Matlab) that is performant and explicit. The benefits of performant code are obvious (faster!) but explicit vectorisation is also a significant benefit. When I first saw Matlab and how you could call the sin with a vector input, I was (slightly) blown away by the usefulness of this. It didn’t take too long for me to realise the limitations though; vectorising a complicated function can require quite a bit of code gymnastics, which doesn’t usually help the readability, particularly for those students who are relatively new to programming. ...