Posts

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 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....

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....

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....

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....

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....

Over the past couple of years or so I’ve been getting into the Julia programming language; it’s been great to watch the language mature over time. Many people proclaim the virtues of its speed (it’s very fast for a dynamic language) but really I like its elegance - it’s a very well designed language that makes full use of multiple dispatch. (Multiple dispatch is something that I doubt most coders know much about but once you are used to it, it’s indispensable!...