Supervision: Adám Gosztolai

Project type: Semester project (master) Master thesis


Background Geometric deep learning has made substantial impact in the machine learning community by generalising convolution operations, previously defined on images, to non-flat domains such as manifolds and graphs. Natural but yet little explored systems where geometric deep learning is likely to have a transformational role are dynamical systems, which appear in many areas of life and physical sciences. Likewise, dynamical systems have had a great impact on the machine learning community by interpreting the evolution of the parameter space during diverse computational tasks (c.f., ref)

The project A particular appeal of studying dynamical systems using machine learning is that one does not need to know the equations of motion. This is known as equation-free or model-free modelling. In particular, dynamical systems can be fully specified as an ensemble of trajectories in state-space, which evolve over a smooth manifold. The project will be about developing a geometric deep learning methods to embed the vector field over a dynamical manifold into a latent space where any change in the underlying dynamical parameters can be interpreted.

Aims This project is available as a semester or master projects and we will adjust the aims accordingly. One particular aim of the project is to detect and classify bifurcations based on the latent representation mentioned above. If this was possible, this could have a significant impact on their experimental detection, which is often difficult due to sparse and incomplete measurements. Time allowing you will also work with neuroscience data to explore how this principle is useful for decoding behavioural states from neural measurements.

Outcome I expect this project to make a substantial impact in both neuroscience, physics and machine learning communities. If you're making good progress, it can likely lead to a conference or journal publication.

My background I am a mathematician (postdoc) with substantial experience in both neuroscience and machine learning (see more on my website). I have worked before in the labs of Pavan Ramdya and Auke Ijspeert and now I work with Pierre Vandergheynst.

Your background I am looking for someone with a quantitative profile (CS, EE, maths, robotics, data science etc). Strength in mathematics is a bonus. Biology knowledge is not necessary, but interest is appreciated.

If this project does not suit you, but you still want to work with me, get in touch and we will figure something out.