Neural Geodesic Flows #23
Description
Your name, department, and University
Lewis O'Donnell, Computer Science, UCL
Name(s) and department(s) of anyone else relevant to this project
Dr Ben Moseley (Imperial), Julian Burge (ETH Zurich)
Please write a brief description of the application area of project
Riemannian geometry, dynamical systems, geometric deep learning, manifold learning, geodesic solver, generative modelling, written in JAX
Please describe the project.
Neural geodesic flows (NGFs), is a framework for discovering and modelling dynamical systems which assumes the system evolves along the geodesics of a latent Riemannian manifold. Both the metric of the manifold and coordinate transforms between observational data and the manifold are simultaneously learned from observational data. Whilst most approaches for dynamical system modelling make rigid physical assumptions, NGFs only assume geometrical properties of the system’s evolution and have the capacity to model a wide range of systems. NGFs are trained in an end-to-end fashion, backpropagating through the coordinate transforms, a numerical geodesic solver on the manifold, and the metric of the manifold, and several techniques such as residual learning and extreme value soft-clipping are required to ensure stable gradient flow. We have shown that NGFs can accurately model particle flow on a sphere and the two-body problem, and can be applied to generative modelling on arbitrary manifolds; with further work, NGFs could provide a powerful geometry-based framework for dynamical systems modelling.
There are many routes to go down with a NGF project: Immedietely some interesting routes could be to add multichart functionallity to the framework as currently it has only been implemented on single charts, develope more efficient versions of the current algorithms in the model (the model is written in JAX and efficiency has been a secondary thought to developing the current version of the model so there is room to improve upon this), develope the use of NGFs in a generative modelling regime using latent flow matching.
We are open to discuss any ideas that people may have or just to meet to discuss NGFs and possible projects that align with your interests.
What will be the outputs of this project?
Potential contribution to publication
Contributions to open source project
Which programming language(s) will this project use?
Python
Links to any relevant existing software repositories, etc.
See repository below for more information
https://github.com/julianbuerge/neural_geodesic_flows
Links to any relevant papers, blog posts, etc.
https://scalable-sciml-lab.org/projects/machine-learning-with-geodesic-flows/
https://www.research-collection.ethz.ch/entities/publication/3f85c3d3-501b-4563-b204-044b54074949
Make project public
- I understand that this project proposal will be public