Geometry is a discipline in pure maths. Geometry and AI have two connections: "-->": geometry is used to invent machine learning algorithms, such as graph neural networks. "<--": machine learning is used to answer questions in geometry, for example by using physics-informed neural networks as a PDE solver.
The structure of the tutorial is: (1) an introduction to Riemannian geometry, (2) positive definite kernels on metric spaces as example of the type "-->", (3) a physics-informed neural network on the circle as an example of the type "<--".
This repository contains the materials for this tutorial. The tutorial is taught on 5 May 2025 at the African Institute of Mathematical Sciences in Cape Town, South Africa.
You can find the notebooks also on Google Colab:
https://colab.research.google.com/drive/1m1gSAV1x3ciwOfzLG7kyd_J2nDbyNX7v?usp=sharing
https://colab.research.google.com/drive/1NarP7Dj7lpcBTWnAfzp_M7Peqt7oEi6i?usp=sharing
https://colab.research.google.com/drive/16WroLn0oeni2wPgz3pf-RHvf2Lg-eBir?usp=sharing