Eikonal solvers, Frechet means, and clustering!

Provided the means to use a machine learning based Eikonal solver to obtain distance functions on arbitrary Riemannian manifolds. This opens numerous opportunities for computing statistics on manifolds. Most notably, with access to a distance function, one can now conduct manifold-based optimisation. Ultimately, this allows us to compute the Frechet mean on the manifold, and conduct unsupervised clustering.

Note

For more information on this, please see the recent preprint:
Computing distances and means on manifolds with a metric-constrained Eikonal approach

Riemax is Born!

Riemax is a JAX library for Riemannian geometry, providing the ability to define induced metrics and operate on manifolds directly. This first release provides functionality for:

1. Computing quantities of interest on the manifold.
2. Defining geodesic dynamics on the manifold
3. Various methods for computing the exponential / log maps, including symplectic approaches.
4. Metropolis-Hastings sampling

and much, much more...

I have also produced documentation, available at https://riemax.danielkelshaw.com. This is currently far from exhaustive, but should give a flavour of what the library can do -- along with some simple examples.

This library is the product of my research, and so is subject to change. Please keep an eye out to see what new features are added!