Discrete Exterior Calculus-based Whittle-Mat\'ern Fields on Meshes

This work presents a sparse precision formulation for Whittle-Mat\'ern fields based on Discrete Exterior Calculus. By treating the $k$-cochain as the latent object to be modeled, we show that a single formulation can produce Whittle-Mat\'ern fields for all $k$ and integer $\alpha$ values. By utilising Whitney maps we can enable a push-forward of the prior on 1-cochains, enabling inference for discrete vector fields. We demonstrate this model on interpolation of vector fields on a sphere.