Earth data are usually not defined on Euclidean spaces. From the obvious spherical geometry of the Earth, to conservation laws, and down to multi-scale invariance, their structure departs from standard Euclidean assumptions.
In this talk, we will explore how ideas centered around geometry, topology, and algebra can become practical tools for deep learning applied to Earth systems.
We will start by looking at Earth system data in non-Euclidean spaces (e.g., spheres, Lie groups, positive semidefinite matrices) and discrete topological domains (e.g. Graphs). Using practical examples, we look at how Riemannian geometry can improve training, loss functions, and model design. We then turn to symmetry and invariance by examining group actions.
We conclude by evaluating the limits of invariant and symmetry-preserving approaches, and by discussing design principles for deciding which structures to respect, which to relax, and when symmetry acts as a limitation rather than an advantage.
Copyright. All Rights Reserved.