SO(3)-equivariant neural networks for meteorological predictions

Abstract: Geometric deep learning is a field that extends traditional deep learning methods to data with an underlying geometric structure, such as graphs and manifolds. It equips neural networks with mechanisms to handle non-Euclidean data and force either invariance or equivariance depending on the type of problem. This means that the result of a prediction does not depend on the symmetries of the underlining geometrical space: rotating a picture of a cat does not produce a picture of a dog and changing atlas for a manifold does not change the manifold. This tackles some of the problems of the black-box nature of neural networks forcing some useful mathematical constraints. We explore the ideas behind geometric deep learning, and we see an application to meteorological data prediction.