SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres
This work addresses the challenge of modeling vector fields on spheres for applications like climate science, though it is incremental as it builds on existing equivariant methods.
The paper tackles the problem of analyzing vector fields on spheres, such as wind patterns, by developing an SO(3)-equivariant neural network architecture that respects rotational symmetries, resulting in lower prediction and reconstruction errors compared to standard and spherical CNNs on rotated data.
Analyzing vector fields on the sphere, such as wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector fields. In this paper, we introduce a deep learning architecture that respects both symmetry types using novel techniques based on group convolutions in the 3-dimensional rotation group. This architecture is suitable for scalar and vector fields on the sphere as they can be described as equivariant signals on the 3-dimensional rotation group. Experiments show that our architecture achieves lower prediction and reconstruction error when tested on rotated data compared to both standard CNNs and spherical CNNs.