SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres

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.

@article{ballerin2025_2503.09456,
  title={ SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres },
  author={ Francesco Ballerin and Nello Blaser and Erlend Grong },
  journal={arXiv preprint arXiv:2503.09456},
  year={ 2025 }
}