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

• URL: http://arxiv.org/abs/2503.09456v1
• Date: Wed, 12 Mar 2025 15:00:32 GMT
• Title: SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres
• Authors: Francesco Ballerin, Nello Blaser, Erlend Grong,
• Abstract summary: Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector fields.<n>We introduce a deep learning architecture that respects both symmetry types using novel techniques based on group convolutions in the 3-dimensional rotation group.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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