E(3)-Equivariant Mesh Neural Networks

• URL: http://arxiv.org/abs/2402.04821v2
• Date: Mon, 19 Feb 2024 01:47:42 GMT
• Title: E(3)-Equivariant Mesh Neural Networks
• Authors: Thuan Trang, Nhat Khang Ngo, Daniel Levy, Thieu N. Vo, Siamak Ravanbakhsh, Truong Son Hy
• Abstract summary: Triangular meshes are widely used to represent three-dimensional objects. Many recent works have address the need for geometric deep learning on 3D mesh. We extend the equations of E(n)-Equivariant Graph Neural Networks (EGNNs) to incorporate mesh face information. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks.
• Score: 16.158762988735322
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric deep learning on 3D mesh. However, we observe that the complexities in many of these architectures does not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information, and further improve it to account for long-range interactions through hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive pre-processing. Our implementation is available at https://github.com/HySonLab/EquiMesh

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