Deep equivariant models use symmetries to improve sample efficiency and generalization. However, the assumption of perfect symmetry in many of these models can sometimes be restrictive, especially when the data does not perfectly align with such symmetries. Thus, we introduce relaxed octahedral group convolution for modeling 3D physical systems in this paper. This flexible convolution technique provably allows the model to both maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in the physical systems. Empirical results validate that our approach can not only provide insights into the symmetry-breaking factors in phase transitions but also achieves superior performance in fluid super-resolution tasks.

通过引入松弛八面体群卷积技术，本文提出了一种用于建模三维物理系统的深度等变模型，该技术在数据一致性的基础上既具备了最高级别的等变性，又能够发现物理系统中微小的破坏对称性的因素。实证结果验证了该方法不仅能够揭示相变中的破坏对称性因素，还在流体超分辨率任务中取得了卓越的性能。

3D物理系统中学习对称破缺的放松八面体群卷积