This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy.

翻译：本文提出了一种新颖的构建方法，用于构造对二维旋转和平移具有等变性的图神经网络，并将其作为非网格化区域上的偏微分方程代理模型。我们证明，将表征与主轴对齐能够避开诸多约束条件，同时保持SE(2)等变性。通过将我们的模型应用于流体流动模拟的代理建模，并与非等变模型进行全面基准测试，我们证明了该方法在数据效率和精度方面均取得显著提升。