Numerical simulation is an essential tool in many areas of science and
engineering, but its performance often limits application in practice or when
used to explore large parameter spaces. On the other hand, surrogate deep
learning models, while accelerating simulations, often exhibit poor accuracy
and ability to generalise. In order to improve these two factors, we introduce
REMuS-GNN, a rotation-equivariant multi-scale model for simulating continuum
dynamical systems encompassing a range of length scales. REMuS-GNN is designed
to predict an output vector field from an input vector field on a physical
domain discretised into an unstructured set of nodes. Equivariance to rotations
of the domain is a desirable inductive bias that allows the network to learn
the underlying physics more efficiently, leading to improved accuracy and
generalisation compared with similar architectures that lack such symmetry. We
demonstrate and evaluate this method on the incompressible flow around
elliptical cylinders.

介绍一种名为 REMuS-GNN 的旋转等变的多尺度模型，它可以用于预测一个输入物理域的输出向量场，改进了在数值模拟中存在的性能限制及深度学习模型在准确性及推广能力方面的不足，实验证明在椭圆柱体不可压缩流动领域具有良好的效果。