REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamics
This work addresses the need for more accurate and generalizable surrogate models in numerical simulations for science and engineering, though it is incremental as it builds on existing graph neural network architectures with added equivariance.
The authors tackled the problem of poor accuracy and generalization in surrogate deep learning models for continuum dynamics simulations by introducing REMuS-GNN, a rotation-equivariant multi-scale model, which improved accuracy and generalization compared to similar architectures lacking such symmetry, as demonstrated on incompressible flow around elliptical cylinders.
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.