REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamics

TL;DR

REMuS-GNN is a rotation-equivariant multi-scale deep learning model that efficiently simulates continuum dynamical systems, improving accuracy and generalisation over traditional surrogate models.

Contribution

The paper introduces REMuS-GNN, a novel rotation-equivariant GNN architecture for simulating continuum dynamics across multiple scales, enhancing physical learning and generalisation.

Findings

Outperforms non-equivariant models in accuracy

Demonstrates improved generalisation to unseen rotations

Effectively simulates flow around elliptical cylinders

Abstract

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.