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

arXiv: https://arxiv.org/abs/2205.07852 · HTML: https://mlsanity.com/paper/2205.07852/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Graph Element Networks: adaptive, structured computation and memory](https://mlsanity.com/paper/1904.09019/) (2019)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Directional Message Passing on Molecular Graphs via Synthetic Coordinates](https://mlsanity.com/paper/2111.04718/) (2021)

## Built on by (most cited first, 3 of 3)

- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [End-to-end Wind Turbine Wake Modelling with Deep Graph Representation Learning](https://mlsanity.com/paper/2211.13649/) (2022)
- [On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods](https://mlsanity.com/paper/2304.00146/) (2023)

## Abstract (arXiv)

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.