# MultiScale MeshGraphNets

arXiv: https://arxiv.org/abs/2210.00612 · HTML: https://mlsanity.com/paper/2210.00612/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [Learning Algebraic Multigrid Using Graph Neural Networks](https://mlsanity.com/paper/2003.05744/) (2020)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [Graph Networks with Spectral Message Passing](https://mlsanity.com/paper/2101.00079/) (2020)
- [Learning ground states of quantum Hamiltonians with graph networks](https://mlsanity.com/paper/2110.06390/) (2021)

## Built on by (most cited first, 30 of 98)

- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamics](https://mlsanity.com/paper/2212.07242/) (2022)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite](https://mlsanity.com/paper/2309.16342/) (2023)
- [Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks](https://mlsanity.com/paper/2504.02843/) (2025)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer](https://mlsanity.com/paper/2512.20399/) (2025)
- [Graph-based Neural Weather Prediction for Limited Area Modeling](https://mlsanity.com/paper/2309.17370/) (2023)
- [Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning](https://mlsanity.com/paper/2302.06186/) (2023)
- [Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer](https://mlsanity.com/paper/2312.12467/) (2023)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [A Manifold Perspective on the Statistical Generalization of Graph Neural Networks](https://mlsanity.com/paper/2406.05225/) (2024)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability](https://mlsanity.com/paper/2305.12871/) (2023)
- [AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamics](https://mlsanity.com/paper/2407.20801/) (2024)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methods](https://mlsanity.com/paper/2301.11378/) (2023)
- [GNN-based physics solver for time-independent PDEs](https://mlsanity.com/paper/2303.15681/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks](https://mlsanity.com/paper/2409.07769/) (2024)
- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)
- [Automotive Crash Dynamics Modeling Accelerated with Machine Learning](https://mlsanity.com/paper/2510.15201/) (2025)
- [Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics](https://mlsanity.com/paper/2409.11899/) (2024)
- [MeshMask: Physics-Based Simulations with Masked Graph Neural Networks](https://mlsanity.com/paper/2501.08738/) (2025)
- [End-to-End Probabilistic Framework for Learning with Hard Constraints](https://mlsanity.com/paper/2506.07003/) (2025)
- [Physics-guided Shape-from-Template: Monocular Video Perception through Neural Surrogate Models](https://mlsanity.com/paper/2311.12796/) (2023)
- [A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations](https://mlsanity.com/paper/2402.13101/) (2024)

## Abstract (arXiv)

In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.