# Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks

arXiv: https://arxiv.org/abs/2409.07769 · HTML: https://mlsanity.com/paper/2409.07769/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 79 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning](https://mlsanity.com/paper/2302.06186/) (2023)
- [Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems](https://mlsanity.com/paper/2109.09510/) (2021)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information using Graph Neural Networks](https://mlsanity.com/paper/2205.04739/) (2022)
- [PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction](https://mlsanity.com/paper/2404.08412/) (2024)
- [NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver](https://mlsanity.com/paper/2104.05829/) (2021)
- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)
- [Importance of equivariant and invariant symmetries for fluid flow modeling](https://mlsanity.com/paper/2307.05486/) (2023)

## Built on by (most cited first, 11 of 11)

- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2506.11398/) (2025)
- [Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence](https://mlsanity.com/paper/2507.00719/) (2025)
- [SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework](https://mlsanity.com/paper/2601.21664/) (2026)
- [Super-resolution of turbulent reacting flows on complex meshes using graph neural networks](https://mlsanity.com/paper/2603.01080/) (2026)
- [Mesh-based Super-resolution of Multiscale Detonation Flows with Graph Transformers](https://mlsanity.com/paper/2511.12041/) (2025)
- [Modeling subgrid scale production rates on complex meshes using graph neural networks](https://mlsanity.com/paper/2603.19841/) (2026)
- [Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations](https://mlsanity.com/paper/2603.23072/) (2026)
- [An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction](https://mlsanity.com/paper/2605.00937/) (2026)
- [Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations](https://mlsanity.com/paper/2605.09284/) (2026)

## Abstract (arXiv)

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor-Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.