# Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks

arXiv: https://arxiv.org/abs/2205.02637 · HTML: https://mlsanity.com/paper/2205.02637/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (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)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [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)
- [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)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [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)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [Graph Element Networks: adaptive, structured computation and memory](https://mlsanity.com/paper/1904.09019/) (2019)
- [Comparing recurrent and convolutional neural networks for predicting wave propagation](https://mlsanity.com/paper/2002.08981/) (2020)
- [Simulating Surface Wave Dynamics with Convolutional Networks](https://mlsanity.com/paper/2012.00718/) (2020)

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

- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Multiscale Neural Operators for Solving Time-Independent PDEs](https://mlsanity.com/paper/2311.05964/) (2023)
- [Multi-GPU Approach for Training of Graph ML Models on large CFD Meshes](https://mlsanity.com/paper/2307.13592/) (2023)
- [A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel components](https://mlsanity.com/paper/2503.17386/) (2025)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming](https://mlsanity.com/paper/2507.11547/) (2025)
- [Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavities](https://mlsanity.com/paper/2509.06041/) (2025)
- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)

## Abstract (arXiv)

Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics in problems encompassing a range of length scales and complex boundary geometries. We demonstrate this method on advection problems and incompressible fluid dynamics, both fundamental phenomena in oceanic and atmospheric processes. Our results show good extrapolation to new domain geometries and parameters for long-term temporal simulations. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than those on which it was trained.