mlsanityData to 7 Oct 2026

Direct Prediction of Steady-State Flow Fields in Meshed Domain with Graph Networks

arXiv 2105.02575 ↗First posted 6 May 2021physics.flu-dyn cs.AIcited by 11

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Abstract (arXiv)

We propose a model to directly predict the steady-state flow field for a given geometry setup. The setup is an Eulerian representation of the fluid flow as a meshed domain. We introduce a graph network architecture to process the mesh-space simulation as a graph. The benefit of our model is a strong understanding of the global physical system, while being able to explore the local structure. This is essential to perform direct prediction and is thus superior to other existing methods.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 11 of its 17 references that are in the map. First posted on arXiv 6 May 2021.

Builds on

11 of 17 references.

References · 11

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  4. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  7. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  8. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  9. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  10. 2016Accelerating Eulerian Fluid Simulation With Convolutional Networkscited by 128
  11. 2018SPNets: Differentiable Fluid Dynamics for Deep Neural Networkscited by 62

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 1; 2025: 2; 2026: 1.

11 papers.

  1. 2022Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNNcited by 43
  2. 2021Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNscited by 38
  3. 2023MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variabilitycited by 15
  4. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  5. 2021Deep Surrogate for Direct Time Fluid Dynamicscited by 5
  6. 2024Large-scale flood modeling and forecasting with FloodCastcited by 5
  7. 2023C(NN)FD -- a deep learning framework for turbomachinery CFD analysiscited by 3
  8. 2023Deep learning modelling of manufacturing and build variations on multi-stage axial compressors aerodynamicscited by 1
  9. 2025C(NN)FD -- Deep Learning Modelling of Multi-Stage Axial Compressors Aerodynamicscited by 0
  10. 2025PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulationscited by 0
  11. 2026Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controlscited by 0