mlsanityData to 7 Oct 2026

Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics

arXiv 2408.06101 ↗First posted 12 Aug 2024cs.LG cs.AI cs.NAcited by 3

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Abstract (arXiv)

This works investigates the generalization capabilities of MeshGraphNets (MGN) [Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICML 2021] to unseen geometries for fluid dynamics, e.g. predicting the flow around a new obstacle that was not part of the training data. For this purpose, we create a new benchmark dataset for data-driven computational fluid dynamics (CFD) which extends DeepMind's flow around a cylinder dataset by including different shapes and multiple objects. We then use this new dataset to extend the generalization experiments conducted by DeepMind on MGNs by testing how well an MGN can generalize to different shapes. In our numerical tests, we show that MGNs can sometimes generalize well to various shapes by training on a dataset of one obstacle shape and testing on a dataset of another obstacle shape.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 15 of its 61 references that are in the map. First posted on arXiv 12 Aug 2024.

Builds on

15 of 61 references.

References · 15

  1. 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,348
  2. 2013Visualizing and Understanding Convolutional Networkscited by 2,278
  3. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  4. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  5. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  6. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  7. 2021Machine learning accelerated computational fluid dynamicscited by 461
  8. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  9. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  10. 2018Sensitivity and Generalization in Neural Networks: an Empirical Studycited by 187
  11. 2022MultiScale MeshGraphNetscited by 94
  12. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
3 more
  1. 2023Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networkscited by 6
  2. 2022An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equationscited by 5
  3. 2022Tensor-product space-time goal-oriented error control and adaptivity with partition-of-unity dual-weighted residuals for nonstationary flow problemscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025TripNet: Learning Large-scale High-fidelity 3D Car Aerodynamics with Triplane Networkscited by 14
  2. 2026Learning Transient Convective Heat Transfer with Geometry Aware World Modelscited by 1
  3. 2025Multiscale Graph Neural Network for Turbulent Flow-Thermal Prediction Around a Complex-Shaped Pin-Fincited by 0