mlsanityData to 14 Oct 2026

Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks

arXiv 2305.15603 ↗First posted 24 May 2023cs.LG physics.flu-dyncited by 12

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Abstract (arXiv)

We contribute to the vastly growing field of machine learning for engineering systems by demonstrating that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models than their non-equivariant counterparts. We benchmark two well-studied fluid-flow systems, namely 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow, and evaluate the models based on different performance measures, such as kinetic energy or Sinkhorn distance. In addition, we investigate different embedding methods of physical-information histories for equivariant models. We find that while currently being rather slow to train and evaluate, equivariant models with our proposed history embeddings learn more accurate physical interactions.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

23 of 40 references.

References · 23

  1. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
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  4. 2016Group Equivariant Convolutional Networkscited by 1,165
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  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
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  10. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
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  12. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
11 more
  1. 2022Message Passing Neural PDE Solverscited by 386
  2. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  3. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  4. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  5. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  6. 2022e3nn: Euclidean Neural Networkscited by 174
  7. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
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  10. 2023Geometric Clifford Algebra Networkscited by 38
  11. 2021Boundary Graph Neural Networks for 3D Simulationscited by 24

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 3; 2026: 4.

12 papers.

  1. 2023LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suitecited by 27
  2. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 27
  3. 2024Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamicscited by 11
  4. 2025Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogatescited by 6
  5. 2024JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Frameworkcited by 4
  6. 2024Mean flow data assimilation using physics-constrained Graph Neural Networkscited by 3
  7. 2025Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Frameworkcited by 2
  8. 2025Reversible GNS for Dissipative Fluids with Consistent Bidirectional Dynamicscited by 1
  9. 2026Learning Mesh-Free Discrete Differential Operators with Self-Supervised Graph Neural Networkscited by 1
  10. 2026FlowSymm: Physics Aware, Symmetry Preserving Graph Attention for Network Flow Completioncited by 0
  11. 2026Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulationcited by 0
  12. 2026Phase-aware video generation for physics-grounded dynamics and interactionscited by 0