mlsanityData to 7 Oct 2026

Importance of equivariant and invariant symmetries for fluid flow modeling

arXiv 2307.05486 ↗First posted 3 May 2023physics.flu-dyn cs.LGcited by 5

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Abstract (arXiv)

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant architectures respecting underlying physical symmetries. However, the effect of rotational equivariance in modeling fluids remains unclear. We build a multi-scale equivariant GNN to forecast fluid flow and study the effect of modeling invariant and non-invariant representations of the flow state. We evaluate the model performance of several equivariant and non-equivariant architectures on predicting the evolution of two fluid flows, flow around a cylinder and buoyancy-driven shear flow, to understand the effect of equivariance and invariance on data-driven modeling approaches. Our results show that modeling invariant quantities produces more accurate long-term predictions and that these invariant quantities may be learned from the velocity field using a data-driven encoder.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 29 of its 54 references that are in the map. First posted on arXiv 3 May 2023.

Builds on

29 of 54 references.

References · 29

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17 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 1.

5 papers.

  1. 2024Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networkscited by 10
  2. 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networkscited by 5
  3. 2024Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modelingcited by 2
  4. 2025Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherencecited by 1
  5. 2026E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPUcited by 0