mlsanityData to 7 Oct 2026

Equivariant geometric convolutions for emulation of dynamical systems

arXiv 2305.12585 ↗First posted 21 May 2023cs.LGcited by 3

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Abstract (arXiv)

Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the laws of physics are relationships between scalars, vectors, and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet, and a UNet. In numerical experiments emulating 2D compressible Navier-Stokes, we see better accuracy and improved stability compared to baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any CNN-based method applied to an appropriate class of problems

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 30 of its 54 references that are in the map. First posted on arXiv 21 May 2023.

Builds on

30 of 54 references.

References · 30

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18 more
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Cited by year (2026 to 7 Oct)

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

3 papers.

  1. 2025Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherencecited by 1
  2. 2026Autoregressive deep learning for real-time simulation of soft tissue dynamics during virtual neurosurgerycited by 0
  3. 2026Loss Landscape Geometry of Partial Differential Equation Emulators: Or, Symmetry Learning via Gradient Alignmentcited by 0