Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates

• URL: http://arxiv.org/abs/2605.18816v1
• Date: Tue, 12 May 2026 10:47:33 GMT
• Title: Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates
• Abstract summary: Neural surrogates enable orders-of-magnitude acceleration of computational fluid dynamics (CFD) simulations.<n>Group-equivariant architectures are a principled way to introduce such bias, yet they can be detrimental when the learning problem itself breaks symmetry.<n>We introduce the Anchored-Branched Geometric Algebra Transformer (AB-GATr), a neural surrogate that integrates scalability and symmetry preservation.
• Score: 1.5465701096936584
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Neural surrogates enable orders-of-magnitude acceleration of computational fluid dynamics (CFD) simulations, with the potential to transform engineering and healthcare workflows. Neural surrogate use in real-world applications requires addressing scalability to large, high-resolution surface and volume meshes, as well as to bespoke architectures, and accounting for limited training data through the use of inductive biases. Group-equivariant architectures are a principled way to introduce such bias, yet they can be detrimental when the learning problem itself breaks symmetry, for example, due to strong distributional alignment in the dataset. In this work, we investigate under which conditions equivariance improves generalization in neural CFD surrogates across tasks with increasing levels of distributional alignment and realism, covering automotive aerodynamics and blood flow (hemodynamics). To systematically assess the added value of equivariance at the limit of problem scaling, we introduce the Anchored-Branched Geometric Algebra Transformer (AB-GATr), a neural surrogate that integrates scalability and symmetry preservation to efficiently model coupled surface and volume quantities in an $E(3)$-equivariant manner. We find that on strongly aligned aerodynamics datasets, i.e., those that break symmetry, enforcing equivariance can degrade in-distribution performance. In contrast, across hemodynamic benchmarks with diverse geometries and varying alignment, equivariance is consistently beneficial. Moreover, across all benchmarks, the explicit equivariance of AB-GATr reliably outperforms implicit symmetry learning through data augmentation. Our findings showcase that equivariance is not universally beneficial across domains, yet it brings tangible advantages in problems lacking strong data regularities.

Related papers

• Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration [71.51826063983434]
  Image restoration is an inherently ill posed inverse problem.<n>We use non strict symmetry as a constraint to formulate the restoration inverse problem.<n>We show that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size.
  arXiv  Detail & Related papers  (2026-05-13T16:22:19Z)
• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Approximate equivariance via projection-based regularisation [1.5755923640031846]
  Non-equivariant models have regained attention, due to their better runtime performance and imperfect symmetries.<n>This has motivated the development of approximately equivariant models that strike a middle ground between respecting symmetries and fitting the data distribution.<n>We present a mathematical framework for computing the non-equivariance penalty exactly and efficiently in both the spatial and spectral domain.
  arXiv  Detail & Related papers  (2026-01-08T15:35:42Z)
• Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution [2.4095472682599417]
  We show that standard convolutional neural networks (CNNs) can partially acquire rotational symmetry without explicit augmentation or specialized architectures.<n>Using 3D channel-flow with differing anisotropy, we find that models trained on more isotropic mid-plane data achieve lower equivariance error.<n>These results clarify when rotational symmetry must be explicitly incorporated into learning algorithms and when it can be obtained directly from turbulence.
  arXiv  Detail & Related papers  (2025-09-25T02:31:56Z)
• Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model [4.79907962230318]
  We show that an equivariant U-shaped neural operator (E-UNO) can learn the evolution of the phase-field variable from short histories of past dynamics.<n>By encoding symmetry and scale hierarchy, the model generalizes better, requires less training data, and yields physically consistent dynamics.
  arXiv  Detail & Related papers  (2025-09-01T09:25:31Z)
• Learning (Approximately) Equivariant Networks via Constrained Optimization [25.51476313302483]
  Equivariant neural networks are designed to respect symmetries through their architecture.<n>Real-world data often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects.<n>We introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model.
  arXiv  Detail & Related papers  (2025-05-19T18:08:09Z)
• Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion [55.95767828747407]
  In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model.<n>We present a framework that reduces training variance and provides a provably lower-variance gradient estimator.<n>We also present a practical implementation of this estimator incorporating the loss and sampling procedure through a method we call Orbit Diffusion.
  arXiv  Detail & Related papers  (2025-02-14T03:26:57Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Learning Layer-wise Equivariances Automatically using Gradients [66.81218780702125]
  Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients.
  arXiv  Detail & Related papers  (2023-10-09T20:22:43Z)
• Equivariant vector field network for many-body system modeling [65.22203086172019]
  Equivariant Vector Field Network (EVFN) is built on a novel equivariant basis and the associated scalarization and vectorization layers. We evaluate our method on predicting trajectories of simulated Newton mechanics systems with both full and partially observed data.
  arXiv  Detail & Related papers  (2021-10-26T14:26:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.