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

2026-05-12

AI Summary

Neural fluid surrogates face significant challenges in real-world scenarios due to limited scalability, data scarcity, and symmetry-breaking effects that hinder generalization. This work systematically investigates the role of E(3) equivariance across computational fluid dynamics tasks with varying degrees of distributional alignment, spanning automotive aerodynamics and hemodynamics. For the first time, it quantifies the performance trade-offs of equivariance in high-fidelity, multi-scale fluid surrogates: while consistently beneficial in geometrically diverse settings, explicit equivariance can degrade in-distribution performance when training data are strongly aligned. To address this, we propose AB-GATr, a novel architecture integrating geometric algebra Transformers, an anchored branching structure, and explicit E(3) equivariance to jointly model surface and volumetric quantities. Experiments demonstrate that AB-GATr substantially outperforms non-equivariant baselines in hemodynamic tasks, and that explicit equivariance consistently surpasses implicit symmetry-learning strategies such as data augmentation.

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.

Problem

• equivariance
• neural surrogates
• computational fluid dynamics
• symmetry breaking
• generalization

Innovation

• equivariance
• neural surrogates
• computational fluid dynamics
• geometric algebra
• E(3)-equivariant