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

TL;DR

This paper investigates when equivariant neural architectures improve fluid dynamics surrogates, demonstrating benefits in diverse, less-aligned datasets and introducing a scalable, equivariant model for coupled surface and volume predictions.

Contribution

It introduces AB-GATr, a scalable E(3)-equivariant neural surrogate, and provides systematic analysis of equivariance benefits across different fluid dynamics tasks.

Findings

Equivariance can degrade performance on strongly aligned datasets.

Equivariance consistently benefits diverse, less-aligned datasets like hemodynamics.

Explicit equivariance outperforms data augmentation for symmetry learning.

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.