研究对称性在流体神经代理中的作用,发现其并非总是有益,但在无强数据规律场景下显著提升性能。
Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates

- 提出AB-GATr模型,同时实现高可扩展性与$E(3)$对称性保持
- 在血流模拟中对称性提升性能,但汽车空气动力学中可能降低精度
- 显式对称性优于数据增强带来的隐式对称学习
神经代理可使计算流体动力学(CFD)仿真提速数个数量级,有望变革工程与医疗流程。实际应用需应对大规模、高分辨率网格及定制架构的可扩展性挑战,并通过归纳偏置缓解训练数据有限问题。群等变架构是引入此类偏置的合理方式,但在学习问题本身破坏对称性时(如数据分布高度对齐),可能产生负面影响。本文系统评估了在不同分布对齐程度和真实度任务中,等变性对神经CFD代理泛化能力的影响,涵盖汽车空气动力学与血流动力学。为在极限规模下评估等变性的价值,提出锚定分支几何代数变压器(AB-GATr),该模型能高效以$E(3)$-等变方式建模耦合表面与体积量。结果表明,在强对齐的空气动力学数据集上,强制等变性会降低分布内性能;而在具有多样几何结构和变化对齐的血流基准测试中,等变性始终有益。所有基准测试中,AB-GATr的显式等变性均优于通过数据增强实现的隐式对称学习。
原文摘要 · Abstract (English)
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.
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