大涡模拟数据驱动亚格子尺度封闭中的旋转等变性与局部性
Rotational equivariance and locality in data-driven subgrid-scale closures
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中文总结 AI 辅助
该研究针对大涡模拟亚格子尺度封闭问题，对比等变与非等变、局部与非局部模型，发现等变非局部模型在泛化性能、参数效率及数据效率上更具优势，等变性与非局部性对该任务均有价值。
中文摘要 AI 辅助
大涡模拟的数据驱动亚格子尺度封闭在众多工程与地球科学应用中备受关注。在此背景下，关于旋转等变性作为学习到的张量映射的归纳偏置的作用，仍存在若干重要问题。我们研究等变性是否能在实际滤波比下提升亚格子尺度建模的准确性、参数效率与泛化能力。针对湍流通道流，我们将数据增强的非等变架构与以等变性为归纳偏置的架构进行对比，同时比较这两类模型的逐点与非局部版本。所有模型在时空、各向异性及雷诺数泛化下，均以匹配的参数数量进行评估。结果显示，未增强的模型可直接从湍流数据中学习到少量等变性，尤其当数据更具各向同性时。等变非局部架构在所有泛化测试中均达到最高相关系数，且参数数量约为非等变对应模型的一半，而逐点架构未优于解析Clark基线。此外，等变模型比非等变模型更具数据效率。等变性的益处随模型感受野增大而提升，表明在实际数据集规模、参数数量及滤波尺寸下，等变性与非局部性对亚格子尺度封闭任务均有用。
英文摘要
Data-driven subgrid-scale closures for large eddy simulation are of significant interest in many engineering and geoscience applications. In this context, several important questions remain about the role of rotational equivariance as an inductive bias for learned tensorial mappings. We investigate whether equivariance improves accuracy, parameter efficiency, and generalization for subgrid-scale modelling at realistic filter ratios. For turbulent channel flow, we compare data-augmented non-equivariant architectures to those with equivariance as an inductive bias. We compare both pointwise and nonlocal versions of these two model classes. All models are evaluated at matched parameter counts across spatiotemporal, anisotropy, and Reynolds number generalization. We show that non-augmented models learn a small degree of equivariance directly from turbulence data, especially when that data is more isotropic. The equivariant nonlocal architecture attains the highest correlation coefficient on every generalization test at approximately half the parameter count of its non-equivariant counterpart, while the pointwise architectures do not improve on the analytical Clark baseline. Additionally, the equivariant model is more data-efficient than a non-equivariant model. The benefit of equivariance grows with the receptive field of the model, indicating that equivariance and nonlocality are both useful for the subgrid-scale closure task at realistic dataset size, parameter counts, and filter size.
