用稀疏传感器重建湍流壁面压力,突破训练域尺度限制。
Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors

- 分块流匹配框架融合短域模拟与稀疏测量,实现跨尺度生成。
- 仅需500个快照(2.5%数据)即可在高雷诺数下重建四倍大域的压力场。
- 适用于稀疏传感场景,尤其适合工程中难以布设密集传感器的流动预测。
在湍流壁面流动中,完整表征壁面压力谱需要同时捕捉粘性尺度高频成分和外层低频成分——这既无法通过短域直接数值模拟(DNS)实现,也难以仅靠稀疏实验测量满足。本文提出分块流匹配(Patched FM),一种生成式框架:从短域DNS学习内尺度壁面压力统计的局部先验,并在推理时通过无需训练的后验采样融合稀疏传感器数据。通过将流匹配向量场进行分块加法分解,生成先验与全局域大小解耦,可实现远超训练配置的域规模重建。以内尺度坐标表达分块先验,使高频压力统计近似雷诺数不变,从而通过仅500个短域快照(仅为基线训练数据的2.5%)实现层级迁移学习,计算成本仅为从头训练的一小部分。该方法应用于可压缩通道流DNS(Re_τ=180, 500, 1000),在长为4倍训练域(L_x^L = 16πδ,对比训练域L_x^S = 4πδ)上,仅需0.25%传感器覆盖率,即能高保真恢复流向上和展向上短域DNS无法获取的低波数谱信息。零样本泛化至未见雷诺数及消融实验证明,内尺度缩放是实现高效雷诺数迁移的物理前提。
原文摘要 · Abstract (English)
Characterizing the complete wall-pressure spectrum in turbulent wall-bounded flows requires simultaneous access to the viscous-scale high-wavenumber content and the outer-layer low-wavenumber content -- a requirement that neither short-domain direct numerical simulation (DNS) nor sparse experimental measurements alone can satisfy. We propose Patched Flow Matching (Patched FM), a generative framework that fuses these two complementary sources by learning a patch-local prior over inner-scaled wall-pressure statistics from short-domain DNS and assimilating sparse sensor measurements at inference time through training-free posterior sampling. The patch-additive decomposition of the flow matching vector field decouples the generative prior from the global domain size, enabling reconstruction on domains arbitrarily larger than the training configuration. By expressing the patch prior in inner-scaled coordinates, where high-wavenumber wall-pressure statistics are approximately Reynolds-number invariant, the framework extends to higher Reynolds numbers through hierarchical transfer learning with as few as $500$ short-domain snapshots ($2.5\%$ of the base training data) at a fraction of the scratch-training cost. Applied to compressible channel-flow DNS at $Re_τ= 180$, $500$, and $1000$, Patched FM reconstructs full-resolution wall-pressure fields on a domain four times larger than the training configuration ($L_x^L = 16πδ$ versus $L_x^S = 4πδ$) from sensor coverage as low as $0.25\%$, recovering the low-wavenumber spectral content inaccessible to short-domain DNS with high fidelity in both streamwise and spanwise directions. Zero-shot generalization to unseen Reynolds numbers and ablation studies further confirm the role of inner scaling as a physical prerequisite for data-efficient Reynolds-number transfer.
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