Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors

2026-06-20

AI Summary

This work addresses the challenge of fully characterizing turbulent wall-pressure spectra, which requires simultaneous resolution of high-frequency viscous-scale and low-frequency outer-layer dynamics—information neither short-domain direct numerical simulations (DNS) nor sparse experimental measurements can capture alone. To overcome this limitation, the authors propose a Patched Flow Matching framework that leverages short-domain DNS to learn an inner-scale local prior and integrates it with patch-based additive flow matching in inner-scaled coordinates, enabling training-free posterior sampling during inference. By fusing sparse sensor data at inference time, the method achieves high-fidelity reconstruction of wall-pressure fields beyond the training domain’s spatial extent. Employing hierarchical transfer learning, the approach generalizes to higher Reynolds numbers (Reτ = 180–1000) using only a few snapshots. Remarkably, with merely 0.25% sensor coverage, it accurately reconstructs full-resolution pressure fields four times larger than the training domain, recovering the low-wavenumber spectral content missing in short-domain DNS.

Abstract

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.

Problem

• wall-pressure reconstruction
• turbulent wall-bounded flows
• sparse sensors
• scale extrapolation
• Reynolds-number invariance

Innovation

• Patched Flow Matching
• inner scaling
• generative reconstruction
• Reynolds-number transfer
• sparse sensor assimilation