Latent attention on masked patches for flow reconstruction

TL;DR

LAMP is an interpretable vision transformer model that reconstructs fluid flow fields from masked data, demonstrating high accuracy in laminar flows and potential for nonlinear extensions.

Contribution

The paper introduces LAMP, a novel transformer-based approach for masked flow reconstruction combining patch-wise PCA and linear regression, with interpretability and modularity.

Findings

LAMP accurately reconstructs laminar wake flows from 90%-masked inputs.

The learned attention maps enable interpretable sensor placement.

LAMP outperforms gappy POD in chaotic flow reconstruction.

Abstract

Vision transformers have shown outstanding performance in image generation, yet their adoption in fluid dynamics remains limited. We introduce the Latent Attention on Masked Patches (LAMP) model, an interpretable regression-based modified vision transformer designed for masked flow reconstruction. LAMP follows a three-fold strategy: (i) partition of each flow snapshot into patches, (ii) patch-wise dimensionality reduction via proper orthogonal decomposition, and (iii) reconstruction of the full field from a masked input using a single-layer transformer trained via closed-form linear regression. We test the method on two canonical 2D unsteady wakes: a laminar wake past a bluff body, and a chaotic wake past two cylinders. On the laminar case, LAMP accurately reconstructs the full flow field from a 90%-masked and noisy input, across signal-to-noise ratios between 10 and 30dB. Further, the learned attention matrix yields interpretable multi-fidelity optimal sensor-placement maps. LAMP's performance on the chaotic wake is limited, but outperforms other regression methods such as gappy POD. The modularity of the framework, however, naturally accommodates nonlinear compression and deep attention blocks, thereby providing an efficient baseline for nonlinear, high-dimensional masked flow reconstruction.