FLRNet: A Deep Learning Method for Regressive Reconstruction of Flow Field From Limited Sensor Measurements

TL;DR

FLRNet is introduced, a deep learning method for flow field reconstruction from sparse sensor measurements that consistently outperformed other baselines, delivering the most accurate reconstructed flow field and being the most robust to noise.

Abstract

Many applications in computational and experimental fluid mechanics require effective methods for reconstructing the flow fields from limited sensor data. However, this task remains a significant challenge because the measurement operator, which provides the punctual sensor measurement for a given state of the flow field, is often ill-conditioned and non-invertible. This issue impedes the feasibility of identifying the forward map, theoretically the inverse of the measurement operator, for field reconstruction purposes. While data-driven methods are available, their generalizability across different flow conditions (\textit{e.g.,} different Reynold numbers) remains questioned. Moreover, they frequently face the problem of spectral bias, which leads to smooth and blurry reconstructed fields, thereby decreasing the accuracy of reconstruction. We introduce FLRNet, a deep learning method for flow field reconstruction from sparse sensor measurements. FLRNet employs an variational autoencoder with Fourier feature layers and incorporates an extra perceptual loss term during training to learn a rich, low-dimensional latent representation of the flow field. The learned latent representation is then correlated to the sensor measurement using a fully connected (dense) network. We validated the reconstruction capability and the generalizability of FLRNet under various fluid flow conditions and sensor configurations, including different sensor counts and sensor layouts. Numerical experiments show that in all tested scenarios, FLRNet consistently outperformed other baselines, delivering the most accurate reconstructed flow field and being the most robust to noise.

Figures (8)

• Figure 1: The overall architecture design.
• Figure 2: Numerical experiment setting for the flow around cylindrical test problem. (a) Dimension of the examined domain. (b) Three different tested sensor layouts.
• Figure 3: Reconstruction result of FLRNet and other baselines at different times of the simulation. FLRNet reconstructed fields are closer to the ground truth compared to other baselines, indicated by the low-value error fields, especially at time $t = 0.82$ (s) and $1.23$ (s).
• Figure 4: Error profile analysis. We computed the average MAE across the whole test dataset at six different horizontal positions over the flow domain. Notice that the average MAE of FLRNet with Fourier feature is constantly the lowest for all examined positions.
• Figure 5: Analysis of the reconstruction error w.r.t the temporal evolution of the flow field. The reconstruction error increases for all models, peaks at around step 20 when the instability arises and gradually reduces as the flow enters its equilibrium. During the whole process, FLRNet with Fourier feature yield the lowest MAE among all baselines.