Tensor-based flow reconstruction from optimally located sensor measurements

TL;DR

This paper presents a tensor-based approach for reconstructing high-resolution flow fields from sparse sensor data, outperforming traditional vectorized methods in accuracy and storage efficiency, especially in high-dimensional flows.

Contribution

The authors introduce a novel tensor-based sensor placement and flow reconstruction method that preserves multidimensional flow information, improving accuracy and reducing storage costs compared to existing vectorized techniques.

Findings

Tensor-based method achieves higher accuracy than vectorized methods.

Error variance is smaller with the tensor approach.

Storage costs are reduced by several orders of magnitude.

Abstract

Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in-situ and satellite measurements of the global sea surface temperature, and 3D unsteady simulated flow around a marine research vessel.