Low-cost singular value decomposition with optimal sensor placement

TL;DR

This paper introduces low-cost SVD (lcSVD), a novel algorithm that enables highly accurate dataset reconstruction with minimal sensors and computational resources, optimized through an optimal sensor placement strategy.

Contribution

The paper presents a new low-cost SVD variant and an optimal sensor placement method that together improve data reconstruction accuracy and efficiency, with practical validation across diverse datasets.

Findings

Maximum speed-up factor of 630 times compared to standard SVD

37% reduction in memory usage

High reconstruction accuracy across various datasets

Abstract

This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD). This algorithm allows to reconstruct a dataset from a minimum amount of points, that can be selected randomly, equidistantly or can be calculated using the optimal sensor placement functionality that is also presented in this paper, which finds minimizing the reconstruction error to validate the calculated sensor positions. This method also allows to find the optimal number of sensors, aiding users in optimizing experimental data recollection. The method is tested in a series of datasets, which vary between experimental and numerical simulations, two- and three-dimensional data and laminar and turbulent flow, which have been used to demonstrate the capacity of this method based on its high reconstruction accuracy, robustness, and computational resource optimization. Maximum speed-up factors of 630 and memory reduction of 37% are found when compared to the application of standard SVD to the dataset. This method will be incorporated into ModelFLOWs-app's next version release.