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.

翻译：本文提出一种新方法，通过奇异值分解（SVD）算法的创新变体（命名为低成本SVD，即lcSVD），能够以极高精度和极低计算成本重构数据集。该算法可从最少数据点（可随机选取、等间距选取，或通过本文提出的最优传感器布局功能计算得出）重构数据集，并基于最小化重构误差验证传感器位置的计算结果。该方法还能确定最优传感器数量，帮助用户优化实验数据采集。通过一系列数据集测试（涵盖实验与数值模拟、二维与三维数据、层流与湍流等场景），验证了该方法在高重构精度、鲁棒性及计算资源优化方面的能力。相较于对数据集应用标准SVD，该方法实现了最高630倍的加速比和37%的内存缩减。该技术将集成至ModelFLOWs-app的下一版本中。