This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase the quality and precision of numerical and experimental data. A combination of two- and three-dimensional, numerical and experimental dasasets are used to demonstrate the reconstruction capacity of the presented methods, showing that these methods can be used to reconstruct any type of dataset, showing outstanding results when applied to highly complex data, which is noisy. The combination of benefits of these techniques results in a series of data-driven methods which are capable of repairing and/or enhancing the resolution of a dataset by identifying the underlying physics that define the data, which is incomplete or under-resolved, filtering any existing noise. These methods and the Python codes are included in the first release of ModelFLOWs-app.

翻译：本文提出一系列新型方法，融合模态分解算法（如奇异值分解和高阶奇异值分解）与深度学习架构，用于修复、增强并提升数值与实验数据的质量及精度。通过二维和三维数值与实验数据集的综合验证，展示了所提方法的重建能力——可重构任意类型的数据集，并在含噪的高复杂度数据中表现优异。这些技术优势的结合形成了一系列数据驱动方法，能够通过识别定义数据的底层物理机制（即使数据不完整或欠采样），在修复和/或增强数据集分辨率的同时滤除现有噪声。上述方法及其Python代码已收录于ModelFLOWs-app的初版发布中。