Deep Learning combined with singular value decomposition to reconstruct databases in fluid dynamics

Fluid Dynamics problems are characterized by being multidimensional and nonlinear. Therefore, experiments and numerical simulations are complex and time-consuming. Motivated by this, the need arises to find new techniques to obtain data in a simpler way and in less time. In this article, we present a novel methodology based on physical principles to reconstruct three-, four- and five-dimensional databases from a strongly sparse sensors as input. The methodology consists of combining Single Value Decomposition (SVD) with neural networks. The neural network used is characterized by a simple architecture based on combining two autoencoders that work in parallel and are joined in the last layer. This new algorithm has been proved with three databases with different dimensions and complexities: in an Atmospheric Boundary Layer (ABL) with a turbulence model and in the flow past a two- and a three-dimensional cylinder. Summarizing, this work proposes a new hybrid physics-based machine learning model with a simple, robust and generalizable architecture, which allows reconstructing databases from very few sensors and with a very low computational cost.