  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.
