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

Abstract

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 databases with three, four and five dimensions, from sparse databases formed by sensor measurements. The methodology consists of combining Single Value Decomposition (SVD), which can extract the main flow dynamics, 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. By applying this methodology, it has been achieved to reconstruct databases of different dimensions obtaining errors of the same order as those obtained in simulations. 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.