Generating Three-Dimensional Fields from Two-Dimensional Soft Computing Strategies.

The main goal of this work is to provide a new tool to reconstruct three-dimensional data from a few two-dimensional planes. To this purpose, spatio-temporal higher order dynamic mode decomposition (HODMD) is applied to a group of vertical and horizontal planes, located at different positions in space. Firstly, the method extracts the relevant frequencies and wavenumbers related to the field analyzed, providing two-dimensional HODMD expansions. Secondly, a system of equations is constructed in the vertical planes using the previous information. Solving this equation system, it is possible to expand the two-dimensional HODMD solutions to recover a three-dimensional HODMD expansion, representing the complete three-dimensional flow field. This method has been successfully tested to reconstruct a three-dimensional toy problem with great precision (error smaller than \(10^{-10}\)). The method could be potentially used in the analysis of turbulent flows (numerical and experimental data), extracting relevant three-dimensional information from the two-dimensional data with reduced computational cost (soft computing).