Physics-informed dimensionality reduction of direct numerical simulations of stratified turbulent flows using convolutional autoencoders

Stratified turbulent flows are multi-scale frameworks characterized by classical small-scale intermittency as well as by the occurrence of large-scale intermittent bursts of vertical velocity and temperature, as it was shown in direct numerical simulations (DNS) of the Boussinesq equations (Rorai et al. 2014, Feraco et al. 2018, 2021). While the research conducted until now - based on short or moderate integration times of DNS runs - allowed to observe the emergence of sporadic, powerful velocity and temperature enhancements in simulations of stratified geophysical flows, an exhaustive characterization of such large-scale intermittent events requires indeed longer integrations, up to 103 - 104 eddy turnover times. This implies the generation of a huge amount of data, which poses serious technical constraints. To address this issue, we implemented new unsupervised clustering and dimensionality reduction techniques based on the use of convolutional autoencoders (CAE). In particular, we employed CAE to extract from the DNS fields the lower dimensional features containing enough information in order to allow the reconstruction of the original inputs (such as the three-dimensional temperature and velocity fields at each time-step of the simulation) from less memory consuming data. The aim of this work is twofold. On one hand, we employ the CAE network trained on DNS datasets of stratified flows (developing large-scale bursts and instabilities) for the purpose of dimensionality reduction. On the other hand, we use the trained CAE as outlier detector, in order to understand what physical parameters can be used to organize more efficiently the data in sub-groups and subsequently improve the accuracy of the reconstruction. Rorai et al., PRE, 2014, Vol. , p. Feraco et al., EPL, 2018, Vol. 123 (4), p.44002 Feraco et al., EPL, 2021, in press, https://arxiv.org/pdf/2106.07574.pdf