# Unsupervised Machine Learning to Teach Fluid Dynamicists to Think in 15 Dimensions

## TL;DR

This paper employs an autoencoder to analyze high-dimensional stratified turbulence data, revealing that vertical velocity is a key indicator of turbulence features, thus offering a new data-driven perspective for fluid dynamicists.

## Contribution

It introduces a novel application of autoencoders to compress and interpret extremely high-dimensional turbulence data, highlighting the importance of vertical velocity in stratified turbulence analysis.

## Key findings

- Vertical velocity is a significant marker for turbulence features.
- Autoencoder errors reveal important flow features.
- Robustness of bleed over across different autoencoder layers.

## Abstract

An autoencoder is used to compress and then reconstruct three-dimensional stratified turbulence data in order to better understand fluid dynamics by studying the errors in the reconstruction. The original single data set is resolved on approximately $6.9\times10^{10}$ grid points, and 15 fluid variables in three spatial dimensions are used, for a total of about $10^{12}$ input quantities in three dimensions. The objective is to understand which of the input variables contains the most relevant information about the local turbulence regimes in stably stratified turbulence (SST). This is accomplished by observing flow features that appear in one input variable but then `bleed over' to multiple output variables. The bleed over is shown to be robust with respect to the number of layers in the autoencoder. In this proof of concept, the errors in the reconstruction include information about the spatial variation of vertical velocity in most of the components of the reconstructed rate-of-strain tensor and density gradient, which suggests that vertical velocity is an important marker for turbulence features of interest in SST. This result is consistent with what fluid dynamicists already understand about SST and, therefore, suggests an approach to understanding turbulence based on more detailed analyses of the reconstruction on errors in an autoencoding algorithm.