Reduced Representations of Rayleigh-B\'enard Flows via Autoencoders

TL;DR

This paper investigates how convolutional autoencoders can effectively reduce the complexity of 2D Rayleigh-Bénard flow data, identifying the minimum latent space dimensions needed to capture key physical features across turbulent regimes.

Contribution

It introduces a novel method for estimating the minimal autoencoder latent space dimension for multiscale flows, highlighting the transition to turbulence around a specific Rayleigh number.

Findings

Minimum autoencoder dimension sharply increases near Ra ~ 10^7

Manually fixing latent space dimension yields best reconstruction results

Estimated dimension does not scale with physical flow scales

Abstract

We analyzed the performance of Convolutional Autoencoders in generating reduced-order representations the temperature field of 2D Rayleigh-B\'enard flows at $Pr=1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range where the flow transitions to turbulence. We present a way of estimating the minimum number of dimensions needed by the Autoencoders to capture all the relevant physical scales of the data that is more apt for highly multiscale flows than previous criteria applied to lower dimensional systems. We compare our architecture with two regularized variants as well as with linear methods, and find that manually fixing the dimension of the latent space produces the best results. We show how the estimated minimum dimension presents a sharp increase around $Ra \sim 10^7$, when the flow starts to transition to turbulence. Furthermore, we show how this dimension does not follow the same scaling as the physically relevant scales, such as the dissipation lengthscale and the thermal boundary layer.