Regularized autoencoders for accurate d* estimation in turbulent multiscale flows

Develop regularized autoencoder architectures that can accurately estimate the minimal latent space dimension d* required to reconstruct all physically relevant scales (up to the Kolmogorov scale) of the temperature field in turbulent, multiscale Rayleigh–Bénard convection at high Rayleigh numbers. Existing regularized variants, including sparsity-inducing autoencoders (SIAE) and implicit rank-minimizing autoencoders (IRMAE), failed to provide accurate d* estimates across the studied Rayleigh numbers, in contrast to fixed-dimension autoencoders that required manual selection of latent dimension.

Background

The paper investigates convolutional autoencoders for reduced-order representations of the temperature field in two-dimensional Rayleigh–Bénard convection across Rayleigh numbers 10^6–10^8. The authors define d* as the minimal latent dimension needed for the autoencoder to accurately reconstruct all physically relevant scales, judged by matching the resolved wavenumbers up to the Kolmogorov scale at a representative height.

They compare a fixed-dimension autoencoder (FdAE) with two regularized variants designed to infer the effective latent dimension after training: a sparsity-inducing autoencoder (SIAE, with L1 penalties) and an implicit rank-minimizing autoencoder (IRMAE, with internal linear layers). While FdAE successfully estimates d* by manual selection of d, both SIAE and IRMAE fail to achieve accurate reconstructions at all scales and produce larger d* estimates where they do work. This motivates the explicitly stated open problem of identifying regularized architectures that can robustly and accurately estimate d* in highly turbulent, multiscale flows.