Decoder Decomposition for the Analysis of the Latent Space of Nonlinear Autoencoders With Wind-Tunnel Experimental Data

TL;DR

This paper introduces a decoder decomposition method to interpret the latent space of nonlinear autoencoders applied to turbulent flow data, enhancing understanding of physical structures and improving model interpretability.

Contribution

The paper proposes a novel decoder decomposition technique for interpreting autoencoders' latent variables in fluid dynamics, demonstrating its effectiveness on synthetic and experimental turbulent flow data.

Findings

Latent space dimension affects interpretability of autoencoders.

The method identifies physical and spurious latent variables.

Decoder decomposition helps rank and select relevant latent variables.

Abstract

Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modelled with a smaller number of degrees of freedom when using the appropriate coordinate system, which is the goal of dimensionality reduction via nonlinear autoencoders. Autoencoders are expressive tools, but they are difficult to interpret. The goal of this paper is to propose a method to aid the interpretability of autoencoders. This is the decoder decomposition. First, we propose the decoder decomposition, which is a post-processing method to connect the latent variables to the coherent structures of flows. Second, we apply the decoder decomposition to analyse the latent space of synthetic data of a two-dimensional unsteady wake past a cylinder. We find that the dimension of latent space has a significant impact on the interpretability of autoencoders. We identify the physical and spurious latent variables. Third, we apply the decoder decomposition to the latent space of wind-tunnel experimental data of a three-dimensional turbulent wake past a bluff body. We show that the reconstruction error is a function of both the latent space dimension and the decoder size, which are correlated. Finally, we apply the decoder decomposition to rank and select latent variables based on the coherent structures that they represent. This is useful to filter unwanted or spurious latent variables, or to pinpoint specific coherent structures of interest. The ability to rank and select latent variables will help users design and interpret nonlinear autoencoders.