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

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.

References in corpus (6)

• On Dynamic Mode Decomposition: Theory and Applications
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Grasping Extreme Aerodynamics on a Low-Dimensional Manifold
• Learning in Sinusoidal Spaces with Physics-Informed Neural Networks

Cited by in corpus (5)

• Compressing fluid flows with nonlinear machine learning: mode decomposition, latent modeling, and flow control
• Real-time forecasting of chaotic dynamics from sparse data and autoencoders
• Compact representation of transonic airfoil buffet flows with observable-augmented machine learning
• Online model learning with data-assimilated reservoir computers
• Latent attention on masked patches for flow reconstruction