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.

利用解码器分解方法进行介电解释和相关的涡流结构的等级和选择过程，以帮助用户设计和解释非线性自动编码器。