  Turbulence is characterised by chaotic dynamics and a high-dimensional state
space, which make this phenomenon challenging to predict. However, turbulent
flows are often characterised by coherent spatiotemporal structures, such as
vortices or large-scale modes, which can help obtain a latent description of
turbulent flows. However, current approaches are often limited by either the
need to use some form of thresholding on quantities defining the isosurfaces to
which the flow structures are associated or the linearity of traditional modal
flow decomposition approaches, such as those based on proper orthogonal
decomposition. This problem is exacerbated in flows that exhibit extreme
events, which are rare and sudden changes in a turbulent state. The goal of
this paper is to obtain an efficient and accurate reduced-order latent
representation of a turbulent flow that exhibits extreme events. Specifically,
we employ a three-dimensional multiscale convolutional autoencoder (CAE) to
obtain such latent representation. We apply it to a three-dimensional turbulent
flow. We show that the Multiscale CAE is efficient, requiring less than 10%
degrees of freedom than proper orthogonal decomposition for compressing the
data and is able to accurately reconstruct flow states related to extreme
events. The proposed deep learning architecture opens opportunities for
nonlinear reduced-order modeling of turbulent flows from data.
