  Simulations of large-scale dynamical systems require expensive computations.
Low-dimensional parametrization of high-dimensional states such as Proper
Orthogonal Decomposition (POD) can be a solution to lessen the burdens by
providing a certain compromise between accuracy and model complexity. However,
for really low-dimensional parametrizations (for example for controller design)
linear methods like the POD come to their natural limits so that nonlinear
approaches will be the methods of choice. In this work we propose a
convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine
linear decoder and consider combinations with k-means clustering for improved
encoding performance. The proposed set of methods is compared to the standard
POD approach in two cylinder-wake scenarios modeled by the incompressible
Navier-Stokes equations.
