  The popularity of deep convolutional autoencoders (CAEs) has engendered new
and effective reduced-order models (ROMs) for the simulation of large-scale
dynamical systems. Despite this, it is still unknown whether deep CAEs provide
superior performance over established linear techniques or other network-based
methods in all modeling scenarios. To elucidate this, the effect of autoencoder
architecture on its associated ROM is studied through the comparison of deep
CAEs against two alternatives: a simple fully connected autoencoder, and a
novel graph convolutional autoencoder. Through benchmark experiments, it is
shown that the superior autoencoder architecture for a given ROM application is
highly dependent on the size of the latent space and the structure of the
snapshot data, with the proposed architecture demonstrating benefits on data
with irregular connectivity when the latent space is sufficiently large.
