A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling

The popularity of deep convolutional autoencoders (CAEs) has engendered effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. However, it is not known whether deep CAEs provide superior performance in all ROM 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.