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

TL;DR

This paper compares different autoencoder architectures for data-driven reduced-order modeling of large-scale dynamical systems, highlighting how architecture choice depends on data structure and latent space size.

Contribution

It introduces a novel graph convolutional autoencoder and systematically compares it with other autoencoders across various data scenarios.

Findings

Deep CAEs excel with irregular connectivity data when latent space is large

Performance depends heavily on data structure and latent space size

Graph convolutional autoencoders benefit specific complex data types

Abstract

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.