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

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.

References in corpus (8)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Semi-Supervised Classification with Graph Convolutional Networks
• Fast Graph Representation Learning with PyTorch Geometric
• Simplifying Graph Convolutional Networks
• Simple and Deep Graph Convolutional Networks
• Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
• PAN: Path Integral Based Convolution for Deep Graph Neural Networks

Cited by in corpus (8)

• Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows
• Deep Learning in Deterministic Computational Mechanics
• An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes
• Physics-aware Reduced-order Modeling of Transonic Flow via $\beta$-Variational Autoencoder
• Low-dimensional Data-based Surrogate Model of a Continuum-mechanical Musculoskeletal System Based on Non-intrusive Model Order Reduction
• A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEs
• Latent assimilation with implicit neural representations for unknown dynamics
• Projection-based model-order reduction via graph autoencoders suited for unstructured meshes