Projection-based model-order reduction for unstructured meshes with graph autoencoders

This paper presents a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) on advection-dominated flows modeled by unstructured meshes. The autoencoder is coupled with the time integration scheme from a traditional deep least-squares Petrov-Galerkin proj...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Magargal, Liam K, Khodabakhshi, Parisa, Rodriguez, Steven N, Jaworski, Justin W, Michopoulos, John G
Format: Article
Language:English
Subjects:
Artificial neural networks
Burgers equation
Euler-Lagrange equation
Flexibility
Galerkin method
Graph neural networks
Graphs
Least squares
Message passing
Model reduction
Time integration
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Summary:This paper presents a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) on advection-dominated flows modeled by unstructured meshes. The autoencoder is coupled with the time integration scheme from a traditional deep least-squares Petrov-Galerkin projection and provides the first deployment of a graph autoencoder into a PMOR framework. The presented graph autoencoder is constructed with a two-part process that consists of (1) generating a hierarchy of reduced graphs to emulate the compressive abilities of convolutional neural networks (CNNs) and (2) training a message passing operation at each step in the hierarchy of reduced graphs to emulate the filtering process of a CNN. The resulting framework provides improved flexibility over traditional CNN-based autoencoders because it is extendable to unstructured meshes. To highlight the capabilities of the proposed framework, which is named geometric deep least-squares Petrov-Galerkin (GD-LSPG), we benchmark the method on a one-dimensional Burgers' equation problem with a structured mesh and demonstrate the flexibility of GD-LSPG by deploying it to a two-dimensional Euler equations model that uses an unstructured mesh. The proposed framework provides considerable improvement in accuracy for very low-dimensional latent spaces in comparison with traditional affine projections.
ISSN:2331-8422