Projection-based model-order reduction for unstructured meshes with graph autoencoders
<|reference_start|>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 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.<|reference_end|>
@article{magargal2024projection-based,
    title={Projection-based model-order reduction for unstructured meshes with
  graph autoencoders},
    author={Liam K. Magargal, Parisa Khodabakhshi, Steven N. Rodriguez, Justin W.
  Jaworski, John G. Michopoulos},
    journal={arXiv preprint arXiv:2407.13669},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13669},
    primaryClass={cs.CE}
}