Scalable Node Clustering for Graph Autoencoders Used in Model-Order Reduction

Graph autoencoders, which have seen growing use for dimensionality reduction of simulations in computational mechanics modeled by unstructured meshes, are dependent upon hierarchical generation of lower-dimensional graphs based on a node-clustering scheme. In earlier studies, the hierarchy of reduced graphs was generated using the spectral clustering algorithm, which leverages graph topology by performing an eigendecomposition of the graph Laplacian to identify clusters aligned with the physical domain's inherent geometry. However, for large graphs, the eigendecomposition can be expensive to compute directly. In this study, we investigate alternative node clustering schemes and assess their respective advantages and disadvantages, with a particular focus on scalability.