Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks
<|reference_start|>Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks: A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor-Green Vortex flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations.<|reference_end|>
@article{barwey2024mesh-based,
    title={Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural
  Networks},
    author={Shivam Barwey, Pinaki Pal, Saumil Patel, Riccardo Balin, Bethany
  Lusch, Venkatram Vishwanath, Romit Maulik, Ramesh Balakrishnan},
    journal={arXiv preprint arXiv:2409.07769},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07769},
    primaryClass={physics.flu-dyn cs.CE cs.LG physics.comp-ph}
}