Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks*

A graph neural network (GNN)-based scientific machine learning framework is developed for mesh-based super-resolution of three-dimensional fluid flows. In this framework, the GNN operates in the context of local interpretation of flow-fields (it acts on local meshes of elements/cells). To facilitate GNN representations in a manner similar to spectral (or finite) element discretizations, the baseline message passing layer is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The multiscale architecture is comprised of a combination of a coarse-scale processor and a fine-scale processor 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 at smaller length scales to produce the super-resolved flow. Demonstration studies are conducted using hexahedral mesh-based data produced by simulations of the Taylor-Green Vortex flow (at Reynolds numbers of 1600 and 3200) performed using NekRS, Argonne's high-order spectral element flow solver. The results show that the GNN architecture is able to produce accurate super-resolved fields for a variety of model configurations.