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

TL;DR

This paper introduces a multiscale graph neural network approach for mesh-based super-resolution of 3D fluid flow data, enabling accurate high-resolution reconstructions from coarse meshes.

Contribution

The work presents a novel multiscale GNN architecture that operates on localized mesh elements and incorporates synchronization for element connectivity, improving fluid flow super-resolution.

Findings

Accurate super-resolution of fluid flows demonstrated on Taylor-Green Vortex and backward-facing step data.

Reconstruction errors increase with Reynolds number, indicating limitations at higher turbulence levels.

Cross-mesh extrapolation shows promising generalization capabilities.

Abstract

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 and backward-facing step 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. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.