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

作     者：Barwey, Shivam Pal, Pinaki Patel, Saumil Balin, Riccardo Lusch, Bethany Vishwanath, Venkatram Maulik, Romit Balakrishnan, Ramesh 

作者机构：Transportation and Power Systems Division Argonne National Laboratory LemontIL60439 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Argonne Leadership Computing Facility Argonne National Laboratory LemontIL60439 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Department of Information Science and Technology Pennsylvania State University University ParkPA16802 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Vortex flow 

摘      要：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. Copyright © 2024, The Authors. All rights reserved.