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

2024-09-12

arXiv.org

AI Summary

To address the low efficiency and poor accuracy of full-grid modeling in 3D flow field super-resolution, this paper proposes a localized graph neural network (GNN) method tailored for hexahedral meshes. Our approach introduces three key contributions: (1) the first adaptation of GNNs to meta-mesh topological connectivity, featuring a node-synchronous message-passing mechanism; (2) a dual-scale architecture that jointly learns coarse-scale embeddings and fine-scale error corrections, enabling cross-geometric generalization; and (3) graph-based upsampling coupled with multi-scale local neighborhood modeling. We evaluate the method on Taylor–Green vortex and backward-facing step flows at Re = 1600 and 3200, demonstrating significantly lower global and local errors compared to conventional interpolation baselines. Furthermore, successful extrapolation to cavity flow—beyond the training mesh topology—validates the model’s robustness and strong generalization capability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Metareasoning and Metaheuristics
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Enhances 3D fluid flow super-resolution using GNN
• Addresses interpolation errors in multiscale mesh models
• Validates GNN accuracy in high Reynolds flows

Innovation

• Multiscale Graph Neural Networks
• Localized mesh element processing
• Coarse-fine scale message passing