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

• URL: http://arxiv.org/abs/2409.07769v2
• Date: Tue, 17 Sep 2024 19:05:17 GMT
• Title: Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks
• Authors: Shivam Barwey, Pinaki Pal, Saumil Patel, Riccardo Balin, Bethany Lusch, Venkatram Vishwanath, Romit Maulik, Ramesh Balakrishnan,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

Related papers

• Point Cloud Denoising With Fine-Granularity Dynamic Graph Convolutional Networks [58.050130177241186]
  Noise perturbations often corrupt 3-D point clouds, hindering downstream tasks such as surface reconstruction, rendering, and further processing. This paper introduces finegranularity dynamic graph convolutional networks called GDGCN, a novel approach to denoising in 3-D point clouds.
  arXiv  Detail & Related papers  (2024-11-21T14:19:32Z)
• Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling [0.0]
  This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications. consistency refers to the fact that a GNN trained and evaluated on one rank (one large graph) is arithmetically equivalent to evaluations on multiple ranks (a partitioned graph) It is shown how the NekRS mesh partitioning can be linked to the distributed GNN training and inference routines, resulting in a scalable mesh-based data-driven modeling workflow.
  arXiv  Detail & Related papers  (2024-10-02T15:22:27Z)
• BLIS-Net: Classifying and Analyzing Signals on Graphs [20.345611294709244]
  Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. We introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. We show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.
  arXiv  Detail & Related papers  (2023-10-26T17:03:14Z)
• Efficient Heterogeneous Graph Learning via Random Projection [58.4138636866903]
  Heterogeneous Graph Neural Networks (HGNNs) are powerful tools for deep learning on heterogeneous graphs. Recent pre-computation-based HGNNs use one-time message passing to transform a heterogeneous graph into regular-shaped tensors. We propose a hybrid pre-computation-based HGNN, named Random Projection Heterogeneous Graph Neural Network (RpHGNN)
  arXiv  Detail & Related papers  (2023-10-23T01:25:44Z)
• Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning [0.0]
  The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications.
  arXiv  Detail & Related papers  (2023-02-13T08:47:11Z)
• A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations [4.984601297028257]
  An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for continuum mechanics simulations. We present a method to construct a hypergraph by connecting the nodes by elements rather than edges. We term this method a finite element-inspired hypergraph neural network, in short FEIH($phi$)-GNN.
  arXiv  Detail & Related papers  (2022-12-30T04:10:01Z)
• EGRC-Net: Embedding-induced Graph Refinement Clustering Network [66.44293190793294]
  We propose a novel graph clustering network called Embedding-Induced Graph Refinement Clustering Network (EGRC-Net) EGRC-Net effectively utilizes the learned embedding to adaptively refine the initial graph and enhance the clustering performance. Our proposed methods consistently outperform several state-of-the-art approaches.
  arXiv  Detail & Related papers  (2022-11-19T09:08:43Z)
• Dynamic Graph Message Passing Networks for Visual Recognition [112.49513303433606]
  Modelling long-range dependencies is critical for scene understanding tasks in computer vision. A fully-connected graph is beneficial for such modelling, but its computational overhead is prohibitive. We propose a dynamic graph message passing network, that significantly reduces the computational complexity.
  arXiv  Detail & Related papers  (2022-09-20T14:41:37Z)
• Graph Ordering Attention Networks [22.468776559433614]
  Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data. We introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. GOAT layer demonstrates its increased performance in modeling graph metrics that capture complex information.
  arXiv  Detail & Related papers  (2022-04-11T18:13:19Z)
• VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization [70.8567058758375]
  VQ-GNN is a universal framework to scale up any convolution-based GNNs using Vector Quantization (VQ) without compromising the performance. Our framework avoids the "neighbor explosion" problem of GNNs using quantized representations combined with a low-rank version of the graph convolution matrix.
  arXiv  Detail & Related papers  (2021-10-27T11:48:50Z)
• Graph Highway Networks [77.38665506495553]
  Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. They suffer from the notorious over-smoothing problem, in which the learned representations converge to alike vectors when many layers are stacked. We propose Graph Highway Networks (GHNet) which utilize gating units to balance the trade-off between homogeneity and heterogeneity in the GCN learning process.
  arXiv  Detail & Related papers  (2020-04-09T16:26:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.