Study on a Fast Solver for Combined Field Integral Equations of 3D Conducting Bodies Based on Graph Neural Networks

• URL: http://arxiv.org/abs/2501.09923v1
• Date: Fri, 17 Jan 2025 02:40:04 GMT
• Title: Study on a Fast Solver for Combined Field Integral Equations of 3D Conducting Bodies Based on Graph Neural Networks
• Authors: Tao Shan, Xin Zhang, Di Wu,
• Abstract summary: We present a graph neural networks (GNNs)-based fast solver (Graphr) for solving combined field integral equations (CFIEs) of 3D conducting bodies.
• Score: 6.506094463237149
• License:
• Abstract: In this paper, we present a graph neural networks (GNNs)-based fast solver (GraphSolver) for solving combined field integral equations (CFIEs) of 3D conducting bodies. Rao-Wilton-Glisson (RWG) basis functions are employed to discretely and accurately represent the geometry of 3D conducting bodies. A concise and informative graph representation is then constructed by treating each RWG function as a node in the graph, enabling the flow of current between nodes. With the transformed graphs, GraphSolver is developed to directly predict real and imaginary parts of the x, y and z components of the surface current densities at each node (RWG function). Numerical results demonstrate the efficacy of GraphSolver in solving CFIEs for 3D conducting bodies with varying levels of geometric complexity, including basic 3D targets, missile-shaped targets, and airplane-shaped targets.

Related papers

• Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks [53.10674067060148]
  Shapley Interactions (SIs) quantify node contributions and interactions among multiple nodes. By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction. We introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly.
  arXiv  Detail & Related papers  (2025-01-28T13:37:44Z)
• 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)
• Graph Transformer GANs with Graph Masked Modeling for Architectural Layout Generation [153.92387500677023]
  We present a novel graph Transformer generative adversarial network (GTGAN) to learn effective graph node relations. The proposed graph Transformer encoder combines graph convolutions and self-attentions in a Transformer to model both local and global interactions. We also propose a novel self-guided pre-training method for graph representation learning.
  arXiv  Detail & Related papers  (2024-01-15T14:36:38Z)
• Predicting Protein-Ligand Binding Affinity with Equivariant Line Graph Network [22.396125176265997]
  Existing approaches transform a 3D protein-ligand complex to a two-dimensional (2D) graph, and then use graph neural networks (GNNs) to predict its binding affinity. We propose a novel Equivariant Line Graph Network (ELGN) for affinity prediction of 3D protein ligand complexes. Experimental results on two real datasets demonstrate the effectiveness of ELGN over several state-of-the-art baselines.
  arXiv  Detail & Related papers  (2022-10-27T02:15:52Z)
• Learning Graph Structure from Convolutional Mixtures [119.45320143101381]
  We propose a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN) GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive.
  arXiv  Detail & Related papers  (2022-05-19T14:08:15Z)
• Hierarchical Graph Networks for 3D Human Pose Estimation [50.600944798627786]
  Recent 2D-to-3D human pose estimation works tend to utilize the graph structure formed by the topology of the human skeleton. We argue that this skeletal topology is too sparse to reflect the body structure and suffer from serious 2D-to-3D ambiguity problem. We propose a novel graph convolution network architecture, Hierarchical Graph Networks, to overcome these weaknesses.
  arXiv  Detail & Related papers  (2021-11-23T15:09:03Z)
• Dense Graph Convolutional Neural Networks on 3D Meshes for 3D Object Segmentation and Classification [0.0]
  We present new designs of graph convolutional neural networks (GCNs) on 3D meshes for 3D object classification and segmentation. We use the faces of the mesh as basic processing units and represent a 3D mesh as a graph where each node corresponds to a face.
  arXiv  Detail & Related papers  (2021-06-30T02:17:16Z)
• Pyramidal Reservoir Graph Neural Network [18.632681846787246]
  We propose a deep Graph Neural Network (GNN) model that alternates two types of layers. We show how graph pooling can reduce the computational complexity of the model. Our proposed approach to the design of RC-based GNNs offers an advantageous and principled trade-off between accuracy and complexity.
  arXiv  Detail & Related papers  (2021-04-10T08:34:09Z)
• Graph-Time Convolutional Neural Networks [9.137554315375919]
  We represent spatial relationships through product graphs with a first principle graph-time convolutional neural network (GTCNN) We develop a graph-time convolutional filter by following the shift-and-sumtemporal operator to learn higher-level features over the product graph. We develop a zero-pad pooling that preserves the spatial graph while reducing the number of active nodes and the parameters.
  arXiv  Detail & Related papers  (2021-03-02T14:03:44Z)
• Distance-Geometric Graph Convolutional Network (DG-GCN) for Three-Dimensional (3D) Graphs [0.8722210937404288]
  We propose a message-passing graph convolutional network based on the distance-geometric graph representation: DG-GCN. It enables learning of filter weights from distances, thereby incorporating the geometry of 3D graphs in graph convolutions. Our work demonstrates the utility and value of DG-GCN for end-to-end deep learning on 3D graphs, particularly molecular graphs.
  arXiv  Detail & Related papers  (2020-07-06T15:20:52Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)

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.