IGA-Graph-Net: Isogeometric analysis-reuse method based on graph neural networks for topology-consistent models

IF 3.8 2区 物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Journal of Computational Physics Pub Date : 2024-10-30 DOI:10.1016/j.jcp.2024.113544
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Abstract

This paper introduces a novel isogeometric analysis-reuse framework called IGA-Graph-Net, which combines Graph Neural Networks with Isogeometric Analysis to overcome the limitations of Convolutional Neural Networks when dealing with B-spline data. Our network architecture incorporates ResNetV2 and PointTransformer for enhanced performance. We transformed the dataset creation process from using Convolutional Neural Networks to Graph Neural Networks. Additionally, we proposed a new loss function tailored for Dirichlet boundary conditions and enriched the input features. Several examples are presented to demonstrate the effectiveness of the proposed framework. In terms of accuracy when tested on the same set of partial differential equation data, our framework demonstrates significant improvements compared to the reuse method based on Convolutional Neural Networks for Isogeometric Analysis on topology-consistent geometries with complex boundaries.
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IGA-Graph-Net:基于拓扑一致性模型图神经网络的等时分析-重复使用方法
本文介绍了一种名为 IGA-Graph-Net 的新颖等距分析复用框架,它将图神经网络与等距分析相结合,克服了卷积神经网络在处理 B-样条数据时的局限性。我们的网络架构结合了 ResNetV2 和 PointTransformer,以提高性能。我们将数据集创建过程从使用卷积神经网络转变为图形神经网络。此外,我们还针对 Dirichlet 边界条件提出了新的损失函数,并丰富了输入特征。我们列举了几个例子来证明所提框架的有效性。在对同一组偏微分方程数据进行测试时,与基于卷积神经网络的等几何分析重用方法相比,我们的框架在具有复杂边界的拓扑一致性几何图形上的准确性有了显著提高。
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来源期刊
Journal of Computational Physics
Journal of Computational Physics 物理-计算机:跨学科应用
CiteScore
7.60
自引率
14.60%
发文量
763
审稿时长
5.8 months
期刊介绍: Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.
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Editorial Board Mesh optimization for the virtual element method: How small can an agglomerated mesh become? A pseudo-spectral time-domain method for ultrasound wave propagation in soft biological tissue Entropy-stable in- and outflow boundary conditions for the compressible Euler equations IGA-Graph-Net: Isogeometric analysis-reuse method based on graph neural networks for topology-consistent models
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