{"title":"IGA-Graph-Net: Isogeometric analysis-reuse method based on graph neural networks for topology-consistent models","authors":"","doi":"10.1016/j.jcp.2024.113544","DOIUrl":null,"url":null,"abstract":"<div><div>This paper introduces a novel isogeometric analysis-reuse framework called IGA-Graph-Net, which combines <em>Graph Neural Networks</em> with <em>Isogeometric Analysis</em> 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 <em>Convolutional Neural Networks</em> to <em>Graph Neural Networks</em>. 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 <em>partial differential equation</em> 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.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.8000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021999124007927","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
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.