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

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.