| 摘 要: 目前,基于深度学习的偏微分方程求解工作聚焦于固定几何区域,存在难以适配几何模型实时变化的问题,因此提出了一种基于主从图神经网络的拓扑一致模型等几何分析重用方法。该方法利用图神经网络预测偏微分方程的解。在自制数据集上进行实验验证,结果表明,即使在复杂几何模型上预测复杂方程,该方法仍能将数值解的相对误差控制在10%以内。这证明了该方法能够高效且精确地在一组拓扑一致的B样条模型上取得光滑连续的数值解,为基于深度学习的偏微分方程求解工作提供了创新思路。 |
| 关键词: 偏微分方程;拓扑一致;重用;等几何分析;主从图神经网络 |
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中图分类号: TP391
文献标识码: A
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| Isogeometric Analysis Reuse Method Basedon Master-SlaveGraph Neural Network for Topology-Consistent Models |
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ZHONG Weizhen, XU Jinlan
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(Department of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China)
weizhenzhong1@gmail.com; jlxu@hdu.edu.cn
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| Abstract: Currently, the work on solving Partial Differential Equations (PDEs) based on deep learning focuses on fixed geometric regions and struggles with problems that require adaptation to real-time changes in geometric models. Therefore, this paper proposes an Isogeometric analysis reuse method based on the Master-Slave Graph Neural Network (MS-GNN) for topology-consistent models. This method utilizes GNN to predict solutions to PDEs. Experiment results conducted on a self-made data set demonstrate that the relative error of numerical solutions can be controlled within 10%, even when predicting complex equations on intricate geometric models. This proves that the proposed method can efficiently and accurately achieve smooth and continuous numerical solutions on a set of topologically consistent B-spline models, providing innovative ideas for the work of solving PDEs based on deep learning. |
| Keywords: PDEs; topology-consistent; reuse; isogeometric analysis; MS-GNN |
