Learning finite element convergence with the Multi-fidelity Graph Neural Network
Learning finite element convergence with the Multi-fidelity Graph Neural Network
复制标题
使用多保真图神经网络学习有限元收敛
DOI：
10.1016/j.cma.2022.115120
复制
发表时间：
2022
影响因子：
7.2
通讯作者：
Najafi, Ahmad R.
中科院分区：
文献类型：
--
作者：
Black, Nolan;Najafi, Ahmad R.
机器学习技术已经成为传统的基于物理的建模和偏微分方程求解器的潜在替代品。在这些机器学习技术中，图神经网络（GNN）通过图模型模拟物理; GNN将相关的物理特征嵌入到图数据结构中，在图中执行消息传递，并基于系统的关系产生新的属性。与许多机器学习框架一样，GNN受到过多数据生成成本和狭窄训练域之外有限的可推广性的限制。为了解决这些限制，我们引入了多保真度图神经网络（MFGNN），这是一种监督机器学习框架，它使用低保真度投影来通知子图表示的任意子域的高保真度建模。我们实现了MFGNN的二维弹性静力学问题的有限元训练数据。MFGNN经过训练，可以在低保真度评估的情况下产生准确的分析，并模拟传统有限元分析（FEA）的收敛行为。通过子域抽象，我们还将MFGNN扩展为训练域之外的新边界条件和材料域的通用模型。
Machine learning techniques have emerged as potential alternatives to traditional physics-based modeling and partial differential equation solvers. Among these machine learning techniques, Graph Neural Networks (GNNs) simulate physics via graph models; GNNs embed relevant physical features into graph data structures, perform message passing within the graphs, and produce new attributes based on the system’s relationships. Like many machine learning frameworks, GNNs are limited by excessive data generation costs and limited generalizability outside of a narrow training domain. To address these limitations, we introduce the Multi-Fidelity Graph Neural Network (MFGNN), a supervised machine learning framework that uses low-fidelity projections to inform high-fidelity modeling across arbitrary subdomains represented by subgraphs. We implement the MFGNN for two-dimensional elastostatic problems with finite element training data. The MFGNN is trained to produce accurate analysis given low-fidelity evaluations and emulate the convergence behavior of traditional finite element analysis (FEA). Through subdomain abstraction, we also extend the MFGNN as a general model for new boundary conditions and material domains outside of the training domain.
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影响因子：
4.1
作者：
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通讯作者：
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第 15 章 – 错误、恢复过程和错误估计
DOI：
--
发表时间：
2013
期刊：
影响因子：
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作者：
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DOI：
10.1016/j.cma.2020.113452
发表时间：
2021-01-01
影响因子：
7.2
作者：
Saha, Sourav;Gan, Zhengtao;Liu, Wing Kam
通讯作者：
Liu, Wing Kam