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arXiv 2212.14545physics.flu-dyncs.LG
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一种受有限元启发的超图神经网络:在流体动力学模拟中的应用

A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations

The University of British Columbia(不列颠哥伦比亚大学)

Rui Gao, Indu Kant Deo, Rajeev K. Jaiman

AI总结:

针对现有图神经网络多基于双边连接的局限,提出受有限元启发的FEIH(ϕ)-GNN超图网络,具备旋转等变性,在流体模拟基准上实现稳定准确的插值预测及适度外推能力。

摘要:

深度学习研究的一个新兴趋势聚焦于图神经网络(GNNs)在基于网格的连续介质力学模拟中的应用。这类学习框架大多在每条边连接两个节点的图上运行。受有限元法中数据连接方式的启发,我们提出了一种通过单元而非边连接节点来构建超图的方法。我们在这种节点-单元超图上定义了一种超图消息传递网络,该网络模拟局部刚度矩阵的计算过程,我们将该方法命名为受有限元启发的超图神经网络,简称FEIH(ϕ)-GNN。我们还为所提出的网络配备了旋转等变性,并探索其对非定常流体流动系统的建模能力。我们在两个常见基准问题(即圆柱绕流和翼型构型流动)上验证了该网络的有效性。使用ϕ-GNN框架可以在插值雷诺数范围内获得稳定且准确的时间滚动预测。该网络还能够向训练范围之外的更高雷诺数域进行适度外推。

英文摘要:

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two nodes. Inspired by the data connectivity in the finite element method, we present a method to construct a hypergraph by connecting the nodes by elements rather than edges. A hypergraph message-passing network is defined on such a node-element hypergraph that mimics the calculation process of local stiffness matrices. We term this method a finite element-inspired hypergraph neural network, in short FEIH($ϕ$)-GNN. We further equip the proposed network with rotation equivariance, and explore its capability for modeling unsteady fluid flow systems. The effectiveness of the network is demonstrated on two common benchmark problems, namely the fluid flow around a circular cylinder and airfoil configurations. Stabilized and accurate temporal roll-out predictions can be obtained using the $ϕ$-GNN framework within the interpolation Reynolds number range. The network is also able to extrapolate moderately towards higher Reynolds number domain out of the training range.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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