A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor–Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.

中文翻译：

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使用多尺度图神经网络对流体流动进行基于网格的超分辨率

这项工作引入了一种图形神经网络 （GNN） 方法，该方法能够对流体流动进行基于网格的三维超分辨率。在这个框架中，GNN 不是一次在基于网格的完整场上运行，而是直接在单元（或单元）的局部网格上运行。为了以类似于频谱（或有限）元素离散化的方式促进基于网格的 GNN 表示，对基线 GNN 层（称为消息传递层，它更新本地节点属性）进行了修改，以考虑重合图节点的同步，从而呈现与常用的基于元素的网格连接性的兼容性。该架构本质上是多尺度的，由粗尺度和精细尺度消息传递层序列（称为处理器）的组合组成，由图形解池层分隔。粗略比例处理器使用粗略比例的同步消息传递元素（以及一定数量的相邻粗略元素）将查询元素嵌入到单个潜在图表示中，而精细比例处理器利用此潜在图上的其他消息传递作来纠正插值错误。使用来自 Taylor-Green Vortex 的基于六面体网格的数据和雷诺数为 1600 和 3200 的后向阶梯流仿真进行演示研究。通过对全局和局部误差的分析，结果最终显示了与粗尺度和多尺度模型配置中的目标相比，GNN 如何能够产生准确的超分场。发现固定架构的重建误差与雷诺数成比例增加。 对单独型腔流配置的几何外推研究表明，超分辨率策略具有很有前途的交叉网格能力。