The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications. To address the first goal of interpretability, the GNN autoencoder achieves reduction in the number nodes in the encoding stage through an adaptive graph reduction procedure. This reduction procedure essentially amounts to flowfield-conditioned node sampling and sensor identification, and produces interpretable latent graph representations tailored to the flowfield reconstruction task in the form of so-called masked fields. These masked fields allow the user to (a) visualize where in physical space a given latent graph is active, and (b) interpret the time-evolution of the latent graph connectivity in accordance with the time-evolution of unsteady flow features (e.g. recirculation zones, shear layers) in the domain. To address the goal of unstructured mesh compatibility, the autoencoding architecture utilizes a series of multi-scale message passing (MMP) layers, each of which models information exchange among node neighborhoods at various lengthscales. The MMP layer, which augments standard single-scale message passing with learnable coarsening operations, allows the decoder to more efficiently reconstruct the flowfield from the identified regions in the masked fields. Analysis of latent graphs produced by the autoencoder for various model settings are conducted using using unstructured snapshot data sourced from large-eddy simulations in a backward-facing step (BFS) flow configuration with an OpenFOAM-based flow solver at high Reynolds numbers.
翻译:这项工作的目标是解决基于自动编码的模型中两个限制: 潜在的空间解释性和与未结构化的 meshes 相兼容性。 完成此目的的办法是开发一个新颖的图形神经网络( GNNN) 自动编码结构, 并演示复杂的流流应用。 为实现第一个可解释性目标, GNN自动编码器通过一个适应性图表缩减程序, 减少了编码阶段中的数字节点的数量。 这个减少程序基本上相当于流地的图形节点取样和感官识别, 并产生以所谓的遮蔽字段的形式为流程重建任务定制的可解释的隐藏图示。 这些隐藏的字段允许用户(a) 在物理空间中显示一个给定的隐藏流的图像神经网络网络, (b) 根据不稳定的流特性的时间变化来解释暗点( 如回溯带区域、 示层层) 。 使用不结构化的图像兼容性直径向直线图结构图结构, 自动解结构结构架构使用一个多层次的模型序列, 与跨层流的图像, 进行每个平流流的滚动, 每个平流, 进行不同的平流, 进行不同的平流, 进行不同的平层流 进行不同的平流流 。