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：本研究旨在解决自编码器模型的两个局限性：潜空间可解释性与非结构化网格兼容性。为此，我们开发了一种新型图神经网络自编码架构，并在复杂流体流动应用中进行了验证。针对可解释性目标，该图神经网络自编码器通过自适应图缩减过程实现编码阶段节点数量的降低。该缩减过程本质上相当于流场条件化节点采样与传感器识别，并以掩码场的形式生成针对流场重建任务的可解释图表示。这些掩码场使用户能够：(a) 可视化特定潜图在物理空间中的活跃区域；(b) 根据域内非定常流动特征（如回流区、剪切层）的时间演化同步解释潜图连接性的动态变化。为满足非结构化网格兼容性需求，自编码架构采用了一系列多尺度消息传递层，每个层建模不同尺度下节点邻域间的信息交换。多尺度消息传递层通过可学习粗化操作增强标准单尺度消息传递，使解码器能够更高效地从掩码场标识区域重建流场。基于高雷诺数条件下OpenFOAM求解器的大涡模拟后向台阶流动配置中的非结构化快照数据，我们分析了不同模型设置下自编码器产生的潜图。