This paper focuses on addressing challenges posed by non-homogeneous unstructured grids, commonly used in Computational Fluid Dynamics (CFD). Their prevalence in CFD scenarios has motivated the exploration of innovative approaches for generating reduced-order models. The core of our approach centers on geometric deep learning, specifically the utilization of graph convolutional network (GCN). The novel Autoencoder GCN architecture enhances prediction accuracy by propagating information to distant nodes and emphasizing influential points. This architecture, with GCN layers and encoding/decoding modules, reduces dimensionality based on pressure-gradient values. The autoencoder structure improves the network capability to identify key features, contributing to a more robust and accurate predictive model. To validate the proposed methodology, we analyzed two different test cases: wing-only model and wing--body configuration. Precise reconstruction of steady-state distributed quantities within a two-dimensional parametric space underscores the reliability and versatility of the implemented approach.

翻译：本文聚焦于计算流体力学（CFD）中常用的非均匀非结构网格所带来的挑战。这类网格在CFD场景中的广泛应用促使我们探索生成降阶模型的新方法。本方法的核心是几何深度学习，特别是图卷积网络（GCN）的运用。通过将信息传播至远端节点并强化关键节点的影响，新型自编码器GCN架构提升了预测精度。该架构包含GCN层与编码/解码模块，基于压力梯度值进行降维处理。自编码器结构增强了网络识别关键特征的能力，从而构建更稳健精确的预测模型。为验证所提方法，我们分析了两个算例：纯机翼模型与机翼-机身构型。在二维参数空间内对稳态分布量的精确重建，充分体现了所实现方法的可靠性与普适性。