Predicting Transonic Flowfields in Non-Homogeneous Unstructured Grids Using Autoencoder Graph Convolutional Networks

TL;DR

The paper tackles predicting transonic flowfields on non-homogeneous unstructured grids by proposing an Autoencoder Graph Convolutional Network (AE-GCN) ROM that uses gradient-based pooling, MWLSI interpolation, and Mahalanobis connectivity to propagate information across the mesh. It combines encoder-decoder compression with four parallel GCNs to output nodewise coefficients such as $C_P$ and the skin friction terms, supervised by a physics-informed loss that includes the pitching moment $C_{M_y}$. Bayesian optimization tunes hyperparameters and the method is validated on two aerospace test cases, BSCW and CRM, showing accurate predictions across a 2D AoA–Mach space and robust extrapolation beyond training data. The approach yields substantial computational savings by enabling rapid per-sample predictions (about 1 s) versus high-fidelity CFD runs that require orders of magnitude more time, while maintaining high fidelity in shock and boundary layer regions, indicating strong potential for online ROM and design optimization.

Abstract

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.

Figures (20)

• Figure 1: Visual comparison between pixelwise convolution on a 2D digital image and graph convolution on a 3D mesh.
• Figure 2: Schematic of the graph autoencoder architecture.
• Figure 3: Visual representation of a graph diagram and its connectivity matrix.
• Figure 4: Pooling and unpooling modules architecture.
• Figure 5: Training, validation and test samples for Mach number and angle of attack.