Predicting transonic flowfields in non–homogeneous unstructured grids using autoencoder graph convolutional networks

Abstract

This paper addresses the challenges posed by non-homogeneous unstructured grids, which are commonly used in computational fluid dynamics. The prevalence of these grids in fluid dynamics scenarios has driven the exploration of innovative approaches for generating reduced-order models. Our approach leverages geometric deep learning, specifically through the use of an autoencoder architecture built on graph convolutional networks. This architecture enhances prediction accuracy by propagating information to distant nodes and emphasizing influential points. Key innovations include a dimensionality reduction module based on pressure-gradient values, fast connectivity reconstruction using Mahalanobis distance, optimization of the network architecture, and a physics-informed loss function based on aerodynamic coefficient. These advancements result in a more robust and accurate predictive model, achieving systematically lower errors compared to previous graph-based methods. The proposed methodology is validated through two distinct test cases—wing-only and wing-body configurations—demonstrating precise reconstruction of steady-state distributed quantities within a two-dimensional parametric space.