Augmenting Hierarchical Graph Convolutional Networks for Aerodynamic Prediction of Shape Variations

Aerodynamic simulation turnarounds are to date the most restrictive bottleneck in the design processes of aerospace or automotive systems. The design development typically entails optimisation of numerous design variables to shape the vehicle, resulting in a vast number of shape configurations to evaluate. Moreover, each configuration requires characterisation of a large number of prescribed loading conditions. New engineering workflows are sought to accelerate the simulation turnarounds and allow the aerodynamics engineers to drive the design progress. In this context, machine learning becomes attractive to devise a predictive system tailored to replicate the high-fidelity aerodynamic solvers but at the fraction of the computational cost. Graph neural networks are particularly designed to execute predictions on discretised domains, making them particularly suited to infer computational fluid dynamics data. This works builds upon previous contributions at the AIAA Aviation Forum 2023 and AIAA Scitech Forums 2024 and 2025, where a graph convolutional and hierarchical-mesh autoencoder framework were developed for modelling of the pressure distribution and shear stresses on an aircraft model across an envelope of freestream conditions. In this work, we extend the developed technology to address predictions on varied shape designs. These models address the aerodynamic shape modelling and optimisation based on two different type of input design: parametric (where the design is defined by a few variables) or topologic (where the geometry variations must be understood purely from the mesh). Various modelling frameworks are proposed aimed at embedding the design geometry into the model. We demonstrate the prediction performance of these frameworks, also compared to the state of the art, by adopting the Agard 445.6 wing as test case. Geometrical variations of this wing are prescribed from structural deflections. The parametric-based models were found to be accurate as the input geometry is easily described by the assigned parametric variables. Furthermore, the implementation of a learnable geometry encoder to describe the geometry from the mesh, was found adequate for the topological based models to achieve a similar performance as the parametric predictions.