Graph neural networks for the prediction of aircraft surface pressure distributions

Abstract

Aircraft design requires a multitude of aerodynamic data and providing this solely based on high-quality methods such as computational fluid dynamics is prohibitive from a cost and time point of view. Deep learning methods have been proposed as surrogate models to predict aerodynamic quantities, showing great potential at significantly reduced cost. However, most approaches rely on a structured grid or are tested only for two-dimensional airfoil cases with a few thousand nodes. During aircraft programs, unstructured grids with millions of nodes are routinely used to model industrial-relevant complex physical systems. Hence, further investigation is required to study the applicability and extension of deep learning methods to industrial cases. In this paper, we use a graph neural network approach applicable to unstructured grids and extend it for the task of predicting surface pressure distributions for complex cases involving several hundreds of thousand of nodes. We compare this approach with proper orthogonal decomposition combined with an interpolation technique and with two other deep learning approaches, namely, a coordinate-based multilayer perceptron for pointwise predictions and its extension using surface normals as additional inputs. Results are first presented for a two-dimensional airfoil case and then for the NASA Common Research Model transport aircraft with an underlying mesh consisting of around 500,000 surface points. The deep learning methods demonstrate in transonic flows the ability to capture shock location and strength more accurately. Furthermore, the proposed graph-based approach with the addition of more geometric information such as connectivity and surface normals seems to provide an additional boost in performance over the coordinate-based multilayer perceptron yielding more realistic pressure distributions.