Investigation of Graph Neural Networks for Prediction of Aerodynamic Quantities in the Frequency Domain

Abstract

Modern aircraft development requires ever-faster evaluations of physical quantities considering large parameter spaces. Conventional computational methods are prohibitive due to the required computational effort. Data-driven surrogate models allow very fast evaluation times, by shifting computational effort to a prior training phase. Deep-learning models have proven capable of capturing high-complexity data. Unsteady aerodynamic effects, e.g. caused by discrete gusts, must be considered during aircraft design. Conventional methods such as the linear frequency domain solver allow computing solutions in the frequency domain. This work investigates the applicability of graph neural networks as surrogate models for such problems. Graph neural networks can use the spatial information given by a computational mesh to enhance the prediction accuracy as prior work on steady aerodynamic problems has shown. Two types of graph neural networks, namely a graph convolutional network with a Residual Gated Graph ConvNets convolution, and the graph network simulator model are compared using only global flow features Mach, angle of attack, and reduced frequency with models using pressure as an additional local flow feature. The complex-valued increment to the pressure coefficient at the airfoil surface is used as the target quantity. An interpolation model and a node-wise predicting fully-connected neural network are used as comparisons. In this work, all models are compared using the NACA 64A010 airfoil as a two-dimensional test case. Therefore, a sampling strategy is described to generate a dataset. Subsequently, the models are optimized towards the available data. Evaluating the models using four different metrics indicates that the two graph neural network approaches using local and global flow features deliver the best predictions. Especially, comparing the deep-learning results to the interpolation model shows advantages in the capability of capturing non-linear flow characteristics in the transonic flight regime. However, with the available dataset and chosen hyperparameters, none of the models delivers satisfactory predictions, especially at low reduced frequency transonic samples. Further investigations test the models behaviours on differently sized datasets, as well as datasets containing subsets of reduced frequencies respectively subsets of Mach numbers and angle of attack. Regarding the computational effort, all data-driven approaches show the potential to evaluate samples approximately four orders of magnitude faster than the linear frequency domain approach. Overall the graph network simulator model using local flow features shows the greatest potential. Finally, ideas regarding further improvements and continuing investigations are given.