Neural network prediction of the flow field in a periodic domain with hypernetwork parametrization

This paper is concerned with fast flow field prediction in a blade cascade for variable blade shapes as well as variable Reynolds number using the machine-learning architecture called convolutional neural network. To generate flow field for a specific Reynolds number, an encoder-decoder convolutional neural network, also called U-Net, is used. The values 500, 1000 and 1500 of the Reynolds number are chosen as the training set. Three U-Nets were trained on CFD results for 100 blade profiles, each U-Net for a different Reynolds number. In order to get a prediction for variable Reynolds number, a so-called hypernetwork in employed. The hypernetwork essentially interpolates between the two trained U-Nets. The architecture of the hypernetwork is fully-connected feedforward neural network with one input neuron correspond-ing to the Reynolds number, one hidden layer and the output layer corresponds to the weights for the interpolated U-Net. The concept of the hypernetwork-based parametrization is tested on a problem of compressible fluid flow through a blade cascade with three unseen blade profiles and unseen Reynolds number