Flow Field Reconstructions With GANs Based on Radial Basis Functions

Abstract

Nonlinear sparse data regression and generation have been a long-term challenge in the field of aerodynamics, flow field reconstruction is an area of specific interest in this article. The high computational costs of computational fluid dynamics (CFD) make large scale CFD data production expensive, which is the reason why cheaper methods are needed. Traditional reduced-order models were promising but they cannot generate a large amount of full domain flow field data (FFD) to execute high-precision flow field reconstructions. Motivated by the problem of existing approaches, and inspired by the success of generative adversarial networks (GANs) in the field of computer vision, we prove a theorem that shows the optimal approximation to a GAN discriminator is a radial basis function neural network when engaged in with nonlinear sparse FFD regression and generation. Based on this theorem, a radial basis function-based GAN (RBF-GAN) and a RBF cluster-based GAN (RBFC-GAN) are proposed for regression and generation purposes. Three different datasets are applied to verify the feasibility of our models. The results show that the performance of RBF-GAN and RBFC-GAN are better than that of GANs and conditional GANs (cGANs) by both the mean square error and the MSPE measurements. In addition, compared with GANs/cGANs, the stability of the RBF-GAN and the RBFC-GAN are improved by 34.62 and 72.31%, respectively. Consequently, our proposed models can be used to generate full domain FFD from limited and sparse datasets to meet the requirements of high-precision flow field reconstructions.