Deep Gaussian Process Enabled Surrogate Models for Aerodynamic Flows

Abstract

Deep Gaussian process (DGP) models are multi-layered hierarchical generalizations of the well-known Gaussian process (GP) models widely used to construct surrogate models of aerodynamic quantities of interest. Combining the desirable features of GP models and deep neural networks (DNN), DGP models are known to perform well when training data is scarce and the behavior of the system response is highly non-stationary. In this paper, the performance of DGP models is evaluated against GP models. Detailed comparisons are made and conclusions are drawn in terms of training time, data requirements, predictive error, and robustness to choice of training design of experiments, among other metrics. Additionally, sensitivity and scalability analyses are conducted for the GP models to evaluate their usability. Finally, an adaptive construction of both models is presented, where the models are built sequentially by selecting points that maximize posterior variance. Several experiments are conducted with canonical test functions at varying input dimensions and a viscous transonic airfoil test case at 42 input dimensions. The experiments suggest that DGP models outperform traditional GP models in terms of accuracy but incur higher computational costs for training.