Automatically Designed Deep Gaussian Process for Turbomachinery Application

Abstract Thanks to their flexibility and robustness to overfitting, Gaussian Processes (GPs) are widely used as black-box function approximators. Deep Gaussian Processes (DGPs) are multilayer generations of GPs. The deep architecture alleviates the kernel dependance of GPs, while complicates model inference. The so-called doubly stochastic variational approach, which does not force the independence between layers, shows its effectiveness in large dataset classification and regression in the literature. Meanwhile, similar to deep neural network, DGPs also require application-specific architecture. In addition, the doubly stochastic process introduces extra hyperparameters, which further increases the difficulty in model definition and training. In this study, we apply doubly stochastic variational inference DGP as surrogate model on high-dimensional structural data regression drawn from turbomachinery area. A discrete optimizer, which is based on classification discriminating good solutions from bad ones, is utilized to realize automatic DGP model design and tuning. Empirical experiments are performed firstly on analytical functions to demonstrate the capability of DPGs in high-dimensional and non-stationary data handling. Two industrial turbomachinery problems with respectively 80 and 180 input dimensions are addressed. The first application consists in a turbine frame design problem. In the second application, DGP is used to describe the correlation between 3D blade profiles of a multi-stage low pressure turbine and the corresponding turbine total-total efficiency. Through these two applications, we show the applicability of the proposed automatically designed DGPs in turbomachinery area by highlighting their outperformance with respect to classic GPs.