58469 - Automatically Designed Deep Gaussian Process for High Dimensional Turbomachinery Application 

Thanks to their flexibility and robustness to overfitting, Gaussian Processes (GPs) are widely used as black-box function approximator. Deep Gaussian Processes (DGPs) are multi-layer generations of GPs. The deep architecture alleviates the kernel dependence of GPS, while complicating 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 as deep neural networks, DGPs also require application-specific architecture. In addition, the double stochastic process introduces extra hyperparameters, which further increases the difficulty in model definition and training. In this study, we apply doubly stochastic variational inference DGPs 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 problems in turbomachinery with respectively 80 and 180 input dimensions are addressed. The first application consists in a multi-profile turbine vane 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 by highlighting their outperformance with respect to classic GPs.