Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Abstract

In recent years, multilayered hierarchical compositions of the well-known and widely used Gaussian process models called deep Gaussian processes are finding use in the approximation of black-box functions. In this paper, the performance of deep Gaussian process models is empirically evaluated and compared against the well-established Gaussian process models with a special emphasis on engineering problems. The work draws conclusions through detailed comparisons in terms of metrics such as computational training cost, data requirement, predictive error, and robustness to the choice of the initial design of experiments. Additionally, the viability and robustness of deep Gaussian process models for applications on practical engineering problems are analyzed through sensitivity to hyperparameters and scalability with respect to the input space dimensionality, respectively. Finally, the models are also compared in an adaptive construction setting, where they are built sequentially by selecting points that maximize posterior variance. Experiments are conducted on canonical test functions with varying input dimensions, an engineering test function, and a practical transonic airfoil test case with a high-dimensional input space. The experiments suggest that deep Gaussian process models outperform traditional Gaussian process models in terms of accuracy at the cost of incurring a significantly higher computational expense for the training procedure. The sensitivity studies indicate that inducing points is the most important hyperparameter that affects deep Gaussian process performance and training time. This work empirically shows that deep Gaussian processes are promising candidates for problems that are known to be nonlinear and high-dimensional, and when limited training data are available.