Principal Component Analysis for High Dimension Stochastic Gaussian Process Model Fitting

Stochastic Gaussian Process models are widely used in stochastic simulation metamodeling to predict the response of noisy simulations. Often, many real-world engineering problems are high-dimensional (more than 10 dimensions), and the Gaussian Process models' prediction for such high-dimensional inputs are computationally expensive due to multiple inversions of the covariance matrix. Therefore, the “curse of dimensionality” on these models prevent them from being used in a high-dimensional setting. To overcome this problem, a methodology for high-dimensional stochastic Gaussian Process models' fitting is proposed in this paper. The input data is first projected onto a reduced set of dimensions found by Principal Component Analysis before being used to fit the model. Numerical experiments prove that the method helps significantly in reducing the computation time.