A Random Fourier Feature Method for Emulating Computer Models With Gradient Information

Abstract

Computer models with gradient information are increasingly used in engineering and science. The gradient-enhanced Gaussian process emulator can be used for emulating such models. Because the size of the covariance matrix increases proportionally with the dimension of inputs and the sample size, it is computationally challenging to fit such an emulator for large datasets. We propose a random Fourier feature method to mitigate this difficulty. The key idea of the proposed method is to employ random Fourier features to obtain an easily computable, low-dimensional feature representation for shift-invariant kernels involving gradients. The effectiveness of the proposed method is illustrated by several examples.

KEYWORDS:

• Computer models
• Gradient-enhanced Gaussian process emulator
• Random Fourier features

Supplementary Materials

We have two supplementary materials online. The first provides proofs of some mathematical results in the article. The second provides the codes for some examples in the article.

Acknowledgments

We would like to thank editor, associate editor, and referees for useful comments that had improved the article.

Additional information

Funding

U. S. National Science Foundation;