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.

摘要

具有梯度信息的计算机模型越来越多地用于工程和科学。梯度增强的高斯过程模拟器可用于模拟此类模型。由于协方差矩阵的大小与输入维度和样本大小成比例地增加，因此将此类模拟器用于大型数据集在计算上具有挑战性。我们提出了一种随机傅立叶特征方法来减轻这个困难。所提出方法的关键思想是采用随机傅立叶特征为涉及梯度的移位不变内核获得易于计算的低维特征表示。通过几个例子说明了所提出方法的有效性。